Free 1 Die Roll Calculator - Calculates the probability for the following events in the roll of one fair dice (1 dice roll calculator or 1 die roll calculator):
* Probability of any total from (1-6)
* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)
* The total being even
* The total being odd
* The total being a prime number
* The total being a non-prime number
* Rolling a list of numbers i.e. (2,5,6)
* Simulate (n) Monte Carlo die simulations.
1 die calculator

A number means an arbitrary variable, let's call it x. The product of 4 and a number is 4x. 12 plus that product is 4x + 12 Is greater than means an inequality, so we set the entire expression greater than 72 4x + 12 > 72

13 more than x means we add: x + 13 This expression is greater than 14, so we write an inequality: x + 13 > 14

13 more than x is greater than 14 13 more than x x + 13 Is greater than 14 [B]x + 13 > 14[/B]

Free 2 dice roll Calculator - Calculates the probability for the following events in a pair of fair dice rolls:
* Probability of any sum from (2-12)
* Probability of the sum being less than, less than or equal to, greater than, or greater than or equal to (2-12)
* The sum being even
* The sum being odd
* The sum being a prime number
* The sum being a non-prime number
* Rolling a list of numbers i.e. (2,5,6,12)
* Simulate (n) Monte Carlo two die simulations. 2 dice calculator

2 is greater than or equal to w and -7 is less than or equal to w Written as an inequality, we have: -7 <= w <= 2

2/3 of a number 17 is at least 29 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x 2/3 of a number means we multiply x by 2/3: 2x/3 The phrase [I]is at least[/I] also means greater than or equal to, so we set up the inequality: [B]2x/3 >= 29[/B]

35 added to n is greater than or equal to the sum of k and 21 Take this algebraic expression in 3 parts: [LIST=1] [*]35 added to n means we have a sum: n + 35 [*]The sum of k and 21 means we add 21 to k: k +21 [*]The phrase [I]greater than or equal to[/I] means an inequality using this sign (>=), so we write this as follows: [/LIST] [B]n + 35 >= k + 21[/B]

50 is more than the product of 4 and w Take this algebraic expression in pieces: The product of 4 and w mean we multiply the variable w by 4: 4w The phrase [I]is more than[/I] means an inequality using the (>) sign, where 50 is greater than 4w: [B]50 > 4w[/B]

6 times a number, x, is at least 22. 6 times a number x: 6x The phrase [I]is at least[/I] means greater than or equal to. So we have an inequality: [B]6x >= 22[/B] <-- This is our algebraic expression [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6x%3E%3D22&pl=Show+Interval+Notation']To solve this for x, paste this into the search engine[/URL] and we get: [B]x >= 3.666667[/B]

-2 times a number x is written as -2x. Less means subtract, so we have 7 less than this is -2x - 7. Finally, greater than or equal to is >=, so our expression becomes: -2x - 7 >= 41

-2 times a number x is denoted as -2x. 7 less than that means we subtract 7: -2x - 7 Finally, that entire expression is greater than or equal to 41 -2x - 7 >= 41

-2 times a number x is denoted as -2x. 7 less means we subtract, so 7 less than that is -2x - 7. Finally, that entire expression is greater than or equal to 41 -2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41 -2 times a number x -2x 7 less than this -2x - 7 Now we set this expressions greater than or equal to 41 [B]-2x - 7 >= 41[/B]

Take this in parts: First, the phrase, "a number" means we pick an arbitrary variable, let's call it x. The product of a number and 7 is 7x. 8 increased by the product of 7x means we add them together. 7x + 8 Finally that entire expression is greater than [U]or equal to[/U] -18 [B]7x + 8 >=-18[/B]

9 is greater than x and x is greater than 3 This is a compound inequality. We write this as: [B]3 < x < 9[/B]

9 subtracted from the product of 3 and a number is greater than or equal to 16 [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]The product of 3 and a number means we multiply 3 times x: 3x [*]9 subtracted from the product: 3x - 9 [*]The phrase is greater than or equal to means an inequality. So we set up an inequality with >= for the greater than or equal to sign in relation to 3x - 9 and 16 [/LIST] Our algebraic expression (inequality) becomes: [B]3x - 19 >= 16[/B]

a 12 sided die is rolled find the probability of rolling a number greater than 7 We assume this is a fair die, not loaded. This means each side 1-12 has an equal probability of 1/12 of being rolled. The problem asks, P(Roll > 7) Greater than 7 means our sample space is {8, 9, 10, 11, 12} If each of these 5 faces have an equal probability of being rolled, then we have: P(Roll > 7) = P(Roll = 8) + P(Roll = 9) + P(Roll = 10) + P(Roll = 11) + P(Roll = 12) P(Roll > 7) = 1/12 + 1/12 + 1/12 + 1/12 + 1/12 P(Roll > 7) =[B] 5/12[/B]

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441? Let the number of tickets above 42 be t. A few things to note on this question: [LIST] [*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality. [*]Earnings = Price * Quantity [/LIST] We're given: Earnings = 4.50 * 42 + 4.5t >= 441 Earnings = 189 + 4.5t >= 441 We want to solve this inequality for t: Solve for [I]t[/I] in the inequality 189 + 4.5t ≥ 441 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 189 and 441. To do that, we subtract 189 from both sides 4.5t + 189 - 189 ≥ 441 - 189 [SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE] 4.5t ≥ 252 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE] 4.5t/4.5 ≥ 252.4.5 [B]t ≥ 56[/B]

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is the better deal Let the number of days be d. We have the inequality below where we show when the day to day cost is greater than the monthly pass: 1.5d > 24 To solve this inequality for d, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.5d%3E24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get: [B]d > 16[/B]

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the month. If he is aiming to earn a minimum of $3200 a month, what is the possible value of sales that will enable this? to start, we have: [LIST] [*]Let the salesman's monthly sales be s. [*]With a 10% discount as a decimal of 0.1 [*]The phrase [I]a minimum[/I] also means [I]at least[/I] or [I]greater than or equal to[/I]. This tells us we want an inequality [*]We want 10% times s + 800 per month is greater than or equal to 3200 [/LIST] We want the inequality: 0.1s + 800 >= 3200 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.1s%2B800%3E%3D3200&pl=Solve']type this inequality into our search engine[/URL] and we get: [B]s >= 24000[/B]

