Basic Math Questions and Answers

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)

For a-b, determine whether the inequality below correctly represents each situation. If so, write "yes." If not, write "no" and the correct inequality for the situation described. 100+ 23.75x ≤ 10+ 43.75x a. Gym A charges members $100 to sign up plus $23.75 each month. Gym B charges members $10 to sign up plus $43.75 each month. After how many months would a membership to Gym A be less expensive than Gym B? b. Moving Company A charges a fee of $23.75 plus $100 per hour. Moving Company B charges a fee of $43.75 plus $10 per hour. How many hours would it take for Moving Company A to be no more expensive than Moving Company B?

Briefly explain why a positive result on a screening test for a disease does not necessarily mean that a patient has the disease. The test may have produced a true negative. true positive. false positive. false negative.

Which denotation of "scholastic" has the best connotation for the sentence below? Students go to school to get an and a diploma. A. sophistication B. education C. edification

A certain forest covers an area of 4100 km². Suppose that each year this area decreases by 8%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.

Use the AC Method to factor 2x² -11x-6 .Split the linear term, writing 2x² -11x-6 as the sum of two binomials: (be careful about how you choose to split-11x, or the AC method won't work!) Factor out the GCF of each binomial: Complete the process of factoring by grouping: I (your answer should now be completely factored!)

Given that the intercepts of a graph are (-8,0) and (0,3), choose the statement that is true. Select the correct choice below. A. The x-intercept is - 8, and the y-intercept is 3. B. The x-intercepts are - 8 and 3. C. The y-intercept is - 8, and the x-intercept is 3. D. The y-intercepts are - 8 and 3.

Digitalis is a technology company that makes high-end computer processors. Their newest processor, the luteA, is going to be sold directly to the public. The processor is to be sold for $5100, making Digitalis a profit of $502. Unfortunately there was a manufacturing flaw, and some of these luteA processors are defective and cannot be repaired. On these defective processors, Digitalis is going to give the customer a full refund. Suppose that for each luteA there is a 12% chance that it is defective and an 88% chance that it is not defective.

Use a formula to find the surface area of each polyhedron described. (a) a rectangular prism that is 3 feet wide, as tall as it is wide, and twice as long as it is tall

The Berry Bakery makes a ratio of 3:4 cookies to muffins. If they make 12 cookies on Monday, how many muffins did they make? A. 9 B. 12 C. 16 D. 24

The 7th term in an arithmetic sequence is 17 and the 50th term is 123. What is the sum of all the terms from the 7th term through the 50th term (including the 7th and 50th terms)? Starting with the 1st term - what is the sum of the first 50 terms?

A set of n = 50 values has average 2,482.06. After all the work is completed, you discover that a value originally recorded as 2,148 should have been 2,418. If you replace the value 2,148 by 2,418, what will be the corrected average?

Each course at college X is worth either 4 or 5 credits. The members of the men's swim team are taking a total of 53 courses that are worth a total of 227 credits. How many 4-credit courses and how many 5-credit courses are being taken? There are 4-credit courses and 5-credit courses being taken.

Find the zeros: f(x) = 2x³ - 3x² - 11x + 6 The zeros are - 2 and 3. The zeros are -2,1/2 and 3 The zeros are -2 and 1/2 The zeros are 1/2 and 3

Medical researchers are excited about a new cancer treatment that destroys tumors by cutting off their blood supply. To date, the treatment has been tried only on mice, but in mice it has been nearly 100% effective in eradicating tumors and appears to have no side effects. What should we conclude about these studies and their ability to provide evidence of the effectiveness of the new treatment in treating cancer in humans? The studies suffer from lack of realism and generalizability. The studies are convincing, assuming that proper randomization and control were used. The studies are convincing, assuming the results have been replicated in a large number of mice. The studies display a high statistical significance, so there is nearly 100% certainty that the treatment will work in humans.

Write an equation of the line that passes through (-5,-3) and is parallel to the line defined by 2x+y=-4. Write the answer in slope-intercept form (if possible) and in standard form (4x+By=C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.

Trent can deliver his newspapers in 10 minutes. It takes Lois 40 minutes to do the same route. How long would it take them to deliver the newspapers if they work together It will take minutes.

Solve the following system of equations by the elimination method. What is the solution of the system? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is B. There are infinitely many solutions. The solution set is C. There is no solution.