Basic Math Questions and Answers

If the equation y = 4(2) is plotted on a semilog scale graph, then the linearized equation will be log(y) = mx + b where

Solve sin(6x) cos(9x) - cos(6x) sin(9x) = -0.7 for the smallest positive solution. Give your answer accurate to two decimal places.

Let the sample space be S=(1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Suppose the outcomes are equally likely. Compute the probability of the event E="an odd number less than 10."

Let the sample space be S= (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Suppose the outcomes are equally likely. Compute the probability of the event E={3, 5, 9}

Convert the degree measurement to radians. Express answer as multiple of π: 45° A.π/5 B. π/4 C. π/6 D.π/3

Suppose you have the following three student loans: $12,000 with an APR of 8.5% for 15 years, $17,000 with an APR of 9% for 20 years, and $14,500 with an APR of 10% for 10 years. a. Calculate the monthly payment for each loan individually. b. Calculate the total you'll pay in payments during the life of all three loans. c. A bank offers to consolidate your three loans into a single loan with an APR of 9% and loan term of 20 years. What will your monthly payments be in that case? What will you total payments be over the 20 years? a. The monthly payment of the $12,000 loan is $118.17. The monthly payment of the $17,000 loan is $152.95. The monthly payment of the $14,500 loan is $ 191.62. b. The total you'll pay in payments during the life of all three loans is $.

Water weighs 62.4 pounds per cubic foot. How much does the water in a tank that measures 7 ft x 4 ft x 9 in, weigh? A. 1,310 lbs B. 1,316 lbs C. 1,573 lbs D. 1,574 lbs

Which of the following statements is false? A. The diagonals of a rectangle are perpendicular. B. The base angles of an isosceles trapezold are congruent. C. A quadrilateral is a polygon with four angles. D. The dlagonals of a rhombus are perpendicular and bisect each other.

A sample of sulfur hexafluoride gas occupies 7.97 L at 242°C. Assuming that the pressure remains constant, what temperature (in °C) is needed to reduce the volume to 3.18 L? Report your answer to the proper number of significant figures.

Find the area of a triangle with legs that are: 15 m, 25 m, and 20 m. A. 150 m² B. 42.4 m² C. 106.1 m² D. 38.2 m²

If each interior angle of a regular polygon measures 108°, how many sides does it have? A. 6 sides B. 5 sides C. 7 sides D. 10 sides

Enter your answer in the provided box. A 86-L sample of dry air cools from 107°C to -24°C while the pressure is maintained at 2.88 atm. What is the final volume?

A line segment that goes from one side of the circle to the other side of the circle and doesn't go through the center is: A. a secant B. a diameter C. a tangent D. a chord

A sandwich shop offers a choice of 5 meats, 3 cheeses, and 4 different breads. How many different combinations of sandwiches are there to choose from which contain one kind of meat, one kind of cheese, and one type of bread? a. 12 b. 15 c. 28 d. 60

You just bought an aquarium for your fish, which is 39.75 inches wide and 11.375 inches deep. The salesman told you to keep the water 2 inches from the top of the tank so the filter to works properly. If the tank is 14 inches high, how many cubic inches of water will it contain once it's filled? A. 5,426 in³ B. 5,087 in³ C. 4,688 in³ D. 5,552 in³

oblems A plumber wishes to cut a piece of pipe 32 inches long into two parts so that the larger part is 4 inches less than three times the smaller part. What are the lengths of the two parts of the pipe?

The half-life of the radioactive element unobtanium-41 is 20 seconds. If 178 grams of unobtanium-41 are initially present, how many grams are present after 20 seconds? 40 seconds? 60 seconds? 80 seconds? 100 seconds?

You have a choice between a 30-year fixed rate loan at 3.5% and an adjustable rate mortgage (ARM) with a first year rate of 2%. Neglecting compounding and changes in principal, estimate your monthly savings with the ARM during the first year on a $175,000 loan. Suppose that the ARM rate rises to 11.5% at the start of the third year. Approximately how much extra will you then be paying over what you would have paid if you had taken the fixed rate loan? What is the approximate monthly savings with the ARM during the first year?

Casey buys a bracelet. She pays for the bracelet and pays $0.72 in sales tax. The sales tax rate is 6%. What is the original price of the bracelet, before tax?

