Math Questions

Given the recurrence relation x₁ = 3, x₁ = 3X(n-1) What is the solution? Xn= 2^n for all negative integers n Xn= 3^n for all negative integers n Xn= 3^n for all positive integers n Xn= 2^n for all positive integers n

An investor bought stock for $20,000. Fourteen years later, the stock was sold for $40,000. If interest is compounded continuously, what annual nominal rate of interest did the original $20,000 investment earn? The annual nominal rate of interest earned is%. (Round to two decimal places as needed.)

Use the ALEKS graphing calculator to find the x-intercept(s) and vertex for the quadratic function. f(x)=x²+5x+1 Round to the nearest hundredth if necessary. If there is more than one x-intercept, separate them with commas. If applicable, click on "None". x-intercept(s): vertex:

Solve the equation for solutions over the interval [0,2x) by first solving for the trigonometric function. 8 sin x + 20 = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an exact answer, using x as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.

Short-term classes: Does taking a class in a short-term format (8 weeks instead of 16 weeks) increase a student's likelihood of passing the course? For a particular course, the pass rate for the 16-week format is 59%. A team of faculty examine student data from 40 randomly selected accelerated classes and determine that the pass rate is 78%. Which of the following are the appropriate null and alternative hypotheses for this research question? A. O Ho: P = 0.59; Ha: p = 0.59 B. O Ho: P = 0.59; Ha: p > 0.59 C. O Ho: p = 0.78; Ha: p = 0.78 D. O Ho: p = 0.78; Ha: p > 0.59

Find the coordinates for the vertex of the following quadratic function algebraically. Be prepared to show your algebraic work. P(x) = -9x + x2 Enter the exact coordinates separately in each blank. (Do not round values.) The vertex is (

Use the sinking fund formula to determine the payment needed to reach the accumulated amount. Round to the nearest cent. Quarterly payments with 5.8% interest compounded quarterly for 3 years, and will accumulate to $82,000. A. $2,285.22 B. $6,305.36 C. $1,657.43 D. $1,789.73

Sets D and H are defined as follows. D = {0, 2, 3, 4, 6} H={-1, 1, 3, 4, 6} Answer each part below. Write your answer in roster form or as Ø. (a) Find. the union of D and H. (b) Find the intersection of D and H.

Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings. How many paintings will Sergio have in his art collection after his donation? Write your answer as an expression. paintings

a. Approximate the given quantity using Taylor polynomials with n=3. b. Compute the absolute error in the approximation assuming the exact value is given by a calculator. e^0.09 a. p3 (0.09) (Do not round until the final answer. Then round to seven decimal places as needed.)

Consider the trigonometric equation 2 sin(0) + 3 = 4, where the angle is measured in degrees. One set of solutions is θ= Another unique set of solutions is θ=

Use the pythagorean theorem to find the length of TI. (leg)2 + (leg) = (hypotemuse)" Enter the answer in simplified form. 245

Given the angle θ= -7π/6 To which quadrant does θ belong? (Write your answer as a numerical value.) Find the reference angle for θ IN RADIANS. Find the point where θ intersects the unit circle.

Consider the graphs of the equations below. y = 3x + 5 (y-7)= 2(x - 1) -12x + 3y = 15 -y = 6x - 5 Select the true statement. A. All four lines cross the y-axis at (0,5). B. All four lines have a positive x-intercept. C. All four lines have a negative x-intercept. D. All four lines cross the x-axis at (5,0).

A robot's body is made up of a rectangular prism with side lengths 48 inches by 24 inches by 36 inches. The head is made up of a cylinder with a height of 24 inches and a radius of 6 inches. What is the volume of the robots head and body in cubic feet? 250.08 ft3 25.57 ft3 51.15 ft3 37.68 ft3

Suppose that $2000 is invested at a rate of 4.7%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 8 years. Do not round any intermediate computations, and round your answer to the nearest cent.

David borrowed money from a credit union for 3 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $1890. How much money did he borrow? If necessary, refer to the list of financial formulas.

Find the monthly payment R needed to have a sinking fund accumulate the future value A. The yearly interest rate r and the time t in years are given below. Interest is compounded monthly. A=$7,000; r=7%; t = 1 R=$ (Round up to the nearest cent.)

Michelle is a sales representative for a publishing company. For the past 16 years, she has exceeded her annual sales goal, primarily by selling mathematics textbooks. Therefore, she will also exceed her annual sales goal this year.

