Math Questions

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

The population of Dublin, Ohio, in 2013 was 43,607 people. The area of the City of Dublin in 2013 was 24.79 square miles. Find the population density of Dublin in 2013 rounded to the nearest person.

Residents of Valentine, a small city in Nebraska, meet for a city council meeting once a week. Meetings are supposed to last no more than 3 hours. However, many residents are complaining that the average meeting is significantly longer than 3 hours (180 minutes). In order to test this, the lengths of the last 15 meetings were recorded in minutes: 147.0, 155.4, 159.6, 162.6, 163.8, 165.0, 167.4, 169.2, 172.2, 172.8, 172.8, 175.8, 175.8, 196.8, 201.6. Using this data, test the null hypothesis at the alpha=0.1 level that the mean length of city council meetings is equal to 3 hours versus the alternative that the average meeting length is greater than 3 hours. Assume that the distribution of meeting lengths is normal. What is the p-value and conclusion of this test? p-value = 0.046; Fail to reject the null hypothesis p-value=0.046; Reject the null hypothesis p-value = 0.990; Fail to reject the null hypothesis p-value = 0.990; Reject the null hypothesis

In how many possible ways can you arrange frults in a row out of a basket of two oranges, one apple, and four lemons? 105 630 5,040 823,543

The number of astronomy papers published increases by 5% every year. If 27,000 astronomy papers were published in a particular year, how many will be published 2 years later?

On a spelling test. Michelle spelled 17 words correctly. There were 20 words on the test. What percent of the words did she spell correctly.

Two similar solids have volumes of 576 in³ and 1125 in³. If the smaller solid has a side length of 12 inches, how long is the corresponding side in the larger solid (in inches)?

This function: f(x)=- 40x4e-x has critical numbers: On the graph of y = f(x) the smallest critical number corresponds to: a local maximum a local minimum neither a local maximum or a local minimum On the graph of y = f(x) the largest critical number corresponds to: a local maximum a local minimum neither a local maximum or a local minimum

A bear is an animal and a zoo contains many animals, including bears. Three classes Animal, Bear, and zoo are declared to represent animal, bear, and zoo objects. Which of the following is the most appropriate set of declarations?

Circle P is dilated to form circle P'. Which of the following statements is always TRUE? A. The length of any chord in circle P is greater than the length of any chord in circle P'. B. The radius of circle P is equal to the radius of circle P'. C. The diameter of circle P is greater than the diameter of circle P'. D. The ratio of the diameter to the circumference is the same for both circles.

The probability of an employee at a large company being out sick on any given day is 0.08, and the probability of an employee at a large company being out sick and there being a fire drill on any given day is 0.0004. a. Find the probability of there being a fire drill given that an employee is out sick. b. If the probability of there being a fire drill is .005, what can you conclude?

At the gym, Diana always spends more minutes running than lifting weights. Part A Which equations describe the relationship between the number of minutes Diana runs, r, and the number of minutes she lifts weights, w. Select all that apply. 12+w=T r=w-12 w= 12 + r r-12= w r+w=12 Part B If Diana spends 25 minutes running at the gym, how many minutes does she spend lifting weights?

Elizabeth rolls a number cube four times such that each roll represents a digit of a four-digit number. Which of the following expressions represents the number of four-digit numbers that are even that Elizabeth could obtain? 6x3 6 x 4 6x6x6x3 6x6x6x6

A basketball player has a free throw percentage of 0.75. In the first half of a game, he made 12 attempts. How can a spinner be created to simulate data collection for this experiment? Create a spinner with two halves where one side represents made shots and one side represents missed shots. Create a spinner with four quarters where two sections represent made shots and two sections represent missed shots. Create a spinner with four quarters where three sections represent made shots and one section represents missed shots. Create a spinner with twelve sections where each section represents a shot.

A four-digit number is divisible by 10 and is smaller than 5,000. Which of the following expressions represents how many possible numbers there are? 4 x 10 x 10 x 1 4 x 10 x 10 x 10 10 × 10 × 10 × 1 10 x 10 x 10 × 10

Which of the following can be classified as a binomial probability experiment? A coin is tossed 10 times. The random variable X is the number of heads that appear. A bag contains 20 marbles. Eight marbles are red, nine marbles are blue, and three marbles are yellow. Three marbles are drawn out of the bag without replacement. The random variable X is the number of blue marbles. Five customers walk into a store. The random variable a represents the number of customers who buy at least one product. A random sample of 30 cars selected from a used car lot and their mileages are recorded.

Caleb was given a gift card for a coffee shop. Each morning, Caleb uses the card to buy one cup of coffee. The original amount of money on the gift card was $45 and after buying 8 cups of coffee, the card had a $25 remaining balance. Write an equation for A, in terms of x, representing the amount money remaining on the card after buying x cups of coffee.

Consider the parabola given by the equation: f(x)=x²-12x + 13 Find the following for this parabola: A) The value of f(-5): B) The vertex = C) The y intercept is the point (0, D) Find the two values of a that make f(x) = 0. Round your answers to two decimal places. Write the values as a list, separated by commas:

Determine whether the planes are parallel, perpendicular, or neither. 3x + 12y - 9z = 1, -15x + 30y + 35z = 0 parallel perpendicular neither If neither, find the angle between them. (If the planes are parallel or perpendicular, enter PARALLEL or PERPENDICULAR, respectively.)

What can the unit fraction 1 meter/3 feet be used for? To convert 25 inches to meters. To convert 15 meters to inches. To convert 5 meters to centimeters. This cannot be used to convert anything.

Owen'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 = 67 + 6x, 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. The change in expected quiz score for every additional one hour students spend on their homework. The number of hours a student should spend on their homework to expect a score of 99 on the quiz.

16. If one student can complete the decoration for the prom in five days working alone, another student can do it in three days, and a third can do it in four days, how long will it take them working together?

The path of a marble rolling off of a desk can be modeled by the parametric equations: x(t)=2.5t y(t)=-16t^2+3 In these equations, the horizontal and vertical positions of the marble x(t) and y(t) are in feet and t is measured in seconds. Use Desmos and scratch paper to complete the following prompts. A. The marble will hit the ground after how many seconds? =0.433 seconds. B. Using your answer to (A), how far (horizontally) from the edge of the table will the marble first hit the ground? C. The parametric equations above can be expressed as the following single rectangular equation:

In how many possible ways can you arrange the digits in the order confirmation number 3018281268? 151,200 301,400 3,628,800 1,000,000

Write the negation of the conditional statement. If she can't take out the trash, then I will. If she can take out the trash, then I can't. She can't take out the trash, and I won't. If she can't take out the trash, then I won't. She can take out the trash and I will.