A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model that represents the number y of muffins that the bakery sells x years after 2010. Find the number of muffins sold after 2010 through 2015: 7,420 - 5,800 = 1,620 Now, since the problem states a linear sales model, we need to determine the sales per year: 1,620 muffins sold since 2010 / 5 years = 324 muffins per year. Build our linear model: [B]y = 5,800 + 324x [/B] Reading this out loud, we start with 5,800 muffins at the end of 2010, and we add 324 more muffins for each year after 2010.

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970 The formula for accumulated value of something with a percentage growth p and years x is: V(x) = Initial Value * (1 + p/100)^x Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have: V(x) = 100 * (1 + 8/100)^50 V(x) = 100 * (1.08)^50 V(x) = 100 * 46.9016125132 V(x) = [B]4690.16[/B]

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m minutes is $21.20. Write an equation that models this situation. Let m be the number of minutes. We have the cost equation C(m): [B]0.25m + 12.95 = $21.20[/B]

A company’s number of personnel on active duty (not on sick leave or vacation leave) during the period 2000 - 2013 can be approximated by the cubic model f(x) = 2.5x^3 - 15x^2 - 80x + 1025, where x = 0 corresponds to 2000. Based on the model, how many personnel were on active duty in 2010? What is the domain of f? If x = 0 corresponds to 2000, when 2010 is 2010 - 2000 = 10. We want f(10): f(10) = 2.5(10)^3 - 15(10)^2 - 80(10) + 1025 f(10) = 2.5(1000) - 15(100) - 800 + 1025 f(10) = 2500 - 1500 - 800 + 1025 f(10) = [B]1,225[/B]

A monster energy drink has 164 mg of caffeine. Each hour your system reduces the amount of caffeine by 12%. Write an equation that models the amount of caffeine that remains in your body after you drink an entire monster energy. Set up a function C(h) where he is the number of hours after you drink the Monster energy drink: Since 12% as a decimal is 0.12, we have: C(h) = 164 * (1 - 0.12)^h <-- we subtract 12% since your body flushes it out [B]C(h) = 164 * (0.88)^h[/B]

A new company is projecting its profits over a number of weeks. They predict that their profits each week can be modeled by a geometric sequence. Three weeks after they started, the company's projected profit is $10,985.00 Four weeks after they started, the company's projected profit is $14,280.50 Let Pn be the projected profit, in dollars, n weeks after the company started tracking their profits. a. What is the common ratio of the sequence? b. Calculate the initial value c. Construct a recurrence relation that can be used to model the value of Pn a. 14,280.50/10,985.00 = [B]1.3[/B] b. 3 weeks ago, the Initial value is 10,985/1.3^3 = [B]$5,000 c. Pn = 5000 * 1.3^n[/B]

a rocket is propelled into the air. its path can be modeled by the relation h = -5t^2 + 50t + 55, where t is the time in seconds, and h is height in metres. when does the rocket hit the ground We set h = 0: -5t^2 + 50t + 55 = 0 Typing this quadratic equation into our search engine to solve for t, we get: t = {-1, 11} Time can't be negative, so we have: t = [B]11[/B]

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in x number of pages, determine a function model that will represent the accumulated writing hours to finish his novel if 3 pages = 5 hours, then we divide each side by 3 to get: 1 page = 5/3 hours per page So x pages takes: 5x/3 hours Our function for number of pages x is: [B]f(x) = 5x/3[/B]

A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost of a yoga membership? Set up the cost function M(c) for classes (c) [B]M(c) = 16 + 7c[/B]

Alyssa has $952 and is spending $27 each week (w) for math tutoring write an algebraic expression to model the situation Alyssa's balance is found by using this expression: [B]952 - 27w[/B]

Bacteria in a petra dish doubles every hour. If there were 34 bacteria when the experiment began, write an equation to model this. Let h be the number of hours since the experiment began. Our equation is: [B]B(h) = 34(2^h)[/B]

