Basic Math Questions and Answers

Jackie has been offered positions by two cable companies. The first company pays a salary of $16000 and a commission of $75 for each cable package sold. The second pays a salary of $13300 plus a commission of $125 for each package sold. How many cable packages would need to be sold to make the total pay the same?

Alexa, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly wages of $390 for 48 hours worked. What is her regular hourly rate? Alexa's regular hourly rate is $ per hour.

The bus fare in a city is $1.50. People who use the bus have the option of purchasing a monthly coupon book for $24.00. With the coupon book, the fare is reduced to $0.50. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book. The bus must be used times.

What is the effect on the graph of f(x) = 1/x when it is transformed to g(x) =1/x -16? A. The graph of f(x) is shifted 16 units up. B. The graph of f(x) is shifted 16 units to the left. C. The graph of f(x) is shifted 16 units to the right. D. The graph of f(x) is shifted 16 units down.

Write the negation of the conditional statement. If there is a storm, then all schools are closed, Choose the correct negation below. A. If there is not a storm, then some schools are not closed. B. There is not a storm and some schools are not closed. C. There is a storm and some schools are not closed. D. There is a storm or some schools are not closed.

A small jet can fly 1650 miles in 3 hours with a tailwind but only 1350 miles into a headwind. Find the speed of the jet in still air and the speed of the wind. Speed of the jet in still air: Speed of the wind:

Graph the given equation by hand by plotting points. Verify your results using a graphing utility. 4x² +9y=36

A typical cup of coffee contains about 80 mg of caffeine and every hour approximately 16% is metabolized and eliminated. (a) Write C, the amount of caffeine in the body in mg as a function of t, the number of hours since the coffee was consumed. mg help (formulas) C(t) =

The two stadiums with the largest capacities are Marshfield Stadium and Bowden Stadium. Marshfield Stadium has a capacity of 4,545 more than Bowden. If the combined capacity for the two stadiums is 210,355, find the capacity for each stadium.

The elements that compose seawater, along with the corresponding percents, are shown in the table. If a sample of seawater contains 30 ml, how many ml of oxygen are in the sample? Seawater Elements Chemical Percent Oxygen 85.84% Hydrogen 10.82% Chlorine 1.94% Sodium 1.08% Magnesium 0.13% Other elements 0.19%

The price of diamond rings. A newspaper advertisement in the Straits Times of Singapore contained pictures of diamond rings and listed their prices, diamond weight (in carats), and gold purity. Based on data for only the 20-carat gold ladies' rings in the advertisement, the least-squares regression line for predicting price (in Singapore dollars) from the weight of the diamond (in carats) is price = 259.63 +3721.02 carats (a) What does the slope of this line say about the relationship between price and number of carats? ( b) What is the predicted price when number of carats=0? How would you interpret this price?

Starting with the graph of f(x) = 9^z , write the formula for the function that results from (a) shifting f(x) 1 units upward. y = (b) shifting f(x) 4 units to the right. y = (c) reflecting f(x) about the x-axis. y =

Tina has been dieting for a total of 13 weeks. She lost 3 pounds on the first week of her diet, but gained back a pound on the second week. On each remaining week of her diet, she lost 2 pounds. How many pounds has Tina lost in all? A. 22 pounds B. 24 pounds C. 26 pound D. 20 pounds

4There are four classes of third graders at Woodbury Elementary School. One class has 24 students, one has 26 students, another has 31 students and the last has 22 students. The principal would like to split the third grade population into two groups for lunch period. Which expression represents the separation of the third grade into two groups? A. 2(24 + 26 +31 +22) B. 24 +26+31+ 22 / 2 C. (24 +26) - (31 +22) D. 2 / 24 +26+31 + 22

In 2011 a country had a population of 143 million and a growth rate of -0.472%. Assuming that this rate remains constant, estimate the population of the country in 2020. In 2020, the country's population will be about

A country's populations in 2000 and 2011 are given below. Use this information and the exponential model A= P(1+r)^n to find the growth rate for the country over this period. population (2000) = 81 million; population (2011) = 109 million

A company manufactures and sells bookcases. The selling price is 53.9 (in dollars) per bookcase. The total cost function is linear, and costs amount to 50,000 (in dollars) for 2000 bookcases and 32, 120 (in dollars) for 800 bookcases. Find the break-even point.

