Basic Math Questions and Answers

Use substitution to solve the system. 3x - 6y = 12 - 3x + y = -4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ○ A. The solution is ▢ (Simplify your answer. Type an ordered pair.) ○ B. There are infinitely many solutions. ○ C. There is no solution.

Use the law of sines, the law of cosines, or the Pythagorean Theorem to solve ∆ABC Round to one decimal place where necessary. (A) C = 90°, a = 7, b = 11 (B) A = 32.5°, B = 57.5°, c = 13 (C) A = 39.4°, B = 85.9°C = 54.7 (D) A = 40.3°, B = 49.7°C, c = 13 (E) no triangle is formed.

If121 people attend a concert and tickets for adults cost $53.75 while tickets for children cost $3.5 and total receipts for the concert was $440.25, how many of each went to the concert?

A football team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $8, deluxe for $3, and regular for $1. The total number of tickets sold was 155, and the total amount of money from raffle tickets was $409. If 19 more deluxe tickets were sold than premium tickets, how many premium tickets were sold?

Evaluate the sum. 12 ∑ (-5-6i) i=4

10 candies cost 100 cents. Which of the following equations will lead you to find the cost of a candy (x)? O 10^x = 100 O x+10 = 100 O x-10 = 100

Graph the solution of the system of linear inequalities. 3x-2y ≤ 6 y ≤ -3

A teacher administers a test to his class of 30 students. The mean score (out of 100 possible points) is 80. From previous studies, you know the population standard deviation is 6. Using the sample data given, calculate a 90% confidence interval for the population mean. (A) 75 - 78 (B) 77 - 83 (C) 78 - 82 (D) 75 - 85

Mr. Hanes, the manager of the local movie theatre, found that the more people attended the movies, the larger his daily bank deposit. a): Can Mr. Hanes conclude that larger attendance results in larger bank deposits? b): Explain.

A water tank that holds 500 gallons and leaks 1/2 gallon of water every hour. (A) What is the rate of change for the function that models the number of gallons in the tank for a given number of hours? (B) Write an equation that represents this function.

Blake is going to invest $34,000 and leave it in an account for 9 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Blake to end up with $50,000?

You deposit $100 each month into an account earning 8.5% interest compounded monthly. How much total interest will you earn after 30 years? a)$129,070.58 b)$165,070.58 c)$36,000 d)$82,623.82

Daniel is going to invest $860 and leave it in an account for 14 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, would be required in order for Daniel to end up with $1,060?

A rare isotope of a nuclear material is very unstable, decaying at a rate of 14% each second. Find how much isotope remains 11 seconds after 5 grams of the isotope is created.

Find the distance between the points (-4, 9) and ( -8,1).

Use the given equivalents, along with dimensional analysis, to convert the given unit to the unit indicated. 87 lb to g

In 2001, the mouse population in a park was measured to be 4,860. By 2009, the population was measured again and was found to be 5,980. Assume the population continues to change line (a) Find a formula for the moose population, P, since 2001. (Let t represent the number of years since 2001.) P(t)=_____ (b) What does your model predict the moose population to be in 2023? _______moose

Convert to Fahrenheit. Use the formula F=(9/5)+C+32 61°C=______ F

Find the restricted values of x for the following rational expression. If there are no restricted values of x, indicate "No Restrictions" (-3x^2 - 6)/6x

Consider the circles shown to the right. Assume one circle is selected at random and each circle is equally likely to be selected. Determine the probability of selecting the number 2, given that the circle is green. 1 2 4 5 6 7 green orange green yellow yellow green The probability of selecting the number 2, given that the circle is green, is_______. (Type an integer or a simplified fraction.)

Assume that a hat contains four bills: a $1, a $ 5, a $10, and a $20 bill. Two bills are to be selected at random with replacement. Find the probability that both bills are $20 if the first selected is a $20 bill? The probability that both bills are $20 if the first selected is a $20 bill is ________. (Simplify your answer. Type an integer or a fraction.)

