Basic Math Questions and Answers

Consider the expression 5b + 3c - 20 + 3b - 15c +4. Part A Simplify the expression. Part B Factor the simplified expression using the GCF. Part C What is the value of the expression when b = 2 and c= -3?

The price of nails is $1.29/lb, the price of washers is $0.79/lb, and the price of bolts is $2.39/lb. Write an expression to represent the total price of n pounds of nails, w pounds of washers, and b pounds of bolts. What is the total cost of buying 2 pounds of nails, 4 pounds of washers, and 3 pounds of bolts?

Use the product rule to simplify the expression. Write your answer in exponential notation. (-6x²)(3x³) Select the correct choice below and fill in any answer boxes within your choice. A. (-6x²)(3x^8) = (Type exponential notation with positive exponents. Simplify your answer) B. The product rule does not apply.

Which of the following best describes the solution to the system of equations below? 3x+6y=10 9x + 18y=30 A. The system of equations has exactly one solution where x = 10/3 and y = 0. B. The system of equations has infinitely many solutions. C. The system of equations has exactly one solution where x = 1 and y = 3/2 D. The system of equations has no solution.

A good example of a positive sanction for conformity is which of the following: Caning Cash Spanking Waterboarding

A sum of $1000 is invested at an interest rate of 4% per year. Find the time required for the amount to grow to $4000 if interest is compounded continuously.

A rectangular auditorium seats 2408 people. The number of seats in each row exceeds the number of rows by 13. Find the number of seats in each row.

Follow the method in Step 1 to determine if the third expression is a perfect square trinomial. The first term and the third term of the third trinomial, h² - 13h + 36, are perfect squares. h² = (h)² 36 = (6)² Because the h-term is negative, if the trinomial is a perfect square, then it is the square of a binomial difference. Find the square of the binomial formed by the difference of the square roots of the perfect squares, (h - 6)². You can use the distributive property to square the binomial. Or you can use the rule for squaring a binomial difference, (a - b)² = a² - 2ab + b², with a = h and b = 6. Compare the original trinomial to the square of the binomial. (h-6)² = (h-6)(h-) =h² - (2)(h) ( ) + (6)² = h² - h + 36

When solving equations using the method of successive approximations, multiple iterations are performed. An approximate solution from three iterations is always an approximate solution from two iterations.

At the Pizza Dude restaurant, a 12-in. pizza costs $3.40 to make, and the manager wants to make at least $2.20 from the sale of each pizza. If the pizza will be sold by the slice and each pizza is cut into 6 pieces, what is the minimum charge per slice?

Select the correct statement in the table. A landscape architect is ordering trees to plant in a park she is designing. The cost of each maple tree is $40, and the cost of each birch tree is $60. Each maple tree requires 15 gallons of water per week, and each birch tree requires 10 gallons of water per week. The architect has a budget of $2,000 to spend on new trees for the park, and the trees must require no more than 400 gallons of water each week. Determine a system of linear inequalities to represent this situation, where x is the number of maple trees and yis the number of birch trees. Then, select the true statement about the system.

How much money does Barbara Mack owe at the end of 6 years if 7% interest is compounded continuously on her $1500 debt? Use the formula A = P ert to solve.

In the accompanying diagram, AB//CD and EF bisects AFG. m∠9 = 42°, find the measure of Each of the numbered angles.

9. (a) Let θ be an angle in standard position. Name the quadrant in which the angle θ lies given that sin θ <0 and sec θ < 0. (b) Let θ be an angle in standard position. Name the quadrant in which the angle θ lies given that cos θ <0 and csc θ > 0.

Samuel is hired at a small sales company. His monthly pay is calculated by the equation P= 150s + 500. s = the number of sales P = Samuel's pay in dollars. Which of the following statements are true? There may be more than one correct answer. Samuel earns a base salary of $500 each month. Samuel earns a base salary of $150 each month. Samuel earns $500 for each sale he makes. Samuel earns $150 for each sale he makes. The vertical intercept is (0, 150).

Completely factor the following polynomial: 90y² + 210y + 490. Factor out the greatest common factor (GCF) of the coefficients.

A. Write the following as whole numbers or decimals, without words. 3.2 thousand 26 thousand 14.5 million a rate of 85 per thousand a rate of 782 per million B. Find the square root of each number, to three decimal places, using your calculator: 0.91 0.452 C. There are two solutions to each of the following equations. What are they? x² = 25. x² = 0.64 x² = 0.0289

Find an approximate irrational solution to 2x = 3. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is {}. (Round to four decimal places.) B. The solution is the empty set.

