Math Questions

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.)

In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch? 17 inches 16 inches 15 inches 14 inches

"Twice the amount of time Jenn ran was 15 minutes more than the amount of time Katie ran." Where J = amount of time Jenn ran (hours) K = amount of time Kati ran (hours) 2J+15= K 2J = K + 15 2J + (1/4)= K 2J = K+ (1/4) 2J+K= 15

Manny owns a home with a front and back lawn. The front lawn is the size of the back lawn. If she mows ½ of her front lawn and 3 of her back lawn, what fraction of her entire lawn was left unmowed?

An author published a book which was being sold online. The first month the author sold 3500 books, but the sales were declining steadily at 12% each month. If this trend continues, how many total books would the author have sold over the first 24 months, to the nearest whole number?

The art club is raising money to go to an art museum. So far they have raised $50 by selling chalk drawings for $5 each. If they need to raise a total of $400, how many more drawings do they need to sell? a. 10 b. 70 C. 80 d. 90

Vicky and Bob went to a store to buy school supplies. Vicky spent a total of $22 on school supplies. She spent $13 on a book and spent the rest of the money on notebooks. The store sells notebooks for $1.50 each. Write an equation that can be used to find the number of notebooks Vicky bought. Use the variable v for the number of notebooks. Solve the equation and show your work.

A ship leaves the Boston Harbor and travels at a bearing of 52° for 200 miles and then changes course and travels for an additional 80 miles at a bearing of 142° to an island location. a). How far is the ship from the Harbor? b) If the ship is able to return home on a direct route from the island to the Harbor, at what bearing should the ship travel?

Select all the studies in which the results may have been skewed by blas. a study with a significantly larger than expected standard deviation about the sample mean a study on the heights of a group of fourth graders, where 90% of the data fell below the population mean a study on employees' commute time, with 90% of the data falling within 1 standard deviation of the population mean a study of the popularity of a particular music genre, with a small standard deviation about the mean a study of the average annual rainfall, with 28% of the data having a z-score greater than 1 a study on the average life span of a type of plant, where 50% of the data fell above the population mean

In a lab experiment, the decay of a radioactive isotope is being observed. On the first day of the experiment the mass of the substance was 1200 grams and mass was decreasing by 11% per day. Write a recursive formula to represent the mass of the radioactive sample on the nth day of the experiment.

The officers of a neighborhood association want to know whether residents are interested in beautifying the neighborhood and, if so, how much money they are willing to contribute toward the costs involved. The officers are considering two methods for gathering data: Method A: Call and survey every tenth resident on the association's roster. Method B: Randomly select and survey 10 residents from among those who come to the neighborhood block party. Which sampling method is most likely to result in a representative sample of the population; Method A or Method B?

A political strategist believes that 58% of voters in a certain state support his candidate. He then commisions a poll of 800 voters and 53% of them support his candidate. Is there evidence at the .05 level of significance to refute the strategist's belief? No, because the test value -3.15 is in the noncritical region. No, because the test value -1.69 is in the noncritical region. Yes, because the test value -2.87 is in the critical region. Yes, because the test value -3.15 is in the critical region.

Members of a student council are designing a school float for a parade. They decide to poll 10% of the student body to get feedback about the theme they have chosen. What would most likely happen if they decided to randomly sample 5% of the student body instead? The sample proportion would more closely model the population proportion. The sample proportion would not be affected. The sample proportion would less closely model the population proportion. There is not enough information to determine how the sample proportion would be affected.

Monica wants to invest $1200 in a savings account. Determine the interest rate (simple interest) required for Monica 's investment to double in value in 20 years. Round your answer to the nearest tenth of a percent.

Thirty percent of consumers prefer to purchase electronics online. You randomly select 8 consumers. Find the probability that the number of consumers who prefer to purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five. (a) Find the probability that the number that prefer to purchase electronics online is exactly five. P(5) =

How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? A. 10 B. 25 C 35 D 45

Determine if the statement is true or false. If the statement is false, rewrite it as a true statement. The expected value of a random variable can never be negative. Choose the correct answer below. A. The statement is false. The expected value of a random variable can be negative. B. The statement is true. C. The statement is false. The expected value of a random variable is always 1. D. The statement is false. The expected value of a random variable is always 0.

A balloon, which always remains spherical, has a variable radius. If the radius is increasing at the rate of 3 units/sec then find the rate at which its volume is increasing with respect to time when its radius is 12 units Note that the volume of the sphere is given by V=4/3 π r^3 A) 48π units^3 / sec C) 576 π units^3 / sec D) 1728π units^3 / sec B) 144π units^3 / sec

A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 4 ft/sec. After 12 seconds, how rapidly is the area inclosed by the ripple increasing? Recall the area of a circle is given by A= πr².

Two rooms in a house are similar rectangles. Room A is 12 ft by 16 ft. The longer side of Room B is 4 ft shorter than twice the length of the shorter side of Room A. What are the dimensions of Room B? A 15 x 20 B. 16 × 20 C. 16 x 16 D. 14 x 16

Using the completing-the-square method, rewrite f(x) = x² + 10x + 7 in vertex form. f(x) = (x + 5)² - 18 f(x) = (x + 10)² +25 f(x) = (x + 5)² +7 f(x)=(x + 5)²