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years. At any time t, the Bangladesh population at year t is: [B]y = 170,000,000(1.015)^t[/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 Basic Statistics Calculator - Given a number set, and an optional probability set, this calculates the following statistical items:
Expected Value
Mean = μ
Variance = σ²
Standard Deviation = σ
Standard Error of the Mean
Skewness
Mid-Range
Average Deviation (Mean Absolute Deviation)
Median
Mode
Range
Pearsons Skewness Coefficients
Entropy
Upper Quartile (hinge) (75th Percentile)
Lower Quartile (hinge) (25th Percentile)
InnerQuartile Range
Inner Fences (Lower Inner Fence and Upper Inner Fence)
Outer Fences (Lower Outer Fence and Upper Outer Fence)
Suspect Outliers
Highly Suspect Outliers
Stem and Leaf Plot
Ranked Data Set
Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range
Root Mean Square
Weighted Average (Weighted Mean)
Frequency Distribution
Successive Ratio

Free Binomial Option Pricing Model Calculator - This shows all 2^t scenarios for a stock option price on a binomial tree using (u) as an uptick percentage and (d) as a downtick percentage

Can a coefficient of determination be negative? Why or why not? [B]Yes, reasons below[/B] [LIST] [*] predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data [*] where linear regression is conducted without including an intercept [*] Yes, negative values of R2 may occur when fitting non-linear functions to data [/LIST]

Consider a probability model consisting of randomly drawing two colored balls from a jar containing 2 red and 1 blue balls. What is the Sample Space of this experiment? (assume B= blue and R=red) The sample space is the list of all possible events [LIST] [*]RRB [*]RBR [*]BRR [/LIST]

Free Dividend Discount Model Calculator - This calculator determines the present value of dividends using the Dividend Discount Model.

Each calendar will selll for $5.00 each. Write an equation to model the total income,y, for selling x calendars income (y) = Price * Quantity [B]y = 5x[/B]

If the correlation between two variables is close to minus one, the association is: Strong Moderate Weak None [B]Strong[/B] - Coefficient near +1 or -1 indicate a strong correlation

In a given year, Houston has good air quality 48% of the days, moderate air quality 41% of the days, and unhealthy air quality 4% of the days. How many days per year do residents have unhealthy air quality? 4% of 365 days in a year = [B]14.6 days. If we are talking full days, we have 14.[/B]

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Which inequality models this situation? Since dimes are worth $0.10 and quarters are worth $0.25, we have: [B]0.10d + 0.25q < 14.75[/B]

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Which inequality models this situation? [U]Let d be the number of dimes and q be the number of quarters[/U] [B]0.1d + 0.25q < 14.75[/B]

Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total amount of money Julio has after x weeks f(x) = Savings per week * number of weeks + starting amount f(x) = [B]10x + 150[/B]

Keith is going to Renaissance Festival with $120 to pay for his admission, food and the cost of games. He spends a total of $85 on admission and food. Games cost $5 each. Which inequality models the maximum number of games Keith can play. Let the number of games be g. Keith can spend less than or equal to 120. So we have [B]5g + 85 <= 120 [/B] If we want to solve the inequality for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=5g%2B85%3C%3D120&pl=Solve']type it in our search engine[/URL] and we have: g <= 7

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI with the following monthly billing policies. Each company's monthly billing policy has an initial operating fee and charge per megabyte. Operating Fee charge per Mb CIVSIN 29.95 0.14 GOMI 4.95 0.39 (i) Write down a system of equations to model the above situation (ii) At how many Mb is the monthly cost the same? What is the equal monthly cost of the two plans? (i) Set up a cost function C(m) for CIVSIN where m is the number of megabytes used: C(m) = charge per Mb * m + Operating Fee [B]C(m) = 0.14m + 29.95[/B] Set up a cost function C(m) for GOMI where m is the number of megabytes used: C(m) = charge per Mb * m + Operating Fee [B]C(m) = 0.39m + 4.95 [/B] (ii) At how many Mb is the monthly cost the same? Set both cost functions equal to each other: 0.14m + 29.95 = 0.39m + 4.95 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B29.95%3D0.39m%2B4.95&pl=Solve']type this equation into our search engine[/URL] and we get: m = [B]100[/B] (ii) What is the equal monthly cost of the two plans? CIVSIN - We want C(100) from above where m = 100 C(100) = 0.14(100) + 29.95 C(100) = 14 + 29.95 C(100) = [B]43.95[/B] GOMI - We want C(100) from above where m = 100 C(100) = 0.39(100) + 4.95 C(100) = 39 + 4.95 C(100) = [B]43.95[/B]

