Math Questions

Which of the following sets of numbers could represent the three sides of a triangle? {10, 21, 32} {14, 24, 40} {13, 17, 32} {13, 16, 27}

A company manufactures electronic components that each must weigh from 29.5 grams to 30.5 grams, inclusive. Which of the following inequalities describes all acceptable weights x, in grams, for each component? (A) |30-x| ≤0.5 (B) |30-x| >0.5 (C) 30-x≤ 0.5 (D)30-x>0.5

Given events A and B are mutually exclusive events, that is, A and B are mutually exclusive events with P(A)=0.2, P(B)=0.3, find P(A∩B).

Michael wishes to give his son a savings bond that will mature in 8 years. He would like the value of the savings bond to be $5,000 at maturity. If he can invest in a bond that has an annual interest rate of 4% compounded monthly, which of the following is the best approximation of the amount he should invest? (A) $3,200 (B) $3,350 (C) $3,500 (D) $3,650

Define a variable and write an inequality. Then sol Marlea received an inheritance of $10,000. She plans to invest some in a stock that pays 7% interest annually. She will deposit the remainder in a savings account that pays 5% interest annually. What is the least amount that Marlea can invest in stock if she wants to earn at least $550 on her investments for the year?

Caitlin had $402 in her bank account. She withdrew $15 each week to pay for a swimming lesson. She now has $237. a.Write an equation that can be used to find the number of swimming lessons that she paid for. b. Find the number of swimming lessons she paid for. C.The cost of a swimming lesson rises to $19. How many lessons can she pay for with the remaining $237?

Assume that a sample is used to estimate a population mean μ. Use the given confidence level and sample data to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place than the sample standard deviation. 95% confidence; n = 51; x = 240; s = 242 143.0 61.3 88.5 68.1

Fabian is 1.65 meters tall. At 12 noon, he measures the length of a tree's shadow to be 18.35 meters. He stands 13.6 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Let U ={a,b,c,d,e,f,8,9,10,11,12,13), X = {a,b,c,9,10,11), and Y = {b,d,f,8,10,12). List the members of the set X'nY', using set braces. X'∩y' = (Use a comma to separate answers as needed.)

Change the logarithmic equation to an equivalent equation involving an exponent. In x = 9 The equivalent exponential equation is

For a project in her Geometry class, Chloe uses a mirror on the ground to measure the height of her school's football goalpost. She walks a distance of 13.65 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then walks 4.7 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.65 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

A newsletter publisher believes that 26% of their readers own a personal computer. Is there sufficient evidence at the 0.01 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario. Answer: Ho: Ha:

A half-century ago, the mean height of women in a particular country in their 20s was 62.4 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.28 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 28 of today's women in their 20s have mean heights of at least 63.33 inches? About of all samples have mean heights of at least 63.33 inches. (Round to one decimal place as needed.)

A boxer needs to lose 3 1/2 kg in a month to be able to compete as a flyweight. In three weeks, he lowers his weight from 55.5 kg to 53.8 kg. How many kilograms must the boxer lose in the final week to be able to compete as a flyweight?

Solve the linear programming problem using the simplex method. Maximize P=2x₁ + 3x₂ + 4x3 X₁ + X3 ≤24 subject to x2 + x3 ≤18 X1, X2, X3 20 Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum value of P is B. There is no optimal solution.

Suppose Robbie is the educational director for a group of teen test prep programs in Nevada. He knows that the mean score on Nevada's mathematics exam is 114 points with a standard deviation of 18 points. Robbie thinks the teens in his program score differently than the population mean on Nevada's mathematics exam. To test his claim, he randomly selects 250 of his students and finds the mean test score of the sample to be 117 points. a. What are Robbie's null (Ho) and alternative (H₁) hypotheses? A. Ho: u 114 pts and H₁: u 114 pts B. Ho: u 114 pts and H₁: u> 114 pts C. Ho: x= 114 pts and H₁: x # 114 pts D. Ho: u 117 pts and H₁: u 117 pts E. Ho: x= 117 pts and H₁:x> 117 pts b. What is the z-statistic? Give your answer precise to two decimal places. c. What is the positive critical value z for a significance level of a= 0.05? Give vour answer precise to at least two decimal places.

The formula D=20 e -0.6h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug was administered. When the number of milligrams reaches 4, the drug is to be administered again. What is the time between injections? The time between injections is hour(s). (Round to two decimal places as needed.)