A cell phone costs $20 for 400 minutes and $2 for each extra minute. Gina uses 408 minutes. How much will it cost? Set up the cost function for minutes (m) if m is greater than or equal to 400 C(m) = 20 + 2(m - 400) For m = 408, we have: C(408) = 20 + 2(408 - 400) C(408) = 20 + 2(8) C(408) = [B]36[/B]

A coin is tossed and a die is rolled. Find the probability pf getting a head and a number greater than 4. Since each event is independent, we multiply the probabilities of each event. P(H) = 0.5 or 1/2 P(Dice > 4) = P(5) + P(6) = 1/6 + 1/6 = 2/6 = 1/3 P(H) AND P(Dice > 4) = 1/2 * 1/3 = [B]1/6 [MEDIA=youtube]ofsbmHmQmjs[/MEDIA][/B]

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation. Perimeter of a rectangle: P = 2l + 2w We have P = 165 and l = x --> x>50 and width y <= 20. Plug these into the perimeter formula [B]165 = 2x + 2y where x > 50 and y <= 20[/B]

a fever is generally considered to be a body temperature greater than 100 F. You friend has a temperature of 37 C. Does you friend have a fever? 37 Celsius equals 98.6 F. Since this is less than 100F, your friend does not have a fever.

A is the set of integers greater than or equal to -5 and less than or equal to -2 [B]-5 <= A <= -2[/B]

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 32 fluid ounces. How many fluid ounces of water are stored in the container? Round your answer to the nearest whole number. 44.9 quarts * 32 fluid ounce / quart = 1,436.8 if we found to the nearest whole number, we round up since 0.8 is greater than 0.5, so we get: [B]1,437 fluid ounces[/B]

a more than b is greater than 6 a more than b: b + a Is greater than 6 means an inequality using the > sign: [B]b + a > 6[/B]

A natural number greater than 1 has only itself and 1 as factors is called a [B]prime number.[/B]

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form Let's review the vitals of this question: [LIST] [*]The probability of heads on a fair coin is 1/2. [*]On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability. [*]So we have a combination of outcomes below: [/LIST] Outcomes [LIST=1] [*]Heads and 4 [*]Heads and 5 [*]Heads and 6 [/LIST] For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities: [LIST=1] [*]P(Heads and 4) = 1/2 * 1/6 = 1/12 [*]P(Heads and 5) = 1/2 * 1/6 = 1/12 [*]P(Heads and 6) = 1/2 * 1/6 = 1/12 [/LIST] Since we want any of those events, we add all three probabilities 1/12 + 1/12 + 1/12 = 3/12 This fraction is not simplified. S[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F12&frac2=3%2F8&pl=Simplify']o we type this fraction into our search engine, and choose Simplify[/URL]. We get a probability of [B]1/4[/B]. By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine: [URL='https://www.mathcelebrity.com/perc.php?num=1&den=4&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']1/4 to decimal[/URL] Alternative Answers: [LIST] [*]For a decimal, we get [B]0.25[/B] [*]For a percentage, we get [B]25%[/B] [/LIST]

A number m is no less than -8 and fewer than 9. No less than means greater than or equal to: m >= -8 Fewer than 9 means less than 9: m < 9 Combine these two inequalities to get [B]-8 <= m < 9[/B]

A number n is no less than 2 and no more than 49. This is a compound inequality. Let's break it into parts. Step 1: No more than 49 means 49 or less. Or, less than or equal to 49 <= 49 Step 2: no less than 2 means 2 or greater. Or, greater than or equal to 2 >=2 Writing this in terms of the number n, we have: [B]2 <= n <= 49[/B]

A number t is no less than 30 and fewer than 40. This is a compound inequality. Take it in 3 parts: Step 1: fewer than 40 means less than (does not include 40) t < 40 Step 2: no less than 30 means greater than or equal to t >= 30 Step 3: Combine these 2 statements into one compound inequality: [B]30 <= t < 40[/B]

A package that is heavier than 11 lbs and 8 oz will have a label that says HEAVY on it. Gloria packed 6 flowerpots to send to her customers. Each of the flowerpots weighs 1 lb and 12 oz. The packing material weighs 5 oz. Will her package be labeled as HEAVY? Calculate weight of flowerpots: Flowerpot weight = Weight per flowerpot * number of flowerpots Flowerpot weight = 1 lb 12 oz * 6 Flowerpot weight = 6 lb and 72 oz Since 72oz = 72/16 = 4 lbs and 8 oz, we have: Flowerpot weight = 6 lb 8 oz + 4 lbs and 8 oz = 12 lb 16 oz Since 16oz = 1 lb, we have: 13lb Add in the 5 oz of packing material, we have: 13lb 5 oz Since this is greater than 11lb 8oz, the package [B]will be labeled as HEAVY[/B]

A pair of dice is rolled. Find the probability of rolling a sum of not less than 5. The phrase [I]not less than[/I] also means greater than or equal to. So we [URL='https://www.mathcelebrity.com/2dice.php?gl=3&pl=5&opdice=1&rolist=+&dby=&ndby=&montect=+']use our 2 dice calculator for a sum roll of 5 or greater[/URL] and we get: [B]5/6[/B]

A parking lot has seventy-one parking spaces numbered from 1 to 71. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 31? Greater than or equal to means including 31 all the way through 71 31-71 is 40 spaces P(s>=31) = [B]40/71[/B]

A parking lot has sixty-eight parking spaces numbered from 1 to 68. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 21? We want P(X>=21). This is also found by taking 1 - P(X <= 20). P(X<=20) = 20/68. Reduced using a [URL='http://www.mathcelebrity.com/gcflcm.php?num1=20&num2=68&num3=&pl=GCF']GCF of 4[/URL], we get 5/17. P(X >=21) = 1 - 5/17 = [B]12/17[/B]

A quantity x is at least 10 and at most 20 The phrase [I]at most[/I] means less than or equal to The phrase [I]at least[/I] means greater than or equal to. So we have the following inequality [B]10 <= x <= 20[/B]

