Math Questions

Public relations specialists create and maintain a favorable public image for the organization they represent. They design media releases to shape public perception of their organization and to increase awareness of its work and goals. The median annual wage for public relations specialists was $55,680 in May 2014. SOURCE: United States. Department of Labor. "Public Relations Specialist." Occupational Outlook Handbook. 17 Dec. 2015. Web. 8 March 2016. A public relations specialist earns $63,500 salary each year. He/she wants to spend no more than three times his/her salary on a house. What is the maximum price of a home that he/she can afford? If a 5% down payment is required, what is the amount financed? If he/she buys a home for the maximum he/she can afford, what is the monthly mortgage payment for a 20 year fixed interest loan at 3.1% compounded monthly?

There are 8000 students at Mountain High School, and 3/10 of these students are seniors. If 1/4 of the seniors are in favor of the school forming a debate team and 5/7 of the remaining students (not seniors) are also in favor of forming a debate team, how many students do not favor this idea?

A cyclist rides her bike at a speed of 2 meters per second. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 4 hours? Do not round your answers. Speed: Distance traveled in 4 hours:

Below, is the sample size, P is the population proportion of successes, and X is the number of successes in the sample. Use the normal approximation and the Cumulative Normal Distribution Table to find the probability. Round the answer to at least four decimal places. n=76, p=0.41 P(X>38) =

Brian's Great-Grandma Pat is turning 100 years old! The family throws her a party, and Brian helps her open a large stack of birthday cards. After opening 46 cards, they stop so Grandma Pat can blow out the birthday candles. Brian and Grandma Pat leave the remaining 55 cards for later. Use an equation to find the total number of birthday cards in the stack. birthday cards

A drug test is accurate 98% of the time. If the test is given to 2400 people who have not taken drugs, what is the probability that at most 50 will test positive, in other words, the test was inaccruate? Round intermediate calculations to two decimal places. Probability = Give your answers to 4 decimal places.

Announcers present music, news, and sports, and may provide commentary or interview guests about these or other important topics. Some act as masters of ceremonies (emcees) or disc jockeys (DJs) at weddings, parties, or clubs. Many announcers work in radio and television studios. Some announcers are self-employed; others work part time. The median annual wage for announcers was $29,010 in May 2014. SOURCE: United States. Department of Labor. "Announcers." Occupational Outlook Handbook. 17 Dec. 2015. Web. 8 March 2016. A newscaster earns $33,100 and wants to invest 10% of his/her monthly salary to save for retirement in 23 years. If he/she invests this money at 5.1% compounded monthly, how much money will he/she have at retirement? a) How much will be saved each year? b) What will be the monthly deposit? c) What will be the amount in the account after 23 years?

11% of all Americans live in poverty. If 47 Americans are randomly selected, find the probability that a. Exactly 3 of them live in poverty. b. At most 4 of them live in poverty. c. At least 2 of them live in poverty. d. Between 4 and 12 (including 4 and 12) of them live in poverty.

In 1993, the moose population in a park was measured to be 4750. By 1999, the population was measured again to be 4030. If the population continues to change linearly: A.) Find a formula for the moose population, P, in terms of t, the years since 1990. P(t) = B.) What does your model predict the moose population to be in 2004?

A new bank customer with $3,000 wants to open an IRA (Individual Retirement Account) to earn money for retirement. The bank is offering a simple interest rate of 11%. How much interest will the customer earn in 20 years? In 30 years? What will be the account balance after 20 years? After 30 years? in interest. In 20 years, the account will earn $ In 20 years, the account balance will be $ In 30 years, the account will earn $ in interest. In 30 years, the account balance will be $

A clothing manufacturer makes denim and hooded fleece jackets. Each denim jacket requires 2 labor-hours for cutting the pieces, 2 labor-hours for sewing, and 1 labor-hour for finishing. Each hooded fleece jacket requires 1 labor-hour for cutting, 4 labor-hours for sewing, and 1 labor-hour for finishing. There are 32 labor-hours for cutting, 60 labor-hours for sewing, and 18 labor-hours for finishing available each day. The profit is $7 per denim jacket and $4 per hooded fleece jacket. Complete parts (a) through (e) below. (b) Let x be the number of denim jackets made each day. Let y be the number of hooded fleece jackets made each day. Refer to the chart, and give three inequalities that x and y must satisfy due to the available labor hours. Give the inequality arising from the available cutting hours. Give the inequality arising from the available sewing hours. Give the inequality arising from the available Finishing hours. (c) Give other requirements that x and y must satisfy. x ≥ y²

Consider a student loan of $25,000 at a fixed APR of 9% for 20 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

An electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. The total cost of the electrician's services can be determined using the equation C = 65+ 60t, where t is the number of hours the electrician spends at the house working. What is the slope of the equation and what is its interpretation in the context of the problem?

