Basic Math Questions and Answers

Janet's car will go 279 miles on 15.5 gallons of gasoline in highway driving. a) How many gallons will it take to drive 1965 miles from her house to a friend's house? b) How far can the car be driven on 135 gallons of gasoline?

Chemicals in butter-flavoring: Workers in a microwave popcorn production plant in Missouri breathe chemicals that are part of the butter-flavoring. Are these workers at greater risk of developing lung problems? To investigate this question, 135 workers at the plant receive a survey, but only 117 respond. Researchers want to compare workers in the popcorn production area with workers who have jobs in other parts of the plant. People in these other jobs are not directly exposed to the butter flavorings. Of the 97 workers in the production area, 30 reported experiences of "shortness of breath. Of the 20 workers in other jobs, only 1 reported "shortness of breath." What can we conclude from this study? Exposure to the chemicals in butter-flavoring is associated with a greater incidence of lung problems, such as shortness of breath. The chemicals in the butter-flavorings are causing shortness of breath because a much larger percentage of workers in the production area have shortness of breath.

The angle of elevation of the sun is 26° from the ground. A business building downtown is 43 m tall. How long is the shadow cast by the building? Round to one decimal place if necessary and do not include units in your answer.

A retired potter can produce china pitchers at a cost of $7 each. She estimates her price function to be p = 17-0.5x, where p is the price at which exactly x pitchers will be sold per week. Find the number of pitchers that she should produce and the price that she should charge in order to maximize profit. Also find the maximum profit. $

Traffic Safety: Here is a passage from a study published by the National Highway Traffic Safety Administration in 2007. "The National Occupant Protection Use Survey (NOPUS) is the only probability-based survey of driver cell phone use in the United States. The survey observes usage as it actually occurs at a random selection of roadway sites, and so provides the best tracking of the extent to which people in this country are using cell phones while driving." NOPUS observed 43,000 drivers in this study. Which question is this observational study designed to answer? Which type of cell phone use is safer to use while driving: hand-held or head set? What proportion of U.S. drivers talk on a cell phone while driving? Does use of a cell phone while driving increase the risk of an accident?

Using Descartes' Rule of Signs, which are possible combinations of zeros for g(x) = 7x4 - 5x³ - 1x² - 2x - 3? Select all that apply: 1 positive, 3 negative, 0 complex 2 positive, 1 negative, 1 complex 1 positive, 1 negative, 2 complex 1 positive, 2 negative, 1 complex 3 positive, 1 negative, 0 complex

Find the derivative of the function. (Simplify your answer completely. Factor, if possible.) g(t) = e^-t / 2t^2 g' (t) =

You are creating an animation in which the characters in one frame of the animation will be standing on the circle. Characters A and B will be on opposite side of the stage from each other and characters C and D will on opposite sides of the stage. There is a chair inside the circle that is 4 feet from Character A, 6 feet from character B, and 3 feet from character C. How far is character D from the chair? 13 feet 1 foot 8 feet

a varies directly as b and inversely as the square of c. If a = 186 when b = 4 and c = 9, find a if b = 5 and c = 6. Round your answer to two decimal places if necessary.

if $5,000 is borrowed with an interest of 12.3% compounded semi-annually, what is the total amount of money needed to pay it back in 3 years? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round your answer.

Simplify the expression. 8x-48/x² - 6x

Researchers studied 208 infants whose brains were temporarily deprived of oxygen due to complications at birth. When researchers detected oxygen deprivation, they randomly assigned babies to either usual care or to a whole-body cooling group. The goal was to see whether reducing body temperature for three days after birth increased the rate of survival without brain damage. What is the response variable? Usual care or whole-body cooling Survival without brain damage ilnfants whose brains are temporarily deprived of oxygen

Water Pollution In a January 2017 Washington Post-ABC News poll, online respondents were asked "There is a proposal to offer nearly 140 billion dollars in tax cuts for private companies if they pay to build new roads, bridges and transportation projects. The companies then could charge tolls for people to use these roads, bridges and transportation. Do you support or oppose this proposal? Do you feel that way strongly or somewhat?" Which question is this observational study designed to answer? What proportion of voters are strongly opposed and what proportion of voters are somewhat opposed to the proposal? What proportion of voters are against giving $140 billion in tax cuts to private companies? What proportion of voters are against either giving $140 billion in tax cuts to private companies or against charging tolls for roads, bridges, and transportation?

