Math Questions

The eccentricity of a hyperbola is defined as e = c/a. Find an equation of a hyperbola with vertices (1,-1) and (-5, -1) and e=5/3 The equation of the hyperbola is

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?

A small motorboat travels 15 mph in still water. It takes 2 hours longer to travel 69 miles going upstream than it does going downstream. Find the rate of the current. (Hint: 15 + x = rate going downstream and 15 - x = rate going upstream.)(Round your answer to the nearest tenth.)

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?

The Earth's Orbit. The maximum distance of the earth from the sun is 9.3 × 10^7 mi. The minimum dis- tance is 9.1 x 10^7 mi. The sun is at one focus of the elliptical orbit. Find the distance from the sun to the other focus.

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.

Line A has a slope of -2/5 and passes through the point (2, 6). Line B has a slope of 1/3 and passes through the point (-33, -2). Find the point where line A intersects line B. A. x = -1, y = 8² B. I = -3, y = 8 C. I = 8, y = -3 D. I = 17, y = 0

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?

Kari is purchasing a home for $260,000. The down payment is 25% and the balance will be financed with a 15 year mortgage at 8% and 4 discount points. Kari made a deposit of $20,000 (applied to the down payment) when the sales contract was signed. Kari also has these expenses: credit report, $70; appraisal fee, $110; title insurance premium, 1% of amount financed; title search, $200; and attorney's fees, $500. Find the closing costs (in $).

A nursing student can be assigned to one of six different floors each day depending on staffing needs. How many different ways can she be assigned during a 4- day work week?

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.

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.