Basic Math Questions and Answers

Which polynomial represents the difference below? (5x^7 +9x^4+3)-(x^4-3x) A. 5x^7 + 8x^4+3x+3 B. 4x^7 + 8x^4 -3x+3 C. 4x^11 +8x³ +3 D. 8x+6

Which of the following is the correct factorization of the polynomial below? 8x3 +64y3 A. (4x+4y)(2x+8y) B.(2x+4y)(4x²-8xy+16y²) C. (4x+2y)(4x²-2xy + 16y²) D. The polynomial is irreducible.

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds. A) .9893 B) .0107 C) .5107 D) .4893

Part C: Write and solve a system of inequalities to model the following situation: An acting company is holding a performance in an arena. They are selling student tickets for $2 and adult tickets for $4. The arena can hold at most 200 people (students and adults). No more than 25% of the people should be adults. The company is hoping to make at least $400 in ticket sales. How many student tickets and how many adult tickets should be sold to maximize the amount of money earned?

The population of a certain city was 4,192 in 2002. It is expected to decrease by about 0.38% per year. Write an exponential decay function, and use it to approximate the population in 2022. The exponential decay function where f(x) is the population of the city x years after 2002 is f(x) = The approximate population of the city in 2022 will be (Round to the nearest whole number as needed.)

Describe and correct the error a student made in identifying the growth or decay factor for the function y = 2.55(0.7)^x Choose the correct answer below and fill in the answer boxes to complete your choice. (Type integers or decimals.) A. The student incorrectly identified the decay factor. The rate of decay is so the decay factor is B. The student incorrectly identified the base. The base is decay factor is , so the C. The student incorrectly identified the function as exponential decay. It represents exponential growth. The rate of growth is so the growth factor is D. The student incorrectly identified the base and incorrectly identified the function as exponential decay. The base is____ So, the rate of growth is___and the growth factor is

Which of the following statements is true? The sum of the exterior angles of a triangle is 360°. The exterior angle at each vertex of a triangle is equal to the sum of the interior angles at the other two vertices. The sum of the interior and exterior angles at any one vertex of a triangle is 180°. All of these.

The area of a rug is represented by the following expression, x² + 4x-12, which of the following expressions represents the width of the rug if the length is x+6. (A ) x-6 (B) x+2 (C) x -2 (D) x+6

Write the contrapositive and negation of the statement. If it is not raining then I will drive. contrapositive: If it is raining then I will not dive. negation: It is raining and I will drive. contrapositive: If I will drive then it is not raining. negation: If it is not raining then I will not drive. contrapositive: If I will not drive then it is raining. negation: It is not raining and I will not drive. contrapositive: If I will not drive then it is not raining. negation: If it is not raining then I will not drive.

Find the sum and enter it in the box below. Enter your answer as a polynomial in descending order, and use the caret (^) for exponents. For example, you would write 4x² as 4x^2. x^5+2x³ +2x² +6x+3 + -3x -3x4 +2x³ +6x

The equation below specifies a function. Determine whether the function is linear, constant, or neither. 2x+3y=7 Choose the correct answer below. A. A constant function is specified by the equation. B. Neither a constant function nor a linear function is specified by the equation. C. A linear function is specified by the equation.

A person places $1380 in an investment account earning an annual rate of = 8.6%, compounded continuously. Using the formula V Pert, where Vis the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 10 years.

One hundred students out of 1200 at a school have been surveyed. Predict the number of students in the population that would answer similarly. Fourteen said they had an after-school job. 114 students 168 students 8571 students 147 students

A boy flying a kite lets out 300 feet of string which makes an angle of 38° with the ground. Assuming that the string is straight, how high above the ground is the kite?

Suppose a city with population 600,000 has been growing at a rate of 6% per year. If this rate continues, find the population of this city in 20 years. The population in 20 years will be approximately (Round to the nearest whole number as needed.)

2) Jasmine is selling fruit for her youth group fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. During the first week, Jasmine sold 14 small boxes and 12 large boxes of oranges for a total of $306. During the second week, Jasmine sold 14 small boxes and 2 large boxes of oranges for a total of $156. What is the cost of a small box of oranges and the cost of a large box of oranges? Let x = Let y = Equation 1: Equation 2: Solution: A small box costs and a large box costs

Determine whether the function represents exponential growth or decay. Write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay. y = 12,600(9/10)x The function y = 12,600(9/10)x represents exponential Rewriting the base in terms of the rate of growth or decay results in the function y = 12,600 ()x In this function, r = which indicates that the value of yby % each time period.