What's my grade? In Professor Krugman's economics course, the correlation between the students' total scores prior to the final examination and their final- examination scores is r = 0.5. The pre-exam totals for all students in the course have mean 280 and standard deviation 40. The final-exam scores have mean 75 and standard deviation 8. Professor Krugman has lost Julie's final exam but knows that her total before the exam was 300. He decides to predict her final- exam score from her pre-exam total. (a) What is the slope of the least-squares regression line of final-exam scores on pre-exam total scores in this course? What is the intercept? Interpret the slope in the context of the problem. (b) Use the regression line to predict Julie's final-exam score. (c) Julie doesn't think this method accurately predicts how well she did on the final exam. Use r2 to argue that her actual score could have been much higher (or much lower) than the predicted value.

Factor. p²(y-v)+2(v-y) Choose the correct answer below. A. (p²-2) (v-v) B. (p²+2) (y + v) C. (p²+2)(y-v) D. (p²+2) (v-y)

Factor by grouping. 15x³−6x² +25x−10

Jerry will pay 6.5% sales tax on a $45 pair of shoes and a $21 shirt. Which expression shows how Jerry can find the total cost after tax? (0.065 x 45 +21) + (45+21) [0.065(45+21)] + (45+21) 2(45+21) x 0.065 0.065 x 45 + 21 +45 + 21

A Tourist Information Center is between a Bus Station and a Train Station. When mapped on a grid, the Tourist Information Center is located at (11,2) and the Bus Station is located at (1.-8). The Train Station is located at point X= y=

Rey wanted to buy a headset worth Php 500 so he saved Php 5 on Monday, Php 6 on Tuesday, Php 7 on Wednesday, and so on. How much would he be able to save in 30 days? Will he be able to buy the headset after 30 days?

Join the following sentences using a transition preceded by a semicolon. I stayed up late last night reading a book. This morning I slept in late. A. I stayed up late last night reading; a book, therefore this morning I slept in late. B. I stayed up late last night reading a book therefore; this morning I, slept in late. C. I stayed up late last night reading a book; therefore this morning I slept in late. D. I stayed up late last night reading a book; therefore, this morning I slept in late.

Solve the equation. 5(4+2x)=9(x-1) Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is (Simplify your answer.) B. There is no solution.

Translate the sentence into an equation. Four more than the product of a number and 8 is 5. Use the variable b for the unknown number.

A woman purchased a used car for $6000. She decided to sell the car for 10% above her purchase price. She could not sell the car so she reduced her asking price by 10%. If she sells the car at the reduced price, will she have a profit or a loss or will she break even? Select the correct choice below and fill in any answer box to complete your answer. A The woman will have a loss of $ B. The woman will have a profit of $ C. The woman will break even.

Salma is putting money into a savings account. She starts with $350 in the savings account, and each week she adds $70. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Salma has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.

Which sentence below correctly punctuates the quote? A. Yeats writes ",She bid me take life easy, as the grass grows on the weirs." B. Yeats writes, "She bid me take life easy, as the grass grows on the weirs." C. Yeats writes "She bid me take life easy, as the grass grows on the weirs," D. Yeats writes, "She bid me take life easy, as the grass grows on the weirs.

An amount of $38,000 is borrowed for 9 years at 4.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back? Use the calculator provided and round your answer to the nearest dollar.

Factor the following trinomial. 12r²-16-44r Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 12r²-16-44r = (Type your answer in factored form.) B. The trinomial is prime.

An object is launched from a platform. Its height can be modeled by the equation h(x) = -7(x+1)(x-8) where h is in meters and x is in seconds. What is it's height just prior to launch? 37 m 42m 47 m 56 m

Solve the quadratic equation by completing the square. 2x² + 5x-7=0 Choose the appropriate process for rearranging the equation, if needed, before completing the square to obtain an equation of the form (x + k)² = d.

Ranger station Q is 7.5 miles due east of ranger station P. Suddenly, a forest ranger at station P sights a fire directly south of his location. A second ranger at station Q sights the same fire at a bearing of S27°W. How far from station P is the fire? 3.40 miles 14.72 miles 3.82 miles 6.68 miles

A tree is broken by the wind. The top of the tree touches the ground 13 feet from its base and makes an angle of 29° with the ground. Find the original height of the tree. 14.86 feet 20,20 feet 7.20 feet 22.07 feet

The length of a rectangle is 5 ft more than twice the width, and the area of the rectangle is 42 ft². Find the dimensions of the rectangle. Length: Width:

A vacuum cleaner dealership sold 310 units in 2011 and 283 units in 2012. Find the percent increase or decrease in the number of units sold. The number of units sold by about%.

