Basic Math Questions and Answers

How much of a(n) 60% orange juice drink must be mixed with 3 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice? The amount of 60% orange juice drink is gallons.

On the first Tuesday of every month, Roth's gives seniors a 15% markdown on everything they purchase including sales merchandise. On the first Tuesday of this month, Jack Graham, a senior, purchased a three-piece suit marked down 40%. If he paid a total of $152.79, including a 7% sales tax, what was the suit's regular selling price?

A pharmacist wishes to mix a solution that is 8% Minoxidil. She has on hand 60 ml of a 3% solution and wishes to add some 10% solution to obtain the desired 8% solution. How much 10% solution should she add?

Select all the expressions that are equivalent (equal) to 2. Show your 8+ (-9) + 3 -4+15-7 -9+8+3 -9-(-12) + (-1) 13-6-3 8- (9+3)

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1800. What was the rate charged per hour by each mechanic if the sum of the two rates was $135 per hour? Note that the ALEKS graphing calculator can be used to make computations easier. First mechanic: $ per hour Second mechanic: $ per hour

Use a graphing utility to complete the table and estimate the limit as x approaches infinity. Then use a graphing utility to graph the function and estimate your answer graphically. (Round your answers to five decimal places.)

Find the real solutions of the equation. 32x4-4x²-1=0 What is the solution set? Select the correct choice below and fill in any answer boxes in your choice. A. B. There are no real solutions.

Suppose two trains leave a station at the same time, traveling in opposite directions. Train B travels 20 mph faster than Train A. In 3.5 hours, the trains are 378 miles apart. Find the speed of each train. The speed of Train A is

In industry, the relationship be- tween wages and the quit ratio of employees is defined to be the percentage of employees that quit within 1 year of employment. The quit ratio of a large restaurant chain that paid its employees the minimum hourly wage ($7.25 per hour) was .2 or 20 employees per 100. When the company raised the hourly wage to $8, the quit ratio dropped to .18, or 18 employees per 100. a. Assuming a linear relationship be- tween the quit ratio Q(x) and the hourly wage x, find an expression for Q(x). b. What should the hourly wage be for the quit ratio to drop to 10 employees per 100?

Use deductive reasoning to arrive at a conclusion based on the assumptions given. (a) ASSUMPTIONS (b) ASSUMPTIONS 1. All Martians have green eyes. 2. Henry is a Martian. 1. The sum of the measures of the angles of a triangle is 180. 2. In a particular triangle, the sum of the measures of two angles is 100. A prime number is any whole number that is divisible only by itself and 1. For example, 7, 11, and 13 are prime numbers. Evaluate the formula n² +n + 17 using all integer values of n from 0 to 9, inclusive. Do you notice a pattern? (a) Using inductive reasoning, draw a conclusion. (b) Is your conclusion true for all values of n? Test n = 16.

Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system. 3x - y = 4 2x + 3y = 21 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The solution is x= 3 and y = 5. B. There are infinitely many solutions. Using ordered pairs, they can be expressed as {(x,y) | x= C. The system is inconsistent.

Evaluate the following polynomial using synthetic substitution! You need to know how to do this question with this method for future quizzes and tests so please don't solve another way. f(x) = x² + 3x - 20; x = 4

A 15 foot ladder is sliding down a building at a constant rate of 2 feet per minute. How fast is the base of the ladder moving away from the building when the base of the ladder is 9 feet from the building?

On a spring day the temperature, T in degrees Fahrenheit, is T = f(h) = 55+1.6h, where h is the number of hours since 8 AM. a) Identify the initial amount and the rate of change of T = f(h). Include units with your answer. b) What do they tell you? c) What is the temperature on a spring day at 4 PM? d) How long did it take for the temperature to reach 63 degrees Fahrenheit?

Solve the system by the addition method. x + 2y = -5 3x + 5y = - 10 Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is. (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Seth plots point B by reflecting point A(3.5, 4) across the x-axis and then reflecting the result across the y-axis. Seth says that point B has coordinates (-4,-3.5). Use words and a graph to show why Seth is incorrect.

