Math Questions

Evan earns $12 an hour plus $15 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week. Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime. Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 30 hours. Part C: Evan earned $510 in 1 week. How many hours (regular plus overtime) did he work?

Moe plays a simplified version of powerball: You either win the entire jackpot of $500,000,000 or you lose the cost to play (i.e., $2). The probability of winning powerball is 1 out of 292,201,338 (the probability of losing is thus 1- 1- 1/292,201,338).What is the expected value of playing this version of powerball?

The formula for the perimeter of a rectangle is P = 2(1 + w) and the formula for the area of a rectangle is A = lw, where / is the length of the rectangle and w is the width. Determine the perimeter and the area of a 3 inch by 5 inch index card.

Solve the quadratic equation by completing the square. x²+8x = -7 To complete the square, what number should be added to both sides of the equation? Type an integer or a simplified fraction.)

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given point. (21,72) sin (= (Type an exact answer in simplified form.) cos (= (Type an exact answer in simplified form.) tan 0 = (Type an exact answer in simplified form.) cot 0 = (Type an exact answer in simplified form.) sec = (Type an exact answer in simplified form.) CSC = (Type an exact answer in simplified form.)

Suppose the weekly cost for the production and sale of bicycles is C(x) = 29x + 3655 dollars and that the total revenue is given by R(x)=81x dollars, where x is the number of bicycles. Write the equation of the function that models the weekly profit from the production and sale of x bicycles. What is the profit on the production and sale of 100 bicycles? Write the function that gives the average profit per bicycle. What is the average profit per bicycle if 100 are produced and sold?

A particular stock is currently trading at $1. An expert market analyst determines that in one year, the price of the stock will be: $2 with a probability of 0.5; $3 with a probability of 0.1; and nothing ($0) with a probability of 0.4. f the random variable X represents the gain or loss in the stock price in one year, what is the expected value of X?

Use a calculator conversion sequence to change the given angle in radians to the equal angle expressed in degrees to the nearest 0.01°. -4.487 rad -4.487 rad ≈ (Round to two decimal places as needed.)

a. The student gets either seven or eight answers correct. The probability the student gets either seven or eight answers correct is (Round to four decimal places as needed.)

A waitress sold 14 ribeye steak dinners and 32 grilled salmon dinners, totaling $598.67 on a particular day. Another day she sold 23 ribeye steak dinners and 16 grilled salmon dinners, totaling $581.98. How much did each type of dinner cost?

The city of Raleigh has 6,500 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 600 randomly selected registered voters was conducted. 224 said they'd vote for Brown, 328 said they'd vote for Feliz, and 48 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Round your answer to four decimal places. This sample statistic suggests that we might expect of the 6,500 registered voters to vote for Brown. Round to the nearest whole number.

The table below describes phone calls made on the planet K-2L last year. The columns show calls dialed by men versus women, and the rows show the distribution of call lengths. (Note that this is not real data.) There were 312,480,000 phone calls made by women that lasted 30 minutes or more. How many calls made by men lasted 0 to 5 minutes?

Find the minimum and maximum values of z= 6x + 5y, if possible, for the following set of constraints. 5x + 4y ≥ 20 x+4y28 x20, y 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is (Round to the nearest tenth as needed.) B. There is no minimum value.

You currently drive 300 miles per week in a car that gets 15 miles per gallon of gas. You are considering buying a new fuel-efficient car for $12,000 (after the trade-in allowance on your current car), which gets 50 miles per gallon. Insurance premiums for the new and old cars are $800 and $600 per year, respectively. You anticipate spending $1200 per year on repairs to the old car and having no repairs on the new car. Assume that gas costs $3.50 per gallon. Over a 5-year period, is it less expensive to keep your old car or buy the new car?

A rectangular piece of plywood 4.00 ft by 8.00 ft is cut from one corner to an opposite corner. What are the angles between the edges of the resulting pieces? Include all resulting angles.

A graphing calculator is recommended. (a) Find the equation for the tangent line to the curve fix) = x² - 3x + 6 at x = 2, writing the equation in slope-intercept form. (b) Use a graphing calculator to graph the curve together with the tangent line to verify your answer.

In camellia plants, flower color is controlled by a single gene with codominant alleles. A camellia plants with red flowers (RR) is crossed with a camellia plant with white flowers (WW). What are the expected phenotypes of the offspring of this cross? A All will have red flowers. B Half will have red flowers and half will have white flowers. C All will have pink flowers. D All will have both red and white flowers.