In June 2008, the Journal of the American Academy of Dermatology reported on the use of an intermittent therapy for flare prevention and long-term disease control of eczema (red, inflamed, itchy skin). Eczema is a chronic skin disease that affects about 10% to 20% of infants and about 3% of adults and children in the United States. Researchers wanted to determine whether intermittent dosing with a specific topical inhibitor is effective in preventing eczema flare-ups in patients with stabilized eczema. Initially, 383 adults and children with moderate to severe eczema were treated with daily doses of the topical inhibitor. After 16 weeks, 197 were disease free and admitted into the maintenance phase of the study. These patients were randomized to a 3-times-weekly treatment with either the topical inhibitor or a placebo for 40 weeks. All tubes of ointments (topical inhibitor and placebo) were packaged in identical boxes and labeled "for investigational use only." Then the packages were sealed with tamper-proof seals and shipped. Neither the researchers not the patients knew who received the topical inhibitor or who received the placebo. During the maintenance phase researchers tracked the number of flare-free days for each patient. What is the purpose of double-blinding in this study? To control the patient's expectations from affecting the outcomes To control both unintentional research bias and patients' expectations To control the researchers' expectations from causing them to unconsciously influence the patient

What value of a makes the equation 3e^6x = 24 true? Round your answer to the nearest tenth. Do not include "x=" in your answer. If necessary, include a leading 0 with any decimals less than 1. For example. 0.5 instead of .5. Provide your answer below:

The revenue in dollars generated from a sale of x picnic tables is given by R(x) = 33x- x2/100 (a) Find the marginal revenue. (b) Estimate the revenue from the sale of the 1001st table by finding R'(1000). (c) Determine the actual revenue from the sale of the 1001st table. (d) Compare your answers for parts (b) and (c). What do you find?

A graphing calculator is recommended. Solve the following exercise on a graphing calculator by graphing an appropriate exponential function (using x for ease of entry) together with a constant function and using INTERSECT to find where they meet. You will have to choose an appropriate window. (Round your answers to one decimal place.) A bank account grows at 7% compounded quarterly. (a) How many years will it take to double? (b) How many years will it take to increase by 50%?

In his Fireside Chat after the attack on Pearl Harbor, how does FDR increase Americans' confidence in the ability of the United States to win the war against the Axis powers? A. He encourages radio stations to focus on patriotism and optimistic news broadcasts. B. He emphasizes how Americans are all on the same team. C. He lists the weaknesses of the enemy's military. D. He focuses on the strengths of each military branch.

The safe load, L., of a wooden beam supported at both ends varies jointly as the width, w, and the square of the depth, d, and inversely as the length, I. A wood 3 in. wide, 8 in, deep, and 4 ft long holds up 14096 lb. What load would a beam 10 in. wide, 4 in. deep, and 19 ft. long, of the same material, support? Round answer to the nearest integer if necessary.

Simplify the following rational expression using long division: x²+4/x-3

Evaluate the expression for the given values. (a) The expression 3c+9v evaluated for c=2 and v= 1/9 is

Miles would like to open up a CD that has an interest rate of 2.4% compounded monthly. His initial deposit is $5,000. How long does he have to keep the money in this account in order to have a balance of $5,500? Round to the nearest tenth of a year.

Solve the rational equation. Make sure to exclude any extraneous solutions. x/x-3 - 18/x^2-9 = -2x/x+3 x = -2, 3 x = -2 x = 3 No solution

Researchers compare two treatments for colon cancer. They examine medical records from 25 large hospitals and compare the survival times for patients who receive the treatments. Is this an observational study or an experiment? observational study experiment

A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than the width. What are the dimensions of this box? Give your answer in the form I, w, h as comma separated values. For example if the box has a length of 1, a width of 2, and a height of 3, you would submit the answer 1, 2, 3.

A bank offers 8% compounded continuously. How soon will a deposit do the following? (Round your answers to one decimal place.) (a) triple (b) increase by 23%

Identify the domain of the following rational expression: x+4 x+4 / x2+x-12 All real numbers except 4 and - 3. All real numbers except -3. All real numbers except 3. All real numbers except -4 and 3.

A trailer in the shape of a rectangular prism has a volume of 3,816 cubic feet. The length of the trailer is 11 feet less than 8 times the width w, and the height is 1 foot more than the width. Find the equation, in terms of w, that could be used to find the dimensions of the trailer in feet. Your answer should be in the form of a polynomial equals a constant.

If an object is projected from a height of 336 ft with an initial velocity of 64 ft per sec, its height after t seconds is given by the following equation h=-16t² +64t+336 Use this information to answer parts (a) and (b) below. (a) After how many seconds is the height 400 feet? (Hint: Let h=400 and solve.)

Use synthetic division to find the result when 2x^4 - 13x³ - 13x² - 13x - 42 is divided by x + 2. Write your answer in the form q(x) + r(x)/d(x)' where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

Your field experience instructor wants to line up 9 cars for transportation to a grade school. Between you and your classmates, there are 26 cars available. How many different groups of 9 cars are possible?

