Basic Math Questions and Answers

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.

Out of 39 students, a survey was taken regarding which pet they own. The results are: 22 have dogs, 17 have cats, 13 have fish, 7 have dogs and fish but not cats, 4 have dogs and cats but not fish, 8 have only dogs, and 5 don't have any of these. How many students have exactly 1 pet?

The endpoints of LF are L(-2, 2) and F(3, 1). The endpoints of JR are J(1, -1) and R(2, -3). What is the approximate difference in the lengths of the two segments? A 2.24 B) 2.86 C) 5.10 D) 7.96

Which sentence below correctly uses an antonym of restrain? A. I could not bridle my excitement when I heard the good news. B. John tried to compel me to tell him the answers to the test, but I said no. C. Though I want to eat that cake, I am going to have to inhibit myself from indulging today. D. The king constrained the courtier from speaking any further, he forced him to stop talking.

Find the exact values of the six trigonometic functions for the following angle. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) sin 45° = cos 45º =

When the theme of a short story is given directly A. the author states his message clearly and explicitly. B. the author uses indirect methods to deliver his message. C. the author teaches us a valuable life lesson.

The recommended daily intake of potassium (K) is 4.725 g. The average raisin contains 3.573 mg K. Fill in the denominators of the fractions, d, and d₂, to complete the conversion factors that can be used to convert between grams and milligrams, given that 1 g is equivalent to 1000 mg. 1g/d₁ mg or 1000mg/d₂ g d₁= mg d₂ = g Assuming that each raisin contains 3.573 mg, how many raisins per day would a person need to eat to meet the recommended daily amount of K, 4.725 g, from consuming raisins alone? amount: raisins/day

Jimmy invited 8 people to his birthday party. Unfortunately he forgot to ask them to RSVP so he doesn't know how many people are coming. How many groups of kids could come if we know that at least one kid comes?

In the mythical kingdom of Permutatus, wizards have special 2-digit license plates. The first digit is greater than 6, and the second digit is odd. The two digits cannot be the same. How many different license plates are possible?

Maya is a software saleswoman. Her base salary is $2200, and she makes an additional $40 for every copy of Math is Fun she sells. Let P represent her total pay (in dollars), and let N represent the number of copies of Math is Fun she sells. Write an equation relating P to N. Then use this equation to find her total pay if she sells 26 copies of Math is Fun. Equation: Total pay if Maya sells 26 copies: $

City Cabs charges a $2.50 pickup fee and $1.50 per mile traveled. Diego's fare for a cross-town cab ride is $20.50. How far did he travel in the cab? Diego traveled miles. Round to the nearest whole number.)

Suppose y = 46(1.08)^x. Use a graphing calculator or some other kind of computer to graphically or automatically solve for x if y = 82. You should be practicing this with whichever device you be allowed to use during part of an exam. Enter the answer correctly to the nearest tenth.

A city has a population of 390,000 people. Suppose that each year the population grows by 7%. What will the population be after 14 years? Use the calculator provided and round your answer to the nearest whole number.

For the linear expression in x, give the constant term and the coefficient of x. 7-3(x + 4) + 8(3x + 1) The constant term is The coefficient of x is

A farmer wishes to fence off two identical adjoining rectangular pens, each with 1936 square feet of area, as shown in the figure. What are x and y so that the least amount of fence is required? x= ft (Type an exact answer.) y =

Solve the following system of equations using the Desmos calculator: 2x+8y = 6 -5x - 20y = -15 True or False: The system of equations has an infinite number of solutions. True False

Determine whether the following the slopes of the lines are parallel, perpendicular, or neither. (-2,13) and (2,1) (3,-4) and (-5,20) Neither Parallel Perpendicular

A map on Rodrigo's phone shows the distances from his apartment building to the nearest restaurants. Restaurant Distance Taco truck 0.3 mi north Café 0.4 mi east Korean bistro 0.7 mi south Sandwich shop 0.8 mi east a. How much farther is it from the taco truck to the Korean bistro than it is from the café to the sandwich shop? Show your work.

During a snowstorm, Connor tracked the amount of snow on the ground. When the storm began, there were 5 inches of snow on the ground. Snow fell at a constant rate of 3 inches per hour until another 9 inches had fallen. The storm then stopped for 7 hours and then started again at a constant rate of 1 inch per hour for the next 6 hours. Make a graph showing the inches of snow on the ground over time using the data that Connor collected.

Find the volume of the largest open box that can be made from a piece of cardboard 31 inches by 17 inches by cutting equal square's from the comers and turning up the sides. in ³. The maximum volume is

Reagan uses the context clue of contrast when talking about "script" in section 1 of "A Time for Choosing"? What does he contrast "script" with in this passage? A. "As a matter of fact" B. "permitted to choose my own words" C. "The sponsor has been identified." D. "the choice that we face in the next few weeks" 3

Does a rhombus fit with proptery #2? No Yes

Including a 8% sales tax, an inn charges $164.16 per night. Find the inn's nightly cost before tax is added.

The wheels on a car have a radius of 15 in. and make 1 revolution every 0.15 sec. What is the average linear speed of the tire? (Round to two significant digits) The average linear speed of the tire is about

Solve the equation by completing the square. x²-11x +30=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.

Marina had $24,500 to invest. She divided the money into three different accounts. At the end of the year, she had made $1,300 in interest. The annual yield on each of the three accounts was 4%, 5.5%, and 6%. If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had she placed in each account?

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 165 grams of a radioactive isotope, how much will be left after 3 half-lives? Use the calculator provided and round your answer to the nearest gram.

Let f(x) = 5x + 4 and g(x) = 5x² + 4x. After simplifying, (fog)(x) =

Investing. How many years will it take $4,000 to grow to $7,100 if it is invested at 6% (A) compounded quarterly? (B) compounded continuously? (A) years (Round to two decimal places.) (B) years (Round to two decimal places.)

Solve the following systems of equations by elimination, if a solution exists. 7x+14y=28 6y-12=-3x Select the correct choice below and fill in any answer boxes in your choice. A. The solution to the system is x = y = 1. B. There are infinitely many solutions. C. There is no solution.

The function h(x) = (x + 6) can be expressed in the form f(g(x)), where f(x) = x^8, and g(x) is defined below: g(x) =