Basic Math Questions and Answers

Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (°F), as the explanatory variable and the number of ice bags sold that day as the response variable. The least squares regression (LSR) line for the data is Y = -135.99 + 2.46X. On one of the observed days, the temperature was 82 °F and 70 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line, Ỹ, when the temperature is 82 °F. Enter your answer as a whole number, rounding if necessary.

Which of the following multiplication problems yield a product that is a rational number? Select TWO that apply. A-2x =5/7 B 2/5x3√2 c 2π X 1/3 5 x -3

You rent an apartment for the academic year (two semesters) with three of your college friends. The rent for the entire academic year is $10,000. Each semester you receive a bill for your share of the rent. If you and your friends divide the rent equally, how much must you pay each semester?

Pedro wants to make a square pen for his goats. He plans that the pen will have a perimeter of at most 60 ft and that a side of the pen will be at least 10 ft long. He has enough money to buy fencing for a pen as large as 40 ft on a side. a. The inequality 4n ≤ 60 models the amount of fence Pedro will use for a pen with side length n ft. Which values from 10 to 40 are solutions of the inequality? Write your answer using two inequalities. b. What do the solutions mean about the amount of fence Pedro will buy?

Until recently, the Zika virus was a rare and mild public health concern and little was known about it. In early 2015, Brazil reported an epidemic of Zika viral infection. Reports soon followed of unusual numbers of neurological disorders such as microcephaly in newborns, a condition characterized by a very small head and poor brain growth. (a) Explain why we cannot conclude from this information alone that Zika infections cause microcephaly in newborns. Select the correct choice from the options. We can conclude causality due to the sheer size of the study. There may be a lurking variable that is causing an increase in both Zika infections and microcephaly in newborns. It may not be Zika virus itself causing the increase of microcephaly in newborns. Some Brazilians are known carriers of the Zika virus, and this prevents us from drawing any conclusions. Correlation and regression lines describe only linear relationships, so no conclusions can be drawn.

Graph the following equation in a rectangular coordinate system. 6x+36=0 Use the graphing tool to graph the line.

A township buys a new asphalt road paver. The paver costs $50,500. The value of the paver decreases each year after purchase. Eventually, it decreases so much in value that it can only be sold for $2,500 for parts.

Which expression is equivalent to 6(x-4)? -6x +4 6x-4 6x-24 -6x + 24

Solve the compound inequality. 2x+4≥-8 and 4x+3<-5 Graph the solution on the number line.

Round the following numbers to the nearest integer. a. 2.22 b. 348.087 c. 10,672.4 d. - 18.2949 a. The number 2.22 rounded to the nearest integer is 2. b. The number 348.087 rounded to the nearest integer is c. The number 10,672.4 rounded to the nearest integer is d. The number - 18.2949 rounded to the nearest integer is

Amy and her husband, Richie, have a joint bank account. Amy and Richie get paid on different days. Amy got paid first and then Richie got paid second. We know that it does not matter in which order they get paid. What property of addition describes this fact?

a.Rewrite the equation 16x-4y-16=0 in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function.

A plane traveling at 300 mph is flying with a bearing of 30°. There is a wind of 50 mph from the south. If no correction is made for the wind, what are the final bearing and ground speed of the plane?

Solve for y, where y is a real number. 3√y=-3

As the 17th century wore on, regional differences continued to crystalize, most notably the continuing rigidity of Puritanism. the use of indentured servants. the importance of slave labor in the South. loyalty to England. the breaking of the Atlanta economy.

Write p2. p without exponents. p2.p= Fill in the blank. p2.p=

Solve for v, where v is a real number. 4√v=-4

Solve for w, where w is a real number. w1/4 = -2 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". W =

What are the degree and leading coefficient of the polynomial? -y6+18y² +20+5y

Suppose that you have $6500 to invest, and you invest x dollars at 12% and the remainder at 8%. Write expressions in x that represent the following values. (a) the amount invested at 8% (b) the interest earned on the x dollars at 12% (c) the interest earned on the money invested at 8% (d) the total interest earned

Graph the solution to the inequality on the number line. |w| > 2

Diane bought new headphones originally listed for $70.99. They are 25% off. Which equation can be used to find the amount Diane will save? Choose one 5 points x = .25(70.99) x = 1.25 (70.99) x = 25 (70.99) x = .75(70.99)

Find the midpoint of the line segment with endpoints (4, -2) and (8,-6).

Your grade in the class consists of 2 midterms 15% each, homework 10%, projects 5%, attendance 10%, and final 30%. Find the weighted mean if your scores are as follows in the class. Midterm 1:85 Midterm 2:90 Final: 80 Homework: 95 Project: 100 Attendace: 75 What is the sum of the weights that is find w=?

