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A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function r(t) = 3t, where t represents time in minutes and r represents how far the paint is spreading. The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2. Part A: Find the area of the circle of spilled paint as a function of time, or A[r(t)]. Show your work. Part B: How large is the area of spilled paint after 10 minutes? You may use 3.14 to approximate π in this problem.

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In a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of the used at least one prescription medication (based on data from “Use of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adults in the United States,” by Qato et al., Journal of the American Medical Association, Vol. 300, No. 24) a. How many of the 3005 subjects used at least one prescription medication? b. Construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.

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At George Washington High School the ratio of graduating seniors that go on to college, as compared to those who do not, is 7 : 4. Last year 28 students went on to college. How large was the graduating class?

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A company plans to sell a new type of cleaner for $280 each. The estimated cost, y, of manufacturing the cleaners is a function with a y-int of 11,000 and a vertex of (500, 24,000). How many must be sold for the company to make a profit?

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Heidi makes stuffed toys. The initial cost for the raw material is $100 for 30 stuffed toys. Every stuffed toy she makes earns her $10. Which graph represents the profit made by Heidi for x number of stuffed toys sold?

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Axel lives in Virginia and makes $54,000 a year. If the median annual income in Virginia is $61,233 and the median annual income in the United States as a whole is $50,233, is Axel likely to qualify for Chapter 7 bankruptcy?

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Lindsie is painting on a canvas with dimensions of 3 ft by 4 ft. She wants to make a display model for a gallery that has twice the area of the original. How much should she increase the length and width by, if she wants to increase them by the same amount? Round your answer to the nearest tenth. A. 10.4 feet B. 1.4 feet C. 3.4 feet D. 8.4 feet

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Is it Exponential distribution? or Geometric distribution? The life times, Y in years of low-grade lightbulbs follow an exponential distribution with a mean of 0.7 years. A tester makes random observations of the life times of this lightbulbs and records them one by one as either a success if the life time exceeds 1 year, or as a failure otherwise. Part a)Find the probability that the first success occurs in the fifth observation. Part b) Find the probability of the second success occurring in the 8th observation given that the first success occurred in the 3rd observation. Part c) Find the probability to 2 decimal places that the first success occurs in an odd-numbered observation. That is, the first success occurs in the 1st or 3rd or 5th or 7th (and so on) observation.

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Women make up 45% of the world’s workforce. What percentage of these women live in poverty? A. 25% B. 40% C. 70% D. 85%

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Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they’ve been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by $80 from what they’ve been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Both options A and B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal.

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Which of the following scale factors results in an enlargement of an image along an opposite ray?

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Silus wants to monitor the temperature of a reaction every 0.5 seconds for 30 minutes. He plans to generate a graph of the temperature values over time and insert the graph into a text document. Which pair of tools would be best for Silus to use? a liquid-based thermometer and a graphing calculator a liquid-based thermometer and a computer an electronic temperature probe and a computer an electronic temperature probe and a graphing calculator

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A consultant needs to make at least $800 this week. She earns $80 for each new written piece and $40 for each review. Which of the following inequalities represents the possible combinations of reviews and new written pieces that she must complete? a. 80x+40y>=800 b. 80x+40y>800 c. 80x+40y

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A basketball player’s free-throw percentage is the ratio of the number of successful shots made to the number of shots attempted. A basketball player has made 13 of the first 20 free throws she has attempted this season. Which rational expression can be used to find the free throw percentage for the season if she successfully makes her next x free-throw attempts?

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So Malik is considering investing $900 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 150%, and a 50% chance that he will lose his initial investment. Determine if Malik should make the investment, and find the expected value of the investment.

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The solution to a system of inequalities is __________. A. a single point that satisfies all inequalities in the system B. a collection of points that satisfy all inequalities in the system C. a single point that satisfies at least one inequality in the system D. a collection of points that satisfy at least one inequality in the system

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Suppose that f(0)=3 and f′(x)≤7 for all values of x. Use the Mean Value Theorem to determine how large f(4) can possibly be.

