Math Questions

The equation above is used to model the relationship between the number of cups, n, of hot chocolate sold per day in a coffee shop and the average daily temperature, T, in degrees Fahrenheit. According to the model, what is the meaning of the 3 in the equation? A) For every increase of 3°F, one more cup of hot chocolate will be sold. B) For every decrease of 3°F, one more cup of hot chocolate will be sold. C) For every increase of 1"F, three more cups of hot chocolate will be sold. D) For every decrease of 1"F, three more cups of hot chocolate will be sold.

After all the taxes are withheld, Jules's take-home pay is about 72% of his total earnings. Estimate his take-home pay if his total earnings for the pay period are $240. 75 120 180 300

Find the standardized test statistic t for a sample with n = 12, x-bar = 18.8, and s = 2.1. Assume that the significance level is a = .01 and the alternative hypothesis is Ha: m : ≠ 19.3. -0.008 -0.037 -0.381 -0.825

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 312, 306, 300, ... Find the 47th term.

An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Assuming that this data is used to test the airline's claim, find the P-value for the test. 0.1499 0.1230 0.3508 0.0746

A person invests money in a savings account that pays 2.5% simple interest. After one year, the person earns $24.25 in interest. How much did this person initially invest in the account (rounded to the nearest dollar)? Use the formula P=1/rtwhere P is the principle, /is the interest earned, r is the interest rate and t is the time, to find the initial investment. $1,230 $125 $1,170 $970

The average life span of one particular brand of refrigerator is 12 years with a standard deviation of 0.8. Find the percentage of refrigerators that last for more than 14 years. 0.62% 6.2% 0.60% 62%

Rey says that this is an obtuse triangle. She is correct, which best describes the reason she justified her answer: 7,24,28 7 + 24 is greater than 28 28² = 7² +24² 28² >7² +24² 28²< 7² +24²

Your candy factory makes Sticker Bars and N&N's. For each case of Stickers, you make $40 profit. For each case of N&N's, you make $55 profit. It takes 2 machine-hours to make Stickers and 5 man-hours to produce one case of candy. It takes 6 machine-hours to make N&N's and 4 man-hours to produce one case of candy. The total number of hours cannot exceed 150 machine-hours and 155 man-hours. Find the number of each type of candy that can be produced in order to maximize profit. Then determine the profit.

A population numbers 11,000 organisms initially and decreases by 2.9% each year. Suppose P represents population, and t the number of years of growth. Write an exponential model, P, in the form P = a b^t

Which statement is true? A. A sample statistic can never be equal to the population parameter. B. Point estimates are defined for both samples and populations. C To calculate a sample proportion, we need to know the population size. D. To calculate a point estimate, we need to know the sample size.

A college requires all incoming freshmen to live on campus. The college has two freshman dormitories, East and West. For an upcoming school year, there are 800 incoming freshmen. Which method evenly assigns the students to the two dormitories so that each Incoming freshman has a fair chance of being selected for either dormitory? A. Using a random number generator, assign each incoming freshman a number, eliminating any duplicate numbers. Assign each incoming freshman with a positive number to East dormitory, and assign each incoming freshman with a negative number to West dormitory. B. Using a two-sided coin, flip a coin for each incoming freshman. If the coin lands on heads, assign the freshman to East dormitory. If the coin lands on tails, assign the freshman to West dormitory. C. Using a random number generator, assign each incoming freshman a number, eliminating duplicate numbers. After each Incoming freshman is assigned a number, list the assigned numbers in ascending order. Assign the first 400 numbers on the list to East dormitory, and assign the last 400 numbers on the list to West dormitory. D.Using a random number generator, assign each incoming freshman a number, eliminating any duplicate numbers. Assign each incoming freshman with an even number to East dormitory, and assign each freshman with an odd number to West dormitory.

The number of hamburgers, and number of sodas, y, that Shaquile can purchase with $12 is represented by the inequality 4x + 2y ≤ 12 Which coordinate pair(s) (x, y) represent a possible number of hamburgers and sodas that Shaquile can purchase? Select all that apply.

Suppose you pay $1.00 to roll a fair die with the understanding that you will get $3.00 back for rolling a 4 or a 2, and nothing otherwise. What is the expected amount you will win? - $1.00 $0.00 $3.00 $0.33 $1.00

Solve the following inequality for x. -4x-6/2 > 5 Do not include spaces in your answer. Write your answer as an inequality statement with x, then the < or > sign, followed by a number.

