Math Questions

You are playing a battle with your character cards. You brought 20 cards with you, but can only choose 5 for the battle. In how many ways can you choose the 5 cards? 1,860,480 20 5 15,504

Use a calculator to find the value of the following expression rounded to two decimal places. cos -1 14/15

A license plate begins with three letters chosen from A to Z. Which of the following represents the number of ways the letters of the license plate can be formed if you can repeat the letters? 26-3 26-26-26 326 26 +3

Put the equation y = x² + 4x - 5 into the form y = (x + h)² + k

Determine the volume of the solid generated by rotating the region bounded by y = x², y = 0 and y = 5 around the line y = 5.

Bag A contains 10 marbles of which 4 are red and 6 are black. Bag B contains 12 marbles of which 8 are red and 4 are black. A ball is drawn at random from each bag. What is the probability that you draw red marbles from both bags?

Jillian has a triangular-shaped garden with side lengths of 11 feet, 12 feet, and 15 feet. Which of the following describes the garden and its shape? Select all that apply. The area of the garden is about 65.2 feet squared. The angle across from the side with a length of 15 feet is about 81.3". The area of the garden is about 20.0 feet squared. The angle across from the side with a length of 15 feet is about 52.3.

Two square pyramids are similar. If the heights of the pyramids are 9 inches and 12 inches, and the volume of the smaller pyramid is 162 in³, what is the volume of the larger pyramid (in cubic inches)?

A car bought for $13000 depreciates at 12% annually. What is its value after 9 years? Do not include the dollar sign in your answer. Round your answer to the nearest cent.

Two square pyramids are similar. If the heights of the pyramids are 9 inches and 12 inches, and the volume of the smaller pyramid is 162 in', what is the volume of the larger pyramid (in cubic inches)?

Leos total bill at the blue lobster came to $45.90. he wanted to leave a 20% tip. How much money would he need to pay in total?

Suppose that a family has 4 children. If the probability of having a girl Is 0.5, which simulation could be used to simulate the probability of having all girls? What is the theoretical probability of having all girls? Let H represent having a girl and T represent having a boy; 4 heads; \P\left(k-4\right)=\frac{41(4Neft(O\right)!\times0.5^40.5^0) Let H represent having a girl and T represent having a boy; 4 tails; Let T represent having a girl and H represent having a boy: 1 tail and 3 heads; \P\left(k-1\right)=\frac[4!) 10.5^3\) [1Meft(3\right)!\times0.5 \P\left(k-4\right)=\frac[41X4Neft(O\right)\times0.5 40.5^0) Let T represent having a girl and H represent having a boy; 2 heads and 2 tails; VP\left(k-2\right)=\frac{2} (2Neft(2\right)!\times0.5^20.5^2)

A certain company's main source of income is a mobile app. The company's annual profit (in millions of dollars) as a function of the app's price (in dollars) is modeled by P(x) = -2(x-3)(x - 11) What would be the company's profit if the app price is 0 dollars?

Seema deposited $800 in a saving account earning 2.05% compounded annually. To the nearest cent, how much will she have in 17 years? Do not include the dollar sign in your answer.

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city. Every year the population drops by 4.5%. What is the population after 3 years? 894 people 1,069 people 854 people 816 people

An electrician charges an hourly rate of $50, but also charges a fixed fee for making house calls regardless of time spend on the job. One day, the electrician earned a total of $250 for a 2 hour job. Write an equation for C, in terms of t, representing the total cost of the electrician's services if the electrician spends t hours at the house working.

Simon has 160 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width 2 (in meters) is modeled by A(z) = -x(x - 80) What width will produce the maximum garden area?

In a neighborhood with 1,269 homes, the exterior of each home must be painted with one of only six colors - white, yellow, grey, blue, green, or brown. There are 234 homes painted white, 125 homes painted yellow, 433 homes painted grey, 207 homes painted blue, 98 homes painted green, and 172 homes painted brown. If a home is randomly selected for an Inspection, what is the probability Is It painted brown? 0.1355 0.1844 0.1720 0.2692

Thomas has graphed the function y = 7x-10 on a coordinate plane. Which of the following statements is true for the function Thomas graphed? A. It has a slope of 10. B. It has a y-intercept of 7. C. It has a negative correlation. D. It assigns exactly one output to each input.