Let U = { 6, 7, 8, 9, 10, 11, 12), A = {8, 10, 11, 12). Use the roster method to write the set A'. (Use a comma to separate answers as needed.)

Write inequalities to represent the situations below. To get the 10% discount, a shopper must spend more than $300. Used to represent the spending (in dollars) of a shopper who gets the discount. The temperature inside the lab refrigerator is no more than 35 °F. Use t to represent the temperature (in °F) of the refrigerator.

Type the missing number to complete the proportion. 18 plants in 1 row 72 plants in rows

A shipment of small lab mice arrives at an animal care facility. A sample of five mice is selected and weighed. The average weight of the sample is 10.2 g, and the standard deviation of weight among mice is 2 g. Find a 95% confidence interval for the mean weight of all the mice in the shipment. 10.2 ±2.48 10.2 ± 11 10.2 ± 2.30 10.2 1.75

A Potating, panoramic camera attached to a helium balloon can capture images of all the airspace below the balloon. The altitude, in feet, of the balloon m minutes after it is released, is equal to 4 more than the square root of the sum of 100m³ and m². A similar camera is attached to a drone and aimed upward to capture images of all the airspace above the drone. The altitude, in feet, of the drone m minutes after it is launched, is equal to the cube root of the sum of m² and 1,600m. Which system of inequalities represents the altitudes, in feet, of airspace which are captured by both cameras after m minutes?

On the graph of f(x) = sin x and the interval [-2π, 0), for what value(s) of x does the graph cross the x-axis? Choose all answers that apply. Select all that apply:

When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Assume a single spin of the roulette wheel is made. Find the probability of winning with the given bet. An example of a dozen bet is betting that the marble will land in a slot numbered 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, or 23. and the number of outcomes in the event is The total number of outcomes is (Type integers or simplified fractions.) The probability of winning with the given dozen bet is (Simplify your answer.)

To pay for an $18,800 camper, Diane made a down payment of $3900 and took out a loan for the rest. On the loan, she paid monthly payments of $267.74 for 5 years. (a) What was the total amount Diane ended up paying for the camper (including the down payment and monthly payments)? How much interest did Diane pay on the loan? (b)

Given events A and B are events with P(-(A u B))=2/3, we can determine the probability of which other event in the list below has the same probability? ANB AUB -AN-B -Au-B -(ANB) -(-AN-B) -(-Au-B)

Consider the following polynomial. f(x) = 4x³ - 21x² + 21x - 4 Step 2 of 2: Use polynomial division and the quadratic formula, if necessary, to identify the actual zeros.

The number of breakfast drive thru customers per day is normally distributed with a mean of 44 and a standard deviation of 6. A. What precent of days have between 38 and 50 breakfast drive thru customers? B. What precent of days have MORE than 50 breakfast drive thru customers? (include percent signs in your answers)

Given that 2 - 2i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x) = x4 - 10x³ + 25x² - 20x - 56

Suppose that events F and S are conditional independent events given D and ~D respectively with p(F|D)=p(S|D)=0.9, p(~F|~D)=p(~S~D)=0.9, and p(D)=0.2. Find p(D|F∩S).

Sandi weighs 175 lb, but she has started a new diet plan that promises she will lose 2 lb per month every month until she reaches her goal weight. Write a Iinear equation that describes how much Sandi weighs, , each month, and then use your equation to find out how many months it will take her to get to 125 lb. use X to denote the number of months since Sandi started her new diet. The linear equation that describes how much Sandi weighs each month is = According to the equation, it w take Sandi months to reach 125 lb

It is known that the function D(h) = 1.225√h models the distance a person can see to the horizon D(h), in miles, if the person is h feet above sea level. Suppose Gregory wanted to be able to see out 76 miles to the horizon. At what elevation would he need to be to see out that far? a) Write an equation that models this situation. Equation: b) Solve the equation to answer the question. Complete the sentence with a number in the first box and an appropriate unit in the second box. You may round your numerical response to two decimal places. Sentence: Gregory would need to be an elevation of

In a conference, 75% of the attendees have been to Germany, and 15% of the attendees have been to both England and Germany. What is the probability that a randomly selected attendee has been to England, if it is known that they have been to Germany? Assume Event E: the attendee has been to England; Event G: the attendee has been to Germany.

