Math Questions

A waitress sold 13 ribeye steak dinners and 24 grilled salmon dinners, totaling $565.26 on a particular day. Another day she sold 20 ribeye steak dinners and 12 grilled salmon dinners, totaling $581.84. How much did each type of dinner cost?

Solve the inequality algebraically. 2x³ > -12x²

A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). What dimensions should be used so that the enclosed area will be a maximum?

Sarah Jones earns $575 per week selling life insurance for Farmer's Insurance plus 4% of sales over $5,750. Sarah's sales this month (four weeks) are $15,500. How much does Sarah earn this month? (Round your answer to the nearest cent.)

A reporter is doing a story on the falling prices of homes in a large neighborhood. The reporter wants to demonstrate how the prices have fallen for all homes, not just the most expensive houses. Which statistic (mean, median, or mode) is most appropriate in this situation? Mean Median Mode

Estimate, then find the sum. Round to the nearest whole number. 2.7+6.87+21.878

An antique table increases in value according to the function v(x)= 750(1.05) dollars, where x is the number of years after 1980. a. How much was the table worth in 1980? b. If the pattern indicated by the function remains valid, what was the value of the table in 1990? c. Use a table or a graph to estimate the year when this table will reach double its 1980 value.

The New York City Marathon is a highly selective race. One way to gain entry into the race is to qualify based on a time from a prior-completed marathon. The NYC Marathon's organizers use this method to limit admission to the top 10% of marathon runners. If the mean completion time of all marathons is 179 minutes with a standard deviation of 17 minutes, what qualifying time should the NYC Marathon organizers set so that only the top 10% of runners will be admitted entry to the NYC Marathon? Round the solution to one decimal place, if necessary. The qualifying time should be set to minutes to ensure that only the top 10% of runners will be

Tara owns a pizza shop. The item purchased most frequently from her shop is a large pizza. For any order, Tara charges $7.00 for each pizza plus $3.00 for delivery services. Tara made a delivery of pizzas to a party for which she charged $45.00. How many pizzas did she deliver? Only an algebraic solution will be accepted.

Oklahoma is a Great Plains state in the south-central part of the United States, a region not historically known for its earthquakes. Seismic records up to 2008 show that Oklahoma has experienced a constant rate about 1.5 perceptible earthquakes (magnitude at least 3) per year, on average. Use the software of your choice to calculate the answers for (a)-(c). (a) Assuming that earthquakes are random and independent, with a constant rate of 1.5 per year, the count of perceptible earthquakes per year in Oklahoma should have a Poisson distribution with mean 1.5. Under this model, what is the probability that Oklahoma had more than 10 perceptible earthquakes in a given year prior to 2008? (Enter your answer rounded to ten decimal places.) P(X> 10) = (b) In 2013, Oklahoma experienced 109 perceptible earthquakes (an average of about 2 events per week). If the rate of 1.5 perceptible earthquakes per year was still true, what would be the probability of recording 109 or more perceptible earthquakes? (Enter your answer rounded to the nearest whole number.)

Analyze the polynomial function f(x) = (x + 7)2 (5-x) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y= for large values of Ix. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Simplify your answer. Type an integer or a fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) of f is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The lesser zero of the function is of multiplicity, so the graph of f the x-axis at x = The greater zero of the function is of multiplicity so the graph of f the x-axis at x =

On a certain day, a cheese packaging facility packaged 480 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws The following table presents the results. minor flaw no minor flaw major flaws no major flaws 19 33 66 362 Find the probability that a randomly selected package of mozzarella cheese from this facility has a minor flaw. 0.177 0.137 0.108 0.235

If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x) = p(1-p)x-1 where p is the probability of success on any one trial. Assume that the probability of a defective computer component is 0.17. Find the probability that the first defect is found in the fifth component tested.

Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y = 65.37x + 79.52 and the r = -0.074. What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.

Destination Weddings Twenty-six percent of couples who plan to marry this year are planning destination weddings. Assume the variable is binomial. In an andom sample of 3 couples who plan to marry, find the probability of the following. Round intermediate calculations and final answers to three decimal places. (a) Fewer than 2 couples will have a destination wedding. (b) At least 2 couples will have a destination wedding.