Last Tuesday, Regal Cinemas sold a total of 8500 movie tickets. Proceeds totaled $64,600. Tickets can be bought in one of 3 ways: a matinee admission costs $5, student admission is $6 all day, and regular admissions are $8.50. How many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?

Ana is working at her sister's pizzeria researching the preparation of different pizza dough recipes. A sample of 27 recipes revealed the following information regarding the linear relationship between cost ($/lb) and preparation time (min). Computer Regression Output for Preparation Time (min) vs. Cost ($/lb) a. Find the equation of the Least Squares Regression Line (LSRL). b. Using an x-axis and y-axis, create a beautiful graph of the LSRL. c. Calculate r, the correlation coefficient.

Greta's Gas Company charges residential customers $9 per month even if they use no gas, plus 64¢ per therm used. (A therm is a quantity of gas.) In addition, the company is authorized to add a rate adjustment, or surcharge, per therm. The total cost of using g therms of gas in a month is given by (a) Which term represents the rate adjustment? What is the rate adjustment in cents per therm? cents per therm (b) Is the expression for the total cost linear? Total cost = 9+0.64g + 0.149g.

A recent study indicated that 44% of the 89 women over age 55 in the study were widows. Round up your answers to the next whole number for the following questions. How large a sample must you take to be 90% confident that the estimate is within 0.05 of the true proportion of women over age 55 who are widows?

Francisco is three years more than twice Jenna's age. Harrison is two years less than three times Jenna's age. If Jenna's age is given by a, then write an expression for Francisco's age, Harrison's age, and the sum of all three ages, in terms of a.

Amienatta has 20 coins in her piggy bank, all dimes and quarters. The total amount of money is $3.05. How many of each coin does she have? Which problem below is the correct system of equation to match this situation is d= number of times and q= number of quarters. d + q = 20 0.10d + 0.25q = 3.05 d + q = 3.05 0.10d + 0.25q = 20 d + q = 20 0.25d + 0.10q = 3.05 d + q = 3.05 0.25d + 0.10q = 20

Husbands and wives. The mean height of American women in their twenties is about 64.3 inches, and the standard deviation is about 2.7 inches. The mean height of men the same age is about 69.9 inches, with standard deviation about 3.1 inches. Suppose that the correlation between the heights of husbands and wives is about r = 0.5. (a) What are the slope and intercept of the regression line of the husband's height on the wife's height in young couples? Interpret the slope in the context of the problem. (b) Draw a graph of this regression line for heights of wives between 56 and 72 inches. Predict the height of the husband of a woman who is 67 inches tall, and plot the wife's height and predicted husband's height on your graph. (c) You don't expect this prediction for a single couple to be very accurate. Why not?

The population of a country has been decreasing for several decades. In 1990, the population was about 175 million people. In 2010, the population was about 169 million people. Determine the percent decrease the country's population during this time period. The country's population decreased by about% during this time period. (Round to one decimal place as needed.)

A dolphin is swimming 3 feet below sea level. It dives down 9 feet to catch some fish. Then the dolphin swims 4 feet up toward the surface with its catch. What is the dolphin's final elevation relative to sea level?

A basic cellular package costs $20/mo. for 60 min of calling, with an additional charge of 20+.30 (x - 60). If you have $0.20/min beyond that time. The cost formula would be C to keep your bill $80 or lower, what is the maximum calling minutes you can use?

Graph the equation by hand by plotting points. Verify your results using a graphing utility. y=2x+9

Which of the following points does not satisfy the equation 2x² - 5y = 20? Select all that apply. A. (0,-4) B. (-5,-14) C. (10,36) D. (5,6)

Which sentence combines these two sentences using a coordinating conjunction? The fountain at the park is just spectacular. Sometime you should go enjoy it. A. The fountain at the park is just spectacular, so sometime you should go enjoy it. B. The fountain at the park is just spectacular, maybe sometime you should go enjoy it. C. The fountain at the park is just spectacular, perhaps sometime you should go enjoy it.