A quarter of a number is greater than or equal to 38. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. A quarter of a number means 1/4, so we have: x/4 The phrase [I]is greater than or equal to[/I] means an inequality, so we use the >= sign in relation to 38: [B]x/4 >= 38 <-- This is our algebraic expression [/B] If you want to solve this inequality, [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=38&propsign=%3E%3D&den1=4&den2=1&pl=Calculate+missing+proportion+value']we type it in the search engine[/URL] to get: x >= [B]152[/B]

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards greater than the width. What is the width of the parking lot? The perimeter of a rectangle is: 2l + 2w = P. We're given 2 equations: [LIST=1] [*]2l + 2w = 152 [*]l = w + 12 [/LIST] Substitute equation (2) into equation (1) for l: 2(w + 12) + 2w = 152 2w + 24 + 2w = 152 Combine like terms: 4w + 24 = 152 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B24%3D152&pl=Solve']type this equation into our search engine[/URL] and we get: w =[B] 32[/B]

A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis? a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day b. Mean of hours that boys studied per day was greater than mean of hours that girls studied per day c. Mean of hours that boys studied per day was smaller than mean of hours that girls studied per day d. Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day [B]a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day[/B] Reason is that in hypothesis testing, you take a position other than what is assumed or what is being tested as the null hypothesis

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package weight. Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1. Set up the price function P(x) [B]P(x) = 0.43 + 0.29(x - 1)[/B]

A standard die is rolled. Find the probability that the number rolled is greater than 3. Using our [URL='http://www.mathcelebrity.com/1dice.php?gl=2&pl=3&opdice=1&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']dice calculator[/URL], the probability is [B]1/2 or 0.5[/B]

A sum greater than 5 A sum implies two variables or more. Let's use 2, x and y [B]x + y > 5[/B]

These are now available as shortcuts. You can type any number or variable in the following forms: [LIST] [*]Absolute value of x less than 8 [*]Absolute value of x less than or equal to 8 [*]Absolute value of x greater than 8 [*]Absolute value of x greater than or equal to 8 [*]Absolute value of x equal to 8 [/LIST]

Alberto’s salary was $1500 greater than 5 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y. Let x be Alberto's salary. Let y be Nick's salary. We have: Let's break this down: [LIST=1] [*]5 times Nick's salary (y), means we multiply the variable y by 5 [*]$1500 greater means we add $1500 to 5y [/LIST] [B]x = 5y - 1500[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y. If Alberto's salary is x and Nick's salary is y, we have: [B]x = 4y + 2000[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y. Let Alberto's salary be x, and Nick's salary be y. We have: [B]x = 4y + 2000[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y. If Alberto's salary is x and Nick's is y, we have: [B]x = 4y + 2000 [/B](since greater than means we add)

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today? Let m be the number of minutes. The phrase [I]at least[/I] means an inequality, also known as greater than or equal to. So we have: m >= 11*6 [B]m >= 66 You can read this as Ali will run 66 or more minutes today. Or at least 66 minutes. Or greater than or equal to 66 minutes[/B]

We have two expressions here, so we need a union since we have the word [U]or[/U]. First, All real numbers less than or equal to -1 is x <= -1. All real numbers greater than 5 is x > 5 So we have x <= -1 U x > 5 [MEDIA=youtube]boOueZTCSuU[/MEDIA]

all real numbers y greater than or equal to 12 Greater than or equal to means we use the sign >= [B]y >= 12[/B]

An ordinary fair die is rolled twice. The face value of the rolls is added together. Compute the probability of the following events: Event A: The sum is greater than 6. Event B: The sum is divisible by 5 or 6 or both. [URL='http://www.mathcelebrity.com/2dice.php?gl=2&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum greater than 6[/URL] = [B]7/12[/B] Sum is divisible by 5 or 6 or both This means a sum of 5, a sum of 6, a sum of 10, or a sum of 12. [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=5&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 5[/URL] = 1/9 or 4/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 6[/URL] = 5/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=10&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 10[/URL] = 1/12 or 3/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=12&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 12[/URL] = 1/36 Adding all these up, we get: (4 + 5 + 3 + 1)/36 [B]13/36[/B]

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum amount of sales you need to make in order to receive a total income of at least $1500 per month. Let the amount of sales be s. The phrase [I]at least[/I] means greater than or equal to. Since 20% is 0.2, We want to know when: 0.20s + 600 >= 1500 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.20s%2B600%3E%3D1500&pl=Solve']type this inequality into our search engine to solve for s[/URL] and we get: s >= [B]4500[/B]

Jason decided that he will sell his stocks if their values per share (x) goes below $5 or above $15. Write a compound inequality represents the values at which Jason will sell his stocks? Below $5 is also known as less than $5: x < 5 Above $15 is also known as greater than $15 x > 15 We write the compound inequality: [B]x < 5 U x > 15[/B]

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use. [U]Define variables[/U] [LIST] [*]Let c be the number of corn plants [*]Let p be the number of potato plants [/LIST] Since cost = price * quantity, we're given two inequalities: [LIST=1] [*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B] [*][B]c + p < 15[/B] [/LIST]

Free Binomial Distribution Calculator - Calculates the probability of 3 separate events that follow a binomial distribution. It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness and kurtosis.
Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor
Calculates moment number t using the moment generating function

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the tank has at least 58 liters. What are the possible numbers of minutes Charmaine could add water? This is an algebraic inequality. The phrase [I]at least[/I] means greater than or equal to. So we have: 6m + 16 >= 58 <-- This is our algebraic expression/inequality. To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=6m%2B16%3E%3D58&pl=Solve']we type this into our search engine [/URL]and we get: [B]m >= 7[/B]

Free Comparison of Numbers Calculator - Compares two numbers and checks to see if they are equal to one another, if the first number is greater than the second number, or the first number is less than the second number. Minimum and maximum.