The population of a certain city was 4,229 in 2005. It is expected to decrease by about 0.34% per year. Write an exponential decay function, and use it to approximate the population in 2028. The exponential decay function where f(x) is the population of the city x years after 2005 is f(x) =

Use the information to answer the following question. A rectangular garden has a length that is 3 feet longer than its width. Let w represent the width of the garden in feet. The entire garden is surrounded by a 2-foot-wide cement walkway. What does the algebraic expression (w + 4)(w + 7) represent in this context? A. the perimeter of the walkway only B. the perimeter of the garden only C. the area of the garden only D. the total area of the garden and walkway

15. What is the volume of a pyramid with a height of 10 units and a rectangular base with dimensions of five units by nine units? A. 55 cubic units B. 150 cubic units C. 300 cubic units D. 450 cubic units

Suppose $12000 is invested at 6% interest compounded continuously. How long will it take for the investment to grow to $24000? Use the model A(t) = Pert and round your answer to the nearest hundredth of a year. It will take years for the investment to reach $24000.

A person receives gifts for her 18th birthday totaling $750. She also saved 5 points $1,500 from her summer job and keeps the money at home in a safe place. She wants to buy a car when she turns 21. She has a part-time job and plans to work full time next summer and save most of that money. She has a monthly cell phone bill and a credit card that she uses for emergencies and then pays the bill in full each month. Which of the following is the most financially wise recommendation for her when it comes to opening bank accounts at this time? She should open a checking account with $1,000 and keep the rest of the money in cash at home for emergencies. She should put $1,500 in a two-year CD, $600 in a checking or NOW account, and keep $150 in cash. She should put $2000 in a five-year CD and open a checking account with the $250 left. She should put $750 into a savings account, $1,000 into a checking account, and keep $500 in cash at home for emergencies.

The Drama club is selling tickets to a theater performance. On the first day of ticket sales the club sold 8 adult tickets and 8 student tickets for a total of $184. The club took in $100 on the second day by selling 1 adult ticket and 8 student tickets. Find the price of each adult ticket and the price of each student ticket. Let x = Let y = Equation 1: Equation 2:

Cindy found a collection of baseball cards in her attic worth $8,000. It is estimated to increase in value by 1.5% per year. Write an exponential growth function and find the value of the collection after 7 years. The exponential growth function that represents this situation is f(x) = . (Simplify your answer.)

The diameter of a circle is 13 m. Find its area to the nearest tenth. A = m2

Which polynomial represents the difference below? ²-3x+10-(9x8+4x) A. 8x¹+x+10 B. -9x¹5+x²+x+10 C. 10x¹5 + 12x+10 D. -9x8+X7-7X+10

What steps do you need to take to solve the equation 1/2x+6=18? Choose the correct answer below. A. Add 6. Then, multiply by 2. B. Subtract 6. Then, divide by 2. C. Add 6. Then, divide by 2. D. Subtract 6. Then, multiply by 2.

Find the sum: (x ^8 + 3x^6-4x^4+10x) + (2x^7-4x^5-x³ + 10). A. 2x² + 4x ^6+ 2x^5-2x^4 -5x³-x² + 17x+17 B. x^8+2x^7+3x^6 - 4x^5 - 4x^4 + x² + 9x+10 C.x^8+2x^7+3x^6-4x^5-4x^4-x³ + 10x + 10 D. 3x^7-7x^5-x² + 20

Find the sum: (x^5-2x^4+3x²-6) + (3x^4 +4x²+x+4). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write 4x² as 4x^2.

A right cylinder has a radius of 3 and a height of 8. A cone has the same radius as the cylinder. Find the height of the cone if the two have the same volume.

Which of the following would produce a similarity transformation? Select all that apply. dilation alone translation followed by rotation rotation followed by a dilation reflection followed by rotation

The Pizza Shack discounts 20% off the regular selling price on the purchase of 3 or more pizzas. What is the sale price on the purchase of 3 pizzas that regularly sell for $10.75, $16.75, and $20.75?