A stained glass window is going to be installed in a semi-circular opening, which is above a 30 inch wide door. If the stained glass window costs $1.40 per square inch, how much will the window cost? Use 3.14 for π as necessary. A. $494.55 B. $1,724.17 C. $389.10 D. $989.10

The domain, range, and Intercepts of a function are shown. Which set of Information could be characteristics of the function's Inverse? domain: x≥-1 y-Intercept: (0,-1) range: y≥-2 x-intercept: (1,0) A. domain: x= -1; range: y = -2; y-intercept: (0,-1); x-intercept: (1,0) B.domain: x= -2; range: y=-1; y-intercept: (0,1); x-intercept: (-1,0) C.domain: x ≥ 1; range: yz 2; y-intercept: (0,1); x-intercept: (-1,0) D.domain: x= -1; range: ye -2; y-intercept: (1,0); x-intercept: (0,-1)

The half-life of the radioactive element unobtanium-37 is 5 seconds. If 80 grams of unobtanium-37 are initially present, how many grams are present after 5 seconds? 10 seconds? 15 seconds? 20 seconds? 25 seconds? The amount left after 5 seconds is 40 grams. The amount left after 10 seconds is grams.

Enter your answer in the provided box. A sample of carbon monoxide occupies 7.36 L at 296.0 K and 772 torr. Find its volume at -47°C and 417 torr.

Enter your answer in the provided box. If 1.97 × 10-3 mol of argon occupies a 96.3-mL container at 31°C, what is the pressure (in torr)?

Solve using the elimination method. Also determine whether the following system is consistent or inconsistent and whether the equations are dependent or independent. 12x - 10y = 3 6x - 5y = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is one solution. The solution of the system is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions of the form (x.). (Simplify your answer.) C. There is no solution. Choose the correct type of solution below. consistent and dependent consistent and independent inconsistent and independent

Enter your answer in the provided box. A sample of sulfur hexafluoride gas occupies 7.97 L at 242°C. Assuming that the pressure remains constant, what temperature (in °C) is needed to reduce the volume to 3.18 L? Report your answer to the proper number of significant figures.

Jose wants to cover his rectangular bathroom floor in tile. The floor measures 3 units by 5 units. Each tile is 1 square unit and costs $4. How much will it cost Jose to cover his entire bathroom floor in tile? Choose 1 answer: A $15 B $20 C $45 D $60

Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures 1.5 radians, what is the length of the curved border? A. 5 yds B. 7.5 yds C. 2 yds D. 0.5 yds

A rectangular prism is changed by doubling its length, halving its width, and tripling its height. How will these changes affect its volume? [Hint: draw a picture] A. The volume is multiplied by 6. B. The volume is multiplied by 3. C. The volume is increased by 3. D. The volume is doubled.

4.2.1: You have saved $400, $350, and $340 so far. After your next and final week of saving, you want to have saved an average of $375 per week. How much do you have to save to get a four week average of $375 per week?

A piece of string that is 132 inches long is cut into 3 pieces. The second piece of string is twice as long as the first piece. The third piece of string is three times as long as the first piece. Find the length of the longest piece of string.

Points A and B are on opposite sides of a lake. A point C is 81.3 meters from A. The measure of angle BAC is 78.33°, and the measure of angle ACB is determined to be 34.167°. Find the distance between points A and B (to the nearest meter). A. 54 m B. 49 m C. 35 m D. 25 m

What is the circumference of a circle whose radius is 13? A. 26 B. 13 C. 13π D. 26π

13. Which steps would transform the parent function f(x) = x to f(x) = -2(x-4)² + 5? a. Reflect across the x-axis, stretch by a factor of 2, translate 4 units to the right and up 5 units. b. A stretch by a factor of 2, translate 4 units to the left and up 5 units. c. Reflect across the x-axis, stretch by a factor of 2, translate 4 units to the left and down 5 units. d. Reflect across the x-axis, stretch by a factor of 2, translate 4 units to the left and up 5 units.

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a $90,000 loan. Option 1: a 30-year loan at an APR of 7.65%. Option 2: a 15-year loan at an APR of 7.25%. Find the monthly payment for each option. The monthly payment for option 1 is $638.56. The monthly payment for option 2 is $ 821.58 (Do not round until the final answer. Then round to the nearest cent as needed.) Find the total amount paid for each option. The total payment for option 1 is $ The total payment for option 2 is $ (Use the answers from the previous step. Round to the nearest cent as needed.)