In 2001 the National Opinion Research Center reported on the National Gun Policy Survey. The results of the survey include information about U.S. adults' opinions of government regulation of firearms. To obtain a random sample of adults in the United States, 1,200 participating households were identified through random digit dialing and then the adult with the most recent birthday (rather than the person who answered the phone) was interviewed. Of those who were interviewed, 78% favored requiring background checks for gun sales between individuals. Which of the following best describes the population of interest in the National Gun Policy Survey? All adults in the United States 78% who favored requiring background checks for gun sales between individuals Adults in each household with the most recent birthday Adults with phone numbers 1,200 U.S. adults

In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded continuously, what will the membership be in 2020? Round the answer to the nearest whole number, and do not include the units in your answer. Provide your answer below:

Given that the polynomial f(x) has 8 turning points, which of the following most accurately describes the degree of f(x) Select the correct answer below. The degree of f(z) is at most 8. The degree of f(z) is at least 9. The degree of f(z) is at least 8. The degree of f(x) is at least 7. The degree of f(z) is at most 7. The degree of f(x) is at most 9.

Which question is best answered by an experiment? Does use of computer-aided instruction in college math classes improve test scores? Is there an association between the number of hours college students spend each week on Facebook and their college GPA? Do the majority of community college students plan to vote in the next presidential election?

A health club charges a one-time sign-up fee and a monthly membership fee. The equation y=23x+35, where y = 0 total cost and a represents the number of months. represents what the health club charges. Find the rate of change. $58 $58 per month $23 $23 per month $12 per month Without the number of months, it cannot be detern $35 per month

The area of a rectangular living room is 450 square feet. The length of the room is 15 feet less than three times the width. Find the equation, in terms of w, that could be used to find the dimensions of the living room in feet. Your answer should be in the form of a polynomial equals a constant.

After wildfires destroyed a portion of a national park, forest service biologists calculated the germination rate of new seedlings. Using a rope as a radius, they marked off a circular area of forest equivalent to one-sixth of an acre. They then counted the number of new seedlings and multiplied by 6 to obtain an estimate of the germination rate in seedlings per acre. What length of rope is needed to create the circle?

An open box is to be constructed by cutting out square corners of x-inch sides from a piece of cardboard 10 inches by 6 inches and then folding up the sides. Express the volume of the box as a function of x. V(x) =

Students want to investigate this question: "Is there a relationship between the number of hours high school students spend each week on Facebook and their high school GPA (grade point average)?" Which study design is most appropriate? Send out a survey to your friends on Facebook. Ask them to take the survey and to forward it to their Facebook friends. In the survey, ask two questions: How many hours do you spend on Facebook each week? What was your GPA in high school? Collect at least 100 responses. Divide high school students into two groups. Flip a coin to decide who is in each group. One group goes onto Facebook for 5 minutes, then takes a short quiz. The other group just takes the short quiz. Go to a local high school and survey students during study hall. In the survey, ask students to estimate the hours they spend on Facebook each week. Obtain the GPA data for these students from the high school counselor.

Consider the graph of the function f(x) =x² +7x/x3-5x2-14x Where is the removable discontinuity? Give only the x-value.

A basketball player has made 12 of his last 20 free throws, which is a free throw percentage of 60%. How many more consecutive free throws would he need to make to raise his free throw percentage to 75%?

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 8 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 16 feet. The length of the ladder is

At the end of a snowstorm, Grace had 15 inches of snow on her lawn. The temperature then increased and the snow began to melt at a constant rate of 2.5 inches per hour. Assuming no more snow was falling, how much snow would Grace have on her lawn 2 hours after the snow began to melt? How much snow would Grace have on her lawn after t hours of snow melting? Snow on lawn after 2 hours: Show on lawn after t hours:

f(x) = -2x² + 4x + 48 Use the Second Derivative Test to locate any local maximum or minimum points in the graph of the given function.

A 20% apple juice drink is mixed with a 100% apple juice drink. The function f(x) = (2)(1.0)+x(0.2) / 2+x concentration of apple juice in the drink after x gallons of the 20% drink are added to 2 gallons of pure juice. What will be the concentration of apple juice in the drink if 6 gallons of 20% drink are added? Give the answer as a percent but do not include the percent sign (%).

Jan spent 3 3/4 hours doing homework last week. She spent 5 1/4 hours doing homework this week. How many more hours did Jan spend on homework this week than last week? A. 1/4 hour C. 1 1/4 hours B. 1/2 hour D. 1 1/2 hours

The amount of simple interest earned, n, varies jointly with the rate of interest, r, and the number of years, t. The simple interest earned is $225 when the rate of interest is 4.5% for 4 years. Using the variables r. and t, find the equation that represents this relationship.

Write an equation and solve the problem. Julia used square tiles to make a design. She laid the tiles in a square, 9 tiles wide by 9 tiles long. Each tile has an area of 1 square inch. What is the area of Julia's tile design?

Evan walks his dog 4 times around the perimeter of a park, for a total distance of 2.8 kilometers. How many kilometers does he walk each time around? Circle the letter of the correct answer. A 0.07 B 0.12 C 0.7 D 0.12