Math Questions

For the following loan, make a table showing the amount of each monthly payment that goes toward principal and interest for the first three months of the loan. A home mortgage of $154,000 with a fixed APR of 6% for 30 years. Fill out the table. End of... Month 1 Interest Payment Toward Principal New Principal

Consider a student loan of $10,000 at a fixed APR of 10% for 3 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Find the critical numbers of the function f(x) = -12x^5 + 15x^4 + 100x³ - 5 and classify them using a graph.

Suppose you have a student loan of $25,000 with an APR of 9% for 40 years. Complete parts (a) through (c) below. a. What are your required monthly payments? The required monthly payment is $ 192.84. (Do not round until the final answer. Then round to the nearest cent as needed.) b. Suppose you would like to pay the loan off in 20 years instead of 40. What monthly payments will you need to make? The monthly payment required to pay off the loan in 20 years instead of 40 is $. (Do not round until the final answer. Then round to the nearest cent as needed.)

Consider the following pair of loan options for a $165,000 mortgage. Calculate the monthly payment and total closing costs for each option. Explain which is the better option and why. Choice 1: 30-year fixed rate at 5.5% with closing costs of $2300 and 1 point. Choice 2: 30-year fixed rate at 5.25% with closing costs of $2300 and 4 points. What is the monthly payment for choice 1? (Do not round until the final answer. Then round to the nearest cent as needed.) What is the monthly payment for choice 2? (Do not round until the final answer. Then round to the nearest cent as needed.)

Someone needs to borrow $14,000 to buy a car and the person has determined that monthly payments of $300 are affordable. The bank offers a 3-year loan at 8% APR, a 4-year loan at 8.5%, or a 5-year loan at 9% APR. Which loan best meets the person's needs? Explain. Which loan best meets the person's needs? (Round to the nearest cent as needed.) A. The first loan best meets the person's needs because the monthly payment of $ budgeted amount of $300 per month. B. The second loan best meets the person's needs because the monthly payment of $ budgeted amount of $300 per month. C. The third loan best meets the person's needs because the monthly payment of $ budgeted amount of $300 per month. D. None of the loans meet the person's needs. is less than the maximum is less than the maximum is less than the maximum

A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will minimize production cost. Helpful information: h: height of can, r: radius of can Volume of a cylinder: V = r²h Area of the sides: A = 2πrh Area of the top/bottom: A = ²

A factory machine is producing Jeans to the length of 49cm. The standard deviation of the population is taken to be 0.3cm. A sample of 50 pairs of jeans is taken and is found to have a mean length of 48cm. Based on a 95% Confidence level interval, should the machine be checked and adjusted? [5]

An isosceles triangle has a vertex angle of 26°. Two sides of the triangle are each 15 ft long. Find the area of the triangle. A. 49.314 sq ft B. 45.543 sq ft C. 9.931 sq ft D. 98.629 sq ft

Use permutations and/or combinations to calculate the probability of getting 3 diamonds and a heart from picking 4 cards from a deck of 52 (assume 4 suites of 13).Verify your answer using fractional probability.

A rancher wants to fence in an area of 3,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

Assume you have a balance of $1100 on a credit card with an APR of 24%, or 2% per month. You start making monthly payments of $200, but at the same time you charge an additional $80 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. The following table shows how you can calculate your monthly balance. Complete and extend the table to show the balance at the end of each month until the debt is paid off. How long does it take to pay off the credit card debt?

A 5000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each pric $148,200?

Solve the system by the addition method. 5x - 4y = 2 2x + 5y = 14 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. There are infinitely many solutions. C. There is no solution.

A 6000-seat theater has tickets for sale at $25 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $190,500?

A radioactive isotope decays rapidly with a half-life of 4 minutes. For a 12 minute test, technicians need at least 6 grams of the isotope to remain at the end of the test. How much must they start with? a) 48 grams b) 12 grams c) 24 grams d) 96 grams

Find the value of z in the solution of the following system: 2x+2y+3z = -107 3x + 2y - 5z = 16 -5x – 2y - 5z = 180

If the derivative f'(x) is negative, decreasing, concave up Then the function f(x) is (not all info may be used): increasing, concave up decreasing, concave up decreasing, concave down increasing, concave down

You are planning to make an open rectangular box from a 6-in. by 6-in. piece of cardboard by cutting congruent squares from the corners and folding up the sides. What are the dimensions of the box of largest volume you can make this way, and what is its volume? Use must use calculus to determine the desired optimal solution to the problem.

Solve the system using Cramer's Rule. -2x - 4y = -22 -x+3y = 14 Find the determinant D (denominator). D= Find the determinant D, associated with z. Dz Find the determinant Dy associated with y. Dy =

Solve the system by the addition method. 5x + 3y = 4 10x+6y=8 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is exactly one solution. The solution set is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. The solution set is {(x,y) |5x+3y=4} or {(x,y)| 10x+6y=8}. C. The solution set is Ø.

A farmer finds that if she plants 90 trees per acre, each tree will yield 60 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 2 bushels. How many trees should she plant per acre to maximize her harvest?

Using the formula A(t) = ae^rt, what is the value of an investment with an initial value (indicated by the variable a) of $1,000 that continuously compounded at 8% (r) over 50 years (t)? (Use 2.718 for the value of e.)

