Math Questions

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?

A resistor and an inductor connected in a series network impede the flow of an alternating current. This impedance Z is determined by the reactance X of the inductor and the resistance R of the resistor. The three quantities, all measured in ohms, can be represented by the sides of a right triangle as illustrated, so Z² = x² + R². The angle is called the phase angle. Suppose a series network has an inductive reactance of X=400 ohms and a resistance of R = 1000 ohms. (a) Find the impedance Z. (b) Find the values of the six trigonometric functions of the phase angle .

Geneva has learned that the expected value of an Insurance payment to a driver to cover the costs of an accident in her state Is $5,200 over the first three years. If her Insurance costs $2,000 a year and the average cost of an accident Is $1,000, which statement is most correct? If Geneva drives more recklessly than most other drivers, the insurance is a good decision for Geneva. If Geneva drives more carefully than most other drivers, the insurance is a good decision for Geneva. Geneva knows she will certainly come out ahead and make money by paying for the insurance. Geneva knows she will certainly lose money by paying for the insurance.

Three hundred students submitted an essay In a nationwide essay contest. The best essay will win a $2,000 scholarship. Ten other students will be given a $1,000 scholarship. What is the expected value of an essay submission? $40 $0.04 $12,000 $1,500

Bob runs each lap in 7 minutes. He will run at most 12 laps today. What are the possible numbers of minutes he will run today? Use for the number of minutes he will run today. Write your answer as an inequality solved for t.

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

Use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle θ. cos θ = 1/11

Suppose the probability of a pitcher throwing a strike (the probability of success) is 0.5. After how any pitches is a strike expected? 1 2 3 5

Describe how you know the difference between a binomial distribution and other probability distributions. Give an example of a scenario involving a binomial distribution not discussed in this lesson.

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?

The critical numbers for the function f(x) = 2x³-21x² + 36x - 7 are: -

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.

A building contractor receives a new contract to consider. From past experience, he estimates that there is a 40% chance of making a $400,000 profit, a 40% chance of losing $300,000 and a 20% chance of losing $250,000. What Is the contractor's expected profit or loss from this contract? $1000 $200,000 -$100,000 -$10,000

You were given a table with the cost of a hamburger In a town and the associated probability of each cost. You found the expected value to be $2.87. Which statement is correct? The average cost of a hamburger is $2.87. You found the expected value by adding up the costs, then dividing by the sum of the probabilities. There are more restaurants that sell a hamburger for $2.87 than there are for any other price. You know the price of a hamburger at every restaurant in town.

Ron makes soap balls and sells them at his local farmers' market. First, he uses a large cylindrical pot to mix and melt the ingredients. The pot has a diameter of 10 inches, and he fills it to a height of 10 inches. When everything is melted, he pours the liquid soap into small spherical soap molds that each have a radius of 1.5 inches. What is the maximum number of soap molds that Ron can fill completely using his soap mixture?

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

Consider the function f(x) = 1/16 x² + 2x + 4. What is the maximum approximation of the area under the curve of f on the interval [-1, 3] with four equal subintervals?

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:

A ferris wheel is 50 meters in diameter and boarded from a platform that is 2 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 6 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 3 minutes?

Guests at a wedding have an appetizer choice of soup or a salad, an entrée choice of chicken, steak, or vegetarian, then a dessert choice of vanilla or chocolate cake. How many different meals are possible?

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

Which of the following correctly describes expected value? the long-term mean of all possible outcomes in a probability distribution the probability distribution of the means of all outcome variables the set of all outcomes in a discrete variable set the first value in a variable set greater than one

In a certain city in Washington, the grass grows at the rate of 1/2 Inch a day on sunny days. On cloudy days, the grass grows at the rate of 1/4 Inch per day. In a typical July, 75% of the days are sunny and 25% are cloudy. Determine the total number of Inches of expected growth In a typical July. 0.43 inches 12.5 inches 15.5 inches 2.34 inches

How can you use a simulation to collect data for an event that has two possible outcomes that each have a probability of 0.5? Use a coin and let heads represent one outcome and tails represent the other outcome. Use a random number generator and let each number represent the different outcomes. Use a deck of playing cards and let number cards represent one outcome and let face cards represent the other outcome. Use a spinner with four sections and let one section represent one outcome and three sections represent the other outcome.