Basic Math Questions and Answers

She receives 70 rewards points just for signing up. She earns 3.5 points for each visit to the movie theater. She needs 105 points for a free movie ticket. Write and solve an equation which can be used to determine v, the number Aria must make to earn a free movie ticket.

A bus traveled on a level road for 6 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 3 hours. Find the average speed on the level road if the entire trip was 498 miles.

After the end of an advertising campaign, the daily sales of a product fell rapidly, with daily sales given by S=3500e-0.12x dollars, where x is the number of days from the end of the campaign. a. What were daily sales when the campaign ended? b. How many days passed after the campaign ended before daily sales were below half of what they were at the end of the campaign?

1. Zachary's final project for a college course took a semester to write and had 95,234 words. Zachary wrote 35,295 words the first month and 19,240 words the second month. a. Round each value to the nearest ten thousand to estimate how many words Zachary wrote during the remaining part of the semester.

Joel sells ice cream cones at the county fair. He has to rent the equipment for $34 and spend $0.53 on ingredients for each cone. Write an inequality and solve it to represent the possible numbers of ice cream cones that he must sell at $1.10 each in order to make a profit.

Mr. Harris has some money in his wallet. He pays the babysitter $12 an hour for 4 hours of babysitting. His wife gives him $10, and he puts the money in his wallet. By how much does the amount in his wallet change?

Three sisters have ages that are consecutive odd integers. The sum of the age of the youngest and three times the age of the oldest is five less than five times the middle sister's age. (a) If x represents the age of the youngest child, then write an equation that models this scenario.

A psychologist finds there is a probability of 0.51 that people have a specific fear. The psychologist then decides to research this further by selecting a random sample of 64 people from the population. (a) What is the mean of the sampling distribution of the sample proportion? n p n(1-P) p (b) What is the value of n*p? Use 2 decimal places in answering this and the next question. (c) What is the value of n*(1 - p)? (d) Determine whether the following statement is true or false. We can conclude that the sampling distribution of the sample proportion is approximately normal. True, both values in (b) and (c) are greater than or equal to 15 and the CLT applies. False, and the CLT does not apply.

At a concession stand, seven hot dog(s) and four hamburger(s) cost $16.00; four hot dog(s) and seven hamburger(s) cost $19.75. Find the cost of one hot dog and the cost of one hamburger. What is the cost of one hot dog? What is the cost of one hamburger?

Stephen makes a base monthly salary of $1500. As a vendor, he must sell $20,000 worth of items per month. He also makes a 4% commission on all sales beyond the monthly quota. If Stephen sold $26,000 worth of items this month, what was his total salary for the month, including base salary and commission, to the nearest dollar? $1740 $240 $1500 $6,000

Explain why 323.202 is less than 323.21 even though 202 is greater than 21.

Newfoundland is a large breed of dog. It weighs about 10 x 10 pounds. Write 10 × 10 using an exponent. Then find the value of the power. How many pounds does the Newfoundland weigh?

A single-serving coffee machine is programmed to dispense 8 ounces of coffee per serving. Occasionally, the machine will start to overfill or underfill cups of coffee and require recalibration. According to the company, the coffee machine requires recalibration if it overfills or underfills cups of coffee by 1.5 or more ounces. Determine the probability that a randomly selected cup of coffee was underfilled or overfilled by more than 1.5 ounces. Assume the distribution of the amounts of all coffee dispensed by the machine are normally distributed with a mean of 8 ounces and a standard deviation of 1.13 ounces. The probability that a randomly selected cup of coffee is overfilled or underfilled by 1.5 ounces is

Suppose payroll tax is 6% of wage/salary income up to $100,000 and 2% of income earned in excess of $100,000. How much payroll tax does a person pay whose salary is $167,000? $7,340 $9,340 $8,000 $13,360

Carson has a smart phone data plan that costs $35 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carson have to pay in a month where he used 3 GB over the limit? How much would Carson have to pay in a month where he used went over by x GB?

Vaccinations are intended to prevent illness. Suppose a flu vaccine is determined to be effective for 52% of patients administered the shot. A random sample of 75 people will be selected from the population. (a) What is the population proportion of success in the above scenario? (b) Calculate the mean of the sampling distribution of the sample proportion of people for whom the shot was effective. (c) Calculate the standard deviation of the sampling distribution of the sample proportion of people for whom the shot was effective. (Round your answer to three decimal places.)

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are in the same condition. List the outcomes of C. [Let "L" designate "locked" and U" designate "unlocked".] {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} (LLL, UUU, LLU, LUL, ULL} LLU, LUL, ULL, LUU, ULU, UUL} O none of these

Find the savings plan balance after 15 months with an APR of 2% and monthly payments of $300.

