Math Questions

You want to start a summer business to earn money. What will you do? You have to consider how much money you can afford to invest in this business, how much it will cost you to make each item, and how much you're going to charge for each item. Research something that would be reasonable to make and sell with the start- up investment you have determined. a. What is the total amount of money you are willing to invest in this business? b. What item are you going to make and sell? Why? c. Describe how your business will work. How much will it cost you to make each item? How much will you sell each item for? d. Do you think your business will be profitable? Explain your answer.

A group of people were asked if Marilyn Monroe had an affair with JFK. 467 responded "yes", and 487 responded "no". Find the probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with JFK. Probability (Please enter a reduced fraction.)

The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5.6 mm. Round values to 4 decimal places when possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the round off error for a jumper's distance is exactly 2.3 is P(x = 2.3) = d. The probability that the round off error for the distance that a long jumper has jumped is between 0 and 5.6 mm is P(1.4 < x < 4.6) = e. The probability that the jump's round off error is greater than 1.32 is P(x > 1.32) = f. P(x> 4.7 x > 0.6) = g. Find the 92nd percentile. h. Find the minimum for the upper quartile.

A geneticist conducts an experiment with peas, one sample of offspring consisted of 458 green peas and 149 yellow peas. Based on these results, estimate the probability of getting an offspring pea that is green. Report the answer as a percent with one decimal place accuracy. (You need not enter the "%" symbol) Probability Is the result reasonably close to the value of 3/4 that was expected? yes no

Raina is choosing between two exercise routines. In Routine #1, she burns 21 calories walking. She then runs at a rate that burns 10.25 calories per minute. In Routine #2, she does only running, burning 15.5 calories per minute. For what amounts of time spent running will Routine #1 burn more calories than Routine #2? Use t for the number of minutes spent running, and solve your inequality for t.

Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 3 mph greaterbthan the speed of the eastbound train. After 3.5 hours, they are 567 miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions. AnswerHow to enter your answer (opens in new window) westbound train: eastbound train:

For the polynomial below, -3 is a zero. h(x) = x³ + x² − 9x-9 Express h (x) as a product of linear factors. h(x) =

Suppose that the weight of an newborn fawn is Uniformly distributed between 1.5 and 3.6 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. a. The mean of this distribution is b. The standard deviation is c. The probability that fawn will weigh exactly 2.6 kg is P(x = 2.6) = d. The probability that a newborn fawn will be weigh between 1.6 and 2.9 is P(1.6 < x < 2.9) = e. The probability that a newborn fawn will be weigh more than 3.12 is P(x > 3.12) = f. P(x> 1.91 x < 2.6) = g. Find the 91st percentile.

For q (x) =-2x² +5x-5/x² +2 (a) Identify the horizontal asymptotes (if any). (b) If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote(s). Separate multiple equations of asymptotes with commas as necessary. Select "None" if applicable. The graph has no horizontal asymptotes. The graph has at least one horizontal asymptote. Equation(s) of the horizontal asymptote(s): y = Crossover point(s):

James receives a gross pay of $1,550 bi-weekly from his employer. If his employer changed his pay period to monthly instead of bi-weekly, calculate the monthly payment that he would receive.

A fish tank of 82 fish is made up of three types of fish. There are 41 betta fish, 18 goldfish and some rainbow fish. How many rainbow fish are in the tank?

Amanda is earning extra money over the summer mowing lawns around her neighborhood. She would like to earn at least $450. She charges $15 for a small yard and $26 for a larger yard. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. . x = the number of small yards mowed . y = the number of larger yards mowed 15x - 26y> 450 26x + 15y > 450 15x + 26y ≥ 450 15x + 26y≤ 450

Kenneth invested his savings in shares of a new company. The company's share price dropped by $1.00 at the end of the first year, and by a further $0.75 at the end of the second year. The share price was $21.63 at the end of the second year. a. Calculate the original share price (at the beginning of the first year). b. Calculate the percent change in the share price over the two-year period.