If a 12-sided regular polygon rotates about its center, at which angle of rotation will the image of the polygon coincide with the preimage?

A Stegosaurus skeleton at a museum has a height of 4 meters. The gift shop at the museum sells a model of the Stegosaurus. The scale used to create the model was 1 cm = 0.16m. What is the height, in centimeters, of the model of the Stegosaurus the gift shop sells?

A curve has area 0.622 to the left of 65 and area 0.378 to the right of 65. Could this curve be a density curve for some variable? Explain your answer. Choose the correct answer below. A. The curve could not be a density curve because the total area under the curve is less than 1. B. The curve could be a density curve because the total area under the curve is equal to 1. C. The curve could not be a density curve because the total area under the curve is greater than 1. D. There is insufficient information to determine if this curve could be a density curve for some variable.

Assume that θ is an angle in standard position whose terminal side contains the point (-7,-24). Find the exact values of the following functions. sin θ= (Simplify your answer. Type an integer or a fraction.) *****

You are buying $48 worth of two types of lawn seed. Ryegrass lawn seed sells for $0.70 per pound and Fescue lawn seed sells for $1.15 per pound. If you bought 25 pounds of Fescue lawn seed, write and solve a linear equation to find the amount of Ryegrass lawn seed purchased.

A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the undesirable behavior. The test is normed so that it has a mean of 140 and a standard deviation of 40. What is the percentile rank of a score of 172, please round to a whole number?

Solve the quadratic equation by completing the square. x^2 +4x=60

Mr. Jones has $10,000 to invest in three types of stocks, low-risk, medium-risk, and high-risk. He invests according to three principles. The amount invested in low-risk stocks will be at most $6,000 more than the amount invested in medium-risk stocks. At least $8,000 will be invested in low- and medium-risk stocks. No more than $6,000 will be invested in medium- and high-risk stocks. The expected yields are 6% for low-risk stocks, 7% for medium-risk stocks, and 8% for high-risk stocks. How much money should Mr. Jones invest in each type of stock to maximize his total expected yield? Mr. Jones should invest $ in low-risk stocks, $ in medium-risk stocks, and $ in high-risk stocks.

A rectangular table seats 14 people: 1 person on each end and 6 on each of the longer sides. Thus, two tables placed end to end seat 26 people. (a) How many people can be seated if n tables are placed in a line end to end? (b) How many tables, set end to end, are required to seat 84 people? (a) If n tables are placed in a line, end to end, people can be seated. (Type an expression using n as the variable. Simplify your answer.) (b) If one table can seat 14 people, tables, set end to end, are required to seat 84 people. (Type a whole number.)

State the two characteristics of the graph of a probability density function. Complete the statements below. 1. The total area under the graph of the equation over all possible values of the random variable must 2. The height of the graph of the equation must be for all possible values equal 0. be positive. equal 1.

A car is traveling at a rate of 48 miles per hour. What is the car's rate in miles per minute? How many miles will the car travel in 10 minutes? Do not round your answers.

write the given common argument form in symbols, then use a truth table to prove that it either is or is not a valid argument.

A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 13.1 inches and standard deviation of 1.2 inches. If a sample of 47 items are chosen at random, what is the probability the sample's mean length is greater than 13 inches? Round answer to four decimal places.

A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in the binomial probability distribution table. (Enter your answers to three decimal places.) (a) Find the probability of getting exactly three heads. (b) Find the probability of getting exactly two heads. (c) Find the probability of getting two or more heads. (d) Find the probability of getting exactly three tails.

In 4 minutes, a conveyor belt moves 100 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 5 minutes. If both belts are used, find how long it takes to move the cans to the storage area. The conveyor belts together can move the 100 pounds of recyclable aluminum from the delivery truck to the storage area in minutes. (Simplify your answer. Type an integer, fraction, or mixed number.)

Before 1918, approximately 50% of the wolves in a region were male, and 50% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 70% of wolves in the region are male, and 30% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.) (a) Before 1918, in a random sample of 11 wolves spotted in the region, what is the probability that 8 or more were male? What is the probability that 8 or more were female? What is the probability that fewer than 5 were female? (b) For the period from 1918 to the present, in a random sample of 11 wolves spotted in the region, what is the probability that 8 or more were male? What is the probability that 8 or more were female? What is the probability that fewer than 5 were female?