Conventionally, the null hypothesis is false if the probability value is: a. Greater than 0.05 b. Less than 0.05 c. Greater than 0.95 d. Less than 0.95 [B]b. Less than 0.05[/B] This is standard in hypothesis testing using p = 0.05

d squared is greater than or equal to 17 d squared means we raise the variable d to the power of 2: d^2 The phrase [I]greater than or equal to[/I] means an inequality. So we set this up using the >= in relation to 17: [B]d^2 >= 17[/B]

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the fries contain 15 grams of fat and the shake contains 9 grams of fat, how many burgers, at 17 grams of fat each, can Dan add to his fries and milkshake if he wants to keep the total fat content of his meal no greater than 69 grams? His original meal is 1 fry and 1 shake. This contains 15 + 9 = 24 grams of fat. To limit his meal to 69 grams of fat, he has 69 - 24 = 45 grams of fat left over. Therefore, he can consume: 17b <= 45 where b is the number of burgers Dividing by 17, we get b = 2.65. Since he does not want to go over 45, he can eat 2 burgers.

difference between 2 positive numbers is 3 and the sum of their squares is 117 Declare variables for each of the two numbers: [LIST] [*]Let the first variable be x [*]Let the second variable be y [/LIST] We're given 2 equations: [LIST=1] [*]x - y = 3 [*]x^2 + y^2 = 117 [/LIST] Rewrite equation (1) in terms of x by adding y to each side: [LIST=1] [*]x = y + 3 [*]x^2 + y^2 = 117 [/LIST] Substitute equation (1) into equation (2) for x: (y + 3)^2 + y^2 = 117 Evaluate and simplify: y^2 + 3y + 3y + 9 + y^2 = 117 Combine like terms: 2y^2 + 6y + 9 = 117 Subtract 117 from each side: 2y^2 + 6y + 9 - 117 = 117 - 117 2y^2 + 6y - 108 = 0 This is a quadratic equation: Solve the quadratic equation 2y2+6y-108 = 0 With the standard form of ax2 + bx + c, we have our a, b, and c values: a = 2, b = 6, c = -108 Solve the quadratic equation 2y^2 + 6y - 108 = 0 The quadratic formula is denoted below: y = -b ± sqrt(b^2 - 4ac)/2a [U]Step 1 - calculate negative b:[/U] -b = -(6) -b = -6 [U]Step 2 - calculate the discriminant Δ:[/U] Δ = b2 - 4ac: Δ = 62 - 4 x 2 x -108 Δ = 36 - -864 Δ = 900 <--- Discriminant Since Δ is greater than zero, we can expect two real and unequal roots. [U]Step 3 - take the square root of the discriminant Δ:[/U] √Δ = √(900) √Δ = 30 [U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U] Numerator 1 = -b + √Δ Numerator 1 = -6 + 30 Numerator 1 = 24 [U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U] Numerator 2 = -b - √Δ Numerator 2 = -6 - 30 Numerator 2 = -36 [U]Step 6 - calculate your denominator which is 2a:[/U] Denominator = 2 * a Denominator = 2 * 2 Denominator = 4 [U]Step 7 - you have everything you need to solve. Find solutions:[/U] Solution 1 = Numerator 1/Denominator Solution 1 = 24/4 Solution 1 = 6 Solution 2 = Numerator 2/Denominator Solution 2 = -36/4 Solution 2 = -9 [U]As a solution set, our answers would be:[/U] (Solution 1, Solution 2) = (6, -9) Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution

Estimate a 15% tip on a dinner bell of $49.76 by first round the bill amount to the nearest $10. Round the bill to the nearest $10 [LIST] [*]$49.76 is in between ($40, $50) [*]1/2 of that interval is (40 + 50)/2 = 90/2 = 45 [*]Since $49.76 is greater than or equal to 45, we round up to $50 [/LIST] Add a 15% tip 50(1 + 0.15) = 50 + 7.50 = [B]$57.50[/B]

Factors of 36 between 2 and 12 We type in [I][URL='https://www.mathcelebrity.com/factoriz.php?num=36&pl=Show+Factorization']factors of 36[/URL][/I] into our search engine and we get: {1, 2, 3, 4, 6, 9, 12, 18, 36} The problem asks for factors of 36 between 2 and 12: Between does not mean inclusive, so we have anything greater than 2 and less than 12: [B]{3, 4, 6, 9}[/B]

Free Find two numbers word problems Calculator - Given two numbers with a sum of s where one number is n greater than another, this calculator determines both numbers.

Five less than a number is at least -7 and at most 7. A number signifies an arbitrary variable, let's call it x. Five less than a number: x - 5 Is at least -7 means greater than or equal to and at most 7 means less than or equal to, so we have a joint inequality: [B]-7 <= x - 5 <= 7[/B]

Four more then double a number is greater than 2 Double a number: A number implies an arbitrary variable, let's call it "x". Double means multiply this by 2 2x Four more than this: 2x + 4 Now, we set this expression as an inequality greater than 2 [B]2x + 4 > 2[/B]

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In rolling a die, the event E is getting a number greater than or equal to 3. What is the complement of the event? The complement E' is everything but the event. So we have: E = P(n >= 3) E' = [B]P(n < 3)[/B]

Yes, it's close to the upper bound. I just wonder what we interpret the below inequality is? y > 10% x + x My two cents: y is greater than 10% upper x What do you say?

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours she needs to work to earn at least $120. A few things to note: [LIST] [*]Earnings = Rate * time [*]Let h be the number of hours worked [*]The phrase [I]at least[/I] means greater than or equal to, so we have the following inequality. [/LIST] We represent this with the following inequality: 7.5h < 120 To solve this inequality for h, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7.5h%3C120&pl=Show+Interval+Notation']type it into our math engine[/URL] and we get: [B]h < 16[/B]

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this. At least means greater than or equal to, so we have: [B]3x + 4y >= 76[/B]

John and Maria bought a medium pizza that has 8 slices. If John ate 2/4 slices and Maria ate 3/8, who ate more pizza? Using our [URL='http://www.mathcelebrity.com/fraction.php?frac1=2/4&frac2=3/8&pl=Compare']compare fractions,[/URL] we see 2/4 is greater than 3/8. So [B]John [/B]ate more pizza.