"There are up to five cookies left." Let c = the number of cookies left c>5 c<5 c≥5 c≤5 c-5

Life expectancy in a country can be approximated with the equation L = 28x0.24 where x is the number of years that the birth year is past 1900. (a) Express this equation with radical notation. L = (b) Use the equation to estimate the life expectancy for a person born in 2019. (Round your answer to one decimal place.)

Solve for y, where y is a real number. y 1/4=3

Solvex=63, where x is a real number. Simplify your answer as much as possible.

Identify the set of values x for which y will be a real number. y=√x-18

Choose the correct translation of the following into symbolic algebra: "five cookies less than the number of cookies left" Let c = the number of cookies left O c>5 Oc<5 O c25 O cs5 O c-5

2 The area of a rectangle is 21 ft², and the length of the rectangle is 1 ft less than double the width. Find the dimensions of the rectangle.

The year that you enter college, your freshman class consists of 760 students. According to statistical studies, about of these students will actually graduate. Approximately how many of 7 your classmates will receive their degrees?

Carry out the indicated operation and give your answer with the specified number of significant digits. 43 x 32.1; 3 significant digits 43 x 32.1≈ (Simplify your answer.)

Solve (w-5)³-48 = 0 where w is a real number. WZL-

2 What are the first two steps to graph y=x+4? What is the first step? A. Plot the point (4,0). Plot the point (0,4). B. OC. Plot the point (3,2). OD. Plot the point (2,3). What is the next step? O A. From this point, move 2 units up (the rise) and 3 units to the right (the run). OB. From this point, move 3 units down (the rise) and 2 units to the left (the run). 2 OC. From this point, move 4 units up (the rise) and units to the right (the run). 3 OD. From this point, move 3 units up (the rise) and 2 units to the right (the run).

Solve for u, where u is a real number. 3=√√2u+15 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

A rental truck costs $45.45 for a day plus 74¢ per mile. (a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the truck for a day. C = X (b) Find the.total.cost of the rental if it was driven 194 miles. C = $ * Enter a number.

Give the slope and y-intercept of the line whose equation is given. Then graph the linear function. 3 f(x) = 5x-7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The slope is ***** (Simplify your answer. Type an integer or a fraction.) OB. The slope is undefined.

A silver dollar is dropped from the top of a building that is 1346 feet tall. Use the position function below for free-falling objects. s(t) = -16t² + vt + so (a) Determine the position and velocity functions for the coin. s(t) = -161² 1346 v(t) = -32t (b) Determine the average velocity on the interval [1, 2]. -48 ft/s (c) Find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = -32 ft/s V(2) = ft/s -64 (d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.) t = 9.17 S (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) 9.147 ft/s

Solve (w+7)²-36 = 0, where w is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click "No solution."

Translate the sentence into an inequality. The difference of twice a number and 10 is greater than or equal to -29. Use the variable b for the unknown number.

The length of a rectangle is 9 yd more than twice the width x. The area is 396 yd². Part 1 of 3 (a) Write an equation in terms of x that represents the given relationship. The equation is xx + 9x (yd) = 396(yd) Part: 1/3 Part 2 of 3 ☐=0 The width is X (b) Solve the equation to find the dimensions of the given shape. yd.

Select the answer that best completes the given statement. The graph of the equation x= 1 is a/an line. standard horizontal undefined vertical regression

Solve your equation in the previous step for y. y = 20- 60-x 3 X P(x) = 3 Step 3 The product P of the two numbers is xy. Use your result from the previous step to write the product as a function of x only. 60x-x² 3 (60-x)x Step 4 Rewrite P(x) by completing the square. P(x) = -1/3 ✔ -1/3 (x-30 30 X )² + 300✔✔ 300) Step 5 Use your result from the previous step to complete the following statements. The maximum value of the product, occurring at the vertex of the graph of P(x), is X. This maximum occurs when x = 30 , and y = Therefore, what are the two numbers? (Enter your answers as a comma-separated list.) 4 X.

Solve for x, where x is a real number. -3 = √2x+6-1 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Use a graphing utility to graph the function and find the absolute extrema of the function on the given interval. (If an answer c not exist, enter DNE.) f(x) = minimum maximum 5 x - 2 (x, y) = (x, y) = (2,7]

Translate the sentence into an inequality. Two times the sum of a number and 16 is at least -21. Use the variable w for the unknown number.

The growth of a company can be described by the equation N = 700(0.06)0.st where t is the number of years the company has been in existence and N is the number of employees. (a) What is the number of employees when t = 0? (This is the number of employees the company has when it starts.) N = employees (b) What is the number of employees when t = 8? (Round your answer to the nearest whole number.) N = employees

You need a 85% alcohol solution. On hand, you have a 65 mL of a 30% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?

A company reimburses its sales representatives $150 per day for lodging and meals plus 37¢ per mile driven. Write a linear equation giving the daily cost C to the company in terms of x, the number of miles driven. How much does it cost the company if a sales representative drives 221 miles on a given day? $ 231.77