Use your graphing calculator to solve the equation graphically for all real solutions. x³4x²-3x + 14 = 0 Solutions: = Make sure your answers are accurate to at least two decimals.

What is the range of the function f(x)=x² f(x) = R ((x) > 0 f(x) ≥ 0 ((x) < 0 ((x) = 0

Andre plays baseball for his university and has a batting average, the probability of successfully hitting the ball, of 0.310. If Andre has 42 turns at bat, what is the probability he successfully hits the ball between 11 and 20 times?

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 11% chance of returning $10,000,000 profit, a 45% chance of returning $2,500,000 profit, and a 44% chance of losing the million dollars. The second company, a hardware company, has a 10% chance of returning $10,000,000 profit, a 44% chance of returning $1,000,000 profit, and a 46% chance of losing the million dollars. The third company, a biotech firm, has a 12% chance of returning $6,000,000 profit, a 29% of no profit or loss, and a 59% chance of losing the million dollars. Order the expected values from smallest to largest. third, first, second second, third, first third, second, first first, third, second second, first, third first, second, third

If f(x) = x² and g(x)=x²-3, how has f(x) been transformed to get g(x)? The graph of f(x) has been shifted up three places The graph of f(x) has been shifted right three places The graph of f(x) has been shifted down three places The graph of f(x) has been shifted left three places The graph of f(x) has been stretched by a factor of 3

Nadia is a stockbroker. She earns 12% commission each week. Last week, she sold $4,500 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011? Last week, she made $ in commission. In 2011, she made $ in commission.

You decide to quit using your credit card and want to pay off the balance of $3,400 in 4 years. Your interest rate is 16.2% compounded monthly. What will your monthly payments be? How much interest do you pay?

The amount of syrup that people put on their pancakes is normally distributed with mean 62 mL and standard deviation 9 mL. Suppose that 44 randomly selected people are observed pouring syrup on their pancakes. Round z-scores to 2 decimal places for use in calculations. Round all other answers to 4 where possible. a. What is the distribution of X? X - N( b. What is the distribution of ? - N( c. If a single randomly selected individual is observed, find the probability that this person consumes is d. For the group of 44 pancake eaters, find the probability that the average amount of syrup is between e. For part d), is the assumption that the distribution is normal necessary?

Ninety percent of individuals have brown/black hair, 8% of individuals have blond hair, and 2% of individuals have red hair. Suppose that of those with black/brown hair, 70% have blue eyes. Of those with blond hair, 85% have blue eyes. Of those with red hair, 60% have blue eyes. What is the probability that a randomly chosen individual does not have blue eyes? Note: Enter your answer in decimals and not percentages. Do not round your answer.

Anusha brings a $20 bill to the store. She purchases 4 pairs of socks for $2.25 each and a new belt for $7.50. How much change will Anusha receive when she pays for her clothes? $3.50 $7.50 $9.00 $16.50

The equation V = -2000t + 24,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $16,000, substitute 16,000 into the equation to find the age of the car. 4 years 5 years 6 years 3 years

On Sunday, a local hamburger shop sold a combined total of 492 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday?

The Magazine Mass Marketing Company has received 12 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.5. What is the probability that more than 8 of the entry forms will include an order? Round your answer to four decimal places.

Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 9x + 2(2x - 5) = 7 - 4x Identity Conditional equation Inconsistent equation

The Stock Market Alexander is a stockbroker. He earns 12% commission each week. Last week, he sold $5,400 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011? Last week, he made $ in commission. In 2011, he made $ in commission.

Name any two points on a horizontal line that is 8 units above the x-axis.

A Food Marketing Institute found that 33% of households spend more than $125 a week on groceries. Assume the population proportion is 0.33 and a simple random sample of 253 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.36? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.36. Round the answer to 4 decimal places.

For a 4-units class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 21 students, and the distribution of total study hours per week is bell-shaped with a mean of 14 hours and a standard deviation of 3.2 hours. Use the Empirical Rule to answer the following questions. a) 68% of the students spend between week. b) 95% of the students spend between week. c) 99.7% of the students spend between week. Check Answer hours and hours and hours and hours on Statistics each hours on Statistics each hours on Statistics each

Abutcher shop knows that it must buy a new machine in 5 years. The machine costs $15,000. In order to accumulate enough money for the machine, the shop owner decides to deposit a sum of money at the end of each 6 months in an account paying 6% compounded semiannually. How much should each payment be? The deposits form an because the deposits are made at the should be used. Each payment should be $ (Do not round until the final answer. Then round to the nearest cent as needed.) of each period. Therefore, the formula

At the beginning of the year, the odometer on an SUV read 37,839 miles. At the end of the year, it read 52,799 miles. If the car averaged 22 miles per gallon, how many gallons of gasoline did it use during the year? A) 14,960 gallons B) 680 gallons C) 329,120 gallons D) 68 gallons

Point Q' is the image of Q(4, -6) under a translation by 1 unit to the right. What are the coordinates of Q'?