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which inequality represents the number of addional games he needs to play in order to score at least 255 points for the season? Let g be the number of games Jordan plays. Total points per game is 17g. And he’s already scored 153. So we need 17g + 153 to be [I]at least [/I]255. The phrase at least means greater than or equal to, so we use the >= operator for our inequality: [B]17g + 153 >= 255[/B]

Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he must score at least 660 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests, n, in order to get an A. We want to know n, such that 556 + n >= 660. <-- We use >= symbol since at least means greater than or equal to. 556 + n >= 660 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=556%2Bn%3E%3D660&pl=Solve']equation/inequality calculator[/URL], we get [B]n >= 104[/B]

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car that keisha wants to buy costs at least $5440. How many hours does Keisha need to babysit to earn enough to buy the car Set up the Earning function E(h) where h is the number of hours Keisha needs to babysit: E(h) = 8h + 1300 The question asks for h when E(h) is at least 5440. The phrase [I]at least[/I] means an inequality, which is greater than or equal to. So we have: 8h + 1300 >= 5440 To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h%2B1300%3E%3D5440&pl=Solve']type it in our search engine[/URL] and we get: h >= [B]517.5[/B]

let x be the variable, an age that is at least 57 years old At least means greater than or equal to x >= 57

Lucas is offered either 15% or $21 off his total shopping bill. How much would have to be spent to make the 15% option the best one? Let the total bill be b. We have: 0.15b > 21 <-- Since 15% is 0.15 Using our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=0.15b%3E21&pl=Show+Interval+Notation']inequality calculator[/URL], we get [B]b>140[/B]. So any bill greater than $140 will make the 15% off option the best one, since the discount will be higher than $21.

Lucy is thinking of a number. The number is greater than two hundred twenty-five. Her number is less than 2 hundreds, 2 tens, and 7 ones. What is Lucy's number? Let the number be n. n > 225 Also: n < 2(100) + 2(10) + 7(1) n < 200 + 20 + 7 n < 227 Combine these, we get: 225 < n < 227 Only one number satisfies this: n = [B]226 [MEDIA=youtube]-LFbAZFy13o[/MEDIA][/B]

M is the set of integers that are greater than or equal to -1 and less than or equal to 2 We include -1 on the left, and include 2 on the right [B]M = {-1, 0, 1, 1, 2)[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be? Let m be Marty's age and w be Warren's age. We have two equations: (1) m = 6w - 3 (2) m + w > 11 Plug (1) into (2) 6w - 3 + w > 11 Combine w terms 7w - 3 > 11 Add 3 to each side 7w > 14 Divide each side by 7 w > 2 which means [B]w = 3[/B] as the youngest age.

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Nia is trying to decide between two possible jobs. Job A pays $2000 a month with a 2% annual raise. Job B pays 24,000 a year with a $500 annual raise. Write a function to represent the annual salary for Job A after x years. Write a function to represent the annual salary for Job B after x years. After how many years would Nia have a greater salary at Job A? Nia Job A salary at time t: S(t) $2,000 per month equals $24,000 per year. So we have S(t) = 24,000(1.o2)^t Nia Job B salary at time t: S(t) $24,000 per year. So we have S(t) = 24,000 + 500t We want to know t when Job A salary is greater than Job B Salary: 24,000(1.o2)^t > 24,000 + 500t Time | A | B 0 | 24000 | 24000 1 | 24480 | 24500 2 | 24969.6 | 25000 3 | 25468.99 | 25500 4 | 25978.37 | 26000 5 | 26497.94 | 26500 6 | 27027.9 | 27000 7 | 27568.46 | 27500 8 | 28119.83 | 28000 9 | 28682.22 | 28500 10 | 29255.87 | 29000 11 | 29840.98 | 29500 12 | 30437.8 | 30000 13 | 31046.56 | 30500

Nine less than a number is no more than 8 and no less than 3 A number is denoted as an arbitrary variable, let's call it x. We have a double inequality: [LIST=1] [*]No more than 8 means less than or equal to 8 [*]No less than 3 means greater than or equal to 3 [/LIST] [B]3 <= x <= 8[/B]

The product of 2 and y means we multiply 2y Nine less than that product means we subtract 9 2y - 9 Finally, the entire expression is not less than 15, which means 15 or more. We use greater than or equal to [B]2y - 9 >= 15 [/B] If you want to solve this inequality and write the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=2y-9%3E%3D15&pl=Solve']our calculator[/URL].

Normal body temperature is 98.6 ̊ F. Write an inequality that describes the temperature, T, of people with above normal temperatures. Above means greater than, so we set up the inequality: [B]T > 98.6 ̊[/B]

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People with a drivers license are at least 16 years old and no older than 85 years old. Set up the inequality, where p represents the people: [LIST=1] [*]The phrase [I]at least[/I] means greater than or equal to. So we use the >= sign. 16 <= p [*]The phrase [I]no older than[/I] means less than or equal to. So we use the <= sign. p <= 85 [/LIST] Combine these inequalities, and we get: [B]16 <= p <= 85[/B] To see the interval notation for this inequality and all possible values, visit the [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=16%3C%3Dp%3C%3D85&pl=Show+Interval+Notation']interval notation calculator[/URL].

(1), how can probability be greater than 1?

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Less than means we do not include 4. But positive means greater than 0, so we have: {1, 2, 3}

Update, this has been added to our shortcuts. You can type any expression in the form, positive numbers less than x where x is any integer. You can also type positive numbers greater than x where x is any integer. Same with less than or equal to and greater than or equal to.

Rhonda raised $245 for her softball team's fundraiser.She wants to raise no less than $455.Write and solve an inequality to determine how much more money Rhonda must raise to reach her goal. Let d represent the amount of money in dollars Rhonda must raise to reach her goal. The phrase [I]no less than[/I] is an inequality using the greater than or equal sign: d >= 455 - 245 d >= [B]210[/B]

Round 12.4263 to the nearest cent [LIST] [*]Work from right to left [*]3 is not greater than 5, so 6 stays the same [*]6 is 5 or more, so we round .42 up to 43. [/LIST] [B]12.43[/B]

Ryan buys candy that costs $4 per pound. He will buy at least 12 pounds of candy. What are the possible amounts he will spend on candy? Clue for you: the phrase [I]at least[/I] means an inequality. Let s be the spend on candy. Cost = Price * quantity Cost = 4 * 12 Cost = 48 The phrase [I]at least[/I] means greater than or equal to: [B]s >= 48[/B]

