Basic Math Questions and Answers

Ana dives into a pool off of a springboard high dive. Her height (in meters above the water), a seconds after diving, is modeled by h(x) = -5(x + 1)(x − 3) How many seconds after diving will Ana hit the water?

By completing the square, the expression x² + 12x + 87 equals (x + A)² + B where A = and B =

Squirrels are running wild on the campus, so Building and Grounds decides to tag 100 of them. In the spring, 50 squirrels are caught and 5 of them are tagged. What is the estimate for the number of squirrels living on campus?

A dance company charges $300 for a package of 20 dance lessons. Research shows that 20 percent of people attend all the lessons. The rest miss an average of 12 lessons. What is the expected value of a single dance for the company? $33.00 $28.00 $24.90 $31.00

In filing his income tax, Raul reported annual contributions of $300 to a public radio station, $180 to a public TV station, $200 to a local food bank, and $300 to other charitable organizations.

Enter values in the t-table for the piecwise function that is shown on the graph. Make sure that you are using the correct equation based for the x-value.

Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of 3.5e^0.05t billion metric tons/year, t years from 1980 (which corre sponds to t = 0). Had it not been for the energy crisis, the rate of production of coal since 1980 might have been only 3.5e^0.01t billion metric tons/year, t years from 1980. Determine how much additional coal was produced between 1980 and 2000 as an alternative energy source.

Amanda needs to buy some pencils. Brand A has a pack of 36 pencils for $8.52. Brand B has a pack of 48 pencils for $9.98. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent.

Suppose you invest $1,000 in an account paying 7% compounded annually. Assuming no other deposits or withdrawals, how many years would it take for the amount in the account to double to $2,000? Round to the nearest 10th

If the distance between the points (-5, − 3) and (x, 45) is 50 then the possible values for x are: List all possible values, separated by commas.

Find the work done by a force F = 8i - 6j + 8k that moves an object from the point (0, 9, 9) to the point (7, 11, 19) along a straight line. The distance is measured in meters and the force in newtons.

Suppose that out of 100,000 male high school baseball players, only one-half percent make it to the Major Leagues. Find the expected number of male high school baseball players who make it to the Major Leagues. 500 50 5,000 100

Abby gets a job at a dress store that pays a salary of $90 per week plus $5 for each dress she sells.. a.) Write an equation to model this scenario. Use function notation. b.) If Abby sells 20 dresses, how much does she get paid? Show your work.

In physics, work is defined as F D where F is the force applied over a distance of D. A box is dragged across 20 meters with a force of 60 Newtons, which are kg m/s2. What calculation will give us the work done, in Joules (which are kg m²/s2)? Choose 1 answer: 20.60 20.1000.60 20/1000.60 20/60

Consider the Quadratic function f(x) = 2x² - 9x - 35. Its vertex is ___, ____; its largest x-intercept is = _____, its y-intercept is y = ____

Consider the Quadratic function f(x) = 3x²-14x -24. Its vertex is its largest x-intercept is a = its y-intercept is y =

An economist wondered if people who go to the movies on weekdays go more or less often on Fridays than any other day. She figured that if it were truly random, 20% of these movie-goers would go on Fridays. She randomly sampled 50 people who go to movies on weekdays and asked them on which day they attend movies most frequently. Of those sampled, 14 indicated that they go on Fridays more often than other days. The economist conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of weekday movie-goers who go most frequently on Fridays is different from 20%. For this test: Ho: p = .2, Ha: p≠2

A couple purchases a home with a $320,000 mortgage at 4% for 30 years with monthly payments. What will the remaining balance on their mortgage be after 10 years? $1527.73 $252,108.84 $213,333.33 $221,866.67 Can't be determined from the given information

Flight FL190 had 120 passenger seats, but 30% of these seats were empty. Therefore, passenger seats were occupied on the flight. 4 30 36 70 84

Find all real solutions of equation 3x² + 6x - 5 = 0. Does the equation have real solutions? Input Yes or No: If your answer is Yes, input the solutions:

Tiffany wants to calculate the volume of her globe. The globe is in the shape of a sphere, as represented in the picture. She measured the circumference of the globe along the equator to be 24 inches. Which of the following measures is closest to the volume of Tiffany's globe? A. 46 cubic inches B. 61 cubic inches C. 234 cubic inches D. 183 cubic inches

Graph y = |x-2|-3. [Hint: what is the vertex? How do you the vertex to plot the remaining points?]

A jet ski is travelling 75 degrees North of East at a constant speed of 43 miles per hour. The water is moving at a rate of 12 miles per hour due East. Represent the movement of the jet ski considering the wind. How far has the jet ski moved horizontally and vertically after 12 minutes?

A radioactive isotope is decaying at a rate of 18% every hour. Currently there are 100 grams of the substance. Part C: When will there be 10 grams left? Justify your answer and round your answer to the nearest hundredth.

A rectangle has vertices (-1, 1), (-4, 1), (−1, 3), and (-4, 3). If the rectangle is reflected over the y-axis, what algebraic rule can be used to find each of the new vertices? Select one: (x,y) → (y, - x) (x,y) → (- x, - y) (z,y) → (-y, − x) (r,y) → (- x, y)

Lucia finds that (3x²+3x+5)+ (7x²−9x+8) – 10x²−12x+13. What error did Lucia make? She found the difference instead of the sum. She combined the terms 3x² and 7x² incorrectly. She combined the terms 3x and -9x incorrectly. She did not combine all like terms.

