Basic Math Questions and Answers

In an orchestra, 25 people can play stringed instruments, 21 can play brass, and 12 can play percussion. Further, 9 of the performers can play both strings and brass, whereas 4 can play both strings and percussion. If no one can play all three types of instruments, what are the maximum and minimum numbers of people in the orchestra? (Hint: Consider expressing the numbers in some of the regions of your diagram in terms of a single unknown, say x.)

Which of the following correctly expresses the exponential model f(x) = 7(4)x with the base e? Select the correct answer below: f(z)=4eln(7) f(x) = 7e4x f(x) = 4e7x f(x) = 7eln(4)x f(x) = 4e7ln(x) f(z) = 7e4h(z)

A pool measuring 8 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 864 square meters, what is the width of the path?

A team of Calculus teachers is analyzing student scores on a final exam compared to the midterm scores. One teacher proposes that they already have every teacher's class averages and they should just work with those averages. Explain why this is problematic. Choose the correct answer below. A. Individual student scores will vary greatly. The class averages will have much less variability and may disguise important trends. B. Individual student scores will not vary greatly. The class averages will have much more variability and may display false trends. C. Individual student scores will not vary greatly. The class averages will have much less variability and may disguise important trends. D. Individual student scores will vary greatly. The class averages will have much more variability and may display false trends.

Notice how the semicolons help the writer to separate different parts of a sentence that also includes commas. Directions: Determine whether or not the following sentences are grammatically correct. Sentence Over the summer we ate pizza with cheese, pepperoni, and olives; hamburgers with bacon, ketchup, and mustard; and barbecued ribs with potato salad, coleslaw, and fresh rolls. I have always tried to be consistent; I never stop changing. Many of the people who live here are seniors however; an underclassmen could get in by filing an application. Correct Incorrect

Each course at Mt. Regis College is worth either 3 or 4 credits. The members of the men's soccer team are taking a total of 48 courses that are worth a total of 155 credits. How many 3-credit courses and how many 4-credit courses are being taken?

The selling price of a car is $18,000. Each year, it loses 15% of its value. Find the exponential function that gives the value of the car t years after its purchase. Write your answer in the form f(t) = a(b)t Provide your answer below:

Acidity is measured on the pH scale. The acidity of a substance is given by pH = -log H, where H is the concentration of Hydrogen ions. If a substance has an H value of 0.00032, which shows a valid step in the process of calculating the pH of the substance? Select the correct answer below: pH = -log 0.0032 -log(3.2 10 4) = pH log(3.2 10 ) = pH log (3.2 10) = -pH pH = log 0.00032

In 2011 the U.S. Department of Transportation reported with 95% confidence that the average length of a motor vehicle trip in the United States was 9.72 miles with a margin or error of 0.22 miles. With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between The level of confidence for this estimate is

An accountant for a corporation forgot to pay the firm's income tax of $725,835.68 on time. The government charged a penalty of 8.4% interest for the 49 days the money was late. Find the total amount (tax and penalty) that was paid. Assume 365 days in a year

If two lines are parallel, the alternate interior angles are congruent. Choose the equivalent statement. A. If alternate interior angles are congruent, the lines are parallel. B. If alternate interior angles are not congruent, then the lines are not parallel. C. If two lines are not parallel, then alternate interior angles are not congruent.

Which of the following statements is not a true statement? A. The legs of a triangle are the sides adjacent to the right angle. B. The hypotenuse is directly across from the right angle. C. The Pythagorean theorem can only be used with right triangles. D. The hypotenuse is always the shortest side length.

Barbara picked 36 apples. She needs to put of the apples in a basket. Barbara says she will put 12 apples in the basket. Is Barbara correct? Explain.

Using the Law of Sines to solve the triangle if ∠A = 40°, ∠C = 68°, b = 25:

Simplify the expression. z²+zx + 3z + 3x / z+ 3

Give the equation of the line with a slope of -1/7 and a y-intercept of - 2.

A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 85% of the time if the person has the virus and 8% of the time if the person does not have the virus. (This 8% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive". a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A/B). Round your answer to the nearest tenth of a percent and do not include a percent sign. b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A' | B'). Round your answer to the nearest tenth of a percent and do not include a percent sign.

The Foster family and the Robinson family each used their sprinklers last summer. The water output rate for the Foster family's sprinkler was 25 L per hour. The water output rate for the Robinson family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1475 L. How long was each sprinkler used?

A tinsmith wants to make a small windowsill planter from a 60 cm x 18 cm sheet of copper. She'll form it by cutting equally sized squares from each of the four corners of the sheet, folding up the resulting flaps to form the sides of the planter, and then soldering the four vertical edges. If she wants the ratio of the planter's width to height to be 7, what will be the ratio of its length to width? Write the exact answer. Do not round.

Karla invests $10,000 into an account with a 2.2% interest that is compounded annually. How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round your answer. Provide your answer below:

Simplify the following rational expression and name the restrictions on the variable, if any: x^2 - 8x + 12 / x^2 - 3x - 18 x-2/x+3, x ≠ 3, 6 x+2/x-3, x ≠ 3 x+2/x-3, x ≠ -6, 3 x-2/x+3, x ≠ -3

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.)