Ajar contains 12 red marbles numbered 1 to 12 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability of the given event, please show your answers as reduced fractions. (a) The marble is red. P(red) = (b) The marble is odd-numbered. P(odd) = (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =

Marwin is selling handmade toys in an online craft boutique. She hopes to earn more than $150 by selling toy planes for $8 each and toy tractors for $12 each. Use the following variables to write an inequality that represents the scenario. . x = the number of toy planes . y = the number of toy tractors

Vail Ski Shop received a $1,210 invoice dated July 17 with 3/10, 2/15, n/60 terms. On July 31, Vail sent a $494 partial payment. a. What credit should Vail receive? (Round your answer to the nearest cent.) b. What is Vail's outstanding balance? (Round your answer to the nearest cent.)

Find five solutions of the equation. Select integer values for x, starting with - 2 and ending with 2. Complete the table of values below. y = − x + 4

A video rental company offers a plan that includes a membership fee of $5 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $25 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? Write a system of equations, graph them, and type the solution.

Macy of New York sold LeeCo. of Chicago office equipment with a $7,100 list price. Sale terms were 1/10, n/30 FOB New York. Macy agreed to prepay the $20 freight. LeeCo. pays the invoice within the discount period. What does LeeCo. pay Macy?

G. Zach deposited $3,000 in a new account at his bank. The bank pays 7.5% interest compounded annually on this account. Zack makes no additional deposits or withdrawals. What will be the balance of Zack's account at the end of 3 years?

In 2004, the population of a district was 26,400. With a continuous annual growth rate of approximately 5%, what will the population be in 2024 according to the exponential growth function? Round the answer to the nearest whole number.

There are a total of 19,153 IRSC students, 61% of which are under the age of 22. In a random sample of 655 students, 68% are found to be under the age of 22. Determine how many students in the population and the sample, respectively, are under the age of 22. Round solutions to the nearest whole number, if necessary. IRSC students are under the age of 22. students in the random sample of 655 IRSC students are under the age of 22:

Verizon offers to sell cellular phones listing for $100.24 with a chain discount of 15/10/5. Cellular Company offers to sell its cellular phones that list at $103.49 with a chain discount of 25/5. If Irene is to buy six phones, how much could she save if she buys from the lower-priced company? (Do not round intermediate calculations. Round all dollar amounts to the nearest hundredth. Round your final answer to the nearest cent.)

How did advances in physics and chemistry dramatically change manufacturing? made large multinational companies possible forced companies to share control of the production process employed fewer workers created research and development divisions

In 2004, the highest spaceplane flight was made in SpaceShipOne. A flight with this altitude can be modeled by the function below, where h is the altitude in meters and t is flight time in seconds. Approximately how long did the flight last? h(t) = -0.17t² + 187t +61,000 t≈1101.3 seconds t≈1363 seconds t≈261.7 seconds t≈1596 seconds

X' is a normally distributed random variable with a mean of 7.0 and a standard deviation of 3.00. Find the value x such that P(X<x) is equal to 0.86. (Note: the diagram is not necessarily to scale.)

Consider the given function f(x) = -3(x+1)² +12. (a) Determine whether the graph of the parabola opens upward or downward. (b) Identify the vertex. (c) Determine the x-intercept(s). (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in interval notation. Write your answers in exact form.

Victoria invests $300 into an account with a 2.5% interest rate that is compounded semiannually. How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar.

The ratio of the number of mystery books to the number of science fiction books is 4:3. The ratio of the number of science fiction books to the number of biographies is 4: 5. If there are 48 science fiction books, find the total number of books.

Two cities have nearly the same north-south line of 97° W. The latitude of the first city is 27° N, and the latitude of the second city is 37° N. Approximate the distance between the cities if the average radius of Earth is 6400 km. The cities are approximately (Round to the nearest integer as needed.) kilometers apart.