If a person can complete the following tasks in the following times, how much of the task can he complete in an hour? In other words, what is his rate at completing the task? a) Mow the lawn, 5 hours, (b) wash the car, 3 hours, (c) write a paper, 1.5 hours. a) The person will have mowed of the lawn in an hour. (Simplify your answer. Type an integer or a fraction)

A student deposits $300 in a savings account that pays 4% annual interest. At the end of 9 years, how much money will be in the savings account? Round your answer to the nearest cent. The savings account will be worth $ at the end of 9 years.

A baseball player comes up to bat 3 times during a league game. He either gets a hit or gets an out. How many different combinations are there for the three at bats? Make a tree diagram to help see the situation. 8 different combinations 7 different combinations 6 different combinations 5 different combinations

In 3 minutes, a conveyor belt moves 600 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 7 minutes. If both belts are used, find how long it takes to move the cans to the storage area.

Two angles are supplementary if the sum of their measures is 180°. Find two supplementary angles such that the larger angle is 148 more than 3 times the smaller angle. (Round to two decimal places if necessary.)

Use the Generalized Power Rule to find the derivative of the function. f(x) = (3x + 1)^4 (3x - 1)^5 f'(x) =

In an election, suppose that 65% of voters support a new tax on fast food. If we poll 187 of these voters at random, the probability distribution for the proportion of the polled voters that support a new tax on fast food can be modeled by the normal distibution pictured below. Complete the boxes accurate to two decimal places.

The midpoint of AB is M(-1,-4). If the coordinates of A are (-3,-7), what are the coordinates of B?

Use the histogram and the normal probability plot of the data to assess the normality of the finger length data. A. Both the histogram and the normal probability plot imply that the data is normal. B. The normal probability plot implies normality but the histogram implies the data is not normal. C. The histogram implies normality but the normal probability plot implies the data is not normal. D. Both the histogram and the normal probability plot imply that the data is not normal.

Simplify sec² (t) - 1 / sec² (t) to an expression involving a single trig function with no fractions. If needed, enter squared trigonometric expressions using the following notation. Example: Enter sin² (t) as (sin(t))².

Which reasoning process is shown in the following example? We examine the email addresses of 100 people. No two individuals from this group of people have identical email addresses. We conclude that for all people, no two people have identical email addresses. A) deductive reasoning B) reasoning by counterexample C) theoretical reasoning D) inductive reasoning

Match the descriptions with the compound interest formulas. A(t) gives the balance in dollars in an account after t years. A(t) = a(1+ r/4)^4t A(4) = a(1 + r/k)^4k A(t) = a(1 + 0.04/k)^kt A(t) = 4(1 + r/k)^kt A(t) = a(1 + 1.04/k )^kt This account starts with 4 dollars. This is the balance in the account after 4 years. This account earns interest at a 4% nominal rate This account earns interest 4 times a year. None of these

A piece of sheet metal, w = 24 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 64 square inches, find the depth of the gutter. (Enter your answers as a comma-separated list.)

A shipping company is buying new trucks. The high-capacity trucks cost $50,000 and hold 340 cases of merchandise. The low-capacity trucks cost $30,000 and hold 200 cases of merchandise. The company has budgeted $1,140,000 for the new trucks and has a maximum of 30 people qualified to drive the trucks. Due to availability limitations, the company can purchase at most 15 high-capacity trucks. How many of each type of truck should the company purchase to maximize the number of cases shipped at one time? To maximize the number of cases of merchandise that can be shipped simultaneously, the company should purchase trucks. high-capacity trucks and low-capacity

A certain store has a fax machine available for use by its customers. The store charges $1.60 to send the first page and $0.45 for each subsequent page. Use an inequality to find the number of pages that can be faxed for $7.00. 44 pages or fewer 16 pages or fewer 4 pages or fewer 13 pages or fewer

A dairy needs 270 gallons of milk containing 4 % butterfat. How many gallons each of milk containing 6% butterfat and milk containing 1% butterfat must be used to obtain the desired 270 gallons?

High school students bound for college take assessment tests. One test measures the verbal and mathematical abilities of prospective college students. Student scores are reported on a scale that ranges from a low of 300 to a high of 700. In one high school graduating class, the scores are as provided in the table provided. Use the technology of your choice to complete parts (a) and (b). Click the link to view the data table.