A guy wire runs from the top of a cell tower to a metal stake in the ground. Juan places a 9-foot tall pole to support the guy wire. After placing the pole, Juan measures the distance from the stake to the pole to be 7 ft. He then measures the distance from the pole to the tower to be 25 ft. Find the length of the guy wire, to the nearest foot.

Assume that the function f is a one-to-one function. (a) If ƒ(7) = 9, find ƒ−¹(9). Your answer is (b) If ƒ−¹( − 2) = – 8, find ƒ( − 8). Your answer is

Select the correct statement and rationale relating the interest rates of traditional banks to those of online banks. Traditional banks offer lower interest rates than online banks because they have higher building costs Traditional banks offer lower interest rates than online banks because they are less risky Traditional banks offer higher interest rates than online banks because they have been around longer Traditional banks offer higher interest rates than online banks because they are not as convenient

At noon, to begin a study, a petri dish had 1800 bacteria cells. Each hour since, the number of cells has increased by 12%. Let / be the number of hours since the start of the study. Let y be the number of bacteria cells. Write an exponential function showing the relationship between y and f.

For the given triangle, find the missing lengths. Give an exact answer and, where appropriate, an approximation to three decimal places. A. Using radicals, the exact length of the other leg is (Simplify your answers.) Find the length of the other leg. Select the correct choice below and fill in the answer box(es) to complete your choice. units. The approximate length of the other leg, up to three decimal places, is B. The exact length of the other leg is units. No approximation is necessary. (Type an integer or a decimal.) Find the length of the hypotenuse. Select the correct choice below and fill in the answer box(es) to complete your choice. units

A building contractor is to dig a foundation 42 feet long, 15 feet wide, and 3 feet deep. The contractor pays $5 per load for trucks to remove the dirt. Each truck holds 7 cubic yards. What is the cost to the contractor to have all the dirt hauled away?

An rock is thrown upward from a platform that is 156 feet above ground at 60 feet per second. Use the projectile formula h = - 16t² + vot + ho to determine when the rock hit the ground. [Recall that vo is the initial velocity of the object and ho is the inital height of the object.] Answer: The rock will hit the ground after Note: Round any numerical responses to two decimal places. If there are multiple answers, separate them with commas.

An 8½" wide by 11" long piece of paper is to be enlarged to poster size. If the width is enlarged to be 34", what is the new measurement of the length? a. 26.2" c. 42" b. 26.3" d. 44"

In 2011, there were 3223 sea otters in Monterey Bay, California. The bay is approximately 77 square miles. To the nearest whole number, what was the density of the sea otter population? A. 41.9 otters/mile2 B. 547.2 otters/mile² C. .02 otters/mile² D. 84.6 otters/mile²

Suppose S={-2, -1, 0, 1, 2} and T={0, 1, 2, 3, 4). Which set represents S∩T? {3,4} {0, 1, 2} {-2, -1} {-2, -1, 0, 1, 2, 3, 4}

In 2005, a city had a population of 310,000 people. Each year since, the population has grown by 4.3%. Let / be the number of years since 2005. Let y be the city's population. Write an exponential function showing the relationship between y and t.

A bag of M&M's has 6 red, 5 green, 7 blue, and 3 yellow M&M's. What is the probability of randomly picking: (give answer as a reduced fraction) 1) a yellow? 2) a blue or green? 3) an orange?

Suppose that an individual has a body fat percentage of 13.1% and weighs 189 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.

A scientist estimated the number of bacteria in a sample every hour and recorded the estimates in the table above. Then the scientist used the data to create the scatterplot above. Based on the information, which of the following functions best models the number of bacteria, f(t), at time t, in hours? (A) f(t)=100(2¹) (B) f(t)=100+2t (C) f(t)=t² +220t+100 (D) ƒ(t)=120 log (t+1)

A homeowner with gas heat in her home has been reviewing her monthly gas bills from the last several years. She has noticed that her highest gas bill is for January, when she owes x dollars. Then, the amount of she owes each month decreases to its smallest size, y dollars, for July. The amount of her gas bill slowly increases back to its maximum amount, x dollars, for the following January. This pattern has continued for all of the years of bills reviewed. Which of the following function types would best model the situation above? A. cube root B. trigonometric C. step D. exponential

Solve the equation. Write the answer in terms of the natural logarithm. e9x + 4 = 6 The solution set is. (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

The width of a rectangular garden is x feet. If 300 feet of fencing is needed to enclose the garden, which of the following represents the length of the garden, in feet? (A) 300-x (B) 300-2x (C) 150-x (D) 150-2x