Basic Math Questions and Answers

Use the following information to answer the questions. The 6th term in the arithmetic sequence is 35 and the 9th term of the arithmetic sequence is 50. What is the common difference? What is a, ? What is the explicit formula? Write in the form 10+4(n-1) where 10 is 1st term, 4 is the common difference

A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation 3x+52 = y. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What is the change per day in the road's length? What was the road's length when the crew started working?

Drag and drop an answer choice into each empty box below. -11 4 -4 11 Consider the points R(6,5) and U(-5,–6). RU undergoes the translation (x, y) → (x + h, y + k), such that R'(-5, 1) and U'(-16, -10). Complete the following algebraic description. Drag the corresponding values. (x, y) → (x+

Estimate the population mean by finding a 99% confidence interval given a sample of size 11, with a mean of 41.7 and a standard deviation of 11.2. Preliminary: a. Is it safe to assume that n < 0.05 of all subjects in the population? b. Is n > 30? Confidence Interval: What is the 99% confidence interval to estimate the population mean? Enter the tri-linear inequality values accurate to one decimal place.

Answer the following. (a) The signal from a certain satellite takes approximately 0.013 seconds to reach Earth. Write this number in scientific notation. (b) The total surface area of South America is approximately 6.89 x 106 square miles. Write this number in standard notation.

Two cities are 2000 km apart and lie on the same north-south line. The latitude of the northernmost city is 53° N. What is the latitude of the other city? The radius of the Earth is approximately 6400 km. The latitude of the other city is approximately N. (Do not round until the final answer.

An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $4600 and his stock in Company B was worth $1000. The stock in Company A has increased 25% since last year and the stock in Company B has increased 22%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).

A store is having a sale on trail mix and jelly beans. For 8 pounds of trail mix and 3 pounds of jelly beans, the total cost is $23. For 2 pounds of trail mix and 5 pounds of jelly beans, the total cost is $10. Find the cost for each pound of trail mix and each pound of jelly beans.

A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ=145° and r= 36 yd. The area of lawn that receives the water is square yards. (Round to the nearest integer as needed.)

Ben walks at a rate of 3 miles per hour. He runs at a rate of 5 miles per hour. In one week, the combined distance that he walks and runs is 170 miles. If Ben walks for 10 hours, how many hours does he run?

Fill in each blank with the appropriate response. (Remember that the vertical stretch or shrink factor is positive.) The graph of y=- 1/5 [x-8]-7 can be obtained from the graph of y = [x] by shifting horizontally units to the vertically shrinking by applying a factor of reflecting across the -axis, and shifting vertically units in the direction. (Type whole numbers.)

Last year, a baseball team purchased new equipment. The equipment manager paid $20 per bat and $12 per glove, spending a total of $552. The manager bought 34 pieces of equipment. Write a system of equations that can represent this situation.

A person's blood type is denoted with the letters A, B, and O, and the symbols + and -. The blood type A+ is read as A positive. The blood type B- is read as B negative. Use the data to write a ratio for the comparison in 3 different ways. AB- donors to AB+ donors

At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? Explain. Write an equation to represent this relationship.

Graph the data. Then find the slope of the line. Explain what the slope represents. At 6 A.M., the retention pond had 28 inches of water in it. The water receded so that at10 A.M. there were 16 inches of water left.

Find (fog)(1), (g o f)(1), (f o g)(x) and (gof)(x). f(x) = x² + 1; g(x) = 3x - 4 (fog)(1) =

As shown in the illustration, Alexa had a negative balance in her checking account before depositing a $47.00 check. What is the new balance of Alexa's checking account? What property did you use to find the sum?

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.