I tried taking the reciprocal of the fraction on the right so I would not have to do division but I could not get the equation to work. The quadratic on the bottom left is unfactorable. What steps would I take to solve this? x2 – 5x – 24 / 2x² - 11x + 24 / 2x² +7x+3 / x²+x-12

Tables in the dining hall are numbered 1-12 for students who eat there. The principal calls out a number for the table that will go through the buffet line first. The other tables follow in order of the table numbers. One student is sure the principal calls certain tables more often. She keeps track of which numbers are called over a 21-day period. Which statistic (mean, median, or mode) is this student using? Mean Median Mode

An actress has a probability of getting offered a job after a try-out of 0.05. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent. Find the probability she will need to attend more than 8 try-outs.

7. How many different 4-letter "words" can be made from the letters j, o, u, r, n, e, y if a. The first letter must be a vowel and repetitions are allowed? Show the computation used to arrive at your answer. b. The first letter must be an y, the last letter must be an r, and repetitions are not allowed? Show the computation used to arrive at your answer.

Richard Gaziano is a manager for Health Care, Inc. Health Care deducts Social Security, Medicare, and FIT (by percentage method) from his earnings. Assume a rate of 6.2% on $128,400 for Social Security and 1.45% for Medicare. Before this payroll, Richard is $1,000 below the maximum level for Social Security earnings. Richard is married, is paid weekly, and claims 2 exemptions. What is Richard's net pay for the week if he earns $1,250? (Use Table 9.1 and Table 9.2). (Round your answer to the nearest cent.) Net pay

The half life of radium-226 is 1620 years. Initially, there are 2-grams in a sample. (a) Half life decay can be modeled by an exponential function: N(t) = N0 ekt. Use the growth equation, kt = ln (N1/N0) to find k. (b) How many grams remain after 10 years? (c) How long will it take for 80% of the 2 grams to decay?

Select the correct answer. The pressure applied on any object can be calculated by using the following equation. P = F/A P = F/A In the pressure equation, P represents the pressure on the object in pascals (Pa), Frepresents the force applied on the object in newtons (N), and A represents the area, in square meters, of the object over which the pressure is applied. What is the pressure applied inside a container having an inner area of 16 square meters over which a force of 1,306 newtons is applied? Note: Answers should be rounded to the nearest whole unit.

The radius of a sphere is measured as 9 centimeters, with a possible error of 0.025 centimeter. (a) Use differentials to approximate the possible propagated error, in cm³, in computing the volume of the sphere. error ± (b) Use differentials to approximate the possible propagated error, in cm2, in computing the surface area of the sphere. error + (c) Approximate the percent errors in parts (a) and (b). (Round your answers to two decimal places.) volume surface area

The distribution of all registered nurses' salaries on the Treasure Coast is known to be normally distributed with a mean of $57, 250 and a standard deviation of $750. Use this information to determine the following two probabilities. Round solutions to four decimal places, if necessary. Find the probability that a single randomly selected nurse's salary is greater than $57,415. P(x > 57, 415) = Find the probability that a random sample of 87 nurses have a mean salary greater than $57,415. P(x > 57, 415) =

What percentage of adults score below 85? 16% 99.7% 68% 0.3% 84% 8% Calling itself "the high IQ society," MENSA requires an IQ score of 130 or higher for membership. What percentage of adults taking the WAIS test qualify for membership? (Enter your answer rounded to the nearest tenth of a percent.)

Two groups of students on a fieldtrip is getting food in a fast food restaurant. The first group bought 8 burgers and 6 soft drinks for $39.76. The second group bought 5 burgers and 7 soft drinks for $29.97. How much does one burger cost? $3.79 per burger $1.86 per burger $1.36 per burger $3.45 per burger

Assume that a national fitness study reports that 15% of millenials exercise daily. Suppose that a researcher surveys a random sample of 200 millenials regarding their daily exercise habits. Assume that X is a binomial random variable that represents the number of millenials in the sample who exercise daily. Compute the mean μ and standard deviation o of the sampling distribution of X. Report μ as a whole number and o as a decimal precise to two decimal places.

You need 250 mL of a 20% alcohol solution. On hand, you have a 5% alcohol mixture and a 55% alcohol mixture. How much of each mixture will you need to obtain the desired solution?

Jason deposits $10,000 into an account paying ____9__(a number between 1.0% and 9.9%, rounded to the tenths place) % interest, compounded monthly. How long will it take for the balance to reach $20,000? Show your set-up and solving steps. Round to the thousandths place.

Three-sevenths of the T-shirts in a T-shirt shop are blue. Seven-eighths of those T-shirts are on sale. One-third of the blue T-shirts that are on sale are size medium. What fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium? Explain.

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.