A fence 6 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

What is the angle of elevation of the sun if a 45 foot tall flag pole casts a 22 foot long shadow? A. 26.1 B. 60.7 C. 63.9 D. 29.3

Suppose that on January 1 you have a balance of $2800 on a credit card whose APR is 14%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. a. Calculate your monthly payments. b. When the card is paid off, how much will you have paid since January 1? c. What percentage of your total payment from part (b) is interest?

Let f(x) = x³ + 3x² - 9x + 15. (a) Use the definition of a derivative or the derivative rules to find f'(x)= (b) Use the definition of a derivative or the derivative rules to find f''(x) = (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing = (e) On what interval is f concave downward (include the endpoints in the interval)? interval of downward concavity = (f) On what interval is f concave upward (include the endpoints in the interval)? interval of upward concavity =

8. Suppose you have borrowed two calculators from friends, but you do not know whether they are set to work in radians or degrees. You ask each calculator to evaluate cos 3.14. One calculator replies with an answer of -0.99999; the other calculator replies with an answer of 0.998499. Without further use of a calculator, how would you decide which calculator is using degrees? Explain your answer.

Find the coordinates of point L that lies along the directed line segment from N(14, 4) to M(2, 8) and partitions the segment in the ratio of 1:3. A. (16, 12) B. (8,6) C. (11,5) D. (-3,1)

Find the midpoint of the segment between the points (8,-10) and (-10,-8). A. (-1,-9) B. (0,0) C. (-1,2) D. (0,-6)

Solve the system of equations, using a matrix or otherwise. If the system has an infinite number of solutions, express them in terms of the parameter z. {5x - 4y +8z = 0 {-10x +9y - 13z= -5 {-2x +2y -2z= -2

Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (12, 0) in the zy-plane, Springfield is at (0, 5), and Shelbyville is at (0, -5). The cable runs from Centerville to some point (x, 0) on the z-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x, 0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of x: f(x) = = We find that f(z) has a critical number at x = To verify that f(x) has a minimum at this critical number we compute the second derivative f''(z) and find that its value at the critical number is , a positive number. Thus the minimum length of cable needed is

The population of Suka is currently 34.88 million people. Suka's current growth rate is 1.1% per year. What will Suka's population be in 5 years? a) 58 774 828 b) 19 477 199 c) 33 003 343 d) 36 841 072

A triangular field has sides of 218.5 m and 213.3 m, and the angle between them measures 58.96°. Find the area of the field. A. 24,032 m² B. 19,966 m² C. 12,016 m² D. 14,332 m²

Which of the following is NOT the equation for a conic section? Enter a, b, c, d, or e. a. 2x² + 5y² - 2x + 7y - 8 = 0 b. y = 3x² + 7x-3 c. y = 2^x + 5 d. x²/9 - (x-3) ²/ 16 =1 e. (x - 2)² + (y + 3)² = 25

While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 40 degrees. After walking 450 ft closer, he guessed that the angle of elevation had increased by 18 degrees. Approximately how tall is the hill? A. 236 feet B. 794 feet C. 496 feet D. 608 feet

Find the midpoint of WX. W = (-1, 5) X = (7,3)

Which of the following would be a good idea as you prepare for a test? A. Stay up late the night before studying. B. Eat a big breakfast right before. C. Put new batteries in your calculator. D. Don't study until the morning of the test.

Jon has quarters, dimes, and nickels in his pocket. The value of his money is $1.75. There are two more dimes than quarters and twice as many nickels as dimes. How many nickels does he have?

If 1800 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

If a virus spreads at a rate that can be modeled by the exponential function A(t) = ae^rt, how many people will be infected after 5 days if the initially 3 people are infected and the growth rate is 40%? (Use your calculator for a precise version of e. If you are not able to use a calculator, you can approximate e as 2.718. Round your answer to the nearest person.)

Solve the following system of equations. If there is no solution, write DNE in each coordinate of the ordered triplet. If there are an infinite number of solution, write each coordinate in terms of z. x-14=y-13 z+6=x+2 y-10=z-7

A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Ho: H0: µ ≥ 3.3 Ha: µ <3.3 What type of test is being conducted in this problem? A. Right-tailed test B. Two-tailed test C. Left-tailed test

If we assume that the conditions for correlation are met, which of the following are true? If false, explain briefly. a) A correlation of -0.98 indicates a strong, negative association. b) Multiplying every value of x by 2 will double the correlation. c) The units of the correlation are the same as the units of y.

If you have $15 and you spend $8 on baseball tickets, what fraction of your money did you spend?

If f(x) = log3(x), what is the transformation that occurs if g(x) = -log3(x)? (Enters for stretch, c for compress, mx for mirrorred across the x-axis, my for mirrored across the y-axis, r for shift right, I for shift left, u for shift up, and d for shift down.)

Select all the correct answers. A biologist models the size of a population of songbirds over time, t, in years, with this function. f(t) 312(0.97)^t Which statements about the population are supported by this function? The population size was initially around 312. The population size was initially around 303. The population size when t=5 is predicted to be 361. The population is increasing by 97% per year. The population is decreasing by 3% per year.

Solve the System. Give answer as (x, y, z). {-1x+5y-5z= -5 {-2x-5y-6z=-6 {4x-5y+2z=2 No solution Infinite number of solutions

Zoe has 8 cups of whole-wheat flour. If each loaf of her favorite bread requires 3/4 of a cup of whole-wheat flour, how many whole loaves of bread can she make using 8 cups? 4 loaves 6 loaves 10 loaves 11 loaves

If the point (2,-5) is reflected in the line y = x, then the image is: A. (-2,5) B. (-5,-2) Oc. (-5,2) D. (5,-2)