Find an expression which represents the difference when (10x-8y) is subtracted from (-4x-9y) in simplest terms.

Ian is going to the amusement park, where he has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money lan will spend is given by the equation y = 20+ 1.5a, where y represents the total amount of money, in dollars and cents, and a represents the number of rides Ian goes on. What is the meaning of the y-value when z = 1? The total amount of money lan will spend if he goes on 100 rides. The change in the total amount of money for every one additional ride he goes on. The total amount of money Ian will spend if he goes on o rides. The total amount of money Ian will spend if he goes on 1 ride.

Suppose that a certain radioactive element has an annual decay rate of 8%. Starting with a 4,329 gram sample of the element, how many grams will be left in 10 years? Round your answer to the nearest gram.

The probability of a sunny day is 3/7 and the probability of a rainy day is 4/7. If It's a sunny day, the probability Paul cycles to work is 7/10, the probability he drives to work is 2/10, and the probability he takes the train to work is 1/10. If It's a rainy day, the probability Paul cycles to work is 1/9, the probability he drives to work is 5/9, and the probability he takes the train to work is 3/9. What is the probability Paul bikes, regardless of the weather today? 0.36 0.48 0.52 0.32

Say that a game consists of two steps. First, you roll a die. If you roll a 1 or a 6, you continue; otherwise, you lose the game. If you rolled a 1 or a 6 and can continue playing the game, the second step is to draw a random card from a standard deck of 52 playing cards. If you draw an ace or a 6, you win. What is the probability that you will win this game? 2/39 1/3 8/52 19/39

Tanya has a garden with a trench around it. The garden is a rectangle with length 2 1/2m and width 2 m. The trench and garden together make a rectangle with length 3 1/2m and width 3 m. Find the area of just the trench. m²

A spinner is used for which it is equally probable that the pointer will land on any one of eight regions. One of the regions is colored blue, four are colored purple, and three are colored brown. If the pointer is spun once, find the probability it will land on brown and then purple. 7/8 3/16 1/8 3/4

Lighthouse Master Jack Simmons is atop his 300 ft lighthouse and spots a boat in the distance at an angle of depression of 18°. How far is the boat from the lighthouse? Round your answer to the nearest Hundredth Distance = Ift

Suppose Solid X and Solid Y are similar. The volume of Solid X is 5145 cm³, and the volume of Solid Y is 10,935 cm³. If Solid X has a height of 28 cm, what is the height of Solid Y in centimeters?

Find all real solutions of the equation 4k² + 15 = 271.

Anthony's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y 57+ 6.3x, where y represents the expected quiz score and a represents hours spent on homework that week. What is the meaning of the x-value when y = 99? A student's expected quiz score if they spent 1 hour on their homework. A student's expected quiz score if they spent 99 hours on their homework. How many hours a student spends studying all year. The number of hours a student should spend on their homework to expect a score of 99 on the quiz.

One pipe can fill a swimming pool 2.8 times faster than a second pipe. If both pipes are open, the pool can be filled in 3 hours. Choose the equation that can be used to determine how many hours, x, it would take to fill the pool if only the slower pipe is used to fill the pool.

Which of the following equations represents a line that passes through the points (-6, 10) and (-8, 16)? I. 3x + y = -8 II. y=-3x -7 Neither II only I only I and II

Consider the parabola given by the equation: Find the following for this parabola: y = x² + 6x - 8 A) The vertex = B) The y intercept is the point (0, C) Find the two values of that correspond to the x intercepts of the parabola and write them as a list, separated by commas: x = Round your answer(s) to two decimal places.

Your little sister is selling scout cookles and you go along with her. Suppose the probability that a person answers the door is 0.4. What is the probability that your first opened door Is at the third house? 0.144 0.240 0.864 0.096

Use the even-odd properties of the trigonometric functions to find the exact value of the given expression. Do not use a calculator. cos (-60°) Select the correct choice below and fill in any answer boxes in your choice. A. cos (-60°)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The answer is undefined.

If two triangles have the same area, what additional information is needed to show that they are congruent? One triangle's altitude is congruent to the other triangle's altitude. The triangles are both isosceles. One triangle has two angles that are congruent to two angles of the other triangle. The triangles each have a right angle.