Calculation Domination: How Anybody Can Explode Their Math Scores Using the Mental Magic of Elon Musk and Warren Buffett. [MEDIA=youtube]RclG-k6itpk[/MEDIA] This audiobook shows you various mental models of the top 5% of math students. Mental models come from the following disciplines: Math Anxiety Science Problem Solving Probability Decision Making Metaphysics Persuasion Math Testing

Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5 to buy the app and then $2.99 for each month that you subscribe (a bargain!). How much would it cost to use the app for one year? Write an equation to model this using the variable “m” to represent the number of months that you use the app. Set up the cost function C(m) where m is the number of months you subscribe: C(m) = Monthly Subscription Fee * months + Purchase fee [B]C(m) = 2.99m + 5[/B]

nandita earned $224 last month. she earned $28 by selling cards at a craft fair and the rest of the money by babysitting. Complete an equation that models the situation and can be used to determine x, the number of dollars nandita earned last month by babysitting. We know that: Babysitting + Card Sales = Total earnings Set up the equation where x is the dollars earned from babysitting: [B]x + 28 = 224[/B] To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B28%3D224&pl=Solve']type it in our math engine[/URL] and we get: x = [B]196[/B]

Free Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index Calculator - Given a series of cash flows C_t at times t and a discount rate of (i), the calculator will determine the Net Present Value (NPV) at time 0, also known as the discounted cash flow model.
Profitability Index
Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activation fee and $40 per month to use the service on the phone. Write an equation that models the number of months he can afford this phone. Let m be the number of months. Our equation is: [B]40m + 75 = 500 [/B] <-- This is the equation [URL='https://www.mathcelebrity.com/1unk.php?num=40m%2B75%3D500&pl=Solve']Type this equation into the search engine[/URL], and we get: m = [B]10.625[/B] Since it's complete months, it would be 10 months.

