Basic Math Questions and Answers

Josh spends of 4/5 his savings to buy 48 shares in a tech company. He has $18 left. Part A: How much does each share of the tech company cost? Show your work. Part B: How many more shares can Josh buy with the remainder of his savings? Explain.

Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cause of childhood deaths before the development of vaccines. Approximately 80% of unvaccinated children who are exposed to whooping cough will develop the infection compared to only 5% of vaccinated children. In 2007, Bob Jones University ended its fall semester a week early because of a whooping cough outbreak; 158 students were isolated and another 1200 given antibiotics as a precaution. Authorities react strongly to whooping cough outbreaks because the disease is so contagious. Because the effect of childhood vaccination often wears off by late adolescence, treat the Bob Jones students as if they were unvaccinated. It appears that about 1400 students were exposed. What is the probability a that at least 75% of these students develop infections if not treated? (Enter your answer rounded to two decimal places.) a=

The daily profit P in dollars of a company making tables is described by the function P = -5x² +245x-2640, where x is the number of tables that are manufactured in 1 day. Use this information to find the profit when x = 20 and x = 28.

The unit cost, in dollars, to produce bins of cat food is $10 and the fixed cost is $8648. The revenue function, in dollars, is R(x)=2x²+288x Find the cost function. C(x) = Find the profit function. P(x) = At what quantity is the smallest break-even point?

Peggy filled her van's gas tank and noted that the odometer read 26,608.8. After the next fill-up, it read 27,025.3. It took 17.5 gal to fill the tank. How many miles per gallon did the van get? The gas mileage of the van is (Type a whole number or a decimal.)

1 Which problems can be solved using the equation 3 x 6 = f? Choose all the correct answers. * Choose only 3* (A) Cleo has 3 times as many bananas as Arianna has. Cleo has 6 bananas. How many bananas does Arianna have? B) Dylan has 6 oranges. Jane has 3 times as many oranges as Dylan. How many oranges does Jane have? (C) Liam has 3 cherries. Brian has 6 times as many cherries as Liam. How many cherries does Brian have? Tina has 3 more peaches than Charlie. Charlie has 6 peaches. How many peaches does Tina have? E Jaclyn has 6 times as many grapes as Kaitlyn. Kaitlyn has 3 grapes. How many grapes does Jaclyn have?

Find the savings plan balance after 9 months with an APR of 4% and monthly payments of $200.

Read each problem and state whether it is P(n,k) or C(n,k). Then evaluate the permutation or combination to determine the answer. Show a step of work when evaluating the permutation or combination prior to using your calculator. a. A race has 21 participants. How many ways can first second, and third place be decided assuming there is no tie? b. Alejandro has 38 other students in his class. He plans to invite 6 students to join a study group. How many ways can he select a group of 6 classmates to join the study group?

In 2004 there were approximately 6960 cinema sites. In 2000 there were 8400 cinema sites. a. Write an equation describing this relationship. Use ordered pairs of the form (years past 2000, number of cinema sites). b. Use this equation to predict the number of cinema sites in 2009.

A farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What are the maximum dimensions that can be enclosed with 84 ft of fence? What is the maximum area of this garden?

A soft drink machine at a local fast food restaurant can be calibrated so that it dispenses an average of ounces per cup. If the ounces of soda dispensed are normally distributed with standard deviation 1.3 ounces, find a value of such that 16-ounce cups will overflow only 10% of the time.

Look at the picture below. What is the person trying to calculate and what mistake did they make in doing so? Be as specific as you can. (4,3) and (5,2) m = 4-5 /3-2

Tyler Herro, a former University of Kentucky player, now plays for the Miami Heat. As a freshman in college, he averaged 14 points per game. If he were to start and play in all 82 NBA games this year, how many points should he expect to score (if he stays at the constant rate he did in college)?

John receives his bank statement for the month. His balance is $430.52. In comparing his checkbook register, canceled checks, and bank statement, he finds that checks #224 and # 250 are outstanding. The amounts are $32.50 and $62.80. What is John's adjusted balance?

6x + 55 = x² 1) Rewrite the equation by completing the square. Your equation should look like (a + c)² = d or (x - c)² = d. 2) What are the solutions to the equation? Choose 1 answer: A. x = -3±8 B. x=3±8 C. x = -8± 3 D. x=8±3

Kaci owns a clothing boutique. She makes a deposit in her business checking account. She has checks to deposit for $234.53 and $495.87. She also has cash consisting of 14 one-dollar bills, 4 five-dollar bills, 8 ten-dollar bills, and 18 twenty-dollar bills. What is Kaci's total deposit?

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8. Convert 68 to a z-score.

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. 3, 2+3i

Since a middle school opened, the girls' basketball team has had the same record every season. The team has won a total of 156 games while losing only 12 games. Find the constant of proportionality of wins to losses.

A bar graph shows that sports books received 9 votes. If the scale is 0 to 20 by twos, where should the bar end for the sports books?

Two stores sell the same refrigerator for the same original price. Store A advertises that the refrigerator is on sale for 15% off the original price. Store B advertises that it is reducing the refrigerator's price by $150. When Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal. Let p represent the refrigerator's original price. Which equation models this situation?

A store advertises that during its Labor Day sale, $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars at 8 a.m. and x > 100, what, in terms of x, is the cost c of Hakeem's purchase?

