Math Questions

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

Drag a value, coordinates, equation, or word to the boxes to correctly complete the statements. Gayle identifies that the vertex of the parabola is! units away from the vertex. The directrix is (3,-1) The directrix of the equation is! (3, 2) Gayle plots the vertex and focus, and graphs the directrix as a dashed line. She then draws the parabola so that the focus sits inside the curve and the directrix does not intersect it.

In a class of 26 students, 17 have a brother and 12 have a sister. There are 5 students who do not have any siblings. What is the probability that a student has a brother given that they have a sister?

The faces of a fair cube are numbered 1 through 6; the probability of rolling any number from 1 through 6 is equally likely. If the cube is rolled twice, what is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll?.

Let a, b, c, d are an increasing A.P. with integer terms and d = a² + b² + c2², then Common difference of A. P. is 2 The value of a + 2b + 3c+4d is 10 The value of 4a + 3b+2c + d is zero Common difference of A.P. is 1

A new computer graphics company employs 10 programmers. The company decides to expand into digital animation and needs to transfer 3 of the programmers into the new department. How many different combinations of 3 programmers can be chosen to transfer to the new department

A particle is moving along a straight line such that the distance traveled (in feet) after t seconds is given by the function s(t) = 8t² + 40t. At t = 6 seconds, what is the velocity of the particle?

A species of snakes studied in a certain area in South America has some exceptionally large individuals, for some reason yet unknown to scientists. The weights of the studied population are strongly right-skewed with mean 36 kg and standard deviation 7 kg. A random sample of 75 snakes is taken. What is the probability that the mean weight of the sample is greater than 37 kg? 0 0.1075 0.4432 cannot say

The water in a pool is evaporating at a rate of 3% per day. If the pool has 21,200 gallons in it today, how many gallons will it have in 10 days? Round your answer to the nearest whole number, if necessary. Answer How to enter your answer (opens in new window) 2 Points

When Bill makes a sandwich, he may choose from among 3 kinds of rolls, 4 varieties of meat, and 2 types of sliced cheese. If he chooses one roll, one meat, and one type of cheese, how many different kinds of sandwiches can he make? (A) 9 (B) 14 (C) 24 3x-420 (D) 288

A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is three inches more than three times the shorter leg. The second template will be in the shape of a rectangle, where one side length is one inch less than three times the length of the triangle's shorter leg, and the other side length is one inch more than twice the width. The carpenter needs the lengths of both diagonals to be the same. Write a system of equations to represent this situation, where y is the length of the diagonals, and x is the shorter leg of the triangle. Which statement describes the number and viability of the system's solutions? A. The system has two solutions, and both are viable because they result in figures with only positive side lengths. B. The system has two solutions, but only one is viable because the other results in a figure with negative side lengths. C. The system has only one solution, and it is viable because it results in a figure with only positive side lengths. D. The system has only one solution, but it is not viable because it it results in a figure with a negative side length.

Karla wants to save up for a prom dress. She figures she can save $9 each week from the money she earns babysitting. If she plans to spend less than $150 for the dress, how many weeks will it take her to save enough money to buy any dress in her price range?

As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 150 milligrams of Medication A with 45 milligrams of Medication B. However this week, the doctor said to only use 6 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?

be worth more or less (including zero) depending on your answer. Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $50, and then they charge her $8 per hour. She has $150 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.) 12 hours 18 hours 13 hours 12.5 hours

You and your classmates create 25 self-portraits to sell at the PTA auction to raise money for your school. In order to pay for the materials you bought to make the self-portraits, you need to sell each of the self- portraits for $1.00. When transporting the self-portraits to the auction, one of your parents accidentally drops three of the self-portraits in the street and they are run over by a school bus. What is the new minimum price you need to set for the remaining self-portraits in order to pay for the materials?

A group of Mathematics faculty at the local college consists of 9 women and 9 men. Five people are to be selected to go to a conference. How many different ways can a group of five people be selected from this group of 18? In how many ways can five women be chosen from the group of 9 women? What is the probability that all women will be chosen to attend the conference? Enter a reduced fraction or decimal.

Kala paid $14.75 for a 2.12-pound bag of shrimp at one store. The following week, she paid $24.99 for a 3.77-pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent. Unit price for the 2.12-pound bag: per pound Unit price for the 3.77-pound bag: per pound The better buy: The 2.12-pound bag The 3.77-pound bag Neither (They have the same unit price)

Find all zeros of f(x) = x³ + 2x² - 6x - 4. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

- Manuel bought 9 pounds of apples. He has eaten 3/4 of a pound so far and has $15 worth of apples left. Write and solve an equation to find the cost of the apples per pound to the nearest dollar. How much did the apples cost per pound?

Arianna invests $5500 in a new savings account which earns 5.6 % annual interest, compounded daily. What will be the value of her investment after 7 years? Round to the nearest cent.

Some species of eagles have been fighting extinction due to environmental hazards such as DDT, PCBS, and dioxin. The problem is with the food chain. Fish or rodents consume contaminated food and/or water. Then the eagles ingest the poison, which in turn affects the durability of the eagles' eggs. It takes only 44 parts per million of certain chemicals to ruin an eagle egg; write this number as a fraction in lowest terms.