Suppose tan(a) = 5/8, where 0 ≤ a ≤ π/ 2. The least solution to tan(3x) = 5/8 in [0, 2π) is x = The greatest solution to tan(3x) = 5/8 in [0, 2π) is x =

Bryce got a job selling glow sticks at the local fairground. He is paid a fixed amount of $480 per week plus $0.82 per item sold. This is represented by the equation P= 0.82n + 480 where P is the amount he is paid for the week and n is the number of glow sticks he sold. a)How much will Bryce be paid if he sells 340 glow sticks? If Bryce sells 340 glow sticks, he will earn $_____for the week. b)How many glow sticks did Bryce sell if he earned $1,177.00? If Bryce has earned $1,177.00, he sold_______glow sticks.

Some checking accounts pay a small amount of interest on the money in the account. In this case, interest is money that is paid to the account holder by the financial institution issuing the checking account. The interest is a percentage of the amount of money in the account. The percentage is called the annual percentage rate. Heather has $1,000 to deposit in an account for 1 year. Compare the following two offers. (A) Bank of Avalon pays 0.7% with no annual fee. (B) Cypress Savings pays 1.3% but charges a $10 annual fee. Which is the better offer?

Use the distributive property to help simplify the numerical expression 8√8 - 8√18 into the form A√C, where A and C are integers.

Let Xn+1 =1.2Xn + 29 be a linear DDS. a) Calculate the equilibrium value for this DDS. b) Suppose the initial value is x₀ = 66. Find the explicit solution. c) Determine the stability of the equilibrium. Choose the correct answer. The equilibrium of this system is Select an answer because (A) the slope is negative. (B) the slope in absolute value is less than 1. (C) the slope in absolute value is greater than I. (D) the slope is positive.

Solve the compound inequality. 0≤2x-5≤7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A). The solution set is_________ B). The solution set is Ø.

Solve the compound inequality. x+8≥8 and x +4≤3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The solution set is ___. (Type your answer in interval notation. Simply your answer. Use integers or fractions for any numbers in the expression) B. The solution set is Ø.

Suppose a computer processor can perform about 3.3 billion operations per second. How many operations can it perform in 0.1 second? It can perform about ______ operations in 0.1 second. (Type a whole number.)

Minimize P subject to the given constraints. P = 16x + 2y constraints x ≥ 0 y ≥ 0 x + 2y ≥ 8 2x + y ≥ 8 a. P =16 at (0, 8) b. P = 8 at (0, 2) c. P = -32 at (-2, 0) d. none of these

You have a summer job that pays time and a half for overtime. That is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal hourly wage of $7. Is the slope an increasing or decreasing rate of change? What does this mean in the context of this situation?

Determine whether the statement mekes sense or does not make sense, and explain your answer. I factored 48x² -196 completely and obtained (7x +14)(7x -14). Choose the correct answer below. (A) It makes sense. Because 49x²-196 is the difference of two squares so the factors are (7x +14)(7x -14). (B) It does not make sense. Because (7x +14)(7x -14) is not completely factored and the complete factors are (7x +14)(7x +14). (C) It does not make sense. Because (7x+ 14)(7x- 14) is not completely factored and the complete factors are (7x -14)(7x -14). (D) It makes sense. There is no common factor in (7x+ 14) and (7x - 14) so these are completely factored.

At what interest rate must $4,800 be compounded annually to equal $8,109.499 after 9 yr?(Round to the nearest percent.) A. 8% B. 7% C. 5% D. 6%

The Family Fine Arts Center charges $22 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 436 people paid admission, the total receipts were $5788. How many who paid were senior citizens? (A) 227 senior citizens (B) 119 senior citizens (C) 209 senior citizens (D) 317 senior citizens

Use the model A = Pe^rt or A = P( 1 + r/n )^nt, where A is the future value of P dollars invested at interest rate r compounded continuously or n times per year for t years. If a couple has $200,000 in a retirement account, how long will it take the money to grow to $1,000,000 if it grows by 6% compounded continuously? Round up to the nearest year.

