Math Questions

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.

Solve the following system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. X + y - z = 6 2x - y + 2z = -5 x + 2y - z = 9 Write the fractions using Cramer's Rule in the form of determinants. Do not evalate the determinants. (Type an integer or simplified fraction for each matrix element.) Select the correct choice below and fill in any answer boxes within your choice. A. Cramer's Rule is applicable. The solution is x = 1, y = [3], and z = -2 (Simplify your answers. Type integers or simplified fractions.) B. Cramer's Rule is not applicable.

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.

Monthly sales of a Jeep Wrangler are expected to increase at a rate of S' (t) = -24t3 Jeep Wrangler per month, where t is time in months and S(t) is the number of Jeep Wranglers sold each month. The Company that makes the Jeep Wrangler plans to stop making them when monthly sales reach 300 Jeep Wranglers. If monthly sales now (t-0) are 1200 Jeep Wranglers, find S(t). How long will the company continue to manufacture this model?

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.

Find the monthly payment (in $) and the total interest (in $) for a mortgage of $48,000 at 5 3/4% for 30 years. Use this table and give the total interest as your answer. (Round your

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.).

A plumbing company charges a $125 just to come out and respond to an emergency call, and an additional $30 for every hour they are working. Find a formula for a linear model that will tell you how much total you need to pay them depending on how long they are working on the plumbing issue.

Kristen's financial advisor has given her a list of 13 potential investments and has asked her to select and rank her favorite four. In how many different ways can she do this?

The equation of line A is y= 7x + 14. Line B is perpendicular to line A and passes through the point (4, 13 3/77). What would be the solution to the system of equations represented by line A and line B? A. The system of equations has no real solutions. B. x = 14, y = 0 C. x = 0, y = 14 D. The system of equations has an infinite number of real solutions.

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 produce buyer for a juice company is buying pears. He makes a choice of either Oregon, California, or imported pears. For this contract he must also choose fancy or extra fancy. Write out the sample space and assume each outcome is equally likely. Then give the probability of the requested outcomes in parts (a) and (b) below. Write out the sample space. Choose the correct answer below. A. S={(California,fancy), (California,extra fancy), (Oregon,fancy), (Oregon,extra fancy), (Michigan, fancy), (Michigan,extra fancy), (imported, fancy), (imported,extra fancy)} B. S={(California,fancy), (California,extra fancy), (Oregon,fancy), (Oregon,extra fancy), (imported, fancy), (imported extra fancy)} C. S={(California,fancy), (Oregon,fancy), (Oregon,extra fancy), (imported extra fancy)} D. S={(California,fancy), (Oregon,extra fancy), (imported,extra fancy)} (a) The pears selected are fancy. (Type an integer or a simplified fraction.) (b) The pears selected are imported or fancy. (Type an integer or a simplified fraction.)

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?

A physical therapist is scheduling appointments for the day. She has five worker's comp cases and six Medicare patients awaiting care. If she chooses nine at random for her morning schedule, find the probability that she'll pick three worker's comp cases and six Medicare patients. Round your answer to five decimal places.

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.

Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth. (1/2)x = 13 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Round to the nearest thousandth as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.

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.)

Follow the method in Step 1 to determine if the fourth expression is a perfect square trinomial. The first term and the third term of the fourth trinomial, 4x^2 + 12x + 9, are perfect squares. 4x² = (2x)² 9 = (3)² Because the x-term is positive, if the trinomial is a perfect square, then it is the square of a binomial sum. Find the square of the binomial formed by the sum of the square roots of the perfect squares, (2x + 3)². You can use the distributive property to square the binomial. Or you can use the rule for squaring a binomial sum, (a + b)² = a² + 2ab + b², with a = 2x and b = 3. Compare the original trinomial to the square of the binomial.

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?

Given that cosα= 2/3 and 0 < α < π/2, determine the exact value of cos α/2

A drill is used to dig down into the earth. After 2 hours, the drill is 12 meters below. the surface. After 5 hours, the drill is 30 meters below the surface. Which equation represents the depth of the drill in meters, y, after x hours of drilling?

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 beverage company announced in the last year that 60% of their products had discounts, 70% of their products were sugar-free and 40% were both. What is the portion of products that either had discounts or were sugar-free? Assume Event A: the product had discounts; Event B: the product was sugar-free.

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, ∞)

2. Use A = Pe^rt to solve the following problem. A sum of $14,000 is invested at an interest rate of 6.85% per year. Find the amount in the account after 10 years if the interest is compounded continuously.

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

A baseball supply store has many inexpensive baseball gloves. In fact, over half of the gloves in stock cost less than $50. However, there are also a few high-end, more expensive gloves in stock. Some of those gloves cost over $300. The store owner wants to advertise her store. She wants to advertise to local children's baseball teams. She wants to advertise that her store is a place to buy reasonably priced items. Which number should she use in the advertisement for the gloves? Median baseball glove price Mean baseball glove price Mode baseball glove price

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.

Use the Venn diagram to answer the question. In 2016, among the top 100 grossing movies in a particular country, 17 were rated PG-13 and earned over $100 million. The number of movies that were rated PG-13 that earned less than $100 million was 21. The number of movies that were not rated PG-13 that earned less than $100 million was 31. What was the number of movies that earned over $100 million and that were not rated PG-13? FERRE The number of movies that earned over $100 million and were not rated PG-13 was (Type a whole number.)

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?

In a group of seven Olympic track stars, three are hurdlers. If three track stars are selected at random without replacement, find the probability that they are all hurdlers. Express your answer as a decimal rounded to four places if necessary. P (All three are hurdlers) =

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?

Easton is working two summer jobs, making $18 per hour tutoring and $9 per hour clearing tables. Last week Easton worked 4 times as many hours tutoring as he worked hours clearing tables hours and earned a total of $162. Graphically solve a system of equations in order to determine the number of hours Easton worked tutoring last week, x, and the number of hours Easton worked clearing tables last week, y.

Use the following system of equations to answer the following: ax + 5y = 2 3x+10y = 4 a. Write both equations in slope-intercept form. (You must show work in order to receive full credit.)

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

➤ 4-19 When she was younger, Mary had to look up at a 68° angle to see into her father's eyes whenever she was standing 15 inches away. How high above the flat ground were her father's eyes if Mary's eyes were 32 inches above the ground?

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.