Math Questions

You have 3,000 square feet of selling space. You want to reserve at least 80 square feet for each product category you will carry. 25% of the space will be used for aisles. How many categories can you carry? a) 15 b) 28 c) 35 d) 75

In order to be elected to student council, Jeremy must have at least 50% of the current council members vote in his favor. If x represents the percent of favorable votes received, which inequality represents the percent of favorable votes that Jeremy needs for election to student council? (hint: Jeremy needs more than 50% votes)

A race has 21 participants. How many ways can first second, and third place be decided assuming there is no tie?

A rental car company is running two specials. Customers can pay $20 to rent a compact car for the first day plus $14 for each additional day, or they can rent the same car for $50 the first day and $8 for every additional day beyond that. Harper notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How much would Harper pay in total? Write a system of equations, graph them, and type the solution.

The San Bernardino County Fair hires about 120 people during fair time. Their hourly wages range from $5.80 to $7.70. California has a state income tax of 9%. Sandy Denny earns $7.70 per hour; George Barney earns $5.80 per hour (assume this is the current minimum wage). They both worked 38 hours this week. Both are married; however, Sandy claims 2 exemptions and George claims 1 exemption. Assume a rate of 6.2% on $128,400 for Social Security and 1.45% for Medicare. a. What is Sandy's net pay after FIT (use the Table 9.1 and Table 9.2), Social Security tax, state income tax, and Medicare have been taken out? b. What is George's net pay after the same deductions? c. How much more is Sandy's net pay versus George's net pay?

Choose a number between 0 and 100 for k. Enter your number in the blank so I know what to use for grading. k=__. Rewrite each exponential equation in logarithmic form. Hint: Use Control and, to do a base of logarithm and Control and . to do an exponent. 18. e^k = v 19. K = 10^x 20. k^x=8

A sports psychologist tests a new coaching method and finds that of the 43 novice athletes who were trained under the new method, they only froze/choked when in high stakes competition 3.5% of the time. If it is known that all novice athletes tend to freeze/choke 6% of the time when in high stakes competition (with a 3.2% average variation from the mean), what would the expected rate of all novice athletes trained using the new coaching method with 92% confidence? Question What is the lower bound estimate for how often all novice athletes would choke if trained under the new method?

Josh spends of 4/5 his savings to buy 48 shares in a tech company. He has $18 left. Part A: How much does each share of the tech company cost? Show your work. Part B: How many more shares can Josh buy with the remainder of his savings? Explain.

Write in simplified form and list all restrictions on the domain. f(y) = 7+ y/y+6 - 6/ y^2-36 f(y)= (Simplify your answer.)

Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the first year is 67%. She obtains a random sample of 98 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year? P

Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cause of childhood deaths before the development of vaccines. Approximately 80% of unvaccinated children who are exposed to whooping cough will develop the infection compared to only 5% of vaccinated children. In 2007, Bob Jones University ended its fall semester a week early because of a whooping cough outbreak; 158 students were isolated and another 1200 given antibiotics as a precaution. Authorities react strongly to whooping cough outbreaks because the disease is so contagious. Because the effect of childhood vaccination often wears off by late adolescence, treat the Bob Jones students as if they were unvaccinated. It appears that about 1400 students were exposed. What is the probability a that at least 75% of these students develop infections if not treated? (Enter your answer rounded to two decimal places.) a=

The daily profit P in dollars of a company making tables is described by the function P = -5x² +245x-2640, where x is the number of tables that are manufactured in 1 day. Use this information to find the profit when x = 20 and x = 28.

The unit cost, in dollars, to produce bins of cat food is $10 and the fixed cost is $8648. The revenue function, in dollars, is R(x)=2x²+288x Find the cost function. C(x) = Find the profit function. P(x) = At what quantity is the smallest break-even point?

For a particular diamond mine, 76% of the diamonds fail to qualify as "gemstone grade". A random sample of 108 diamonds is analyzed. Find the standard deviation. 0.041 0.96 0.24 0.76

Peggy filled her van's gas tank and noted that the odometer read 26,608.8. After the next fill-up, it read 27,025.3. It took 17.5 gal to fill the tank. How many miles per gallon did the van get? The gas mileage of the van is (Type a whole number or a decimal.)

1 Which problems can be solved using the equation 3 x 6 = f? Choose all the correct answers. * Choose only 3* (A) Cleo has 3 times as many bananas as Arianna has. Cleo has 6 bananas. How many bananas does Arianna have? B) Dylan has 6 oranges. Jane has 3 times as many oranges as Dylan. How many oranges does Jane have? (C) Liam has 3 cherries. Brian has 6 times as many cherries as Liam. How many cherries does Brian have? Tina has 3 more peaches than Charlie. Charlie has 6 peaches. How many peaches does Tina have? E Jaclyn has 6 times as many grapes as Kaitlyn. Kaitlyn has 3 grapes. How many grapes does Jaclyn have?

Find the savings plan balance after 9 months with an APR of 4% and monthly payments of $200.

Read each problem and state whether it is P(n,k) or C(n,k). Then evaluate the permutation or combination to determine the answer. Show a step of work when evaluating the permutation or combination prior to using your calculator. a. A race has 21 participants. How many ways can first second, and third place be decided assuming there is no tie? b. Alejandro has 38 other students in his class. He plans to invite 6 students to join a study group. How many ways can he select a group of 6 classmates to join the study group?

a. If x is increased from 2 to 3, how much does 1 + x/2 + x change by? change = b. Does the function increase or decrease when x goes from 2 to 3? The function ?

In 2004 there were approximately 6960 cinema sites. In 2000 there were 8400 cinema sites. a. Write an equation describing this relationship. Use ordered pairs of the form (years past 2000, number of cinema sites). b. Use this equation to predict the number of cinema sites in 2009.

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