Math Questions

44% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) a least four, (c) less than eight. (a) P(3)= (Round to three decimal places as needed.) (b) P(x24)= (Round to three decimal places as needed.) (c) P(x<8)= (Round to three decimal places as needed.)

Which of the following statements best summarizes the Side-Splitter Theorem? If a line is perpendicular to one side of a triangle and intersects the two other sides, the line divides the two sides of the triangle proportionally. If a line is parallel to one side of a triangle and intersects the two other sides, the line will always form a right angle. If a line is parallel to one side of a triangle and intersects the two other sides, the line divides the two sides of the triangle proportionally. If a line is congruent to one side of a triangle and intersects the two other sides, the line divides the two sides of the triangle proportionally.

Two similar solids have surface areas of 112 in2 and 175 in2. If the smaller solid has a side length of 20 inches, how long is the corresponding side in the larger solid (in inches)?

Sheena claims that all quadrilaterals are rectangles. Which of the statements below disproves Sheena's claim? Quadrilaterals have four sides. Quadrilaterals are polygons. A square is a quadrilateral. A trapezoid is a quadrilateral.

In the example of rats playing musical chairs, how would the probability of a certain rat being in a certain chair change in the case of five rats and four chairs, compared to five rats and five chairs? A fifth chair or no chair makes no difference for calculating the probability. The probabilities are only different if there is only one chair. The probability would become greater; there are fewer chairs. The probability would become less; there are fewer chairs.

Mr. Cook gave a history quiz last week. The scores from his class are shown below. 78, 82, 91, 75, 76, 86, 90, 88, 70, 72 A student was absent on the day of the quiz and scored a 50 on the make-up quiz. What is the approximate difference in the class' mean score before and after the make-up quiz? A 3 points B. 4 points c. 5 points D. 6 noints

Among a group of twenty students, eight have been to Mexico and six have been to Canada. Three students have been to both countries. What is the probability that a student from this group went to Mexico or Canada? 11/20 17/20 14/20 8/20

In a survey of women in a certain country (ages 20-29), the mean height was 65.4 inches with a standard deviation of 2.77 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 95th percentile? (b) What height represents the first quartile? (a) The height that represents the 95th percentile is inches. (Round to two decimal places as needed.) (b) The height that represents the first quartile is inches. (Round to two decimal places as needed.)

Write the quadratic function in the form g(x)= a (x −h)² + k. Then, give the vertex of its graph. g(x)=x² + 4x +3

When the Dragons have lost their most recent game, 200 fans buy tickets. For each consecutive win the Dragons have, the number of tickets fans buy increases by a factor of 1.1.Write a function that gives the number of tickets fans buy to Dragons games after the Dragons have had consecutive wins.

Max sleeps in 4 out of 5 days in a week. If he wakes up late, the probability that he's late for school is 9/10. If he doesn't wake up late, the probability he's late for school Is 3/10. What percent of days does he get to school on time? 11/50 13/50 22/50 7/10

Two transformations of quadrilateral PQRS are described below. • First transformation: (x,y) → (x+1, y-2) • Second transformation: (x+1, y-2) → (x+1, 2-y) Which transformations were used on quadrilateral PQRS? O a reflection over y-axis, then a translation O a translation, then a reflection over x-axis O a translation, then a reflection over y-axis O a reflection over x-axis, then a translation

Find all real solutions of the equation (9x + 2)² = 36. Write your answers as a list of integers or reduced fractions in the form A/B. For example, if your answers are 2/3 and 5, you would enter 2/3,5

Graph the following system. Use the line tool to graph both lines then use the point tool to plot the point of intersection. Write the point of intersection as an (x, y) ordered pair. If there is no solution or infinite solutions, leave the answerbox blank. y = 2x + 2 y= - 3x + 7

A population of fish grows exponentially by 8% each year. If the starting population is 100, what will be the size of the population in 5 years? How long will it take the population to reach 1000 fish?

Consider these statements. • All squares are equiangular. • Some rhombuses are squares. Which conclusion can be made using both statements? Some rhombuses are rectangles. A rhombus is always equiangular. All rhombuses are squares. Some rhombuses are equiangular.

A spinner has eight equal-sized sections labeled A, B, C, D, E, F, G, and H. What is the number of possible outcomes if you spin the spinner three times and the first spin is a vowel? 8 24 128 512

A box has four cards numbered 1, 2, 3, and 4 Rafael will toss a coin once and record the toss as heads (H) or tails (T). Then he will randomly pick a card from the box and record the number chosen. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the number chosen is 3.

What was President Eisenhower's position on the Vietnam Conflict? He worked to keep the US neutral. He believed the only way to get out of the conflict was to win; so he ordered increased military action He believed the US had to maintain peaceful relations in the Indochina Region. He believed we had to get involved because if one nation fell to communism, we would lose the whole reg

A chemist has three different acid solutions. The first acid solution contains 25 % acid, the second contains 40% and the third contains 60 %. They want to use all three solutions to obtain a mixture of 96 liters containing 50 % acid, using 3 times as much of the 60 % solution as the 40 % solution. How many liters of each solution should be used?

In an online poll, 197 people voted for Coach as the best job at the Super Bowl. The job of Announcer received 205 more votes than the Coach. Write and solve an equation to find how many votes the job of Announcer received.

Find all real solutions of equation 4x² + 5x - 4 = 0. Does the equation have real solutions? Input Yes or No: If your answer is Yes, input the solutions:

Given the function g(x) = 6x³ +54x² + 90x, find the first derivative, g'(x). g'(x) = Notice that g'(x) 0 when a = 5, that is, g'(-5) = 0. Now, we want to know whether there is a local minimum or local maximum at x = -5, so we will use the second derivative test. Find the second derivative, g''(x). g''(x) = Evaluate g''(-5). g''(-5) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = -5? At x = -5 the graph of g(x) is Based on the concavity of g(x) at x =-5, does this mean that there is a local minimum or local maximum at x = -5? At x = - 5 there is a local

There are 25 students in your class. Your teacher wants to choose a group of 5. In how many ways can she form a group of 5 students? 5 25 53,130 6,375,600

Miss Crawford wants to buy a new car. She is considering elther a hybrid or an electric car. She can choose a standard or a luxury model. There are red, silver, black, and white colors available to choose from. How many possible cholces does Miss Crawford have If she chooses one Item from each group? 4 8 16 24

Samantha has some dimes and quarters. She has 7 more dimes than quarters and the collection of coins is worth $10.15. How many dimes and quarters does Samantha have? Write an equation(s) to represent the situation and then solve. Be sure to define your variable(s) and clearly answer the question.

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