Math Questions

A toy manufacturer determines that the daily cost, C, for producing x units of a dump truck can be approximated by the function C(x) = 0.01x²-x+104. a. How many toy dump trucks must the manufacturer produce per day in order to minimize the cost? b. What is the minimum daily cost?

The Wechsler Adult Intelligence Scale (WAIS) is the most common IQ test. The distribution of scores for adults taking the WAIS is approximately Normal with a mean of 100 and a standard deviation of 15. Use the 68-95-99.7 rule to answer the questions about WAIS scores. What percentage of adults score above 100? 68% 32% 84% 2.5% 50% 0.3%

A farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What are the maximum dimensions that can be enclosed with 84 ft of fence? What is the maximum area of this garden?

Consider statements p and q. p: The path is in the park. q: A tree branch is above us. (a) Write each statement below in symbolic form using p and q. Statement 1: A tree branch is not above us or the path is not in the park. Statement 2: If a tree branch is above us, then the path is not in the park.

A soft drink machine at a local fast food restaurant can be calibrated so that it dispenses an average of ounces per cup. If the ounces of soda dispensed are normally distributed with standard deviation 1.3 ounces, find a value of such that 16-ounce cups will overflow only 10% of the time.

The unit cost, in dollars, to produce tubs of ice cream is $3 and the fixed cost is $8918. The price-demand function, in dollars per tub, is p(x) = 283 - 2x Find the cost function. C(x) = Find the revenue function. R(x) = Find the profit function. P(x) = At what quantity is the smallest break-even point?

Look at the picture below. What is the person trying to calculate and what mistake did they make in doing so? Be as specific as you can. (4,3) and (5,2) m = 4-5 /3-2

Tyler Herro, a former University of Kentucky player, now plays for the Miami Heat. As a freshman in college, he averaged 14 points per game. If he were to start and play in all 82 NBA games this year, how many points should he expect to score (if he stays at the constant rate he did in college)?

John receives his bank statement for the month. His balance is $430.52. In comparing his checkbook register, canceled checks, and bank statement, he finds that checks #224 and # 250 are outstanding. The amounts are $32.50 and $62.80. What is John's adjusted balance?

Graph the line that passes through the points (5,0) and (-5, 4) and determine the equation of the line.

Suppose that the functions and s are defined for all real numbers x as follows. r(x)=3x-5 s(x) = 6x Write the expressions for (r-s) (x) and (r+s) (x) and evaluate (r.s) (2). (r-s)(x) = (r+s)(x) = (r.s) (2) =

6x + 55 = x² 1) Rewrite the equation by completing the square. Your equation should look like (a + c)² = d or (x - c)² = d. 2) What are the solutions to the equation? Choose 1 answer: A. x = -3±8 B. x=3±8 C. x = -8± 3 D. x=8±3

Kaci owns a clothing boutique. She makes a deposit in her business checking account. She has checks to deposit for $234.53 and $495.87. She also has cash consisting of 14 one-dollar bills, 4 five-dollar bills, 8 ten-dollar bills, and 18 twenty-dollar bills. What is Kaci's total deposit?

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8. Convert 68 to a z-score.

Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 7-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 3.8% or largest 3.8%. What is the minimum head diameter that will fit the clientele? What is the maximum head diameter that will fit the clientele?

Find the area under the standard normal curve within three standard deviations of the mean. Round the solution to four decimal places, if necessary.

Rita have a decorative M&M's dispenser in her house. When a guest activates the dispenser, this person gets a randomly selected M&M out of the container. The container has 10 Red M&M's, 8 Blue M&M's and 13 yellow M&M's.

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. 3, 2+3i

Since a middle school opened, the girls' basketball team has had the same record every season. The team has won a total of 156 games while losing only 12 games. Find the constant of proportionality of wins to losses.

A bar graph shows that sports books received 9 votes. If the scale is 0 to 20 by twos, where should the bar end for the sports books?

The lines L₁, L2, L3,... L2₂0 are distinct. All the lines L4, L8, L12, L16 and L20 are parallel. All the lines L₁,L5, L9, L13, L17 pass through a given point A. The maximum number of points of intersection of these 20 lines is

Two stores sell the same refrigerator for the same original price. Store A advertises that the refrigerator is on sale for 15% off the original price. Store B advertises that it is reducing the refrigerator's price by $150. When Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal. Let p represent the refrigerator's original price. Which equation models this situation?

A store advertises that during its Labor Day sale, $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars at 8 a.m. and x > 100, what, in terms of x, is the cost c of Hakeem's purchase?

Discuss the validity of the following statement. If the statement is true, explain why. If not, give a counter example. Every polynomial function is one-to-one. Choose the correct choice below.