Write down everything you know about the equation y = mx + b. You should include what this general equation represents, as well as what each of the different letters represents. Be as thorough as possible.

You are seeking to be emancipated from your parents. You are looking for an apartment. There are two final choices. Apartment A has a $1000 security deposit and costs $1200 each month. Apartment B has a $1500 and costs $1175 each month. How many months, m, will it take for the costs to be the same?

A balloon is rising straight up at a rate of 9 ft/sec. An observer is on the ground 120 feet from the point of lift-off. How fast is the angle of elevation changing at the moment the balloon is 50 feet in the air?

Jill plots point G with coordinates (a, b) in the coordinate plane. She reflects that point across the y-axis. In which quadrant is the reflection of point G in the coordinate plane? A Quadrant l B Quadrant II C Quadrant III D Quadrant IV

Claire is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof (point A) is 20°, and the angle of elevation from her eyes to the top of the antenna (point B) is 39°. If her eyes are 1.62 meters from the ground, find the height of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.

Rewrite log (5x³ - 5x²) as a sum of terms. log (5) + log (x²) + log(x − 1) log (5) + log(x) + log(x) + log(x - 1) log (5) + log(x) + log(x) + log(x) - log (1) log (5) + log(x) + log(x) - log(x - 1)

Which sentence below uses a colon correctly? A. It is important to: eat well, sleep enough, drink water, and exercise. B. It is important to keep healthy habits: eat well, sleep enough, drink water, and exercise. C. It is: important to keep healthy habits, eat well, sleep enough, drink water, and exercise.

What must you do here before using long division on this polynomial problem? Put both polynomials in descending order. Find the least common multiple of both the divisor and the dividend. Use a place holder. Determine the prime factorization of the dividend.

Evaluate without using a calculator. Write "undefined" or "imaginary" if your result is not a real number.4√1/16 Write "undefined" or "imaginary" if your result is not a real number. Give your answer as a reduced fraction. No decimals.

The profit P (in thousands of dollars) for a company spending an amount s (in thousands of dollars) on advertising is shown below. Find the amount of money the company should spend on advertising in order to yield a maximum profit.

Jacob invests $3,500 in an account that has an annual interest rate of 4.8% compoundec monthly. Addison invests $4,200 in an account that has an annual interest rate of 3.2% compounded continuously. Which of the following statements is true when comparing the amount of money in the two accounts after 10 years? After 10 years Addison has about $700 more than Jacob. After 10 years Jacob has about $74 more than Addison. After 10 years Addison has about $133 more than Jacob. After 10 years Addison and Jacob have the same amount of money in their accounts.

According to Sampling techniques, identify the type of sample obtained on each situation given below: 1) A pollster uses a computer to generate 500 random numbers, then interviews the voters corresponding to those numbers. [Select]

Given the parent function f(x) = x5, write an equation for the function g(x), in which f(x) is shifted down by 3, left by 1, and vertically stretched by a factor of 2. g(x) = 2(x + 1)5 - 3 g(x) = (x + 1)5 - 3 g(x) = 2(x + 1)5 +3 g(x) = 2(x - 1)5 - 3

Consumer Reports compared the effectiveness of an antiwrinkle cream with that of a plain moisturizer in reducing the appearance of wrinkles. The researchers enrolled 79 subjects with moderate to marked wrinkles, and instructed them to use both products, one on each side of the face, every morning for 12 weeks. The subjects didn't know which products they were using. At the end of the study, panelists examined before and after photos of the subjects to assess wrinkle appearance. The panelists did not know which product the subjects had used. Which of the statements is true? This study was a double-blind experiment, but not a randomized experiment. This study was a randomized, double-blind experiment. This study is just anecdotal. This study was an experiment, but not a double-blind experiment.

Find two positive numbers that satisfy the given requirements. The sum is S and the product is a maximum.

Steve is a nuclear physicist that is studying one radioactive element. Initially, he has 100 kg of that element, but he discovered that that amount decreases following the equation Nt 100(2.72)-0.06t However, for his experiments it is better to express this equation in the form N(t) = 100* a. Help Steve to find the adequate value for a. Round your answer to the nearest hundredth.