Discuss the validity of the following statement. If the statement is true, explain why. If not, give a counter example. Every polynomial function is one-to-one. Choose the correct choice below.

f(x) = (x+7)²(x+9)(x-12)² List each zero of faccording to its multiplicity in the categories below.

At lunch a waiter had eleven customers and five of them didn't leave a tip. If he got Ssix each from the ones who did tip, how much money did he earn?

A 1.000-g sample of chromium metal reacted with oxygen gas to give 1.462 g of product. Calculate the empirical formula of the chromium oxide.

In a random sample of 200 cars of a particular model, 3 have a manufacturing deficit. At this rate, how many of 10,000 cars of the same model will have a manufacturing deficit? (A) 150 (B) 200 (C) 250 (D) 300

An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are worth five points. How many two point questions are on the test? How many five point questions are on the test?

Caleb bought 3 orders of cheese dip to share with his friends. How much did he spend on cheese dip?

Assume you intend to create a stratified sample of 250 from a population of 920 trucks, 1540 subcompact cars, 1320 sedans, 450 motorcycles, 110 R.V.'s, 550 luxury cars, and 780 sports cars. How many subcompacts should you have in your sample? a 65 b 60 C 68 d 70

A small business sells custom oak moldings in 12-foot lengths. One molding type has the revenue function R(x) = 59x and the cost function C(x) = 2800+ 45x. Find the number of 12-foot lengths of this molding that must be sold to break even. X = lengths

The speed of light is approximately 6.71 a 10 miles per hour. Which of the following options shows this number correctly written in standard notation?

A hiker is walking down a mountain. She walked 5,978 feet in 17 minutes. In that time, she descended 1,024 feet from the top of the mountain. She then walked 3,972 feet in 7 minutes. In that time, she descended 500 more feet. Express the average rate of change in altitude of the hiker from her starting point to her ending point as a unit rate.

Combine like terms to simplify the expression below. -6y + 7y = 1y 32 + y - 2y² Now, re-write the equation with the variable with the highest exponent first.

Two cities have nearly the same north-south line of 101° W. The latitude of the first city is 23° N, and the latitude of the second city is 36° N. Approximate the distance between the cities if the average radius of Earth is 6400 km.

Sadie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5 hours and charged her $77 for parts. The total was $302. Which equation could be used to determine x, the cost of labor per hour? r

Junior is saving money in his piggy bank. He starts with 10 cents and adds two pennies each day. Create an x → y table and a graph for the function for which x represents the number of days since Junior started saving money and y represents the total money he has saved.

A pennant is shaped like a right triangle with hypotenuse 10 feet. The length of one side of the pennant is 2 feet longer than the length of the other side. Find the length of the two sides (legs) of the pennant. Enter your answers as a comma separated list.

You have tablets with a strength of 2.37 mg, and you must give 0.16 g. How many tablets will you need? Less than 1 Exactly 1 More than 1

- A boat leaves port A and travels 40 knots for 2 hours on a bearing of N 62° W then travels at the same speed for 3 hours on a bearing of N 28° E to port B. Find the distance and bearing from port B to A.

The city of Raleigh has 11,900 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 600 randomly selected registered voters was conducted. 353 said they'd vote for Brown, 219 said they'd vote for Feliz, and 28 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Round your answer to four decimal places. This sample statistic suggests that we might expect of the 11,900 registered voters to vote for Brown. Round to the nearest whole number.

In 2012, the population of a city was 5.62 million. The exponential growth rate was 2.48% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 9 million? d) Find the doubling time. of the number of years since 2012

Alexis de Tocqueville observed American society during the beginning of industrialization. Which of the following best characterizes his observations? a) Americans are insufficiently focused on their careers and miss opportunities to advance in the job market. b) Americans need to be more like people who live in the Old World and lighten their spirits. c) Americans regularly participate in government elections but cannot agree on which path is the best one to follow. d) Americans have become so obsessed with accumulation that they have no time left to enjoy life and participate in their free political system.

In a recent survey of college-educated adults, 102 indicated that they regularly work more than 45 hr a week. If this represents 34% of those surveyed, how many people were in the survey? There were people in the survey.

Your patient is to receive a dosage of 15 mg and you have only 1 tablet labeled 5 mg. How many more mg are needed?

A rope is 60 in in length and must be cut into two pieces. If one piece must be three times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary. The length of the smaller piece is in. The length of the larger piece is in.

Complete the proof of the statement, "If a figure is a rectangle, then it must me a parallelogram". Use the diagram provided to help you. Angles A and D are supplementary [Select] transversal AD, so lines DC and AB are parallel by the [Select] Similarly, angles A and B are [Select] same side interior angles formed by transversal AB which makes lines AD and BC also parallel. Finally, ABCD must be a parallelogram because we have just proven both pairs of opposite sides are [Select]

Find the angular speed w for the following. a wind turbine with blades turning at a rate of 15 revolutions per minute The angular speed for a wind turbine with blades turning at a rate of 15 revolutions per minute is minutes. radians. radians per minute.

(a) Find the domain of the following function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. x², if 0<x≤2 f(x)= x+2, if 2<x<5 7, if x ≥ 5

Permutation and combination: What are your chances of winning the Lucky Millions Lottery if you You pick 4 numbers from 1 to 40 without replacement and 1 number from 1 to 30. Answer format: