Basic Math Questions and Answers

Use graphing technology to find the domain of the function f(x) = √(x - 2) - 2.

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function C(x)-0.1x²-56x+24,712. How many machines must be made to minimize the unit cost? Do not round your answer.

A cookie company uses one cup of sugar for every 20 cookies it makes. Let S represent the total number of cups of sugar used, and let N represent the number of cookies made. Write an equation relating S to N, and then graph your equation using the axes below.

In a national survey conducted by the Centers for Disease Control to determine health risk behaviors among college students. Asked "How often do you wear a seat belt when driving a car"? Response frequency I do not drive a car 249 Never 118 Rarely 249 Sometimes 345 Most of the time 716 Always 3093 b) What percentage of respondents answered "Always"?

In a survey people are asked "Which brand of toothpaste do you prefer?" The data gathered from this question would be what type of data? A. categorical B. quantitative C. continuous

How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 20-foot radius?

The point P(1,0) lies on the curve y = sin(107/2). If Q is the point (z, sin(107/2)), find the slope of the secant line PQ (correct to four decimal places) for z = 2, 1.5, 1.4, 1.3, 1.2, 1.1, .5. .6, .7.8.9. (Do the slopes appear to be approaching a limit?)

A group of friends will go on a weekend camping trip and split the cost of gas equally. The cost that each person will pay for gas is inversely proportional to the number of people who go on the trip. If four friends go on the trip, each person pays $23 for gas. Write an equation that describes the relationship between cost (c) that each person pays for gas, and the number of people on the trip (n).

What is the value of the expression below when w =7 and x=6? 5w-x

Suppose the function f(t) = et describes the growth of a colony of bacteria, where t is hours. Find the number of bacteria present at 5 hours. A) 59.598 B) 148.413 C) 79.432 D) 8.155

Lily has an account that pays 3.48% simple interest per year and wants to accumulate $4,000 in interest from it over the next 12 years. How much money should Lily invest in this account to meet her goal?

Choose the measurement closest to 50 liters: 14 gal, 140 gal or 50 gal. Choose the correct answer below. 140 gal 50 gal 14 gal

Choose true or false. Explain your answer. For a dilation, corresponding angles of the image and preimage are congruent. Choose the correct answer below. A. True, because the image and preimage are congruent, so the corresponding angles are congruent. B. False, because the image and preimage are congruent, so the corresponding angles are similar. C. True, because the image and preimage are similar, so the corresponding angles are congruent. D. False, because the image and preimage are similar, so the corresponding angles are similar, not congruent.

Michael is mixing two types of candy for a party. The chocolate pieces cost $0.40 per ounce, and the hard candy costs $0.20 per ounce. How many ounces of each type of candy should he purchase if he wants a mixture that is 50 ounces and costs $0.35 per ounce?

Determine the volume and the surface area of the three-dimensional figure. Use the key on your calculator. The volume is 696.91 cm³. (Simplify your answer. Type an integer or a decimal rounded to the nearest hundredth as needed.) The surface area is (Simplify your answer. Type an integer or a decimal rounded to the nearest hundredth as needed.)

Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(p) = -4p² +12,000p. What unit price should be established for the dryer to maximize revenue? What is the maximum revenue? The unit price that should be established to maximize revenue is $ 1500 (Simplify your answer.)

A local minimum of a function is its A) largest value of the function over its entire domain. B) smallest value of the function over its entire domain. C) smallest value for a given interval. D) largest value for a given interval.

Your factory produces lemon-scented widgets. You know that each unit is cheaper, the more you produce. But you also know that costs will eventually go up if you make too many widgets due to the costs of storage of the overstock. The new head of accounting says that your cost for producing x thousands of units a day can be approximated by the formula C = 0.2x² - 4.02x + 253. Find the daily production level that will minimize your costs.

For the following stirred tank reaction, carry out the following analysis. a. Write an initial value problem for the mass of the substance. b. Solve the initial value problem. A 400-L tank is initially filled with pure water. A copper sulfate solution with a concentration of 20 g/L flows into the tank at a rate of 2 L/min. The thoroughly mixed solution is drained from the tank at a rate of 2 L/min.

A principal of $2700 is invested at 5.5% interest, compounded annually. How many years will it take to accumulate $6000 or more in the account? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

Barry is going to the movies and wants to buy drinks and candy for his friends. Drinks represent x and drinks are $3 each. Candy represents y, and candy is $6 each, Barry has $24 total to spend. Which equation below in Standard Form represents the situation. (Standard Form: Ax+ByC) 3x+2y=6 6x + 3y - 24 24x+6y=3 3x+6y=24

Consider the following implication: "If you drink coffee then you won't be able to sleep." Which of the following is the contrapositive of this statement? If you can't sleep then you drank coffee. If you can sleep then you didn't drink coffee. If you don't drink coffee then you will be able to sleep. Which of the following is the inverse of this statement? If you can sleep then you didn't drink coffee. If you don't drink coffee then you will be able to sleep. If you can't sleep then you drank coffee. Which of the following is the converse of this statement? If you can sleep then you didn't drink coffee. If you don't drink coffee then you will be able to sleep. If you can't sleep then you drank coffee.

The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at the given point. 9x² + 4xy + 6y² + 11y-9=0,(-1,0) (a) Give the equation of the line that is tangent to the curve at the given point. y = 18/7x + 18/7 (b) Give the equation of the line that is normal to the curve at the given point.

You are going to the mall with your friends and you have $200 to spend from your recent birthday money. You discover a store that has all jeans for $25 and all dresses for $50. You really, really want to take home 6 items of clothing because you "need" that many new things. How many jeans and dresses can you buy? Define your variables and show all your work below.

