Basic Math Questions and Answers

The vertices of a rectangle are M(-5,-5), N(-1,-5), O(-1,1), and P(-5,1). A rotation about the origin maps P' to the point (1, 5). The rotation was _degrees. 90° clockwise 90° counterclockwise 180° counterclockwise 45° clockwise 180° clockwise 270° clockwise 270 counterclockwise

A 2012 Gallup survey of a random sample of 1014 American adults indicates that American families spend on average $151 per week on food. The report further states that, with 95% confidence, this estimate has a margin of error of +$7. (a) This confidence interval is expressed in the form: "estimate + margin of error." What is the range of values (lower bound, upper bound) that corresponds to this confidence interval? (Enter your answers as a whole number.) lower bound: upper bound:

At a certain school 40 of the 90 boys and 28 of the 63 girls signed up for the senior trip. Is there an association between going on the trip and gender?

At a sale this week, a sofa is being sold for $741. This is a 24% discount from the original price. What is the original price?

The widespread addition of fluoride to tap water in the United States and other countries has been credited with a drastic decrease in tooth decay. However, there is always some concern over possible harmful effects of any kind of treatment. Most studies so far have failed to show a negative impact of water fluoridation on health, but one study did report a significant decrease in IQ among individuals exposed to extra fluoride as children compared with individuals not exposed to this treatment. Commenting on this study in a news article on National Public Radio, Dr. Myron Allukian of the Harvard School of Dental Medicine said that the effect on IQ was small, accounting for only about a half-point difference. He further explained that a half-point difference in IQ is meaningless, just like a difference in adult heights of half a millimeter. (a) Why is it important to know the size of an effect and not just if the effect was statistically significant? Because importance is the same as statistical significance while practical application is not. Because practical application is the same as statistical significance while importance is not. Because practical application and importance are not the same as statistical significance. None of the options are correct.

An investment of $1000 is placed in a savings account with an annual interest rate of 3%. After 1 year, how much interest has been earned, and what is the value of the account?

A set of children's blocks contains three shapes: longs, flats, and cubes. There are 3 times as many longs as cubes, and 30 fewer flats than longs. If there are 600 blocks in all, how many longs are there?

Find the value of the expression (2x − 12) + (1/2 xy - 10) for x = 4 and y = 7. 0 -16 6 8

Andrea, Anthony, and Amy were in the orchard picking apples. Andrea picked 3/4 of a bushel, Anthony picked 3/8 of a bushel, and Amy picked 1 ½ bushels. How many bushels of apples did they pick?/

SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?

Find an approximation of the area of the region R under the graph of the function f on the interval [1, 3]. Use n = 4 subintervals. Choose the representative points to be the right endpoints of the subintervals. f(x) = 4/X

A musician charges c(x) = 25x + 12,000, where x is the total number of attendees at the concert. The venue charges $55 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?

How many times greater is 5.96 x 104 than 2.98 x 10³ ? Write the answer in standard form. A 5 B 50 C 20 D 2

A cylindrical jelly jar is 9 inches across the top and about 12 inches high. How many cubic inches of jelly could it hold (to the nearest hundredth)? Use π = 3.14. A. 763.02 in ³ B. 678.24 in ³ C. 3,052.08 in ³ D. 1,526.04 in³

If Biff wins the lotto then he will not buy a used car. If Biff buys a used car then he did not win the lotto. If Biff does not buy a new car then he won the lotto. If Biff does not win the lotto then he will buy a used car.

A horse pulls a 350 kg cart to get it going with a force of 2000 N and accelerates for 30 seconds. Afterwards the horse and cart move at constant speed. What is the momentum while the cart is at this constant speed?

Solve the following logarithmic equation. log 5x = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is {}. (Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.) B. There is no solution.

Add. Simplify by collecting like radical terms if possible, assuming that all expressions under radicals represent nonnegative numbers. √√2a +8√8a³

Solve the system by the method of your choice. x²+2y² = 441 x+y = 21

A figure drawn on a coordinate plane has vertices at (1, 2), (1, 4), (-4, 4), and (-2,2). On the coordinate plane below, plot the vertices of the figure after a rotation of 270° clockwise about th origin.

A farmer bought a number of pigs for $168. However, 4 of them died before he could sell the rest at a profit of 2 per pig. His total profit was $12. How many pigs did he originally buy? He originally bought pigs.

A few years ago, Sarah acquired a parcel of land valued at $16,500. Today, that same parcel of land has a value of $18,975. Find the percent increase in the property's value. Round your answer to the nearest hundredth, if necessary.

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 12 cubic feet. There were twice as many small boxes shipped as large boxes shipped and the total volume of all boxes was 168 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.

A landscaper planted 9 flats of impatiens, 11 flats of snapdragons, and 13- flats of phlox. How many flats, did she plant altogether? 14 She plant altogether flats. (Simplify your answer. Type a mixed numeral, if possible. Otherwise, type á whole number or a fraction.)

A landscaper planted 82 flats of impatiens, 12 flats of snapdragons, and 13; flats of phlox. How many flats, did she plant altogether? She plant altogether flats (Simplify your answer. Type a mixed numeral, if possible. Otherwise, type a whole number or a fraction.)

O A department store has a discount on shoes based on a percentage of the price. Suppose one pair of shoes is marked down from $60 to $48. What is the price for a $80 pair of shoes after the discount is applied?