Solve by the elimination method. 4x - y = 1 x + 3y = 10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

An artist creates a right prism whose bases are regular decagons. He wants to paint the surface of the prism. One can of paint can cover 32 square feet. How many cans of paint must he buy if the height of the prism is 11 ft and the length of each side of the decagon is 2.4 ft? Make sure to round to the nearest whole can.

Solve the rational equation. If the equation has no solution, so state. 32/(x² - 25) + 8/(x + 5) = 4/(x - 5) (A) The solution set is { } (B) There are infinitely many solutions. (C) There is no solution.

Graph the linear equation. f(x) = -(1/3)x. Use the graphing tool to graph the equation.

The demand equation for a certain product is 8p² +5q² = 1400, where p is the price per unit in dollars and q is the number of units demanded. (a) Find and interpret dq/dp. (b) Find and interpret dp/dq. (b) How is ap/dq calculated? A. Use implicit differentiation. Differentiate with respect to q and assume that p is a function of q. B. Use implicit differentiation. Differentiate with respect to q and assume that q is a function of p. C. Use implicit differentiation. Differentiate with respect to p and assume that p is a function of q. D. Use implicit differentiation. Differentiate with respect to p and assume that q is a function of p. Find and interpret dq/dp, Select the correct choice below and fill in the answer box to complete your choice.

The height of a cylinder is three times the diameter of the base. The surface area of the cylinder is 126π ft^2? What is the radius of the base?

Solve the compound inequality. - 2x < -8 and x-4 <5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set of the compound inequality is ___ . (Type your answer in interval notation.) B. The solution set is Ø.

Use Gauss-Jordan elimination to find the solution to the following system of equations. 9x + 20y + 4z = 11 4x + 9y + 3z = -3 X+ 2y – 2z = 5 Select the correct choice below and fill in any answer boxes within your choice. A) There is one solution. The solution is x= ______, y= _____and z= ______. (Simplify your answer.) B) There are infinitely many solutions. If z is any real number, x= _____ and y= _______. (Type an expression using z as the variable.) C) There is no solution.

A company uses two vans to transport workers from a free parking lot to the workplace between 7:00 and 9:00 a.m. One van has 5 more seats than the other. The smaller van makes two trips every morning while the larger one makes only one trip. The two vans can transport 65 people, maximum. Let x be the seats in the small van and y the seats in the large van. How many seats does the larger van have?

Pythagoras and Esky both put $400 into a bank at the same time. Pythagoras's bank calculates 5% interest compounded annually. Esky's bank compounds continuously using 4.5% interested. Who will have more after 10 years and by how much? Pythagoras will have $24.24 more Esky will have $24.24 more Pythagoras will have $21.24 more Esky will have $36.15 more

Solve the compound inequality. -2x≤-8 or 7x-21≥21 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A). The solution set is _____. B). The solution set is Ø.

Consider the quadratic equation y = x² + 2x + 9. Complete the square to express the quadratic in standard form y = a(x – h)²+k a =_______ h =_______ k =_______

Oliver wants to have $13,000 in 15 years after investing in an account that earns 4.2% compounded quarterly. How much should he invest?

Write an algebraic expression to represent each of the scenarios below. Your answers must be simplified completely. Scenario Algebraic Expression a)Sales tax is currently 9.1 %. Write an algebraic expression to represent the total amount paid for an item that costs D dollars after tax is added to the purchase. b)A store is having a 45% off sale. Write an algebraic expression to represent the sale price for an item that is originally priced at D dollars. c)Carmen receives a 3% raise every year. Write an algebraic expression to represent Carmen's salary after one year if her current salary is S dollars. d)Let B represent the bill for dinner at your favorite restaurant. You decide to leave a 18% tip. Write an algebraic expression to represent the total amount paid for dinner, including tip.

Fill in the blank with the appropriate word. A group that also satisfies the commutative property is called a(n)___________ (or abelian) group. A group that also satisfies the commutative property is called a(n) __________ (or abelian) group. → finite → commutative → associative → infinite