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200? Set P(t) = 19,200 0.7t^2+6t+15,000 = 19,200 Subtract 19,200 from each side: 0.7t^2+6t+4200 = 0 The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B] t 0.7t^2 6t Add 15000 Total 1 0.7 6 15000 15006.7 2 2.8 12 15000 15014.8 3 6.3 18 15000 15024.3 4 11.2 24 15000 15035.2 5 17.5 30 15000 15047.5 6 25.2 36 15000 15061.2 7 34.3 42 15000 15076.3 8 44.8 48 15000 15092.8 9 56.7 54 15000 15110.7 10 70 60 15000 15130 11 84.7 66 15000 15150.7 12 100.8 72 15000 15172.8 13 118.3 78 15000 15196.3 14 137.2 84 15000 15221.2 15 157.5 90 15000 15247.5 16 179.2 96 15000 15275.2 17 202.3 102 15000 15304.3 18 226.8 108 15000 15334.8 19 252.7 114 15000 15366.7 20 280 120 15000 15400 21 308.7 126 15000 15434.7 22 338.8 132 15000 15470.8 23 370.3 138 15000 15508.3 24 403.2 144 15000 15547.2 25 437.5 150 15000 15587.5 26 473.2 156 15000 15629.2 27 510.3 162 15000 15672.3 28 548.8 168 15000 15716.8 29 588.7 174 15000 15762.7 30 630 180 15000 15810 31 672.7 186 15000 15858.7 32 716.8 192 15000 15908.8 33 762.3 198 15000 15960.3 34 809.2 204 15000 16013.2 35 857.5 210 15000 16067.5 36 907.2 216 15000 16123.2 37 958.3 222 15000 16180.3 38 1010.8 228 15000 16238.8 39 1064.7 234 15000 16298.7 40 1120 240 15000 16360 41 1176.7 246 15000 16422.7 42 1234.8 252 15000 16486.8 43 1294.3 258 15000 16552.3 44 1355.2 264 15000 16619.2 45 1417.5 270 15000 16687.5 46 1481.2 276 15000 16757.2 47 1546.3 282 15000 16828.3 48 1612.8 288 15000 16900.8 49 1680.7 294 15000 16974.7 50 1750 300 15000 17050 51 1820.7 306 15000 17126.7 52 1892.8 312 15000 17204.8 53 1966.3 318 15000 17284.3 54 2041.2 324 15000 17365.2 55 2117.5 330 15000 17447.5 56 2195.2 336 15000 17531.2 57 2274.3 342 15000 17616.3 58 2354.8 348 15000 17702.8 59 2436.7 354 15000 17790.7 60 2520 360 15000 17880 61 2604.7 366 15000 17970.7 62 2690.8 372 15000 18062.8 63 2778.3 378 15000 18156.3 64 2867.2 384 15000 18251.2 65 2957.5 390 15000 18347.5 66 3049.2 396 15000 18445.2 67 3142.3 402 15000 18544.3 68 3236.8 408 15000 18644.8 69 3332.7 414 15000 18746.7 70 3430 420 15000 18850 71 3528.7 426 15000 18954.7 72 3628.8 432 15000 19060.8 73 3730.3 438 15000 19168.3 74 3833.2 444 15000 19277.2

Free Population Growth Calculator - Determines population growth based on an exponential growth model.

Sam has x model planes. Anton has 8 more planes than Sam does. How many model planes Does Anton have? how many planes do they have together? Sam has x Anton has [B]x + 8[/B] since the word [I]more[/I] means we add The word [I]together[/I] means we add, so we have: Sam + Anton = x + x + 8 Grouping like terms, we have: Sam + Anton = [B]2x + 8[/B]

Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her account. Write a linear equation to model this situation? Enter your answer in y=mx b form with no spaces. Let x be the number of hours Sarah baby sits. Then her account value y is: y = [B]30x + 300[/B]

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Suppose that Candidates A and B have moderate political positions, while Candidate C is quite liberal. Voter opinions about the candidates are as follows. 35% want A as their first choice, but would also approve of B. 31% want B as their first choice, but would also approve of A. 20% want B as their first choice, and approve of neither A nor C. 10% want C as their first choice, and approve of neither A nor B. [LIST=1] [*]If all voters could vote only for their first choice, which candidate would win by plurality? [*]Which candidate wins by an approval vote? [/LIST] [U]Plurality Voting:[/U] [LIST] [*]A: 35% [*]B: 31% + 20% = 51% [*]C: 10% [/LIST] [B]Candidate B wins[/B] using the plurality voting method and a majority [U]Approval Voting:[/U] [LIST] [*]A: 35% + 31% = 2 approvals [*]B: 35% + 31% + 20% = 3 approvals [*]C: 10% = 1 approval [/LIST] Therefore, [B]Candidate B wins[/B] using the approval voting method

Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an average of 4 cars arrive at a toll bridge each second. If it is assumed that cars arrive randomly, and can thus be modeled with Poisson distribution, what is the probability that in the next second, [U][B]NO[/B][/U] cars will arrive? Use the [I]Poisson Distribution[/I] with λ = 4 and x = 0 Using the [URL='http://www.mathcelebrity.com/poisson.php?n=+10&p=+0.4&k=+0&t=+3&pl=P%28X+=+k%29']Poisson Distribution calculator[/URL], we get P(0; 4) = [B]0.0183[/B]

The cost of tuition at Johnson Community College is $160 per credit hour. Each student also has to pay $50 in fees. Model the cost, C, for x credit hours taken. Set up cost equation, where h is the number of credit hours: [B]C = 50 + 160h[/B]