Starting at noon, Kennedy observed the amount of snow on her lawn during a blizzard. She wrote an equation to represent 8, how many inches of snow were o lawn: 8= 0.012x +4.5, where x represents the number of minutes past noon. What could the number 4.5 represent in the equation? The amount of snow on the lawn when the blizzard ended. How much more snow is added to the lawn every minute. The amount of snow on the lawn at noon. The amount of snow on the lawn at 12:01 p.m.

In a sample of 40,000 first-born babies, 7 were found to have a certain syndrome. Find the empirical probability that a family's first child will be born with this syndrome. The empirical probability is.

Sebastian signed up for a streaming music service where there's a fixed cost for monthly membership and a cost per song downloaded. His total cost per month is given by the equation c = 1.25x + 4.99, where a represents the number of songs he downloads and c represents the total cost, in dollars and cents. What is the meaning of the c-value when x = 1? The cost to use the service for one month if zero songs are downloaded. The total cost per month assuming one song is downloaded. The cost to download 100 songs. How much the streaming service charges per downloaded song.

A shuttle bus arrives at a hotel every 40 minutes to take guests into town. If a guest walks out the door at a random time, find the probability of each waiting time. a) P(at least 15 min) b) P(no more than 10 min)

A license plate is to consist of 3 letters followed by 5 digits. Determine the number of different license plates possible if the first letter must be an K, L, M, N or P and repetition of letters and numbers is not permitted. 90,720,000 272,160,000 54,522,000 9,072,000

49. Validate the biconditional statement. A game can be classified as a card game if and only if it is played with a deck of cards. The biconditional statement is false because the conditional statement and the converse are false. The biconditional statement is false because the conditional statement is false. The biconditional statement is false because the converse is false. The biconditional statement is true because the conditional statement and the converse are true.

Constellation Party Supplies makes different types of cylindrical glow sticks. A regular glow stick has a volume of 26.5 cubic centimeters. A thin glow stick for bracelets has 1/4 the volume of a regular one and a diameter of 0.64 centimeters. What is the length of a thin glow stick?

f(x) = 3x - 7, g(x) = 6 - x (a) (f+g)(x) = (b) (f-g)(x) = (c) (fg)(x) = (d) (f/g)(x) = What is the domain of f/g?

Joseph is in the business of manufacturing phones. He must pay a daily fixed cost of $1000 to rent the building and equipment, and also pays a cost of $50 per phone produced for materials and labor. Make a table of values and then write an equation for C, in terms of p, representing total cost, in dollars, of producing p phones in a given day.

A Ferris wheel has a radius of 80 feet. Two particular cars are located such that the central angle between them is 165º. To the nearest tenth, what is the length of the intercepted arc between those two cars on the Ferris wheel?

Kyla bought a raffle ticket at a charity event. Five raffle ticket winners are chosen every 45 minutes. If Kyla steps out to take a phone call at a random time, what is the probability that she has at least 10 minutes before winners are called again? A. 22.2% B. 77.8% C. 66.7% D. 75%

The quadratic y = (x - 3)(x + 5) is horizontally translated left by 4 units. Which of the following gives the equation of the transformed quadratic? (A) y = (x-7)(x + 1) (B) y = (x + 1)(x + 9) (C) y = (x + 1)(x + 9) - 4 (D) y = x² + 2x - 11

In order to test the efficacy of a program designed to attract more women to STEM fields in college, 700 female students who completed the program were compared to 1200 female students who did not complete the program. Of the 700 women who completed the program, 125 of them majored in a STEM field in college. Of the 1200 women who did not complete the program, 174 of them majored in a STEM field. Perform a hypothesis test to see if there is statistically significant evidence that the proportion of women who completed the program is significantly greater than the proportion who did not complete the program. Perform the test at the alpha = 0.05 level. What is the p-value and conclusion of this test? p-value = 0.026; Fail to reject the null hypothesis p-value = 0.026; Reject the null hypothesis p-value = 0.053; Fail to reject the null hypothesis p-value = 0.053; Reject the null hypothesis

Suppose the probability that a basketball player makes a foul shot (the probability of success) Is 0.35. Would you use a binomial distribution or geometric distribution to determine the probability that the basketball player makes the first foul shot on the fifth attempt? What is that probability? binomial; 0.010 geometric; 0.010 binomial; 0.062 geometric; 0.062