A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. To test the claim, the manufacturer randomly selects 497 homes in Omaha, and finds that 340 of them had one or more lawn mowers. Find the p-value for this test. 0.0252 0.1118 0.0505 0.0555

Denis examined the records of the clients who had joined his gym more than six months ago, and he found the following: P(joined in January) = 0.12 P(member for over 6 months) = 0.5 P(over 6 months and joined in January) = 0.024 Find the probability that a client remained a member for more than 6 months, given that the client joined in January, and write the equation in proper notation.

III. Always, Sometimes, or Never. 29. A diameter is a chord. 30. A segment with both endpoints on a circle is a radius.. 31. A secant to a circle a tangent to the same circle. 32. A chord of a circle can be a radius. 33. Two externally tangent circles can have more than two common tangents. Two tangents to a circle at the ends of a diameter are parallel.

student draws a circle with a radius of 3 inches and highlights an are on the circle that measures inches. What is the radian measure of the central angle that is subtended by the highlighted arc? A 5π/6 radians B 18π/5 radians C 15π/6 radians D 5π/18 radians

Does a system of linear equations always have a solution? What about the following system? x + 3y = 1; 2x+6y=3 If we think of the two equations in the above system as two "straight lines" in the plane, can you explain why the system doesn't have a solution?

Three starting youth basketball players are ages 8, 10, and 9. Solve for the probability that a sample of two is randomly chosen. Show your work and explain the steps you used to solve.

A wire is attached to the top of the tower and to a point on the ground that is 35 m from the base of the tower. If the wire makes a 65° angle with the ground, how long is the wire?

The student council at a high school is conducting a survey to get feedback from students about a recent school event. This is one of the questions the student council included on the survey: Yes or no? Would you attend another school event that included the same food and entertainment? Which statement is true about the question? A. The question is an appropriate survey question. B. The question is an inappropriate survey question because it uses absolute language. C. The question is an inappropriate survey question because it is a leading question. D. The question is an inappropriate survey question because it is a double-barreled question.

Enrollment in a business seminar increased from 71 people to 81 people. What was the percent of increase? Round to the nearest tenth of a percent.

A student council wants to know whether students would like the council to sponsor a mid-winter dance or a mid-winter carnival this year. Classify each sampling method. a. Survey every tenth student on the school's roster. b. Survey all students in three randomly selected homerooms. c. Survey a random selection of those who happen to be in the cafeteria at noon. d. Survey those who ask the council president for a questionnaire.

A 20 foot ladder is leaning against a house. The bottom of the ladder is 3ft. from the house. To the nearest tenth of a foot, about how high does the top of the ladder reach? 19.2 ft 19.8 ft 19.4 ft 19.6 ft

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3025 feet and Plane B is just taking off. Plane A is gaining altitude at 25.25 feet per second and Plane B is gaining altitude at 85.75 feet per second. How many seconds will pass before the planes are at the same altitude? seconds What will their altitude be when they're at the same altitude? feet

A glider flies 8 miles south from the airport and then 15 miles east. Then it flies in a straight line back to the airport. What was the distance of the glider's last leg back to the airport? 17 miles 18 miles 19 miles 16 miles

Juan runs a company that makes pens. He notices that 1 out of every 9 pens are faulty. He uses a standard deck of cards to model the situation, with all the 10s representing faulty pens. Which statement about his model is true? a. His model cannot be improved. b. His model can be improved the most by removing all the hearts from the deck. c. His model can be improved the most by removing all face cards from the deck. d. His model can be improved the most by removing all the face cards and aces from the deck.

The fare for a taxi cab is a $2 flat fee plus an additional $1.50 for each mile. Which equation represents the total cab fare in dollars? A y+2=1.5x,y represents miles traveled, x represents the total fare B. y = 1.5x + 2y represents the total fare, x represents miles traveled C. 1.5y=x+2y represents the total fare, x represents miles traveled D. y = (1.5+ 2)x,y represents miles traveled, x represents the total fare

Jesse drives to work. The distance Jesse's car travels (d) on a number of gallons of gas (g) is given by the equation d = 25g. The constant of proportionality in terms of distance traveled per gallon of gas is ______ ("distance traveled per gallon of gas" is your clue!)