The measurement of the radius of the end of a log is found to be 16 inches, with a possible error of 1/8 inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.

Solve the system by the addition method. 2x + 15y = 4 2x - 15y = 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. There are infinitely many solutions. c. There is no solution. (Type an ordered pair.)

The vertices of triangle KLM are K(1,2), L(0,0), and M(4,0). A translation of triangle KLM (pre-image) results in triangle K'L'M' (image) with vertices K'(2,1), L'(1,-1), and M'(5,-1). Graph the figure and use words and coordinate notation to describe the translation.

Which sentence uses the semicolon correctly? A. The basketball team will fly to Seattle; for the game on Sunday, B. The team played well in the game, and Seattle is a fun place to visit. C. The team lost the game, they were exhausted on the bus home.

In order to develop a more appealing cheeseburger, a franchise uses taste tests with 6 different buns, 8 different cheeses, 2 types of lettuce, and 2 types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?

Solve the system by the substitution method. x+y = -9 y = - 4x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. There are infinitely many solutions. C. There is no solution.

If n is an odd integer, which equation can be used to find three consecutive odd integers whose sum is -3? 1) n+(n+1)+(n+3)=-3 2) n+(n+1)+(n+2) = -3 3) n+(n+2)+(n+4)=-3 4) n+(n+2)+(n+3)=-3

What are the zeros of the polynomial y = x² + 3x? (0, 0) (3,0) (0,3) (0, 0) and (-3, 0) (3,-3)

A study examined the impact of THC, the active ingredient in marijuana, on various physiological and psychological variables. The study recruited a sample of 18 young adults who were habitual marijuana smokers. Participants came to the lab 3 times, each time completing the entire series of tests and questionnaire, but each time smoking a different marijuana cigarette: one with 3.9% THC, one with 1.8% THC, and one with no THC, a placebo. The order of the conditions was randomized and participants were not told how much THC was in the cigarette they smoked until after all the data were collected. This is an example of A. a completely randomized experiment. B. a case-control observational study. C. a matched pairs or repeated measures experiment. D. an anecdotal evidence.

Graph the line containing the point P and having slope m. P=(4,-6); slope undefined Use the graphing tool to graph the line.

Find the quadratic function y = ax +bx+c whose graph passes through the given points. (-2,-24), (1,-3), (3,-19)

Solve. 1/2(4y + 2)-20 <-1/3(9y-3)

The force required to compress a spring varies directly as the change in the length of the spring. If a force of 18 pounds is required to compress a certain spring 4 inches, how much force is required to compress the spring 7 inches?

Plot the pair of points and determine the slope of the line containing them. Graph the line. (-4,1); (0,-5) What is the slope of the line containing the points (-4,1) and (0,-5)? Select the correct choice below and fill in any answer boxes within your choice. A. The slope is (Type an integer or a simplified fraction.) B. The slope is undefined.

Differentiate the given function y with respect to x. The possible relative extrema can be found by setting y' equal to zero, and are as follows. We will need to check test intervals to determine if these are actual extrema. Earlier we found that y'= 7x6 - 7. Differentiate y' with respect to x. So, y" 0 when x = and the possible point of inflection is as follows. We will need to check test intervals to determine if it is an actual inflection point.

Find the value of $15,000 at the end of one year if it is invested in an account that has an interest rate of 3.60% and is compounded in accordance with the rules below. a. compounded monthly b. compounded daily (assuming a 365-day year) c. compounded quarterly a. What is the value if the money is compounded monthly? (Do not round until the final answer. Then round to the nearest cent as needed.) b.What is the value if the money is compounded daily? $ (Do not round until the final answer. Then round to the nearest cent as needed.) c. What is the value if the money is compounded quarterly? $ (Do not round until the final answer. Then round to the nearest cent as needed.)

Describe the effect that the transformations y = 1.5. f(x - 5) + 4 have on the graph of y = f(x). Your numerical answers should all be positive. help (numbers)

Evaluate the given expression if x = -1 and y = 2. 6x + 3y/ 1+ 4y