Basic Math Questions and Answers

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

Find R and θ given the components Rx = 15.07 and Ry = 5.29. R=

Use synthetic division to find the result when 2x³-9x² - 16x-2 is divided by x + 1. 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.

Use the model Q(t)=Qoe-0.000121t for radiocarbon dating to answer the question. A sample from a mummified bull was taken from a certain place. The sample shows that 76% of the carbon-14 still remains. How old is the sample? Round to the nearest year.

A boiler room has the shape of a rectangular prism. The area of the floor of the room is 112 square feet. The length of the room is 2 feet more than twice the width. The height is 1 foot greater than the width. What is the volume of the room in cubic feet? Do not include units in your answer. Provide your answer below:

The cost of a four-year private college education (after financial aid) has been estimated to be $50,000.+ How large a trust fund, paying 4% compounded quarterly, must be established at a child's birth to ensure sufficient funds at age 18? (Round your answer to the nearest cent.)

The math department faculty at a large university wanted to know what portion of the student body believes students should be able to enroll in any math class without meeting a prerequisite. The statistics departmer offered to cooperate in conducting a survey, and a simple random sample of 500 students was selected fro the students enrolled in statistics classes. A survey form was sent by email to these 500 students and 236 responded. What is the population of interest for this study? all students enrolled in a statistics class 500 students who received the email survey all students at the university 236 students who responded to the email survey

Provide an appropriate response. The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1100 miles What is the probability a particular tire of this brand will last longer than 58,900 miles? 0.8413 0.1587 0.2266 0.7266

Given that the degree of the polynomial f(a) is 7, which of the following most accurately describes the number of a intercepts that f(a) has? Select the correct answer below: f(x) has at least 8 a-intercepts. f(x) has at least 6 a-intercepts. f(x) has at most 8 ar-intercepts. f(x) has at most 6 x-intercepts. f(x) has at most 7-intercepts f(x) has at least 7 ar-intercepts.

Given that the polynomial f(x) has degree 9, which of the following most accurately describes the number of turning points of f(x)? Select the correct answer below: The graph of f(x) has at most 10 turning points. The graph of f(x) has at most 9 turning points. The graph of f(x) has at most 8 turning points. The graph of f(x) has at least 8 turning points. The graph of f(x) has at least 10 turning points. The graph of f(x) has at least 9 turning points.

The sum of two nonnegative numbers is 20. Find the numbers a. if the product of one number and the square root of the other to be as large as possible. b. if one number plus the square root of the other is to be as large as possible.

Find all the zeros of f(x) = 2x³ + 30x² + 18x + 270

Tremayne is saving for his daughter's college education. If the savings account earns 4% Interest compounded monthly, and he wants to have $50,000 in 15 years, what must the principal be? Round your answer to the nearest dollar. Do not round until your final step.

A fish tank in the shape of a rectangular prism has a volume of 24 cubic feet. The length of the fish tank is 2 feet less than twice the width w, and the height is 1 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the fish tank in feet. Your answer should be in the form of a polynomial equals a constant. Provide your answer below:

Which is an equation of the degree 3 polynomial function with real coefficients having zeros (roots) located at x = = 2 with multiplicity 1 and x = -6 with multiplicity 1? The function also has a y-intercept located at (0, -36). Select the correct answer below: y=(x-2)(x-3)(x+6) y= (x+2)(x+3)(x-6) y=(x-2)(x+3)(x+6) y=(x+2)(x-3)(x-6)

A shed in the shape of a rectangular prism has a volume of 910 cubic feet. The length of the dumpster is 7 feet less than twice the width w, and the height is 3 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the shed in feet. Your answer should be in the form of a polynomial equals a constant.