Math Questions

You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow changes. The college conducts a lottery, and whichever number is drawn, represents the value. Your plot has a length which is four more than five times and the width is two less than three times .x. a.) What are the dimensions of your mowing plot? Length: Width: b.) What is the area of your plot (area= length x width)? Area: c.) If x= 12 meters, how many square meters is your plot? Area:

A bank offers a CD that pays a simple interest rate of 11.5%. How much must you put in this CD now in order to have $3,000 for a home-entertainment center in 2 years. The present value that must be invested to get $3,000 after 2 years at an interest rate of 11.5% is (Round up to the nearest cent.)

Determine the effective annual yield for each investment. Then select the better investment. Assume 360 days in a year. 14% compounded monthly; 14.25% compounded annually The effective annual yield for a 14% compounded monthly investment is %.

The city of Raleigh has 9,200 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 350 randomly selected registered voters was conducted. 180 said they'd vote for Brown, 157 said they'd vote for Feliz, and 13 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. Preview This sample statistic suggests that we might expect Round to the nearest whole number. Preview of the 9,200 registered voters to vote for Brown.

A student is taking a true-false exam with 10 questions. Assume that the student guesses at all 10 questions. Use the accompanying tables to complete parts a through c. a. The student gets either seven or eight answers correct. The probability the student gets either seven or eight answers correct is _____ b. The student gets between four and eight answers correct, inclusive. The probability the student gets between four and eight answers correct, inclusive is _____

After you build 1 shelf, your friend wonders how long it will take you to build 9 shelves. How much time will it take to build 9 shelves, if you work at a constant rate?

A major coffee supplier has warehouses in Seattle and San Jose. The coffee supplier receives orders from coffee retailers in Salt Lake City and Reno. The retailer in Salt Lake City needs 600 pounds of coffee, and the retailer in Reno needs 450 pounds of coffee. The Seattle warehouse has 1000 pounds available, and the warehouse in San Jose has 700 pounds available. The cost of shipping from Seattle to Salt Lake City is $2.50 per pound, from Seattle to Reno $3 per pound, from San Jose to Salt Lake City $4 per pound, and from San Jose to Reno $2 per pound. Find the number of pounds to be shipped from each warehouse to each retailer to minimize the cost. Ship pounds of coffee from Seattle to Salt Lake City. pounds of coffee from Seattle to Reno, pounds of coffee from San Jose to Reno. pounds of coffee from San Jose to Salt Lake City, and

You must decide whether to buy a new car for $23,000 or lease the same car over a three-year period. Under the terms of the lease, you can make a down payment of $2000 and have monthly payments of $150. At the end of the three years, the leased car has a residual value (the amount you pay if you choose to buy the car at the end of the lease period) of $11,000. Assume you can sell the new car at the end of the three years at the same residual value. Is it less expensive to buy or to lease?

Suppose that $5000 is deposited into an account that earns 3.5% interest compounded Semiannually. Let f(t) represent the value (in dollars) of the account at t years after depositing the $5000. Find the value of the account at t = 4 years. (Round your answers to two decimal places.) {Round your final answer to two decimal places}

A study finds that the carapace length of an adult spider is normally distributed with a mean of 19.55 mm and a standard deviation of 1.29 mm. Let x denote carapace length for the adult spider. VIIHNEN an permaye vi avvn sprecio a vapadorongan u THREE CER IV TREG The percentage of adult spiders that have carapace lengths between 17 mm and 18 mm is equal to the area under the standard normal curve between 1.98 and - 1.20. (Round to two decimal places as needed.) e. Find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 21 mm. The percentage of adult spiders that have carapace lengths exceeding 21 mm is equal to the area under the standard normal curve that lies to the right of (Round to two decimal places as needed)

The population of weights of a particular fruit is normally distributed, with a mean of 228 grams and a standard deviation of 12 grams. If 26 fruits are picked at random, then 7% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.

A nature center charges a $5 admission charge for children who are 12 years old or younger and $10 for those 13 years old and older. On Tuesday, the petting zoo took in $1620 from ticket sales and sold a total of 232 tickets. How many tickets of each type were sold? a. Clearly write the unknown quantities you're being asked to find and assign variables to represent each of them. Let x = Let y = b. Using the information in the problem, write a system of equations representing this scenario. You may consider making a table to organize the known and unknown quantities to help you write the system.

For the arithmetic sequence with a, = 2 and d=5, find each: (a) the first five terms The first five terms of the arithmetic sequence are (b) the 12th term The 12th term in the arithmetic sequence is (c) the sum of the first 12 terms The sum of the first 12 terms of the arithmetic sequence is

How is a normal probability plot used to detect outliers? Choose the correct answer below. A. All observations are used to construct the normal probability plot, and any observations above 0 may be outliers. B. All observations are used to construct the normal probability plot, and any observations that have a normal score greater than 2 in magnitude may be outliers. C. All observations are used to construct the normal probability plot, and any observations that fall well outside the overall pattern of the data may be outliers. D. All observations are used to construct the normal probability plot, and any observations that do not fall on a straight line may be outliers.

Based on a recent study, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.26 and standard deviation of 0.15. Find the percentage of preterm infants who have the following arterial cord pH levels. a. pH levels between 7.00 and 7.50 b. pH levels over 7.34. a. The percentage of arterial cord pH levels that are between 7.00 and 7.50 is (Round to two decimal places as needed.)

A car traveling at speed v miles per hour on a dry road should be able to come to a full stop in the distance of D(V) = 0.055v² + 1.1v feet.+ Find the stopping distance required for a car traveling at 45 mph. (Round your answer to the nearest whole number.)

You invest $1950 in an account paying 5.9% interest compounded daily. What is the account's effective annual yield? Assume 360 days in a year.

Fill in the blanks below: a. If an ellipse has a major axis length of 8, then its semi-major axis length is_ b. If an ellipse has a minor axis length of 6, then its semi-minor axis length is c. If an ellipse has vertices at (0, 2) and (0, 2) then its major axis length is semi-major axis length is d. If an ellipse has co-vertices at (0, 1) and (0, 1) then its semi-minor axis length is Is this ellipse a horizontal ellipse or a vertical ellipse? e. If a vertical ellipse has a major axis length of 4, its vertices are at f. If a horizontal ellipse has a semi-minor axis length of 3, its co-vertices are at

You own 18 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? The probability that the CDs are in alphabetical order is

For the geometric sequence with a 32 and r= -1/4, find each (a) the first five terms (b) the 12 term (c) the sum of the first 12 terms, rounding values to two decimal places, if necessary

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.