The average family spends $112 at the grocery store each week with a standard deviation of $35. Assuming that the amount a family spends on groceries follows a normal distribution, solve for the percentage of families that spend: 1. less than $56? 2. more than $131? 3. between $56 and $131 Include your work with your answer to receive full credit.

In a company's first year in operation, it made an annual profit of $127,000. The profit of the company increased at a constant 29% per year each year. How much total profit would the company make over the course of its first 28 years of operation, to the nearest whole number?

An employee joins a certain company and earns a beginning salary of $95000. At the end of each year, this employee receives a 6% raise. An explicit formula y= A. B^x can be written to model this situation. For this model, the value of A is type your answer... and the value of B is type your answer...

The equation 2w + 5j = 60 is used to determine the number of water bottles w and the number of juice bottles j that can be bought for $60. If you purchase 4 bottles of juice, how many bottles of water can you buy? A 10 B. 15 C. 20 D. 25

The formula for the area of a triangle is A =1/2 bh where b is the base of the triangle and h is the height of the triangle. What is the length of the base if the area is 22 cm^2 and the height is 8 cm? A. 4.5 cm B. 5 cm C. 5.5 cm D. 6 cm

Jackson was offered a job that paid a salary of $93, 000 in its first year. The salary was set to increase by 1% per year every year. If Jackson worked at the job for 16 years, what was the total amount of money earned over the 16 years, to the nearest whole number?

At the state fair, admission at the gate is $8. In addition, the cost of each ride is $2. Suppose that Frank will go on x rides. Frank wants the total number of dollars he spends on admission and rides to be fewer than t. Using the values and variables given, write an inequality describing this.

37% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities. (a) P(3) (Round to the nearest thousandth as needed.) (b) P(x≥4)=(Round to the nearest thousandth as needed.)

Renee is going bowling. The cost per game is $2.50. Renee will need to rent a pair of bowling shoes for $1.50. She can spend up to $16.00 to bowl and rent a pair of shoes. What is the maximum number of games that Renee can bowl?

The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 3 square flower beds, one on each side of the playground. The length of the playground is I and its width is w. The length of each side of the flower beds is a. Assume that the playground and beds do not overlap. The total fencing material required to fence the playground and all three flower beds is:

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $60/ft and on the other three sides by a metal fence costing $50/fL. If the area of the garden is 182 square feet, find the dimensions of the garden that minimize the cost. Length of side with bricks x = Length of adjacent side y =

"The difference between the circumference and the sum of 6 feet and the radius is zero." Where C = the circumference (feet) r = the radius (feet) C-6+r C-6=r C/(6 + r) C/(6+r)=0 C-(6+r)=0 C-(6+r)

A rectangular picture frame has a length of 7 inches and a width of 5 inches. What is the length of the diagonal of the picture frame? 8.2 inches 8.4 inches 8.6 inches 8.8 inches

Which statement is true regarding the line y = -4x + 13? The line has a slope of -13. The line has a slope of 4. The line passes through the point (0, 13). The line passes through the point (0, - 4).

Dustin and Melanie are playing a game where they roll 2 standard 6-sided number cubes and find the sum of their outcomes. Each player gets a chance to guess the correct sum, and the player who guesses the correct sum wins the game. Dustin decides to guess a sum of 6. Melanie decides to guess a sum of 7. Which player made the better decision?

Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using the drug. It is thought that regular exercise might help reduce the headaches. If a random sample of 209 patients using diltiazem exercised regularly and only 16 had headaches, would this indicate a reduction in the population proportion of patients having headaches? Use a 1% level of significance.

Eddie is practicing wind sprints during his summer break. He's able to run 100 meters in 28 seconds. If d represents distance and t represents time, write two equations that represent this proportional relationship: Start with the proportion: ___ = ___ Then solve for one of the variables: Then solve for the other variable:

Carlie runs two different business. She needs to pay $100 for materials, and pay her associates $12 per hour for her childcare business. And for her lawn care business, she has to pay $275 for materials, and pays her associates $10 per hour. Write two functions, C(x) and L(x), to represent the amount of money she will need to run her childcare business and her lawn care business. Complete the equations by filling in the blanks. Childcare business: C(x) = Lawn care business: L(x) =

A gym charges $35 per month for full access to their workout equipment. Mrs. Lewis has a $140 gift certificate to the gym. For how many months can Mrs. Lewis work out using the gift certificate? A 3 months B. 4 months C. 5 months D. 6 months