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MATH SOLVE
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At a factory that produces pistons for cars, Machine 1 produced 392 satisfactory pistons and 98 unsatisfactory pistons today. Machine 2 produced 360 satisfactory pistons and 240 unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today's batch. What is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory ?
General
4 months ago
Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. P =
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4 months ago
After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t) = 1.35te−2.802t † models the average BAC, measured in mg/mL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink). What is the maximum average BAC during the first 6 hours? (Round your answer to three decimal places.)
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4 months ago
A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach?Let X1= the number of radio ads purchasedX2= the number of television ads purchasedMaximize3,000X1+7,000X2(maximize exposure)Subject to:200X1+500X2≤40,000(budget constraint)X1≥10(at least 10 radio ads purchased)X2≥10(at least 10 television ads purchased)X1≥X2(# of radio ads ≥ # of television ads)X1, X2≥0(non-negativity constraints)
General
4 months ago
The following data represent the length of life in years, measured to the nearest tenth, of 30 similar fuel pumps: 2.0 3.0 0.3 3.3 1.3 0.4 0.2 6.0 5.5 6.5 0.2 2.3 1.5 4.0 5.9 1.8 4.7 0.7 4.5 0.3 1.5 0.5 2.5 5.0 1.0 6.0 5.6 6.0 1.2 0.2 (a) Construct a stem-and-leaf plot for the life in years of the fuel pumps, using the digit to the left of the decimal point as the stem for each observation. (b) Set up a relative frequency distribution. (c) Compute the sample mean, sample range, and sample standard deviation.
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4 months ago
A clown bought 5 bags of round balloons with 24 balloons in each bag. The clown also bought 3 bags of long balloons with 36 balloons in each bag.Part 1How many more round balloons than long balloons did the clown buy?The clown bought 12 more round balloons than long balloons.Part 2 out of 2The clown also bought 3 bags of heart-shaped balloons with 14 balloons in each bag. When the clown blew up all of the round, long, and heart-shaped balloons, 23 balloons burst.How many blown-up balloons were left? Explain your answer. blown-up balloons were left.First, I found the number of heart-shaped balloons, 3 × = . Next, I added that number to the number of round balloons and long balloons, + 120 + 108 = balloons in all. Last, I subtracted the number of burst balloons, so − 23 = balloons left./
General
4 months ago
If exactly 220 people sign up for a charter flight, Leisure World Travel Agency charges $282/person. However, if more than 220 people sign up for the flight (assume this is the case), then every fare is reduced by $1 times the number of passengers above 220. Determine how many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 220. Show that the revenue function R is given by R(x)
General
4 months ago
A dog weighs two pounds less than three times the weight of a cat. The dog also weights twenty-two more pounds than the cat. Write and solve an equation to find the weights of the cat and the dog.
General
4 months ago
A family has a huge array of solar panels to make electricity. If each month they sell back 420 kWh for $0.07 per kWh, how much money could they make in a year
General
4 months ago
A farmer wants to fence in a rectangular field that encloses 3600 square feet. One side of the field is along a river and does not require fencing. The fencing costs $3.50 per foot. Express the total cost C(x) of the fencing (in dollars) as a function of x.
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4 months ago
Zoya asked the students of her class their baseball scores and recorded the scores in the table shown below: Baseball Scores Score Number of Students 0 1 1 2 2 5 3 3 4 6 5 7 6 9 Based on the table, what is the mean baseball score
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4 months ago
The graph represents the atmospheric pressure, in pounds per square inch, as a function of altitude in miles above sea level.Which statements accurately reflect this relationship?Select each correct answer. The atmospheric pressure gets close to 14 lb/ft2as the altitude continues to increase.The atmospheric pressure is 14 lb/in2at sea level.As the altitude approaches sea level, the atmospheric pressure increases.As the altitude increases, the atmospheric pressure increases.
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4 months ago
7/2x−1/2y=9/23x−y=5What is the solution of the system of equations?
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4 months ago
which shows the graph of the solution set of y -1/2 x – 3
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4 months ago
Misty has several pieces of construction paper that each measure 4 inches long and 9 inches wide. She needs to create the smallest possible square without cutting or overlapping. What is the measure of the square's side lengths?
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4 months ago
The circumference of the Earth is approximately 25,000 miles. What is this number expressed in scientific notation? A) 2.5 x 10^4 B) 2.5 x 10^3 C) 25 x 10^3 D) 2.5 x 10^4
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4 months ago
Let f(x)=3^x .Which function represents a transformation of f(x) by a vertical stretch with factor 6?g(x)=1/6 ⋅ 3^xg(x)=3^1/6xg(x)=3^6xg(x)=6 ⋅ 3^xLet f(x)=5^x .Let g(x)= 5^x − 7 .Which statement describes the graph of g(x) with respect to the graph of f(x) ?A. g(x) is translated 7 units left from f(x) .B. g(x) is translated 7 units up from f(x) .C. g(x) is translated 7 units right from f(x) .D. g(x) is translated 7 units down from f(x) .
General
4 months ago
The graph represents the atmospheric pressure, in pounds per square inch, as a function of altitude in miles above sea level. Which statements accurately reflect this relationship? Select each correct answer. The atmospheric pressure gets close to 14 lb/ft2 as the altitude continues to increase. The atmospheric pressure is 14 lb/in2 at sea level. As the altitude approaches sea level, the atmospheric pressure increases. As the altitude increases, the atmospheric pressure increases.
General
4 months ago
Which numbers are a distance of 5 units from 8 on a number line?Select the location on the number line to plot each point.
General
4 months ago
The graph shows the number of albums sold as a function of the number of albums produced. Which statement is true? As the number of albums produced decreases, the number of albums sold increases without bound. There is no limit to the number of albums produced, but there is a limit to the number of albums sold. As the number of albums produced increases without bound, the number of albums sold increases without bound. As the number of albums sold increases without bound, the number of albums produced decreases without bound.
General
4 months ago
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