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next week, Sarah is scheduled to work 8 hours at the daycare center. Which of the following inequalities represents the number of hours (h) that Sandra needs to work at the restaurant next week to earn at least $156 from these two jobs? Set up Sarah's earnings function E(h) where h is the hours Sarah must work at the restaurant: 12h + 9(8) >= 156 <-- The phrase [I]at least[/I] means greater than or equal to, so we set this up as an inequality. Also, the daycare earnings are $9 per hour * 8 hours Multiplying through and simplifying, we get: 12h + 72 >= 156 We [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B72%3E%3D156&pl=Solve']type this inequality into the search engine[/URL], and we get: [B]h>=7[/B]

Set C is the set of two-digit even numbers greater than 72 that do not contain the digit 8. First, two-digit numbers mean anything less than 100. Let's, list out our two-digit even numbers greater than 72 but less than 100. C = {74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98} The problem asks for numbers that do not contain the digit 8. Let's remove those numbers from the list. C = {74, 76, [S]78[/S], [S]80, 82, 84, 86, 88[/S], 90, 92, 94, 96, [S]98[/S]} [B]C = {74, 76, 90, 92, 94, 96} [MEDIA=youtube]_O6nXX0V4zo[/MEDIA][/B]

Seven subtracted from the product of 3 and a number is greater than or equal to -26 [LIST=1] [*]A number means an arbitrary variable, let's call it x. [*]The product of 3 and a number is written as 3x [*]Seven subtracted from 3x is written as 3x - 7 [*]Finally, that entire expression is greater than or equal to -26: [B]3x - 7 >= - 26[/B] [/LIST]

First, the phrase [I]a number[/I] means we choose an arbitrary variable, let's call it x. Twice a number means we multiply it by 2. 2x Six less than that means we subtract 6 2x - 6 Now, the last piece, we set up an inequality. At least -1 means greater than or equal to 1. At most 1 means less than or equal to 1. Notice, for both points, we include the number. -1 <= 2x - 6 <= 1

List out the sums greater than 8: (4, 5) (4, 6) (5, 5) (5, 6) (6, 6) (5, 4) (6, 4) (6, 5) Since there are 6 * 6 = 36 total outcomes, we have the probability of the sum greater than 8 as: 8/36 = 2/9

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed. a. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months? b. What is the average precipitation of 5 randomly selected years for the first 7 months? c. What is the probability of 5 randomly selected years will have an average precipitation greater than 18 inches for the first 7 months? [URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=1&pl=P%28X+%3E+Z%29']For a. we set up our z-score for[/URL]: P(X>18) = 0.7088 b. We assume the average precipitation of 5 [I]randomly[/I] selected years for the first 7 months is the population mean μ = 19.32 c. [URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=5&pl=P%28X+%3E+Z%29']P(X > 18 with n = 5)[/URL] = 0.8907

the average, a, is at least 85 At least is an inequality. It also means greater than or equal to, so we have: [B]a >= 85[/B]

The charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.4 hours, 3 hours, and 8.5 hours. Set up the cost function C(h), where h is the number of hours to rent the trailer. We have, for any hours greater than 2: C(h) = 30 + 9(h - 2) Simplified, we have: C(h) = 9h - 18 + 30 C(h) = 9h + 12 The question asks for C(2.4), C(3), and C(8.5) [U]Find C(2.4)[/U] C(2.4) = 9(2.4) + 12 C(2.4) = 21.6 + 12 C(2.4) = [B]33.6 [/B] [U]Find C(3)[/U] C(3) = 9(3) + 12 C(3) = 27 + 12 C(2.4) = [B][B]39[/B][/B] [U]Find C(8.5)[/U] C(8.5) = 9(8.5) + 12 C(8.5) = 76.5 + 12 C(8.5) = [B]88.5[/B]

The difference between A and B is no less than 30 The difference between means we subtract. No less than means greater than or equal to, so we have the following inequality; [B]A - B >= 30[/B]

the difference between A and B is no less than 30. The difference between a and b: a - b The phrase [I]no less than[/I] means an inequality. You can also say this as [I]greater than or equal to[/I]. [B]a - b >= 30[/B]

The difference of twice a number and 4 is at least -27. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x Twice a number means multiply the number by 2 2x [I]and 4[/I] means we add 4 to our expression: 2x + 4 [I]Is at least[/I] means an inequality. In this case, it's greater than or equal to: [B]2x + 4 >= -27 [/B] To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B4%3E%3D-27&pl=Solve']type it in the search engine[/URL].

The domain of a relation is all even negative integers greater than -9. The range y of the relation is the set formed by adding 4 to the numbers in the domain. Write the relation as a table of values and as an equation. The domain is even negative integers greater than -9: {-8, -6, -4, -2} Add 4 to each x for the range: {-8 + 4 = -4, -6 + 4 = -2. -4 + 4 = 0, -2 + 4 = 2} For ordered pairs, we have: (-8, -4) (-6, -2) (-4, 0) (-2, 2) The equation can be written: y = x + 4 on the domain (x | x is an even number where -8 <= x <= -2)

The larger number b exceeds the smaller number c by 45. Exceeds means greater than or more than, so we have: [B]b = c + 45[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden. Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given: [LIST=1] [*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I] [*]2l + 2w = 72 [/LIST] We substitute equation (1) into equation (2) for l: 2(3w + 4) + 2w = 72 Multiply through and simplify: 6w + 8 + 2w = 72 (6 +2)w + 8 = 72 8w + 8 = 72 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get: w = [B]8 [/B] To solve for l, we substitute w = 8 above into Equation (1): l = 3(8) + 4 l = 24 + 4 l = [B]28[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters A garden is a rectangle, which has perimeter P of: P = 2l + 2w With P = 72, we have: 2l + 2w = 72 We're also given: l = 3w + 4 We substitute this into the perimeter equation for l: 2(3w + 4) + 2w = 72 6w + 8 + 2w = 72 To solve this equation for w, we t[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B8%2B2w%3D72&pl=Solve']ype it in our search engine[/URL] and we get: w =[B] 8[/B] Now, to solve for l, we substitute w = 8 into our length equation above: l = 3(8) + 4 l = 24 + 4 l = [B]28[/B]

The longest bridge in america is 1700 ft long. Write an inequality that describes the length of every bridge. Let the bridge length be b. Since no bridge will ever be greater than 1700 ft, we have: [B]b <= 1700[/B]

