Math Questions

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

Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99 7 rule to find the percentage of buyers who paid between $150,000 and $156,000, if the standard deviation is $2,000 A. 49.85% B. 47.5% C. 99.7% D. 34%

A community theater uses the function p (d)=-4d^2 + 200d - 100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each. Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend.

Which of the following could be the equation of an ellipse? (More than one answer may be possible) (x-4)² = 24 (y + 8) (x-4)² + (y + 8)² = 1 (x-4)²/2 - (y + 8)² =1 (x-4)²/2+ (y + 8)²/16 =1

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 6.5%, and the tax in the second city was 4%. The total hotel tax paid for the two cities was $480. How much was the hotel charge in each city before tax? Note that the ALEKS graphing calculator can be used to make computations easier. Second city: $ First city:

Select the correct answer. It is estimated that approximately one-half of all aluminum cans will be recycled each year. If a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function? Nt = 350,000(0.52)^t A. 87,500 B. 25,591 C. 175,000 D. 21,875

Rock music accounts for 64% of the CD sales of True Tones Record Company. If next year's production is planned at 300,000 CD's, estimate how many of the CD's will be of rock music? 150,000 200,000 240,000 500,000

A 6-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6). Find the probability of rolling a number less than 8. The probability of rolling a number less than 8 is

Which recursive sequence would produce the sequence 10, -25, 45, ...? a₁ = 10 and an = -3an-1 + 5 a₁ = 10 and an =-5an-1-2 a₁ = 10 and an = -2an-1-5 a₁ = 10 and an = 5an-1-3

Determine whether the side lengths could form a triangle. Prove your answer with an inequality. 5 ft., 2 ft., 10 ft. 37 in., 18 in., 25 in. Given the measures of two sides of a triangle, find the range of values for the third side. 3 km, 48 km 11 ft ,24 ft

manager of the customer service department of an e-commerce company wants to know the average hold time for customers who call the department. The department receives about 850 calls each hour. The following data set shows the hold time, in minutes, for 10 calls picked at random. 2, 1, 4, 5, 3, 3, 7, 4, 3, 2 Calculate the approximate hold time for all customers who call the customer service department. The approximate hold time for all customers who call the customer service department

Lucy has an unpaid balance of $1200 on her credit card. The credit card company requires a minimum payment of 4.5% and charges an annual interest rate of 30%. Calculate Lucy's minimum payment, the amount of interest paid that month, and her unpaid balance. Round each to the nearest cent. The minimum payment is $ The amount of interest paid is $ The unpaid balance is $

In Ventura County, the height measurements of ten-year-old children are approximately normally distributed with a mean of 54.7 inches, and standard deviation of 5.1 inches. Let X be the height of a randomly chosen child in Ventura County. a. What is the distribution of X?X - ? Please show the following answers to 4 decimal places. b. If a Ventura County child is randomly chosen, find the probability that the height is at least 57.3 inches. c. If a Ventura County child is randomly chosen, find the probability that the height is between 57.3 and 65 inches. Please show the following answer to 1 decimal place.

A real estate office pays its salespeople a weekly retainer of $220 plus a commission of 2.5% for the first $200 000 of the value of each property sold and 2% of each amount after that. Calculate the commission received if a house is sold for $540,000.

Outworkers who sew T-shirts together are paid a wage of $3 per hour plus $1.45 for each T-shirt sewn together. Calculate the average hourly wage for each of the following workers. A) Kellie, who sews 90 T-shirts over 8 hours B) Nicole, who sews 47 T-shirts over 6 hours C) David, who sews 116 T-shirts over 10 hours

A map is placed on a coordinate grid. Cincinnati is located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? 15.4 16.6 16.2 15.8

Which statement is true? Point estimates are used to make Inferences about population parameters. When we use the population mean and proportion to summarize information about the entire population, we call them point estimates. The population mean and proportion are always equal to their corresponding point estimates. The sample mean and sample proportion of a population are called population parameters.

A sports academy decides to survey athletes at the academy about how closely they follow their recommended nutrition plan. Coaches at the academy are responsible for administering the surveys. Each coach will have a one-on-one discussion with each of their athletes in which they will ask the athlete the survey questions and write down their responses. What is a source of bias in this sampling method? A. It is less likely athletes will reveal to their coach that they do not follow their nutrition plan. B. Some athletes may be injured that day and unable to complete the survey. C. Most athletes do not follow recommended nutrition plans. D. Some athletes may be sick that day and unable to complete the survey.

Select the best choice for the definition for vertex. A. The graph of a quadratic function that is a U-shaped curve. B. Is defined by an ordered pair and is considered the minimum point or the maximum point. C. A vertical line that passes through the vertex of the graph of a quadratic function. D. A term that describes the x-intercept(s) of the graph of a quadratic function.

A bag contains 4 red balls, 6 blue balls, and 8 yellow balls. If you replace each ball after you see it's color, find the probability of removing a blue ball, then a red ball, and then a yellow ball. Write your answer as a fraction simplified to lowest terms (reduced).

Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to the starting point? 10 miles 9.8 miles 9.6 miles 9.4 miles

Use the ALEKS graphing calculator to solve the system of equations. x² + y² = 22 y=9/7 x+ 5/7 Round to the nearest hundredth. If there is more than one solution, use the "or" button. If applicable, click on "No solution". (x,y)= No solution

Cool Down 2-24 Is this a polynomial identity? Show that this is or is not a polynomial identity: (a + b)(a²-ab + b²) = a³ + b³

Find the equation of the axis of symmetry of the following parabola algebraically. y = 2x² + 32x + 136

Part 2: Complete these problems and show work clearly (formulas used and what values you typed into the calculator). When asked for, state your answers or findings in a complete sentence. Again, limited/no help from teacher, MathLab, Learning Commons for Part 1 and Part 2). 1. In October of 1981, average interest rates were the highest they've ever been in America: 18.3% on 30-year mortgages AND 16.7% on 15-year mortgages a. Without using the table, calculate the monthly payment for a loan of $175,000 for 30 years. State your answer in a sentence.

You rent an apartment that costs $900 per month during the first year, but the rent is set to go up $90 per year. Write a recursive formula to show what the rent is during the nth year of living in the apartment.

Jacob is a teacher and takes home 58 papers to grade over the weekend. He can grade at a rate of 15 papers per hour. Write a recursive sequence to represent how many papers Jacob has remaining to grade after working for n hours. ao an

Describe a situation with an output of area in square feet that can be modeled using the function f(x) = (x)(2x + 5).

Total blood volume in ml per body weight in kg, is important in medical research. For healthy adults, the red blood cell volume is about μ = 28 ml/kg. Suppose Roger has had seven blood tests and the mean red blood cell count was 32.7 ml/kg. Assume that x has a normal distribution and o = 4.75. Do the data indicate that Roger's red blood cell volume is different either way from μ = 28 ml/kg? Use a = 0.01.

A system of equations is shown below. 3x - 2y = 7 9z - 6y = k What statement is true about the relationship between the value of k and the number of solutions for the system of equations? For any value of k, the system of equations has no solution. For any value of k, the system of equations has infinitely many solutions. If k is equal to any value other than 21, the system of equations has no solution. If k is equal to any value other than 21, the system of equations has infinitely many solutions.

The length of a rectangle is increasing at a rate of 9 cm/sec while the width w is decreasing at a rate of 9 cm/sec. When t= 8 cm and w= 15 cm, find the rates of change of the area, the perimeter, and the lengths of the diagonals of the rectangle. Determine which of these quantities are increasing, decreasing, or constant. The rate of change of the area of the rectangle is___cm² /sec. (Simplify your answer.)