Basic Math Questions and Answers

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

The lengths (in inches) of fish caught by two groups of fishermen are shown. Group 1: 20, 14, 14, 17, 23, 21, 9, 18 Group 2: 13, 14, 24, 12, 20, 20, 26, 7 Find the range of the fish lengths for each group. Compare your results.

A shipping container in the shape of a rectangular prism must have a volume of 25,000 cubic feet. The client tells the manufacturer that, because of the contents, the length of the container must be 10 feet longer than twice the width w, and the height must be 5 feet greater than the width. Find the equation, in terms of w, that could be used to find the dimensions of the container in feet. Your answer should be in the form of a polynomial equals a constant.

Explain why the initial value of any function of the form f(x)= a(bx) is equal to a.

Use synthetic division to find the result when 2x4 - 8x³ + 10x² − 6x – 49 is divided by x + 2. Write your answer in the form g(x) + d(x), where g(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

Solve the following rational inequality. 3/x+2 ≥ -1 x ≤ -5 or x>-2 x< -5 or x≥-2 x < -5 or x>-2 x≤-5 or x≥-2

The number of computers N (t) (in millions) infected by a computer virus can be approximated by N (t)=2.8 / 1+17e^-0.8t where t is the time in months after the virus was first detected. (a) Determine the number of computers initially infected when the virus was first detected. Round t

Consider the line with the equation: y = x + 1 Give the equation of the line parallel to Line 1 which passes through (-3, 2): Give the equation of the line perpendicular to Line 1 which passes through (-3,2)

Solve the following rational equation, and make sure to exclude any extraneous solutions. x/x-3 + 2x/ x+3 = 3

Divide using long division: 24x³ - 31x² - 71x - 25 / 8x + 3 where Q(x) + R(x) / D(x)' where Q(x) is the polynomial quotient, R(x) is the remainder, and D(x) is the given divisor

Solve the rational equation by graphing. Make sure to exclude any extraneous solutions. 2x+1/x = x/x-2 No solution. x≈-0.6, 3.6 x≈ 3.6 0-0.6

Express the following fraction in simplest form using only positive exponents. 3v8/2(v)²

One weekend, there were 98 pizzas ordered for the sophomore dorm. That weekend 19 customers ordered their pizza with just pepperoni, 16 customers ordered their pizza with just sausage, 20 ordered theirs with just onions, 15 ordered theirs with pepperoni and sausage, 9 ordered theirs with sausage and onions, 17 ordered theirs with pepperoni and onions, and 2 ordered theirs with all three items. How many customers ordered their pizza with pepperoni or sausage (or both)? A) 35 B) 72 C) 13 D) 50

A bank features a savings account that has an annual percentage rate of 3.4% with Interest compounded quarterly. Ashley opens one of these brand new savings accounts and deposits $2,000 into the account. What is her account balance after 4 years, rounded to the nearest cent?

Use synthetic division to find the result when 2x4 - 10x² + 16x + 13 is divided by x - 3. 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 divison