Basic Math Questions and Answers

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

A bank loaned out $16,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%? How much of the $16,000 did the bank loan out at 7%?

One hundred volunteers who have agoraphobia are available for a study. Fifty are selected at random and are given the drug imipramine, which is believed to be effective in treating agoraphobia. The other 50 are given a placebo. A psychiatrist evaluates the symptoms of all volunteers after two months to determine if there has been substantial improvement in the severity of their symptoms. What would make this study double-blind? Neither the volunteers nor the psychiatrist were allowed to see each other during the session when the psychiatrist evaluated symptom severity. Neither the volunteers nor the psychiatrist knew which subjects received the placebo. All of these answers are correct. Neither drug had any identifying marks on it.

Where does the polynomial y = x² + 4x + 6 cross the y-axis? (0,6) (6,0) (0, -6) and (-6, 0) (0, 3) and (6, 0) (0, 0) and (0, -6)

A customer went to a garden shop and bought some potting soil for $17.50 and 4 shrubs. The total bill was $53.50. Write an equation to find the price of each shrub (p). What is the price of each shrub?

The formula A = 21.2 e 0.0417t models the population of a US state, A, in millions, t years after 2000. a. What was the population of the state in 2000? b. When will the population of the state reach 29.8 million? a. In 2000, the population of the state was 21.2 million. b. The population of the state will reach 29.8 million in the year (Round down to the nearest year.)

Vera is currently using 16,000 MB of storage on her phone, and she is deleting 2.2 MB of music each minute. Keira is currently using 11,275 MB of storage on her phone, and she is adding 16.7 MB of music each minute. Write an inequality that could be used to find the number of minutes it will take for Vera to be using no more than the amount of storage that Keira is using.

Graph y=6x-6 by plotting points. Based on the graph, determine the intercept(s) Use the graphing tool to graph the equation.

Determine whether Rolle's Theorem can be applied to fon the closed interval [a, b]. (Select all that apply.) f(x)=9-x-91, [0, 18] Yes, Rolle's Theorem can be applied. No, because fis not continuous on the closed interval [a, b]. No, because fis not differentiable in the open interval (a, b). No, because f(a) = f(b). If Rolle's theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)

Avicenna, a major insurance company, offers five-year life insurance policies to 65-year-olds. If the holder of one of these policies dies before the age of 70, the company must pay out $21,300 to the beneficiary of the policy. Executives at Avicenna are considering offering these policies for $938 each. Suppose that for each holder of a policy there is a 4% chance that they will die before the age of 70 and a 96% chance they will live to the age of 70. (If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the beneficiary. Avicenna can expect to make money from offering these policies. In the long run, they should expect to make dollars on each policy sold. Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose dollars on each policy sold. Avicenna should expect to neither make nor lose money from offering these policies.

A laptop computer is purchased for $2150. After each year, the resale value decreases by 35%. What will the resale value be after 5 years? Use the calculator provided and round your answer to the nearest dollar.

Marcus wants to set up a special fund so he can go to some concerts throughout the year. If his ticket purchases last year totaled $620, estimate how much he should save each month to have approximately the same amount available for tickets this year.

Solve the equation. x / x+7 = 5/4 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.

Find two positive numbers satisfying the given requirements. The product is 1200 and the sum of the first plus three times the second is a minimum. (first number) (second number)