Math Questions

A tank that is 8 feet deep, with a square bottom with sides 4 feet each, has 1 foot of water that weighs 62.3 lb/ft³ in it. How much work, to the nearest whole unit (in ft-lb), will it take to pump the water to the rim of the tank?

The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by m(x) = -2(x-4) What is the maximum possible number of mosquitoes?

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

Suppose that a family has 5 children. How could you simulate the probability of having a girl or boy using colns? What outcome would show the outcome of all girls? Let H represent having a girl and T represent having a boy: HHHHH Let H represent having a girl and T represent having a boy: TTTTT Let T represent having a girl and H represent having a boy; HHHHH Let T represent having a girl and H represent having a boy: HTTTH

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.

Which of the following is NOT a characteristic of the chi-square distribution? The chi-square curve approaches, but never touches, the positive horizontal axis. The mean of the chi-square distribution is located to the left of the peak. The chi-square curve is nonsymmetrical. As the degrees of freedom increases, the chi-square curves look more and more like a normal curve.

There are twelve songs on your playlist. Six of them are country and six are pop. With random shuffle and no repetition, you listen to six songs. What is the probability that you listened to all country songs?

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

How can you use a simulation with a number cube to collect data for an event that has two possible outcomes that each have a probability of 0.5? Select all that apply. Let the odd numbers represent one outcome and the even numbers represent the other outcome. Let numbers 1-3 represent one outcome and numbers 4-6 represent the other outcome. Let number 1 represent one outcome and number 6 represent the other outcome. Let numbers 1 and 2 represent one outcome and numbers 3-6 represent the other outcome. Let numbers 1-4 represent one outcome and numbers 5 and 6 represent the other outcome.

A parabola has a vertex at the point (-2, -3) and an x-intercept at (1, 0). Find the other x-intercept. You must justify your answer for credit.

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

A tile is drawn at random from the tiles below. What is the probability that it is a consonant and has a point-value that is less than 3? Write your answer as a fraction in simplest form.

A brand of jeans comes in nine different washes, five different fit styles, and three different height options. If two of the wash options are out of stock, how many ways can someone order a single pair of jeans? A. 95 B. 105 C. 120 D. 15

Captive primates, such as spider monkeys, often experience fractured bones. The probability distribution from a study of the X-rays of 500 captive spider monkeys shows that half of them had one healed fracture; one-quarter had two healed fractures; ten percent had three healed fractures; and fifteen percent had four healed fractures. About how many healed fractures would you expect a randomly selected captive spider monkey to have based on this probability distribution? 01 02 03 04

The function is defined as follows for the domain given. h(x) = 2x+1, domain = (-5, -1, 2, 3) Write the range of h using set notation. Then graph h.

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

The diameters of apples from a certain farm follow the normal distribution with mean 4 inches and standard deviation 0.4 inch. Apples can be size-sorted by being made to roll over mesh screens. First the apples are rolled over a screen with mesh size 3.5 inches. This separates out of all the apples with diameters less than 3.5 inches. Second, the remaining apples are rolled over a screen with mesh size 4.3 inches. During that first step, what proportion of apples have a diameter of less than 3.5 inches? Round your answer to four decimal places.

Graph, label, and connect the following points: S(3, 2), D(6, 8), I(2, 8), and E(15, 2) to form polygon SIDE. a. Name the type of polygon. b. Find the length of the height. c. Find the area of the figure named SIDE. d. Calculate the lengths of segments SI and DE. e. Calculate the perimeter of SIDE. f. Find the slopes of SI and DE.

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?

What must the probabilities of all the branches add up to? 0.5 1 100 2

Consider the quadratic function f(x)= -x2 - x +20 Determine the following: (enter all numerical answers as integers, fractions, or decimals): The smallest (leftmost) -intercept is = The largest (rightmost) a-intercept is= The y-intercept is y= The vertex is The line of symmetry has the equation

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.

The monthly cost of operation at a company, C, given in dollars as a function of the number of units produced per month, u, is given below. C= $3,173 + $31u If the company wants to keep the cost of operation under $18,000 per month, what is the maximum number of units they can produce? A. 4,780 B. 4,781 C. 478 D. 479

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)

If the parent function is f (x) = log5 (x), identify the transformations of the parent function given f (x) = -5 log5 (x+2)-3. (select all that apply) A vertical stretch of 5 B vertical shift down 3 c vertical compression of 1/5 D reflection over the y-axis E horizontal shift left 2 F reflection over the x-axis G horizontal shift right 2 H vertical shift up 3

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.

If the expected value for a probability distribution from a study of penguin births recorded In U.S. zoos in 2018 equals 2.4578, what does this value tell you? expect that any randomly selected U.S. zoo had between 24 and 25 penguin births in 2018 expect that all U.S. zoos had 2.4578 penguins born in 2018 expect that about 2.5% of U.S. zoos had a penguin birth in 2018 expect any randomly selected U.S. zoo recorded between 2 and 3 penguin births in 2018

Algebraically find the vertex & build a table of 5 values for the following absolute value function: y = 3x - 1| +7

A construction worker, 36 feet up on a scaffold, lifts a 4-lb rope hand over hand up to the scaffold to raise a cement block weighing 8 pounds off the ground. (Assume the rope is 36 feet long.) How much work (in ft-lb) is required to pull the rope and the block up to the scaffolder?

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

How is P(x) calculated in the process of determining an expected value using a probability distribution? by dividing the count for each outcome (x) by the total count of outcomes in a sample by multiplying the count for each X times the total count by adding all counts and dividing that total by N by subtracting the count of each X from the EX

What is the total probability of getting one of the two following outcomes with three number generators, assuming the number generators are binary? (0, 1, 0) and (1, 0, 1) 1/4 1/8 3/4 3/4

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?

8 A radioactive isotope is decaying at a rate of 18% every hour. Currently there are 100 grams of the substance. Part B: How much will be left one day from now? Round your answer to the nearest hundredth.

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)

8. A card is chosen at random from a standard deck. Find each probability as a fraction (in simplest form). decimal, and percent. a) P(ace) c) P(face card or 8) b) P(black or queen) d) P(red jack)

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?

There are 15 candidates for three positions at a restaraunt. One position is for a cook. The second position is for a food server. The third position is for a cashier. If all 15 candidates are equally qualified for the three positions, in how many different ways can the three positions be filled?

Solve using the quadratic formula. 0= 4x² + 11x + 4

A certain lottery requires players to select 5 different numbers, in any order, from 1 to 48 inclusive. How many different sets of 5 numbers can be chosen? The 5 numbers can be chosen in different ways.

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?