The lowest score that is greater than 25% of the scores. [B]This is defined as the 25th percentile.[/B]

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An average sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement? Let a be the number of apples required. The phrase [I]at least[/I] means greater than or equal to, so we have the inequality: 6a >= 50 To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6a%3E%3D50&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get: [B]a >= 8.3333 apples or rounded up to a full number, we get 9 apples[/B]

the number of students allowed on a trip cannot be greater than 85 let s represent the number of students x <= 85

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio? Perimeter of a rectangle is: P = 2l + 2w We're given l = w + 3 and P = 54. So plug this into our perimeter formula: 54= 2(w + 3) + 2w 54 = 2w + 6 + 2w Combine like terms: 4w + 6 = 54 [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 12[/B] Plug this into our l = w + 3 formula: l = 12 + 3 [B]l = 15[/B]

Let's take this by pieces. The product of 8 and a number k is written as: 8k. Since it's greater than 4, but not more than 16, we include this in the middle of an inequality statement. 4 < 8k <= 16 Notice no more than has an equal sign, it means less than or equal to. Greater does not include an equal sign.

the product of a number and 15 is not less than 15 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. x the product of a number and 15 means we multiply x by 15 15x The phrase [I]not less than[/I] means greater than or equal to. We set 15x greater than prequel to 15 [B]15x >= 15 <-- This is our algebraic expression [/B] [U]If the problem asks you to solve for x:[/U] Divide each side by 15: 15x/15 >= 15/15 [B]x >= 1[/B]

The product of a number b and 3 is no less than 12. A number b is just written as b. So we have: The product of b and 3 is no less than 12. take this in parts: [LIST] [*]The product of b and 3: 3b [*]The phrase [I]is no less than[/I] means an inequality, so we have greater than or equal to. We set 3b greater than or equal to 12 [/LIST] [B]3b >= 12[/B]

The product of two consecutive integers is greater than 100 Take an integer x. Next consecutive integer is x + 1 The product of those integers is: x(x + 1) This product is greater than 100 which gives us the algebraic expression of: x(x + 1) > 100 IF we want to solve for x: x^2 + x > 100 Subtract 100 from each side: x^2 + x - 100 > 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-100%3E0&pl=All&hintnum=+0']Solve this quadratic:[/URL]

The product of x and 7 is not greater than 21 The product of x and 7: 7x Is not greater than means less than or equal to, so we have our algebraic expression: 7x <= 21 If you want to solve this inequality and interval notation, use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=7x%3C%3D21&pl=Show+Interval+Notation']calculator[/URL]. [MEDIA=youtube]pyYaiKSI0ZQ[/MEDIA]

The product of x and u is not greater than 21 The product of x and u xu Not greater than means less than or equal to: xu <= 21

We write the quotient: m/-2, but move the negative sign to the top. -m/2 Next, greater than 24 means we use the > sign -m/2 > 24

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk [I]m[/I] and cups of juice [I]j[/I] a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone? Total calcium = Milk calcium + Juice Calcium Calculate Milk Calcium: Milk Calcium = 299m where m is the number of cups of milk Calculate Juice Calcium: Juice Calcium = 261j where j is the number of cups of juice The phrase [I]meet or exceed[/I] means greater than or equal to, so we have an inequality, where Total Calcium is greater than or equal to 1000. So we write our inequality as: Milk calcium + Juice Calcium >= Total Calcium [B]299m + 261j >= 1000[/B]

The science club charges 4.50 per car at their car wash. Write and solve and inequality to find how many cars they have to wash to earn at least 300 Let x be the number of cars they wash. Set up our inequality. Note, at least 300 means 300 or greater, so we use greater than or equal to. [U]Inequality:[/U] [B]4.50x >= 300 [/B] [U]So solve for x, divide each side by 4[/U] [B]x >= 66.67[/B]

The sum is greater than 7, the sum is divisible by 2 2 dice sum greater than 7 means 8, 9, 10, 11, 12. Now take this set, and intersect it with sums divisible by 2. [B]8, 10, 12[/B]

The sum of 2x and y is at least 20 The sum of 2x and y: 2x + y The phrase [I]is at least[/I] means an inequality. We write this as >= or greater than or equal to: [B]2x + y >= 20[/B]

The sum of 3 consecutive integers is greater than 30. Let the first consecutive integer be n The second consecutive integer is n + 1 The third consecutive integer is n + 2 The sum is written as: n + n + 1 + n + 2 Combine like terms: (n + n + n) + (1 + 2) 3n + 3 The phrase [I]greater than[/I] means an inequality, which we write as: [B]3n + 3 > 30[/B]

[I]Is at least [/I]means greater than or equal to: 5x + 2x >= 70 If we combine like terms, we have: 7x >=70 We can further simplify by dividing each side of the inequality by 7 x >=10 If you want the interval notation for that, use the [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3E%3D10&pl=Show+Interval+Notation']interval notation calculator[/URL].

The sum of a number b and 3 is greater than 4 and no more than 16 The sum of a number b and 3: b + 3 Greater than 4 and no more than 16 means we have a combo inequality: [LIST] [*]Greater than 4 means we use a > sign [*]No more than 16 means less than or equal to, so <= [/LIST] [B]4 < b + 3 <= 16[/B]

The value of 3 times the quantity of 4 + x is greater than 6 less than x. 3 times the quantity 4 + x 3(4 + x) 6 less than x x - 6 3 times the quantity 4 + x is greater than x - 6 [B]3(4 + x) > x - 6[/B]

The Waist to Hip Ratio (WHR) is commonly expressed as a decimal. WHR has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Jonia has a WHR greater than 1, she is at “high risk” for cardiovascular problems. Jonia’s waist measurement is 42 inches and her hip measurement 2 inches less. Jonia's WHR: WHR = W/H WHR = 42/(42 - 2) WHR =4 2/40 WHR = [B]1.5 which is high risk[/B]

There are 113 identical plastic chips numbered 1 through 113 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is greater than 44? We want 45, 46, … 113 The formula to get inclusive number count between and including 2 numbers is: Total numbers = L - S + 1 Total numbers = 113 - 45 + 1 Total numbers = 69 That is 69 possible numbers. We draw this out of a total of 113 [B]P(Number > 44) = 69/113 [B]P(Number > 44) [/B]= 0.610619 [MEDIA=youtube]BLBVcpdHqXU[/MEDIA][/B]