A guitar factory has a cost of production C(x) = 75x + 50,000. If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar, and write the revenue function.

Divide. 7√1862 Select the correct choice below and fill in any answer boxes in your choice. A. The quotient is with no remainder. B. The quotient is with remainder C. The quotient is undefined.

On a shelf at a gaming store, there are nine Sony Playstations and seven Nintendo Wii consoles left. If one gaming system is selected at random, find the probability that the system is a Wii console.

Recently, a certain bank offered a 5-year CD that earns 2.32% compounded continuously. Use the given information to answer the questions. (a) If $10,000 is invested in this CD, how much will it be worth in 5 years? approximately $ (Round to the nearest cent.) (b) How long will it take for the account to be worth $35,000? approximately years (Round to two decimal places as needed.).

Federal rules state that a drone cannot fly within 5 miles of an airport. If a drone is 2.71 miles east and 3.92 miles north of the nearest corner of an airport and is flying at a height of 0.07 miles above the ground, is it in violation of the rule? Yes, because it is approximately 4.77 miles from the nearest corner of the airport. Yes, because it is approximately 4.84 miles from the nearest corner of the airport. No, because it is approximately 6.56 miles from the nearest corner of the airport. No, because it is approximately 6.70 miles from the nearest corner of the airport.

A company announced mailing coupons to its loyal customers. 25% of the coupons are for icecream only and 20% of the coupons are for pizza only. Given that a customer can get at most one coupon, what is the probability that they get coupons for both pizza and icecream? Assume Event A: getting a coupon for icecream; Event B: getting a coupon for pizza.

Ohm's law of electricity states that V = IR, where V is voltage represents the resistance. a. Rewrite the equation to isolate I. b. If V 220 volts and R = 4 ohms, what is the value for l? c. Rewrite the equation to isolate R. d. If V = 550 volts and I= 1.5 amperes, what is the value of resistance?

Alex deposits $9,000 in a Certificate of Deposit (CD) with an APR of 1.2%, compounded monthly. How much will be in the CD in 9 years, to the nearest dollar? The formula for compound interest is given below. A = P(1 + r/100)nt

Suppose the charge account of Strong's Mailing Service at the local supply store had a 1.8% interest rate per month on the average daily balance. Find the average daily balance if Strong's had an unpaid balance on March 1 of $184.10, a payment of $50 posted on March 11, and a purchase of $26.50 posted on March 24. The billing cycle ends March 31.

A small motorboat travels 14 mph in still water. It takes 5 hours longer to travel 31 miles going upstream than it does going downstream. Find the rate of the current. (Hint: 14+x=rate going downstream and 14 - x = rate going upstream.) (Round your answer to the nearest tenth.)

James has a mortgage of $94,500 at 8% for 30 years. The property taxes are $3,900 per year, and the hazard insurance premium is $764.50 per year. Find the monthly PITI payment (in $). (Round your answer to the nearest cent. Use this table as needed.)

The percentage of Americans who are retired has been increasing over the last decade. This is causing some concern because health care, social security, and other costs will be the responsibility of a smaller group of people. That is, as the percentage of retired people increases, the percentage of working age people decreases. The following model predicts the percentage of retired people based on demographic data: R=t/873.36-2.15 where R is the percentage (as a decimal) of Americans who are retired in the year t (for example, the year 1995 would be t = 1995). Use the formula to predict the percentage of retired people in 2028. Give the answer as a percent, rounded to the nearest tenth of a percent.

For the new fall season, a network president has 12 shows in development, and 8 openings in the prime time schedule. In how many ways can she arrange new shows to fit into the schedule?

Solve the logarithmic equation. Express all solutions in exact form. 2 Inx=14 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is { (Type an exact answer in simplified form. Use a comma to separate answers as needed.) B. The solution is the empty set.

A. Write the hypotheses for each situation below. a. In Fall 2019, 19.3% of all CSUN students were in the College of Social and Behavioral Sciences (CSBS). You want to test whether the percentage is larger this semester. In a random sample of 150 current CSUN students, 33 are in CSBS. Ho: Ha: b. Same as part a except you want to test whether the percentage has changed this semester. Ho: Ha: B. In part A, what does the symbol in your hypotheses stand for? Circle the best words: The symbol stands for the NUMBER / PROPORTION of CSUN students IN THE SAMPLE / AT CSUN during FALL 2019/ THIS SEMESTER who are in CSBS. C. Compute the test statistic, z, for this test. Round final answer to two decimal places. D. Based just on this value of z, should you reject the null hypothesis in A, part b? Explain.