Find the horizontal and vertical asymptotes of f(x). Then graph f(x). x+4 x+2 f(x) = If there is a horizontal asymptote, what is it? Select the correct choice below and fill in any answer boxes within your choice. CA. The horizontal asymptotę is 1. (Type an equation.) OB. There is no horizontal asymptote. 45 If there is a vertical asymptote, what is it? Select the correct choice below and fill in any answer boxes within your choice. OA. The vertical asymptote is (Type an equation.) OB. There is no vertical asymptote.

Determine which ordered pairs given are solutions of the linear inequality in two variables. 3x - 5y ≤ - 5; (-1,-2), (4,0) Is the ordered pair (-1-2,) a solution to the inequality? No Yes O Is the ordered pair (4,0) a solution to the inequality? No Yes E

A website received 9,347 visits during the !rst month of its launch. The third month witnessed three times the number of visits than the second month. If the website received 13,455 visits over the three month period, how many visits did it witness during the second month? O 22802 O 4108 O 11401 8216 O 1027

Use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.) C = 4.1√x + 19,000, R = 6.24x

Working alone, Abhasra can pick forty bushels of apples in 10 hours. Elisa can pick the same amount in 11 hours. How long would it take them if they worked together? 4.27 hours ○ 4.86 hours 4.82 hours ○ 4.64 hours O 5.24 hours

The Garden Center ordered 10 ounces of marigold seed and 7 ounces of carnation seed paying $257.50. On a different day, they ordered another 15 ounces of marigold seed and 14 ounces of carnation seed, paying $428.95. Find the price per ounce for each type of seed.

A physician orders 0.7 oz of magnesia and alumina oral suspension antacid 4 times per day for a patient. How many milliliters is the patient to ingest in a day? Note that 1 oz 29.57 mL.

Let f(x) = x² + 2x +1 Evaluate the function for the following, write your answers in standard form, a + A

If n = 420 and p = 0.6, construct a 99% confidence interval about the population proportion. Round your answers to three decimal places. Preliminary: a. Is it safe to assume that n < 0.05 of all subjects in the population? O No O Yes b. Verify np (1-p) ≥ 10. Round your answer to one decimal place. np (1 - p) = Confidence Interval: What is the 99% confidence interval to estimate the population proportion? Round your answer to three decimal places. <p<

Write an equation of the line perpendicular to the given line that contains P. P(8, − 4); y = x/4+5

Garrett can order stickers from two companies. Company A charges a $30 design fee plus $0.80 per sticker. Company B charges a $14 design fee plus $1.20 per sticker. How many stickers would Garrett have to order for the cost at both companies to be the same?

Given the cubic function f(x)=3x³-5x²-34x + 24: a) Show that x=4 is a zero off. Use this zero to write down a factor of f b) Use polynomial long division to find the other zeros off. Show your algebraic work.

C(f)=16-5f a.) Find m b.) What is the C-intercept? c.) Find C(3)

Find the domain of the function y = 3 tan(2x/3).

Julia has $5.00 to spend on lemons. Lemons cost $0.59 each, and there is no tax on the purchase. Which of the following inequalities can be used to represent a, the number of lemons Julia can buy?

A twelve-sided die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number greater than 9? Write your answer as a fraction.

The supply and demand curves for a business dealing with wheat are Supply: p= 1.45 +0.00014x² Demand: p= (2.373 -0.007x)² where p is the price in dollars per bushel and x is the quantity in bushels per day. Use a graphing utility to graph the supply and demand equations and find the market equilibrium. (The market equilibrium is the point of intersection of the graphs for x > 0. Round your answers to two decimal places.)

A rectangular prism has a height of 3 inches and a volume of 27 cubic inches. The height of this prism is changed to 6 inches, and the other dimensions stay the same. What is the volume of the prism with this change?

For the following infinite series, find the first four terms of the sequence of partial sums. Then make a conjecture about the value of the infinite series. 3+0.8+0.08 +...

The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 180 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store. number of items - continuous; total time - continuous number of items - continuous; total time - discrete number of items - discrete; total time - discrete number of items - discrete; total time - continuous

In sailing, it is not possible to head straight into the wind. In order to get upwind, a sailboat simply sails at an angle to the wind and then turns to sail back toward where it wants to go. Assume that a boat needs to get directly upwind 6000 m. If it sails off at a 45 degree angle to the wind and then turns back 90 degrees towards the original goal, how far would it have to sail to get directly upwind 6000 meters? Round to the nearest tenth. Distance to get directly upwind 6000 meters: meters 8485.3 010392.3 4242.6 6000

A landfill has 60,000 tons of waste in it. Each month it accumulates an average of 360 more tons of waste. What is a function rule that represents the total amount of waste after m months? Let W represent the total amount of waste and m represent months. A. W = 360m + 60,000 B.W = 60,000m + 360 C.W = 360m - 60,000 D.W = 60,000m - 360

Determine whether the conclusion follows logically from the premises. If my jeans are tight, then I will go on a diet. My jeans are tight. Therefore, I will go on a diet. Valid argument Invalid argument If I win the lottery, then we can all go on a cruise. I won the lottery. Therefore, we can all go on a cruise. Valid argument Invalid argument

A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10 adults over 50, what is the probability that at least six wear sunglasses? 0.700 0.006 0.850 0.200