Solve the following system of equations. 5a - 30b= 3 10a + 30c = 34 60b + 20c = 22 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is one solution. The solution is (Type integers or simplified fractions.) B. There are infinitely many solutions. The solutions are (, ,c). (Type integers or simplified fractions.) C. There is no solution.

Answer parts a through c based on a study showing that late in the semester, procrastinating students reported more symptoms of physical illness than their nonprocrastinating peers. a. At the beginning of the semester, procrastinators reported an average of 2.75 symptoms, increasing at a rate of 0.35 symptoms per week. Write a function that models the average number of symptoms after x weeks. y= 2.75 +0.35x (Use integers or decimals for any numbers in the expression.) b. At the beginning of the semester, nonprocrastinators reported an average of 3.75 symptoms, increasing at a rate of 0.15 symptoms per week. Write a function that models the average number of symptoms after x weeks. y= 3.75 +0.15x (Use integers or decimals for any numbers in the expression.) c. By which week in the semester did both groups report the same number of symptoms of physical illness? For that week, how many symptoms were reported by each group? By week in the semester both groups reported the same number of symptoms of physical illness. Each group reported symptoms.

A baseball player hit 59 home runs in a season. Of the 59 home runs, 17 went to right field, 21 went to right center field, 8 went to center field, 12 went to left center field, and 1 went to left field. (a) What is the probability that a randomly selected home run was hit to right field? (b) What is the probability that a randomly selected home run was hit to left field? (c) Was it unusual for this player to hit a home run to left field? Explain.

The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 146. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 12. Ten more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.

You need a loan of $155,000 to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices. Choice 1: 15-year fixed rate at 5% with closing costs of $2400 and no points. Choice 2: 15-year fixed rate at 4.5% with closing costs of $2400 and 4 points. What is the monthly payment for choice 1? $1,225.73 (Do not round until the final answer. Then round to the nearest cent as needed.) What is the monthly payment for choice 2? $1,185.74 (Do not round until the final answer. Then round to the nearest cent as needed.) What is the total closing cost for choice 1?

12. An object is launched at 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is h(t) = -4.91² + 19.6t+ 58.8, where his in meters. When does the object strike the ground? a. t= -2 sec and t = 6 b. t=0 sec c. t = 2 sec d. t = 6 sec

The coordinates of three vertices of parallelogram ABCD are A(-3,-2), B(0,2), and C(2,2). What are the coordinates of vertex D? A. (1,-2) B. (1,2) C. (-1,2) D. (-1,-2)

Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 80 yd from B and 104 yd from A, with angle ACB measuring 51.2°. How far apart are A and B (to the nearest yard)? A. 82 yards B. 109 yards C. 100 yards D. 101 yards

What is the radius of a circle whose circumference is 36π? A. 36 B. 12 C. 18 D. 9

The exponential model A = 520.1e0.006 describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was million.

The Tennis Club has 5 new members. Each member buys a racket and a tube of balls. If 6 rackets cost $186.00 and 6 tubes of balls cost $27.00, how much do the 5 people pay for rackets and balls?

The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find the area of the triangle. A. 496.08 ft² B. 153.45 ft² C. 494.35 ft² D. 107.24 ft²

What is the circumference of a circle (to the nearest whole number) whose diameter is 12? A. 12 B. 19 C. 38 D. 113

When estimating a population mean, are you more likely to be correct when you use a point estimate or an interval estimate? Explain your reasoning. Choose the correct answer below. A. If n ≤30 an interval estimate is more accurate. If n > 30 a point estimate is more accurate. B. You are more likely to be correct using a point estimate because an interval estimate is too broad and contains many possible values. C. You are more likely to be correct using an interval estimate because it is unlikely that a point estimate will exactly equal the population mean. D. There is no difference between an interval estimate and a point estimate in terms of accuracy.

Suppose you want to borrow $95,000 and you find a bank offering a 20-year loan with an APR of 5%. a. Find your regular payments if you pay n = 1, 12, 26, 52 times a year. b. Compute the total payout for each of the loans in part (a). c. Compare the total payouts computed in part (b). a. The payment for n = 1 would be $ 7,623.05. The payment for n = 12 would be $ 626.96. The payment for n = 26 would be $289.18. The payment for n = 52 would be $144.55. (Do not round until the final answer. Then round to the nearest cent as needed.) b. For n = 1, the total amount paid is $, for n = 12, the total amount paid is $, for n = 26, and for n = 52, the total amount paid is $ the total amount paid is $ (Round to the nearest dollar.)