An astronaut is returning to Earth in a spacecraft. If the spacecraft is descending at a rate of 13.81 kilometers per minute, what will be its change in height after 51/2 minutes? Round your answer to the nearest kilometer. 76 km -76 km 760 km -760 km

According to a goverment statistics department, 19.8% of women in a country aged 25 years or older have a Bachelor's Degree, 15.8% of women in the country aged 25 years or older have never married; among women in the country aged 25 years or older who have never married, 23.8% have a Bachelor's Degree; and among women in the country aged 25 years or older who have a Bachelor's Degree, 19.0% have never married. Complete parts (a) and (b) below.

The function fis defined as follows. f(x) = -x² +6 If the graph of fis translated vertically downward by 3 units, it becomes the graph of a function g. Find the expression for g (x).

Consider the system of equations. x+2y=8 -3x-2y=12 How do you solve the system of equations with Cramer's rule? Drag a value or determinant expression into each box to correctly solve the system using Cramer's rule.

Angle is in standard position and (-6, -4) is a point on the terminal side of θ What is the exact value of secθ in simplest form with a rational denominator?

Solve the equation for x. x² - 12x +32 = 0

Assuming the population has a bell-shaped distribution, if a sample size n = 19 has a sample mean x̄ = 33 with a sample standard deviation s = 7, find the margin of error at a 95% confidence level. Round the answer to two decimal places.

Carmen is choosing between two exercise routines. In Routine #1, she burns 44 calories walking. She then runs at a rate that burns 16.3 calories per minute. In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 18.5 calories per minute. For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #2? Use t for the number of minutes spent running, and solve your inequality for t

Using the verbal description below, write the original function and it's inverse. Explain your solution strategy. 1. Starting with a number x, subtract 5 2. Take the square of that quantity 3. Divide by 3

The number of bats in a colony is growing exponentially. After 2 years, there were 207 bats. After 4 years, there were 1863 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 11 years? Do not include units in your answer.

A die is rolled 3 times. What is the probability of showing a (n) 2 on every roll?

The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4,720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6,300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?

Liz does screen-printing. When she screen-prints a batch of T-shirts, there is an initial set-up time of 15 minutes. After that, it takes 3 minutes to print each shirt. How long does it take to screen-print a batch of 14 shirts?

A coach bought 3 jerseys and 2 pairs of shorts for each of the 14 players on her soccer team. The jerseys cost $15 each, and the shorts cost $12 each. The coach used a $100 coupon to hel pay for the uniforms. Rewrite the numerical expression with parentheses to model the total cost, $866. 14 x 3 x 15 +2 x 12 + 100

A contractor is in charge of hiring people for a construction project. The number of days it would take to complete the project with a full time workers can be found using the function f(x) = 234. Assume once workers are assigned to the project, no workers may be added or taken off the project until it is finished. Find and interpret the given function values and determine an appropriate domain for the function. f(-1) = meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. of the problem. f(2)= meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. f(6.5) = meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is

Given g(x)=x²-4x, find the equation of the secant line passing through (-4, g (-4)) and (2, g (2)). Write your answer in the form y=mx+b.

In Fall 2020, 10.5 million undergraduate students attended a 4-year institution full- time. Of those, 9,240,000 were under age 25, 945,000 were ages 25-34, and 315,000 were age 35 and older. Answer the questions below. Label your answers with a, b, c. a. What percent of the students were under age 25? b. What percent of the students were ages 25-34? c. What percent of the students were age 35 and older?

Express 9.603603603... as a rational number, in the form p/q where p and q have no common factors.

A circle has the equation x2 + y² + 6x-4y-23=0. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is (Type an ordered pair, using integers or decimals.) The radius of the circle is (Type an integer or a decimal.) (b) Use the graphing tool to graph the circle. (c) What are the intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed. Type exact answers for each coordinate, using radicals as needed. Simplify your answer.) B. There is no intercept.

A point on the unit circle in the third quadrant has an x-value of -1/4, and makes an angle of a with the positive x-axis. (a) Draw the unit circle and plot the point. Indicate a.