1. Dora has an after school job at the Children's Zoo. She notices that at one meal, 3 cats will eat 2 cans of food. a How much food does 1 cat eat? b. Write a formula that Dora can use to determine how many cans of food to use for any given number of cats? (You can use the table method to develop the formula) c. If there are 12 cats in the Zoo, how many cans of food should Dora use at each meal time?

At noon, a barista notices that she has $30 in her tip jar. If she makes an average of $0.45 from each customer, how much will she have in her tip jar if she serves n customers during her shift? How much will she make if she serves 134 customers? How many customers did she serve by noon?

The line of best fit through a set of data is y = - 55.765 - 2.454x According to this equation, what is the predicted value of the dependent variable when the independent variable has value 10? y = Round to 1 decimal place. The attached video is from questions 3 and 4 and applies to this question, too.

Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible. Through (-4,7), perpendicular to the y-axis What is the equation of the line?

Find composite numbers that have the following characteristics: a. A number greater than 40 whose prime factorization contains 3 prime numbers that do not repeat . b. A number greater than 1000 whose prime factorization contains 1 prime number that does not repeat, 1 prime number that repeats 3 times, and 1 prime number that repeats twice.

f(x) = 2x and g(x) = 2.^x Graph the functions on the same coordinate plane. What are the solutions to the equation f(x) = g(x) Enter your answers in the boxes.

The state of New York reported 1484 live births in which the infants had Down syndrome (trisomy 21) between 2006 and 2010, which averages to about 5.7 cases per week. While the causes of Down syndrome are not fully understood, it is reasonable at this point to assume that live births are independent and the weekly rate is constant. Let X be the count of babies born with Down syndrome in the state of New York in a given week. (a) What values could X take? Notice how there is no clear limit to this range. None of the options are correct. X can take on any positive real number above the mean of X. X can take on any negative integer value. X can take on any non-negative whole number.

ΔBCD What is the length of the other leg? Enter your answer, as a decimal rounded to the nearest tenth, in the box. is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.

Andy is scuba diving. He starts at sea level and then descends 10 feet in 2 1/2 minutes. Part A How would you represent Andy's descent as a unit rate? Express your answer as an integer. Enter your answer in the box. feet per minute Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes?

So far this season, the university's football team has executed 147 running plays, 134 passing plays, and 21 "trick" plays. What is the probability that the team will execute a passing play? 0.444 0.477 0.556 0.487

Which of the following expressions are equal to 1,-1, or to neither of those? List the corresponding letter(s), separated by commas if there are more than one. a. a - 4 / - a + 4 b. -4 + a / a- 4 c. a + 4 / a - 4 d. a - 4 / 4 - a e. a + 4 / 4 + a f. -a - 4 / a + 4

Solve the inequality algebraically. 2x³ > -12x²

Sarah Jones earns $575 per week selling life insurance for Farmer's Insurance plus 4% of sales over $5,750. Sarah's sales this month (four weeks) are $15,500. How much does Sarah earn this month? (Round your answer to the nearest cent.)

Estimate, then find the sum. Round to the nearest whole number. 2.7+6.87+21.878

An antique table increases in value according to the function v(x)= 750(1.05) dollars, where x is the number of years after 1980. a. How much was the table worth in 1980? b. If the pattern indicated by the function remains valid, what was the value of the table in 1990? c. Use a table or a graph to estimate the year when this table will reach double its 1980 value.

The New York City Marathon is a highly selective race. One way to gain entry into the race is to qualify based on a time from a prior-completed marathon. The NYC Marathon's organizers use this method to limit admission to the top 10% of marathon runners. If the mean completion time of all marathons is 179 minutes with a standard deviation of 17 minutes, what qualifying time should the NYC Marathon organizers set so that only the top 10% of runners will be admitted entry to the NYC Marathon? Round the solution to one decimal place, if necessary. The qualifying time should be set to minutes to ensure that only the top 10% of runners will be

Oklahoma is a Great Plains state in the south-central part of the United States, a region not historically known for its earthquakes. Seismic records up to 2008 show that Oklahoma has experienced a constant rate about 1.5 perceptible earthquakes (magnitude at least 3) per year, on average. Use the software of your choice to calculate the answers for (a)-(c). (a) Assuming that earthquakes are random and independent, with a constant rate of 1.5 per year, the count of perceptible earthquakes per year in Oklahoma should have a Poisson distribution with mean 1.5. Under this model, what is the probability that Oklahoma had more than 10 perceptible earthquakes in a given year prior to 2008? (Enter your answer rounded to ten decimal places.) P(X> 10) = (b) In 2013, Oklahoma experienced 109 perceptible earthquakes (an average of about 2 events per week). If the rate of 1.5 perceptible earthquakes per year was still true, what would be the probability of recording 109 or more perceptible earthquakes? (Enter your answer rounded to the nearest whole number.)