[SIZE=4]There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more than 14 pencils. Which of the following could be the total number of pencils in all 5 cases? A) 35 B) 45 C) 65 D) 75 [U]Determine the minimum amount of pencils (At least means greater than or equal to):[/U] Minimum Amount of pencils = Cases * Min Quantity Minimum Amount of pencils = 5 * 10 Minimum Amount of pencils = 50 [SIZE=4][U]Determine the maximum amount of pencils (Not more than means less than or equal to):[/U] Maximum Amount of pencils = Cases * Min Quantity Maximum Amount of pencils = 5 * 14 Maximum Amount of pencils = 70[/SIZE] So our range of pencils (p) is: 50 <= p <= 70 Now take a look at our answer choices. The only answer which fits in this inequality range is [B]C, 65[/B]. [B][/B][/SIZE]

There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than 7. First Event: P(1, 3, 5, 7, 9) = 5/10 = 1/2 or 0.5 Second Event: P(8, 9, 10) = 3/10 or 0.3 Probability of both events since each is independent is 1/2 * 3/10 = 3/20 = [B]0.15 or 15%[/B]

This is a double inequality. Let's take it by pieces: Three more than 2x is denoted as 2x + 3. We add since we see the phrase, [I]more than[/I]. Because it's greater than or equal to 1, we have: 1 <= 2x + 3 Finally, that same phrase is [U]also[/U] less than or equal to 11. 2x + 3 <= 11. Piecing these two inequalities together, we have: 1 <= 2x + 3 <= 11.

This is a two-part inequality. Let's take it piece by piece. Three more than 2x means we add. 2x + 3 It's greater than or equal to 1, denoted below: 1 <= 2x + 3 It's also less than or equal to 11, denoted below 2x + 3 <= 11 Piece these two inequalities together: 1 <= 2x + 3 <= 11

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be? Let my current age be a. We're given: 4/5a > 3/4(a + 1) Multiply through on the right side: 4a/5 > 3a/4 + 3/4 Let's remove fractions by multiply through by 5: 5(4a/5) > 5(3a/4) + 5(3/4) 4a > 15a/4 + 15/4 Now let's remove the other fractions by multiply through by 4: 4(4a) > 4(15a/4) + 4(15/4) 16a > 15a + 15 [URL='https://www.mathcelebrity.com/1unk.php?num=16a%3E15a%2B15&pl=Solve']Typing this inequality into our search engine[/URL], we get: a > 15 This means the smallest [I]integer age[/I] which the problem asks for is: 15 + 1 = [B]16[/B]

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260 person-hours per week. Tom has one part-time employeewho works 20 hours per week. Each full-time employee works 40 hours per week. Write an inequality to determine n, the number of full-time employees Tom must schedule, so that his employees will work at least 260 person-hours per week. Set up the inequality: [LIST] [*]Add the part-timer's hours of 20 [*]Full time hours is 40 times n employees [*]At least means greater than or equal to, so we use the >= sign [/LIST] [B]40n + 20 >= 260[/B]

Translate and solve: 30 times m is greater than −330. (Write your solution in interval notation.) 30 times m: 30m is greater than -330 30m > -330 Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=30m%3E-330&pl=Show+Interval+Notation']equation and interval solver[/URL], we get: m > -11

Two dice are rolled. Determine the probability of the following. Rolling an even number or a number greater than 6 We want P(X = Even) or P(X>6) With 2 dice, our die totals are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Evens are: 2, 4, 6, 8, 10, 12 > 6 = 7, 8, 9, 10, 11, 12 When the problem states [I]or[/I] it means either of the sets. When we take the union of both sets, we get: 2,4,6,7,8,9,10,11,12 This is 9 possible entries out of 12: 9/12 We can simplify this by dividing top and bottom by 3: P(X = Even) or P(X>6) = [B]3/4 or 0.75[/B]

two unbiased dice are thrown. find the probability that the total number on the dice is greater than 10 [URL='http://www.mathcelebrity.com/2dice.php?gl=2&pl=10&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']From our 2 dice calculator[/URL]: We have (5,6),(6,5),(6,6) P(Sum) > 10 is [B]1/12[/B]

Let x be our variable: We write x, such that x is greater than 4 below: [B]{x | x > 4}[/B]

what is the smallest number greater than 400 that is divisible by 9? 400/9 = 44.4444 Round down to 45. 45 * 9 = [B]405[/B]

X is at least as large as 4. This is an algebraic expression, where the phrase [I]at least as large as[/I] means greater than or equal to: [B]x >=4[/B]

x is smaller than 9 and greater than 4 Written as: 4 < x < 9 To display the interval notation, use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=4%3Cx%3C9&pl=Show+Interval+Notation']interval notation calculator[/URL].

X is such that X belongs to rational numbers and X is less than or equal to 1 and greater than 0 Greater than 0 means we don't include 0 0 < less than or equal to 1 means we include 1: [B]0 < x <= 1[/B]

You have to pay 29 a month until you reach 850 how many months will that take. Let m be the number of months. We set up the inequality: 29m > = 850 <-- We want to know when we meet or exceed 850, so we use greater than or equal to [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=29m%3E%3D850&pl=Show+Interval+Notation']Type this inequality into our search engine[/URL], and we get: m >= 29.31 We round up to the next integer month, to get [B]m = 30[/B].

you must be 65 or older to join inequality Let a be the age. 65 or older means greater than or equal to 65: [B]a >=65[/B]

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of rolling these two dice, given that the red die shows an even number and the green die shows an odd number greater than 1? [LIST] [*]Red Die Sample Space {2, 4, 6} [*]Green Die Sample Space {3, 5} [*]Total Sample Space {(2, 3), (2, 5), (4, 3), (4, 5), (6, 3), (6, 5)} [*]The sie of this is 6 elements. [/LIST]

Your grade must be at least 60 to pass this class Assumptions and givens: [LIST] [*]The phrase [I]at least[/I] means greater than or equal to. [*]Let g be your grade [/LIST] We have: [B]g >= 60[/B]