You are at Pie 5 ordering a one toppling pizza. You have 5 options for the crust, 4 choices for the sauce, 5 options for cheese, and 10 options for the topping. How many different pizzas can you make?

At a certain zoo, the average mass of one blue whale is measured to be,190000 kilograms. Use scientific notation to express the mass of 60 blue whales.

Which of the following is typically the least important factor to consider when conducting a statistical analysis of data? Context of the data Formula calculation Source of the data Sampling method

1) Find dy/dx for 2y² - 144 = 22² 2) Sales, x, of Michael Myers masks and their price, p, are related by p = 20. x² 4500 - 5p². If the price is decreasing at a rate of $1 per day, find the rate at which sales will change per day if

A given line has the equation 10x+2y=-2. What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y=-5x+12. 5x+y=12 y-12=5(x-0) 5x+y=-1

Find the difference. - 67x² +68x + 25) - (31x² + 49) =

At a certain zoo, the average mass of one elephant is measured to be 3800 kilograms. Use scientific notation to express the mass of 160 elephants.

You give a test to 100 students and determine the median score. After grading the test, you realize that the 10 students with the highest scores did exceptionally well. You decide to award these 10 students a bonus of 5 more points. The median of the new score distribution will be that of the original score distribution. A. lower than B. equal to C. higher than D. depending on skewness, higher or lower than

Find the sum. (36x5 + 21x³ - 15) + (7x5 + 15x³ + 25) =

You look at an ant under a magnifying glass. Find the actual length of the ant. The image of the ant is 5 times the ant's actual size and has a length of 2.5 cm. The ant's actual length is (Type an integer or a decimal)

The sum of 36 times a number and the reciprocal of the number is positive. Find the numbers which satisfy this condition.

An engineer measured the dimensions for a rectangular site by using a wooden pole of unknown length x. The length of the rectangular site is 2 pole measures increased by 3 feet, while the width is 1 pole measure decreased by 4 feet. If the perimeter of the site is 70 ft., what are the real dimensions of the site?

Find the vertex and axis of symmetry of the quadratic function. (b) Determine whether the graph is concave up or concave down. (c) Graph the quadratic function. g(x) = -2(x - 2)² +1 (a) The vertex is (2,1). (Type an ordered pair.) The axis of symmetry is (Type an equation.)

Find the amplitude, the period, any vertical translation, and any phase shift of the graph of the following function. y=8-sin 6x + ( 6x + π/4) What is the amplitude of the function? (Type an integer or a simplified fraction.) *****

Last year 762 students voted in the student council election at San Bruno Middle School. This year 721 students voted. What was the percent of change in the number of students that voted to the nearest tenth?

For the equation x/3 = 15, a student found the value of x to be 5. Complete the explanation of the error. What is the correct answer?

A party rental company has chairs and tables for rent. The total cost to rent 12 chairs and 2 tables is $43. The total cost to rent 3 chairs and 5 tables is $40. What is the cost to rent each chair and each table?

Consider the following functions. f(x)= x³ + 2 and g(x) = x - 3 Step 1 of 2: Find the formula for (f + g)(x) and simplify your answer. Then find the domain for (f + g)(x). Round your answer to two decimal places, if necessary.

George was absent for the last accounting test, For those who took the test, the mean was 75.8, the median was 74, and the mode was 81. When George took the test later, his score was different from all the other students' scores, and the class mean went up to exactly 76.6. What effect, if any, did George's score have on the class mode? A. None, the mode stayed the same. B. It decreased the mode exactly 0.8 points. C. It increased the mode exactly 0.8 points. D. It increased the mode more than 0.8 points. E. The effect of George's score on the mode cannot be determined from the given informa- tion.

Yusuf broke a cell sample into 8 batches, each weighing 4.2 x 10-⁹ grams. How much did the original sample weigh? Use scientific notation to express your answer.

Stock in Company A sells for $87 a share and has a 3-year average annual return of $23 a share. The beta value is 1.06. Stock in Company B sells for $81 a share and has a 3-year average annual return of $19 a share. The beta value is 1.18. Derek wants to spend no more than $14,000 investing in these two stocks, but he wants to earn at least $2100 in annual revenue. Derek also wants to minimize the risk. Determine the number of shares of each stock that Derek should buy.

Suppose you are the president of a student government. You wish to conduct a survey to determine the student body's opinion regarding student services. The university provides you with a list of the names and phone numbers of the 19,935 students. Discuss the procedure you would follow to obtain a simple random sample of 25 students.

You are offered two different sales jobs. The first company offers a straight commission of 3% of the sales. The second company offers a salary of $ 450 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good?

Express each phrase as a rate and unit rate. (Round your answer to the nearest hundredth.) 1) 9 pencils for 11 dollars 2) 110 miles on 9 gallons of gas 3) 4 calculators cost $160.00 4) 8 dollars for 4 cans of tuna 5) 19 dollars for 6 books

Wendy is a waitress and has $15,000 to invest, and wishes to gain $4,200 in interest over the next eight years. Approximately what is the minimum simple interest rate Wendy needs to reach her goal?

The zeros of a fifth-degree polynomial function, Q, include -5(multiplicity 3) and 3+i. In addition, Q(0)=2500. Write the function in standard form. 2x5 +22x4 - 20x³ +300x² + 2500 2x5+21x4+ 25x3 + 75x² + 1250 2x5 + 9x4 - 5x3 - 175x² + 1250 2x5 + 18x4 - 10x3 - 350x² + 2500