The distribution of heights of both five-year old boys and seven-year old boys is approximately Normal. The mean height of a five-year old boy is 43 inches and the standard deviation is 1.8 inches. The mean height of a seven-year old boy is 48 inches and the standard deviation is 2.1 inches. John's height was 44 inches on his fifth birthday, and today, on his seventh birthday, he measures 49 inches tall. What can you conclude about the rate of John's growth when compared to other boys his age?

f(x) = (x+7)²(x+9)(x-12)² List each zero of faccording to its multiplicity in the categories below.

At lunch a waiter had eleven customers and five of them didn't leave a tip. If he got Ssix each from the ones who did tip, how much money did he earn?

The profit for a product can be described by the function P(x)=202x-5000-x² dollars, where x is the number of units produced and sold. To maximize profit, how many units must be produced and sold? What is the maximum possible profit?

A 1.000-g sample of chromium metal reacted with oxygen gas to give 1.462 g of product. Calculate the empirical formula of the chromium oxide.

In a random sample of 200 cars of a particular model, 3 have a manufacturing deficit. At this rate, how many of 10,000 cars of the same model will have a manufacturing deficit? (A) 150 (B) 200 (C) 250 (D) 300

An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are worth five points. How many two point questions are on the test? How many five point questions are on the test?

Caleb bought 3 orders of cheese dip to share with his friends. How much did he spend on cheese dip?

Angela Montery has a five-year car loan for a Jeep Wrangler at an annual interest rate of 5.9% and a monthly payment of $595.50. After 3 years, Angela decides to purchase a new car. What is the payoff on Angela's loan? (Round your answer to two decimal places.)

What percentage of the general U.S. population are high-school dropouts? The Statistical Abstract of the United States, 120th Edition, gives the percentage of high- school dropouts by state. For convenience, the data are sorted in increasing order.

Assume you intend to create a stratified sample of 250 from a population of 920 trucks, 1540 subcompact cars, 1320 sedans, 450 motorcycles, 110 R.V.'s, 550 luxury cars, and 780 sports cars. How many subcompacts should you have in your sample? a 65 b 60 C 68 d 70

A small business sells custom oak moldings in 12-foot lengths. One molding type has the revenue function R(x) = 59x and the cost function C(x) = 2800+ 45x. Find the number of 12-foot lengths of this molding that must be sold to break even. X = lengths

A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 10 in /min, how fast is the thickness of the ice decreasing when it is 3 in. thick? How fast is the outer surface area of ice decreasing?

The speed of light is approximately 6.71 a 10 miles per hour. Which of the following options shows this number correctly written in standard notation?

College students average 7.1 hours of sleep per night with a standard deviation of 45 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 8.1 hours?

A hiker is walking down a mountain. She walked 5,978 feet in 17 minutes. In that time, she descended 1,024 feet from the top of the mountain. She then walked 3,972 feet in 7 minutes. In that time, she descended 500 more feet. Express the average rate of change in altitude of the hiker from her starting point to her ending point as a unit rate.

Combine like terms to simplify the expression below. -6y + 7y = 1y 32 + y - 2y² Now, re-write the equation with the variable with the highest exponent first.

A ball is thrown upward from the top of a 48-foot-high building. The ball is 64 feet above ground level after 1 second, and it reaches ground level in 3 seconds. The height above ground is a quadratic function of the time after the ball is thrown. Write the equation of this function.

Two cities have nearly the same north-south line of 101° W. The latitude of the first city is 23° N, and the latitude of the second city is 36° N. Approximate the distance between the cities if the average radius of Earth is 6400 km.

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53 inches, and standard deviation of 6.8 inches. What is the probability that the height of a randomly chosen child is between 39.9 and 54.9 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

Sadie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5 hours and charged her $77 for parts. The total was $302. Which equation could be used to determine x, the cost of labor per hour? r

Junior is saving money in his piggy bank. He starts with 10 cents and adds two pennies each day. Create an x → y table and a graph for the function for which x represents the number of days since Junior started saving money and y represents the total money he has saved.

A pennant is shaped like a right triangle with hypotenuse 10 feet. The length of one side of the pennant is 2 feet longer than the length of the other side. Find the length of the two sides (legs) of the pennant. Enter your answers as a comma separated list.

Given nt+1= = nt + 3.6 and n4 = 12.6: a) Make a table for the first five terms. b) Find n20 and n_22. c) Find the t for which n 102.6 and nt = -70.2. d) Write an algebraic representation for this sequence.

It is given to you that an equation of the tangent line to the graph of y = g(x) at x = 16 is 6x + 9y = 15 It follows that y = ___ and that y is the equation of the tangent line to y = g(x²) at x = 4 iand that y = ____ the equation of the tangent line to y = (g(x))² at x = 16.

Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function? Select all correct answers. Select all that apply: {(2, 10), (8,8), (-4,7), (3, 10)} {(8,6), (-2,-1), (-4,-2), (-2, 8)} ((-3,4), (7,6), (0, 1), (0,8)} ((9,6), (6,0), (1,-5), (0,6)} {(2,1), (2,0), (9, 14), (-3,8)}