Analyze the polynomial function f(x) = (x + 7)2 (5-x) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y= for large values of Ix. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Simplify your answer. Type an integer or a fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) of f is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The lesser zero of the function is of multiplicity, so the graph of f the x-axis at x = The greater zero of the function is of multiplicity so the graph of f the x-axis at x =

Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y = 65.37x + 79.52 and the r = -0.074. What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.

I tried taking the reciprocal of the fraction on the right so I would not have to do division but I could not get the equation to work. The quadratic on the bottom left is unfactorable. What steps would I take to solve this? x2 – 5x – 24 / 2x² - 11x + 24 / 2x² +7x+3 / x²+x-12

An actress has a probability of getting offered a job after a try-out of 0.05. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent. Find the probability she will need to attend more than 8 try-outs.

Richard Gaziano is a manager for Health Care, Inc. Health Care deducts Social Security, Medicare, and FIT (by percentage method) from his earnings. Assume a rate of 6.2% on $128,400 for Social Security and 1.45% for Medicare. Before this payroll, Richard is $1,000 below the maximum level for Social Security earnings. Richard is married, is paid weekly, and claims 2 exemptions. What is Richard's net pay for the week if he earns $1,250? (Use Table 9.1 and Table 9.2). (Round your answer to the nearest cent.) Net pay

The half life of radium-226 is 1620 years. Initially, there are 2-grams in a sample. (a) Half life decay can be modeled by an exponential function: N(t) = N0 ekt. Use the growth equation, kt = ln (N1/N0) to find k. (b) How many grams remain after 10 years? (c) How long will it take for 80% of the 2 grams to decay?

Select the correct answer. The pressure applied on any object can be calculated by using the following equation. P = F/A P = F/A In the pressure equation, P represents the pressure on the object in pascals (Pa), Frepresents the force applied on the object in newtons (N), and A represents the area, in square meters, of the object over which the pressure is applied. What is the pressure applied inside a container having an inner area of 16 square meters over which a force of 1,306 newtons is applied? Note: Answers should be rounded to the nearest whole unit.

What percentage of adults score below 85? 16% 99.7% 68% 0.3% 84% 8% Calling itself "the high IQ society," MENSA requires an IQ score of 130 or higher for membership. What percentage of adults taking the WAIS test qualify for membership? (Enter your answer rounded to the nearest tenth of a percent.)

Two groups of students on a fieldtrip is getting food in a fast food restaurant. The first group bought 8 burgers and 6 soft drinks for $39.76. The second group bought 5 burgers and 7 soft drinks for $29.97. How much does one burger cost? $3.79 per burger $1.86 per burger $1.36 per burger $3.45 per burger

You need 250 mL of a 20% alcohol solution. On hand, you have a 5% alcohol mixture and a 55% alcohol mixture. How much of each mixture will you need to obtain the desired solution?

Jason deposits $10,000 into an account paying ____9__(a number between 1.0% and 9.9%, rounded to the tenths place) % interest, compounded monthly. How long will it take for the balance to reach $20,000? Show your set-up and solving steps. Round to the thousandths place.

Three-sevenths of the T-shirts in a T-shirt shop are blue. Seven-eighths of those T-shirts are on sale. One-third of the blue T-shirts that are on sale are size medium. What fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium? Explain.

You have 3,000 square feet of selling space. You want to reserve at least 80 square feet for each product category you will carry. 25% of the space will be used for aisles. How many categories can you carry? a) 15 b) 28 c) 35 d) 75

In order to be elected to student council, Jeremy must have at least 50% of the current council members vote in his favor. If x represents the percent of favorable votes received, which inequality represents the percent of favorable votes that Jeremy needs for election to student council? (hint: Jeremy needs more than 50% votes)

The San Bernardino County Fair hires about 120 people during fair time. Their hourly wages range from $5.80 to $7.70. California has a state income tax of 9%. Sandy Denny earns $7.70 per hour; George Barney earns $5.80 per hour (assume this is the current minimum wage). They both worked 38 hours this week. Both are married; however, Sandy claims 2 exemptions and George claims 1 exemption. Assume a rate of 6.2% on $128,400 for Social Security and 1.45% for Medicare. a. What is Sandy's net pay after FIT (use the Table 9.1 and Table 9.2), Social Security tax, state income tax, and Medicare have been taken out? b. What is George's net pay after the same deductions? c. How much more is Sandy's net pay versus George's net pay?