What is the length of the the midsegment of a trapezoid with bases of length 13 and 29?

At your high school, you are trying to determine the probability that a student takes Spanish given that the student is taking Marketing? How would you determine this probability? Explain your thinking.

70% of the voters favor Ms. Stein. If 300 voters are chosen at random, what is the expected number of voters who indicate favoring Ms. Stein?

When looking at the association between the events "owns a car" and "owns a pet," if the events are independent, then the probability P(owns a pet | owns a car) is equal to which of the following? A. P(owns a pet) x P(owns a car) B. P(owns a pet) C. P(owns a pet) + P(owns a car) D. P(owns a car)

Justin is pouring a concrete walkway around his grandmother's rectangular garden. He wants the walkway to be 3 feet wide all the way around. If his grandmother's garden is 25 feet by 42 feet, what is the area of the top of the walkway?

Marle Spector is the star basketball player on the University of Florida's women's basketball team. Marle has sprained her ankle and the team doctor estimates that there is a 50% chance that Marle will be well enough to play in the next game. The team coach estimates that with Marle, the team will score 80 points. Without Marle, the coach estimates the team will score 64 points. What Is the number of points the team can expect to score? 72 points 68 points 71 points 64 points

A machinist creates a solid steel part for a wind turbine. The part has a volume of 1,015 cubic centimeters. Steel can be purchased for $0.29 per kilogram and has a density of 7.95 g/cm³. If the machinist makes 500 of these parts, what is the total cost of the steel?

You are on a treasure-diving ship that is hunting for gold and silver coins. You reel in a wire basket that contains gold and silver coins, among other things. The basket holds no more than 50 pounds of material. Each gold coin weighs about 0.5 ounce, and each silver coin weighs about 0.25 ounce. You want to know the different numbers of each type of coin that could be in the basket. Write an inequality that models the weight in the basket. Give three solutions to the inequality you wrote above

Solve 9t2 + 30t + 25 = 36 by using the square root method. Enter each solution in the box below as a reduced fraction or integer. If there is more than 1 solution, separate the values with a comma (example: -3, 2).

A relative has set up an account for you to have access to in 15 years. The account is at a bank which pays 2% interest and compounds quarterly. If the original amount placed in the account is $10,000, how much will be in the account after 15 years?

If a 43.08 gram piece of brass which has a specific heat of 0.38 J/gºC absorbs 1,979.56 J of energy, how much did the temperature change? Round your answer to 2 numbers after the decimal and include the correct units.

Find all real solutions of the equation (4j-1)² = 25. Write your answers as a list of integers or reduced fractions in the form A/B. For example, if your answers 2/3 are and 5, you would enter 2/3,5

Solve 25t2-64-0 by using the square root method. Enter the solution(s) in the box below as reduced fractions or integers. If there is more than 1 solution, separate the values with a comma (example: 11/7, 11/7). The solution set fort is

The quadratic equation is in factored form. y = − 1.1(x+6)(x − 7) What are the x-intrecepts for the graph of this equation? Enter the left-most intercept first: Enter the right-most intercept next:

Consider a student loan of $15,000 at a fixed APR of 9% for 30 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Acme Life Insurance charges $650 for a $1,000,000 life Insurance policy. Historical research shows that 1 In 11,000 policyholders will dle and the company is forced to pay out $1,000,000. On average, what is the expected profit of Acme Life Insurance per policy? $649.94 $591.00 $559.03 $62.01

Jenny runs a daycare center and charges $60 per day for each child. There are currently 50 children enrolled at the daycare. At a recent conference, Jenny was advised to lower her rates in order to stay competitive in her area. For each price decrease of $4 per day, the number of children enrolled at the center increases by two. Write the equation that can be used to determine the number of price decreases, x, in dollars, for which the daycare center has a daily revenue of $2,800. A. (60-4x)(50 + 2x) = 2,800 B. (60-2x)(50 +4x) = 2,800 C. (60+ 2x)(50-4x) = 2,800 D. (60+4x)(50-2x) = 2,800

Michael uses a blend of dark chocolate and milk chocolate to make the ice cream topping at his restaurant. He needs to buy 100 kg of chocolate in total for his next order. Dark chocolate costs $12 per kilogram, milk chocolate costs $10 per kilogram, and he wants to spend $1120 total. Let d be the number of kilograms of dark chocolate he buys and m be the number of kilograms of milk chocolate he buys. Which system of equations represents this situation?

An item is regularly priced at $95. It is now priced at a discount of 45% off the regular price. Use the ALEKS calculator to find the price now.

A ferris wheel is 20 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? What is the Midline? y What is the Period? How High are you off of the ground after 4 minutes?

Sarah has two tests at school next week, a math test and a physics test. Let A represent the event that she passes her math test and B represents the event that she passes her physics test. If A and B are independent events with P(A) = 0.30. and P(A and B) = 0.21, find P(B). Give your answer as a decimal rounded to two decimal places.

Charlie has to carry 272 apples from a farm to the market. How many baskets will he need, given that each basket can hold 49 apples?

The height of a right cylindrical can of peas is greater than the diameter of the base of the can. The can is sliced into two equal parts through its bases. Which of the following figures BEST describes the cross section of the cylinder? A. circle B. rectangle C. triangle D. semicircle

In a large city's recent mayoral election, 131,506 out of 309,153 registered voters actually turned out to vote. If 20 registered voters are randomly selected, find the probability that 7 of them voted in the mayoral election. Use TI-84 (plus) calculator to find the binomial probability. Round your answer to three decimal places.