The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and the ticket price are in dollars. What is the maximum profit, and how much should the tickets cost? Take the [URL='http://www.mathcelebrity.com/dfii.php?term1=-30x%5E2+%2B+360x+%2B+785&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']derivative of the profit function[/URL]: P'(x) = -60x + 360 We find the maximum when we set the profit derivative equal to 0 -60x + 360 = 0 Subtract 360 from both sides: -60x = -360 Divide each side by -60 [B]x = 6 <-- This is the ticket price to maximize profit[/B] Substitute x = 6 into the profit equation: P(6) = -30(6)^2 + 360(6) + 785 P(6) = -1080 + 2160 + 785 [B]P(6) = 1865[/B]

The observation which occurs most frequently in a sample is the [B]mode[/B]

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. What is the median recovery time? a. 2.7 b. 5.3 c. 7.4 d. 2.1 [B]b. 5.3 (mean, median, and mode are all the same in a normal distribution)[/B]

The polynomial function P(x) = 75x - 87,000 models the relationship between the number of computer briefcases x that a company sells and the profit the company makes, P(x). Find P (4000), the profit from selling 4000 computer briefcases. Plug in 4,000 for x: P(4000) = 75(4000) - 87,000 P(4000) = 300,000- 87,000 P(4000) = [B]213,000[/B]

The population of goats on a particular nature reserve t years after the initial population was settled is modeled by p(t) = 4000 - 3000e^-0.2t. How many goats were initially present? [U]Initially present means at time 0. Substituting t = 0, p(0), we get:[/U] p(0) = 4000 - 3000e^-0.2(0) p(0) = 4000 - 3000e^0 p(0) = 4000 - 3000(1) p(0) = 4000 - 3000 [B]p(0) = 1000[/B]

The revenue for selling x candles is given by f(x)=12x. The teams profit is $40 less than 80% of the revenue of selling x candles. write a function g to model the profit. Profit = Revenue - Cost We are given the revenue function f(x) = 12x. We are told the profit is 0.8(Revenue) - 40. Our profit function P(x) is: P(x) = 0.8(12x) - 40 Simplifying, we have: [B]P(x) = 9.6x - 40[/B]

The store is selling apples for $0.49 per pound. Write a function to model the cost of "p" pounds of apples. Let p be the pounds of apples. Our cost function is: [B]C(p) = 0.49p[/B]

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet. We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets: C(b) = nb + 9 We are given C(9) = 72 and b = 9 9n + 9 = 72 [URL='https://www.mathcelebrity.com/1unk.php?num=9n%2B9%3D72&pl=Solve']Run this through our equation calculator[/URL], and we get [B]n = 7[/B].

Free Trade Cost Calculator - Calculates the saved hours under the electrician/carpenter model of specializing in jobs as well as opportunity cost.

Free Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM) Calculator - Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.

Which of the following is NOT TRUE about the distribution for averages? a. The mean, median, and mode are equal. b. The area under the curve is one. c. The curve never touches the x-axis. d. The curve is skewed to the right. Answer is d, the curve is skewed to the right For a normal distribution: [LIST] [*] The area under the curve for a standard normal distribution equals 1 [*] Mean media mode are equal [*] Never touches the x-axis since in theory, all events have some probability of occuring [/LIST]

Write a model that utilizes all three explanatory variables with no interaction or quadratic terms. Choose the correct answer below. A. y i = B₀ + B1x1 + B2x2 + B3x3 + e i B. y i = B₀ + B1x1 + B2x2 + B3x3x2 + e i C. y i = B1x1 + B2x2 + B3x3 + ei D. None of the above equations satisfy all of the conditions [B]A. y i = B₀ + B1x1 + B2x2 + B3x3 + e i[/B]

you start with 150$ in year bank account if you save $28 a year with equation would model your savings find equation. We create a savings function S(y) where y is the number of years since the start. S(y) = Savings per year * y + initial savings [B]S(y) = 28y + 150[/B]