Basic Math Questions and Answers

Simplify the exponential expression: (2x³y²) ³ (3y³ w)² 72w²x9y12 -1w²x9y 17wx6y10 w²x²y6

Evaluate the function at the given values of the independent variable and simplify. f(x)=6x²-1/x² (a) f(4) (b) f(-4) (c) f(-x)

The measure of an angle is five times the measure of its complementary angle. What is the measure of each angle? ____ and ___

Accounts payable would appear on the balance sheet as a a. current liability. b. long-term liability. c. current asset. d. disclosure in the notes only.

James spent one-half of the money in his account on car repair. Then he spent a third of the remaning amount on his rent. He did not add any money to his account or use the money in his account for any other reason. If we want to know how much is left in his account now, what other information do we need? The name of his bank The starting amount of money in his account What his other expenses are James' age

The dimensions of a triangular lot are 165 feet by 49 feet by 154 feet. If the price of such land is $3 per square foot, how much does the lot cost? The lot costs $ (Do not round until the final answer. Then round to the nearest cent as needed.)

Use the echelon method to solve the following system of two equations in two unknowns. Check your answer. 7x+3y= -28 6x-3y=-24 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Type an ordered pair.) B. There are infinitely many solutions. The general solution is (y), where y is any real number. C. There is no solution.

Jennifer just got a new job. The starting salary for the new job is $45,000. The job comes with a choice of two promotion packages. A promotion package is a plan that explains in writing how much Jennifer will make in salary if she continues to do a good job at the company. Jennifer has to decide which of the two promotion packages she wants. The first package increases her salary by 3% each year. The second package increases her salary by $2000 each year. Jennifer plans to stay with the company for 5 years. Which option should she choose? There is not enough information to determine which package is better. Both options would yield the same salary after 5 years. The 3% increase per year yields a higher salary after 5 years. The $2000 increase per year yields a higher salary after 5 years.

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 11% chose chocolate pie, and the margin of error was given as ±5 percentage points. Describe what is meant by the statement that "the margin of error was given as ±5 percentage points." Choose the correct answer below. A. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11% ± 5%. B. The statement indicates that the study is 100% -5% = 95% confident that the true population percentage of people that prefer chocolate pie is 11%. C. The statement indicates that the study is only 5% confident that the true population percentage of people that prefer chocolate pie is exactly 11%. D. The statement indicates that the interval 11% ± 5% is likely to contain the true population percentage of people that prefer chocolate pie.

Which of the following are statements? Choose each correct answer. Select all that apply: 3+7 I will go for a walk later today. Every prime number has exactly two factors. Papaya is my favorite fruit.

The city of Raleigh has 10200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 300 randomly selected registered voters was conducted. 96 said they'd vote for Brown, 187 said they'd vote for Feliz, and 17 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not a percent. This sample statistic suggests that we might expect of the 10200 registered voters to vote for Brown.

Rewrite the following polar equation in rectangular form. r=11/4sinθ-6cosθ

One half of a cantaloupe was shared equally among 3 people. What fraction of the whole cantaloupe did each person get? Explain how you found your answer.

Let p(x) = x³ - x² + 2x - 5. p(-3) can be computed via synthetic division by filling in for the letters α through g in the table 1-1 2-5 b d f a c e g where

Perform the indicated operation. Write the answer in scientific notation, rounding to two decimal places. Then write the rounded answer in decimal notation as well. (4.8x10³) (9.6×102) Write the answer in scientific notation, rounding to two decimal places. (4.8 x 10-3 )(9.6 x 10-2) = x 10

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 6th term is -10; 15th term is -46 a₁ = 10, d = 4, an = an-1 + 4 a₁ = 10, d = -4, an = an-1-4 a₁ = -30, d = 4, an = an-1 + 4 a₁ = -10, d=-4, an = an-1-4

If f(x) = x² + 4, g(x) = x − 3 and h(x) = √z, then f(g(h(x))) =

Factor the trinomial completely. If the polynomial cannot be factored, say it is prime. x2+10x +25 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x²+10x + 25 = __ (Type your answer in factored form.) B. The polynomial is prime.

The data can be modeled by the following system of linear equations. {- 5x+ 20y = 140 Equation 1 {x + 4y = 178 Equation 2 Equation 1 is modeled for the percentage of never-married American adults, y, x years after 1970 and Equation 2 is modeled for the percentage of married American adults, y, x years after 1970. Use these models to complete parts a and b. a. Determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately what percentage of Americans, rounded to the nearest percent, will belong to each group? In year the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately % percentage of Americans will belong to each group.

Karina and Perry are cleaning up litter in the park for community service hours. Karina and to Perry both claim they have covered the greatest area. Who is correct? Justify your answer using mathematical reasoning.

A graphic artist is designing a poster to advertise an upcoming event. The only restrictions regarding the poster size is that it must have a length of 7x inches and a width of 2x + 3 inches. Find a simplified expression for the area of the poster.

Use the balanced equation to answer the following question. 6CUNO3 + Al2(SO4)3 -> 3Cu₂SO4 + 2AI(NO3)3 Molar mass of CUNO3 125.56 g/mol Molar mass of Al(NO3)3 213.01 g/mol How many grams of copper (I) nitrate (CUNO3) are required to produce 44.0 grams of aluminum nitrate (Al(NO3)3)? 0.619 g CUNO3 24.88 g CUNO3 77.81 g CUNO3 155.62 g CUNO3

Find the missing coefficient. (2d-6)(2d + 4) = 4d² + __ d-24 a -2 b -4 c 4 d 20

Armando's goal is to find a job that provides an income of $45,000 a year. Natalie's Furniture offers him a job paying a base salary of $28,000 a year, plus a commission of 6% of his sales. Determine what Armando's total sales will need to be for him to have a yearly income of $45,000. If Armando takes the job with Natalie's Furniture, he will need to make $ _________ in total sales in order to have a yearly income of $45,000 per year. Round your answer to the nearest cent.

