Basic Math Questions and Answers

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.

Find the x- and y-intercepts. -8x-7y=56 Write each intercept as an ordered pair. If there is more than one intercept, use the "and" button. Select "None" if applicable.

If we draw the relative frequency histogram for x where: x = 5, 5, 3, 6, 6, 6, 9, 10 class start = 2.5 class width=2 what is the relative frequency of the class: 6.5 to 8.5 Give answer to nearest thousandth (3 decimal places).

Solve the following equation. |-2x| = |14| Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. B. There is no real solution.

Identify the population and the sample: A survey is conducted to determine the opinion of Illinois residents about cell phones. From the 350 IL residents surveyed, 140 think law should prohibit the use of cell phones in public places. Population: [Select] Sample: [Select]

The sum of three numbers is 2. The first number minus the second plus the third is -2. The first minus the third is 2 more than the second. Find the numbers. What is the first number? What is the second number? What is the third number?

A basic cellular package costs $40/month for 60 minutes of calling with an additional charge of $0.20/minute beyond that time. The cost function C(x) for using z minutes would be • If you used 60 minutes or less, i.e. if if x ≤ 60, then C(z) = 40 (the base charge). • If you used more than 60 minutes, i.e. (z - 60) minutes more than the plan came with, you would pay an additional $0.20 for each of those (x - 60) minutes. Your total bill would be C(x) = 40 +0.20 (x- 60). If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use?

Use shifts and scalings to graph the given function. Then check your work with a graphing utility. Be sure to identify an original function on which the shifts and scalings are performed. f(x) = (x+3)²-3 What is the original function? y = (Type an expression. Simplify your answer.)

Start with the parent function: f(x) = (x - h)² + k Choose your own horizontal shift: h = Choose your own vertical shift: k = Write the resulting vertex form of the function: Write the resulting standard form of the equation: Where is the vertex? Where is the y-intercept?

Two trains leave stations 252 miles apart at the same time and travel toward each other. One train travels at 85 miles per hour while the other travels at 95 miles per hour. How long will it take for the two trains to meet?

Find the inverse function and graph both f(x) and f(x) on the same set of axes. Check your work by looking for the required symmetry in the graphs. f(x) = 1-8x The inverse function is f¹(x) =

Solve using the elimination method. 3r-5s=-26 5r+ 3s = 36 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is r=- OB. There are infinitely many solutions. The solution set is {(r,s)|3r-5s = - 26}. C. There is no solution.

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.

Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer. Then, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. B. There are infinitely many solutions. C. There is no solution. What is the decimal approximation for the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution set is A. The solution set is B. There are infinitely many solutions. C. There is no solution.

Solve the equation. 5x-3=2+3x The solution is x =

A college student takes the same number of credits each semester. Before beginning college, the student had some credits earned while in high school. After 3 semesters, the student had 41 credits, and after 6 semesters, the student had 68 credits. If C(t), is the number of credits after t semesters, write the equation that correctly models this situation. Provide your answer below: c(t)=

Use synthetic division to divide. 5- 4x + 3x²x3 / + 1

Solve the equation. 2x-(6x+6)=3x-34 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is B. There is no solution.

Using the given equation, (a) find the intercepts of its graph and (b) graph the equation. -2x+4y=16 (a) What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The x-intercept is -8 (Type an integer.) B. There is no x-intercept. What is the y-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is 4 (Type an integer.) B. There is no y-intercept

Tum-Tum has three times as much money as Binky. Po-Po has $150 more than Binky. If Tum-Tum doubled his money and both Binky and Po-Po earned another $200 each, they would have exactly enough to buy a pair of Saints season tickets which cost $2150. How much money do each of them have?

Solve the given equation for the variable. (Enter your answers as a comma-separated list.) 5³ - 3x