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The intersection of a right cylinder and a plane makes an oval cross section. Which option is true about the plane of intersection? The right cylinder is cut with a plane parallel to the base. The right cylinder is cut with a plane perpendicular to the base and passing through the center. The right cylinder is cut with a plane perpendicular to the base but not passing through the center. The right cylinder is cut with a plane that is neither parallel nor perpendicular to the base.

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Crystal earns $5.50 per hour mowing lawns. a. Choose the rule that describes how the amount of money m earned is a function of the number of hours h spent mowing lawns. b. How much does Crystal earn if she works 3 hours and 45 minutes?

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Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 4 and a horizontal side of 10. The other triangle has a vertical side of 12 and a horizontal side of 30. Could the hypotenuses of these two triangles lie along the same line? No, because they are not similar triangles No, because one is larger than the other Yes, because they are similar triangles Yes, because they are both right triangles

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The Widget Company is planning to produce widgets. The company has rented space for its manufacturing operation at $4,000 per month. Each widget requires $32 worth of materials and $44 worth of labor. Find the total cost if it makes 350 widgets in a month.

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A company manufactures 2,000 units of its flagship product in a day. The quality control department takes a random sample of 40 units to test for quality. The product is put through a wear-and-tear test to determine the number of days it could last. If the product has a lifespan of less than 26 days, it is considered defective. The table gives the sample data that a quality control manager collected. 39 31 38 40 29 32 33 39 35 32 32 27 30 31 27 30 29 34 36 25 30 32 38 35 40 29 32 31 26 26 32 26 30 40 32 39 37 25 29 34 Which statement is true about the population proportion of defective pieces in the 2,000 items? a 5 pieces must be defective. b 100 pieces must be defective. c More than 100 pieces must be defective. d The population proportion of defective pieces must be equal to the sample proportion. e There is insufficient data to calculate the proportion of defective pieces.

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1. Ron makes $1,659 a month. What is the maximum monthly rent he can afford? $414.75 $447.93 $464.52 $774.80 2. You should be able to spend a little over 1/4 of your gross monthly pay on rent. True False 3. If Michelle makes $3,780 in monthly gross pay, what is the maximum she can afford to pay for rent? $1,058.40 $1,020.60 $907.20 $793.80

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Wendy is logging the number of video game levels she wins per hour. She has determined the function to be f(x) = 6x + 9, where x represents hours and f(x) represents the number of video game levels won. Which of the following options describes the restrictions to the domain and range correctly?

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1.Work the following pricing problems for services rendered. (Round to hundredths( Hourly rate, worker A = $15.00 Hourly rate, worker B = $8.00 Hourly rate, worker C = $5.25 Labor time, worker A = 2 1/2 hours Labor time, worker B = 1 hour Labor time, worker C = 3/4 hour Overhead rate = 75% Retail price of goods = $125.50 What is the total cost of job?

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Luis, Marlon, and Victoria are counting money. They each have the same amount in dollar bills, quarters, dimes, nickels, and pennies. They take turns matching amounts in different ways. Luis sets aside two dollars in dollar bills. Marlon makes the same amount with eight quarters. Victoria makes the same amount with one dollar bill and 10 dimes. This exercise best illustrates which function and which characteristic of money? Standard and divisibility Store of value and durability Medium of exchange and portability Measure of value and scarcity

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Which test point holds true for 3/2y – 2x>1? A. (1/4, 1) B. (4, 1) C. (1, 1/4) D. (1, 0) E. (1/4, 3/4)

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Tim has a picture frame that is 30 cm long and 24 cm wide. He wants to make a picture frame that is similar in shape but is 18 cm long. How wide should this second picture frame be? cm

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An artist wants to make alabaster pyramids using a block of alabaster with a volume of 576 cubic inches. She plans to make each pyramid with a square base area of 3 square inches and a height of 4 inches. At most, how many pyramids can the artist make from the block of alabaster? 136 144 154 166 172

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The amount of water flowing into a tank doubles every minute. The tank is full in an hour. When was the tank half full?

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