You performed a simulation to examine mutation proportions. You put fifty candies in each of two bags. You hit both bags with a book to simulate a genetic mutation occurring. The first bag had five broken candles and the second bag had ten broken candies. Which statement is correct? Your sample size was too small to use the z-test to compare proportions. The proportions of candies in the bags were not statistically significantly different at the 90% confidence level. The proportions of candies in the bags were statistically significantly different at the 90% confidence level. The proportions of candies in the bag could not be determined.

Multiplying by a number flips the graph of a function over the x-axis.

Determine whether the function represents exponential growth or decay. Write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay. y=460.4^x

You are given the choice between a yearly payment of $3,405 that increases by $151 every year or a yearly payment of $3,405 that increases by 2.8% compounded annually. How much money would you make after 13 years if you chose the exponential payment? Do not include the dollar sign in your answer. Round to the nearest cent.

You have two job offers that you are considering. Offer 1: You earn a yearly salary of $47,130 that increases by $3,791 every year. Offer 2: You earn a yearly salary of $47,130 that increases by 2.4% compounded annually. How much money would you make after 21 years if you chose the linear payment? Do not include the dollar sign in your answer. Round to the nearest cent.

The diameter of a circle is 14 m. Find its area to the nearest tenth.

A test of significance with a = 0.05 results in a p-value of 0.1. What do you conclude? A. The null hypothesis is rejected. B. The null hypothesis is not rejected. C. The alternative hypothesis is not rejected. D. The null hypothesis is accepted.

A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $40 per acre. Seed for crop B costs $20 per acre. The farmer can spend at most $1600 on seed. If crop B brings in a profit of $90 per acre, and crop A brings in a profit of $60 per acre, how many acres of each crop should the farmer plant to maximize her profit?

For the line 3x - 4y -12 = 0, which statement is true? The x-intercept is 3, and the y-intercept is 4. The x-intercept is 3, and the y-intercept is -4. The x-intercept is 4, and the y-intercept is 3. The x-intercept is 4, and the y-intercept is-3.

The radius of a circle is 5 cm. Find its area to the nearest tenth.

9.) The equation y= 19x + 350 represents the relationship between the total 1 point cost, in dollars, y, to rent a banquet hall for a party, and the number of people attending, x. Select all true statements. * The y-intercept is 19. The y-intercept is 350 The slope is 350. The slope is 19. The y-intercept represents the cost per person attending. The y-intercept represents the initial cost. The slope represents the cost per person attending. The slope represents the initial cost. Y represents the total cost to rent the banquet hall.

Match the following shapes with their correct description. 1. rectangle 2. triangle 3. circle 4. trapezoid a. a slice of a rectangular pyramid perpendicular to the base but not through the apex b. the cross section of a cone parallel to the base c. the cross section of a rectangular prism perpendicular to the base d. the cross section of a triangular pyramid parallel to the base

Jacy is 12 years old and weighs 82 lb. Assume that his weight increases at a rate of 16% each year. Write an exponential function to model the increase. What will he weigh after 5 years?

21. Which of the following is the only triangle whose sides form a right triangle? A. a=2 units b=4 units c=12 units B. a=3 units b=4 units c=7 units C. a=5 units b=5 units c=√10 units D. a=2 units b=1 units c= √5 units

Tatianna is choosing what foods to eat for breakfast. Let A denote the event "at least one red food is chosen" and B denote the event "at least one piece of fruit is chosen". Which of the following represents the event "at least one food that is chose is red or at least one food that is chosen is a fruit"? a) A' ∪ B' b) A ∪ B c) A ∩ B d) A' ∩ B'

Bryan Berg built an 83-storey house of cards. He used 27000 playing cards to accomplish this feat. At this same rate, about how many cards would it take to build a 100-storey house of cards? Round your answer to the nearest integer. 30 750 44 900 2400 32 530

Which of the following best describes transformation by dilation? A dilation only enlarges the size of a figure. A dilation takes place in either a horizontal or a vertical direction. Dilations preserve size, but not shape. The pre-image and image of a dilation will remain the same shape, even if they are not the same size.

A mobile phone company determined with 95% confidence that the a teenager with a mobile phone send an average of 180 text messages 20 messages each day. Which of the following statement is most likely to be true based on the study? There is a 95% probability that every student with a mobile phone sends at least 160 messages a day. There is a 95% probability that every student with a mobile phone sends at most 200 messages a day. There is a 95% probability that the true average of text messages sent by a teenager is somewhere between 160 and 200 text messages a day. There is a 95% probability that the true average of text messages sent by a teenager is 180 text messages a day.