The function A = Age -0.00866x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 200 pounds of the material are placed in the vault, how much time will need to pass for only 65 pounds to remain? Round to nearest whole number. A. 260 years B. 140 years C. 130 years D. 135 years

A researcher wants to learn the effects sleep deprivation has on a person's reflexes. The volunteers were broken into two separate groups. In the first group, forty volunteers were only allowed to sleep for 2 hours a night for five days in a row. In the second group, forty volunteers slept their normal sleep patterns for the same five days. On the sixth day, the researcher tested each participant on his/her reflexes. Control Group: Experimental Group: Treatment: Variable of Study:

Journal entries based on the bank reconciliation are required in the depositor's accounts for a. bank errors. b. NSF items. c. deposits in transit. d. outstanding checks.

Find the vertical, horizontal, and oblique asymptotes, if any, of the following rational function. G(x)=x4 - 1/6x² - 6x *** Find the vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The funct has one vertical asymptote, ____ (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymptote is __(Type equations. Use integers or fractions for any numbers in the equations.) C. The function has no vertical asymptote.

The position function of an object is given by s³ + t²s = 2t, where the position, s, is a function of time, t, for t ≥ If ds/dt=2-2st/3s^2+t^2 determine why the acceleration is not defined at t = 0. 2-2st = 0 for t = 0 and s = 0 2-2st=0 for t = 0 and s = 1 (3s² +1²)² = 0 for t = 0 and s = 0 (3s² + 2)2 = 0 for t = 0 and s = 1

Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded 2 times per year. What will the account balance be after 6 years? Round to the nearest hundredth. A = P(1+ r/n)ⁿᵗ

Suppose that $8500 is placed in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. $ (b) Find the amount in the account at the end of 2 years. $

Find the distance between the pair of points (-3,-4) and (1,-3). If necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is __ units. (Simplify your answer. Type an exact answer, using radicals as needed.)

Sophia says that you can solve the problem in the Example by multiplying both quantities in the ratio 60:36 by 1/6. Is Sophia correct? Explain.

Find the distance between the points (9, 10) and (-1, 6).

Which statement about the end behavior of the logarithmic function f(x) = log(x + 3) - 2 is true? A. As x decreases, y moves toward the vertical asymptote at x = -3. B.As x decreases, y moves toward the vertical asymptote at x = -1. C.As x increases, y moves toward negative infinity. D.As x decreases, y moves toward positive infinity.

5. Brianna works at the Steve Lindquist Aquatic Center during her summer vocation. She is paid $10 per hour for teaching swim lessons and $20 per hour for teaching water aerobics She can work a maximum of 35 hours per week, and would like to earn at least $400 this week. If x represents the number of hours teaching swim lessons and y represents the number of hours teaching water aerobics. a. Write a system of inequalities that could be used to represent the given conditions. b. Insert a picture of the graph. (Sketch the graph if you're writing on paper.) c. Pick 2 ordered pairs, explain what they represent in terms of the problem, and how much money she would earn that week.

Lizbeth has two choices for her retirement account. She starts with $12,000. Choice A account choice is to have her investment compounded quarterly at 6%. Choice B account is to have her investment compounded biannually at a rate of 7.5%.Which choice will give her more money to retire with?

Graph the solution to the inequality on the number line. |v-8] <2

Give the following number in Base 10. (11011)2= [?]10

Which of the following is false? Enter a, b, c, d, or e. a. Every whole number is a natural number. b. Some rational numbers are whole numbers. c. O is an integer. d. No irrational numbers are integers. e. ∛729 is not irrational.

Which of the following is NOT irrational? Enter a, b, c, d, or e. a. π b. √7 c. √49 d. 7.313113111311113... e. √7-√3

Let f(x) = (x² + 1)² and g(x) = What is the slope of the curve og'(4) = 8 o g'(4) = // og'(4) = - 8 og'(4) = -1/ 4 f'(x). g(x) = f (x) at the point(4, 1)?

Person A can paint the neighbors house 6 times as fast as person B The year A and B worked together, it took them one day. How long would it take each to paint the house? find the how many days person A would tale and find how many days person B would take. there are two answers.

The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true? A) 30x = 2 B) 2x = 30 C)2x = 30 D) x + 30 = 2

Cost of goods sold is reported as a(n) a. current liability. b. long-term asset. C. current asset. d. expense.

What is a measure of central tendency (also known as a measure of center)? A. A number that separates the lower P% of the data from the upper (1-P)% of the data. B. A value that can stand in for and fairly represent all the data values in a large set of numbers; a typical value C. A value that can summarizes the spread or dispersion of a set of data D. A value that represents the probability of generating a test statistic at least as extreme than than the one you already hav E. A value equal to a data value's standard deviations from the mean

Which of the following sets of numbers could not represent the three sides of a right triangle? {36, 77,85} {24, 45, 51} {7, 24, 25} {65, 72,96}

Which of the pairs of events below is dependent? Select the correct answer below. drawing a 7 and then drawing another 7 with replacement from a standard deck of cards rolling a 1 and then rolling a 6 with a standard die rolling a 3 and then rolling a 4 with a standard die drawing a heart and then drawing a spade without replacement from a standard deck of cards

A certain radioactive substance has a half-life of five days. How long will it take for an amount A to disintegrate until only one percent of A remains?

What is the solution set for |s+4| = 6? s=-2 and s=2 s=-10 and s=2 s=-10 and s= 10 s= 2 and s=10