Which of the following numbers best describes inequality above? A) [0,4/3) B)[4/3, ∞) C) (-∞, ∞) D) (-∞, -4]u[3, ∞)

Write the first term of the given expression as a perfect cube. The number 125 is a perfect cube which can be written in exponential form. 125 = 5 x 5 x 5 Substitute the exponential form found above into the given expression. Then, use the power of a product rule for exponents to write the first term in the form a³. 125x³ 1 = ( )^3 (x)³ - 1 = ( )^3 - 1

Determine which situation could be represented by the following system of linear equations. x + y = 70 8x + 5y = 410 A. Evaporated milk comes in eight-ounce cans and five-ounce cans. A grocery store sold 410 ounces of evaporated milk in 70 cans. B. At the floral shop, Mary buys eight large bouquets and five small bouquets for a total of $410. Mark buys one large bouquet and one small bouquet for $70 less than Mary pays. C. Packs of file folders cost $8 each and boxes of pens cost $5. An office manager ordered 70 more boxes of pens than packs of file folders and paid a total of $410. D. Each student at an elementary school is required to have five notebooks and eight pencils. One grade has a total of 70 school supplies and another grade has a total of 410 school supplies.

Which expression is equivalent to the given expression? 10g + 5 5q +5g +5 10q+5+5 5g + 10 5q +5

Can the following be factored? If so, factor it: 16x6-80y² Yes, (4x³+8y)(4x³-10y) Yes, (4x³+20y)(4x³-20y) Yes, (4x³+20y2)(4x³-20y²) Yes, (4x3+40y)(4x³-40y) Cannot be simply factored.

Solve the word problems using the RDW strategy. Show all of your work. Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it and gave the leftovers to his friends. What fraction of the pie did he give to his friends?

An entertainment center is financed at a total cost of $2,364.99 including a down payment of $300. If the center is financed over 24 months, find the monthly payment. The monthly payment is $(Round to the nearest cent as needed.)

The weights of the fish in a certain lake are normally distributed with a mean of 11 lb and a standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 8.6 and 14.6 lb? 0.3270 0.4032 0.0968 0.6730

This equation can be used to predict the population p (in thousands) of Barbaria, a mythical country, for a given year,t where t is the number of years since 1950: p = 15,498 + 446t a. To find the predicted population in 2020, what should you use for t? Compute the population predicted for 2020. Write the answer using the word "thousands." Without using the word "thousands." b. Compute the population predicted for 2021. In the answer, don't use "thousands." c. How much does the population increase each year?

Factor the difference of cubes. Recall that a difference of cubes can be rewritten such that a³ b³ = (a - b)(a² + ab + b²). Factor the difference of cubes. Then, simplify the terms. (4x³)3 - (3y)3

Serafina is solving a number puzzle that involves three integers, e, f, and g, where e is negative. The product of e and fis-15. The product of e and g is 6. The product of f and g is -10. What are the values of e, f, and g? Show your work.

Suppose the charge account of Black's Mailing Service at the local supply store had a 1.7% interest rate per month on the average daily balance. Find the Black's finance charge on April 1 if Black's had an unpaid balance on March 1 of $148.96, a payment of $25.00 posted on March 12, and a purchase of $27.06 posted on March 22. The billing cycle ends March 31. The Black's finance charge is (Round to the nearest cent as needed.)

Let B={-20, -19, 0, 19, 20}, and D = {-19}. Insert C or to make the following statement true. D ____ B Choose the correct answer below. A. Not every element of D is also an element of B, so D B. B. Every element of D is also an element of B, so D B. C. Not every element of B is also an element of D, so D B. D. Every element of B is also an element of D, so D B.

Oscar, Renee, Penny and Hugo, all turkeys, are wandering through the beautiful forest. They spot seven bees and five cockroaches, and in the trees, they see eight spiders. There are also four deer and four boars. Behind a bush, they can see a pair of antlers. How many legs are there in total?

ALGAE Ronald owns a fish tank in the shape of a rectangular box. The tank is 18 inches high, 14 inches deep, and 30 inches long. Ronald went on a one-month vacation. When he returned he found that the sides and bottom of his fish tank were covered with algae. What is the area that was covered?

In a random sample of 25 students at college, the average IQ was x = 103. Assume that the IQ of a student in college follows a Normal distribution with unknown mean and standard deviation = 15. A 90% confidence interval for u is (78, 128). (97, 109). (98, 108). (102, 104).

A bird traveled 72 miles in 6 hours flying at constant speed. At this rate, how many miles did the bird travel in 5 hours? 12 30- 60 14.4 I don't know (I need help with these type of questions)