A light bulb factory finds that 5 out of every 200 light bulbs are defective. If 5 bulbs are sampled, what's the probability of observing at most 1 defective bulbs? Note: Round to the nearest thousandth.

Stuart Daniels estimates that he will need $22,000 to set up a small business in 9 years. (a) How much (in $) must Stuart invest now at 8% interest compounded quarterly to achieve his goal? (b) How much compound interest (in $) will he earn on the investment?

Infotron Inc makes electronic hockey and soccer games. Each hockey game requires 2 labor-hours of assembly and 2 labor-hours of testing. Each soccer game requires 3 labor-hours of assembly and 1 labor-hour of testing. Each day there are 57 labor-hours available for assembly and 35 labor-hours available for testing. How many of each game should Infotron produce each day to maximize its total daily output? Infotron should produce hockey games and soccer games

If s= 7 cm and t = 24 cm, what is the length of r? A. 38 cm B.31 cm C. 28 cm D. 25 cm

Reasoning Tommy earned $14.80 in interest after 4 years on a principal of $100. His simple interest rate is 3.7%. Jane earned $136.80 in interest after 3 years on a principal of $1,200. Her simple interest rate is 3.8%. Which bank would you rather use, Tommy's or Jane's? Explain your reasoning. Which bank would you rather use? A. Jane's because her bank accepted a smaller principal. B. Jane's because her bank offers a better interest rate. C. Tommy's because his bank paid more interest. D. Tommy's because his investment took less time.

Translate the sentence into an inequality. Nine subtracted from the product of 2 and a number is at most 15. Use the variable y for the unknown number.

Element X decays radioactively with a half life of 14 minutes. If there are 230 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 3 grams? y = a(.5)

Determine if the sequence is arithmetic. If it is, find the common difference and the explicit formula. -22, 122, -222, -322, ..

Arrows An Olympic archer is able to hit the bull's-eye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what's the probability of each of the following results? a) Her first bull's-eye comes on the third arrow. b) She misses the bull's-eye at least once. c) Her first bull's-eye comes on the fourth or fifth arrow. d) She gets exactly 4 bull's-eyes. e) She gets at least 4 bull's-eyes. f) She gets at most 4 bull's-eyes.

At time t seconds, the position of a body moving along the s-axis is s = (³-12t² + 45t) m. (a) Find the acceleration of the body each time the velocity is zero. Enter your answer as a list if necessary. Answer: -6,6 (b) Find the speed of the body each time the acceleration is zero. Enter your answer as a list if necessary. (c) Find the total distance traveled by the body from t=0 tot = 4. Σm

The population of Mathville is increasing exponentially . (a) Find a function that represents the population of Mathville, if in 2014 the population was 51,430, and the population last year was 76,600.

Noah is solving an equation and one of his moves is unacceptable. Here are themoves he made. 2(x+6)-4 = 8 + 6x original equation 2x + 12-4 = 8 + 6x apply the distributive property 2x+8 = 8 + 6x combine like terms 2x = 6x subtract 8 from both sides 2=6 divide each side by x Which answer best explains why the "divide each side by x step" is unacceptable? A. When you divide both sides of 2x = 6x by x you get 2x² = 6x² B. When you divide both sides of 2x = 6x by x it could lead us to think that there is no solution while in fact the solution is x = 0. C. When you divide both sides of 2x = 6x by x you get 2 = 6x. D. When you divide both sides of 2x = 6x by x it could lead us to think that there is no solution while in fact the solution is x = 3.

What is the fourth step in construction of perpendicular bisector of the line segment AB? Draw a line segment using the ruler. Label it AB. Draw a line from X to Y. The line XY is the perpendicular bisector of the line segment AB. Without changing the compass setting, place the pointed end of the compass on B. Draw arcs above and below the line segment to cut the first two arcs. Mark the points where these arcs meet. Call them X and Y. Place the pointed end of the compass on A and draw arcs above and below the line segment.

Claire has received scores of 85, 88, 87, and 75 on her algebra tests. What is the minimum score she must receive on the fifth test to have an overall test score average of at least 83? A) 80 B) 79 C) 81 D) 78

A Food Marketing Institute found that 29% of households spend more than $125 a week on groceries. Assume the population proportion is 0.29 and a simple random sample of 343 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.31. Round the answer to 4 decimal places.

A computer company makes desktop and laptop computers at factories in three states - California, Texas, and New York. The California factory produces 40% of the company's computers, the Texas factory makes 25% and the remaining 35% are made in New York. Of the computers made in California, 75% are laptops. Of those made in Texas and New York, 70% and 50%, respectively, are laptops. Find the following probabilities: P(computer is a laptop) 90% 65% 19.5% 75%