Lauren's science class is taking a field trip to the nearest natural history museum. The museum is 62.5 miles from Lauren's school. The class plans to stop after 30 minutes, or 0.5 hours, to visit a local wildlife refuge. The bus driver plans to drive at an average speed of 50 miles per hour. How many hours will the second part of the trip take? Write your answer as a whole number or a decimal. hours

Considering only the values of ß for which sin ß tan ß sec ß cot ß is defined, which of the following expressions is equivalent to sin ß tan ß sec ß cot ß? Select the correct answer below: sec ß cot β tan β cot tan β tan ß csc ß sec ß

f(x) = 2x and g(x) = x + 3 Step 1 of 2: Find the formula for (f + g)(x) and simplify your answer. Then find the domain for (f + g)(x). Round your answer to two decimal places, if necessary. Answer (f + g)(x) = Domain=

Given that f(x) = x² + 2x and g(x) = x + 2, calculate (a) (fog)(-2)= (b) (gof)(-2)= Enter an integer or decimal number [more..]

-6z² +6z +140/ (z + 5)² (3z-5) Determine the correct partial fraction decomposition for the expression above. Provide your answer below:

Teresa wants to save $600 to buy a TV. She saves $17 each week. The amount, A (in dollars), that she still needs after w weeks is given by the following function. A (w)=600-17w Answer the following questions. (a) If Teresa still needs $277, how many weeks has she been saving? weeks (b) How much money does Teresa still need after 7 weeks?

The following exercise presents problems similar to exercises from the previous sections of this chapter. Use Newton's Method to approximate the solution. the point on the graph of f(x) = 8 - x² that is closest to the point (1, 0). (Round your answer to three decimal places.)

Fill in the blanks below in order to justify whether or not the mapping shown represents a function. The mapping diagram above a function since where there

A certain species of fish is to be introduced into a lake, and wildlife experts estimate the population will grow to P(t) = (684)2^1/3, where t represents the number of years from the time of introduction. Step 1 of 2: What is the doubling-time for this population of fish?

Solve the following equation for B, where -π ≤ β < π. sec^2β-1/tan(-β) = -√3/3 Select the correct answer below: β = π/6 β = -π/6 β = -5π/6 and π/6 β = -π/6 and 5π/6

Let x represent the number of hours Trenton spends studying algebra, and let y represent the number of hours he spends studying history. For parts (a) - (e), write an inequality to represent the given statement. (a) Trenton has a total of at most 6 hr to study for both algebra and history combined. An inequality that represents this statement is

You have 80 yards of fencing to enclose a rectangular region. a) Write a function for the area of the rectangular region in terms of x. b) Find the dimensions of the rectangle that maximize the enclosed area. c) What is the maximum area?

A ball is thrown from a height of 160 feet with an initial downward velocity of 12 ft/s. The ball's height h (in feet) after t seconds is given by the following. h=160-12t-167² How long after the ball is thrown does it hit the ground? Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

The average score of all golfers for a particular course has a mean of 70 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 71. 0.1293 0.0228 0.4772 0.3707

Each year, Giselle plants and grows tomatoes in her backyard garden. Her plants typically produce a total of around 300 tomatoes during the season. However, each week approximately 4 tomatoes are not usable due to destruction by local wildlife. Write an equation to represent the average number of usable tomatoes, t, produced per week over the course of wweeks in the growing season. A. t = 300/w-4w B. t = 300/4w C. t= 300-4w/w D. t= 300+4w/w

Online photos: A poll surveyed 1802 internet users and found that 843, of them had posted a photo or video online. Can you conclude that less than half of internet users have posted photos or videos online? Use the a 0.05 level of significance and the critical value method. State the null and alternate hypotheses. Ho: H₁: The hypothesis test is

In the Bible, Joash was 7 years old when he became king; Uzziah was 16; Ahaz was 20; Manasseh was 12; Josiah was 8; and Jehoiachin was 18. What was the average age of these young men when they became kings of Judah? Write the remainder as a fraction. On the blank, write the answer in simplest form.

For f(x) = x² +4 and g(x)=√x-2, find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice. A. The domain of fog is {x}. (Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The domain of f o g is all real numbers. (b) (gof)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice.

Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not. D = Ga +3h³a

Use the Quotient Rule of Logarithms to write an expanded expression equivalent to log2(4x+1/x). Make sure to use parenthesis around your logarithm functions log(x + y). Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button. Provide your answer below:

A pet store has 7 puppies, including 4 poodles, 2 terriers, and 1 retriever. Rebecka and Aaron, in that order, each select one puppy at random without replacement. Find the probability that Aaron selects a retriever, given Rebecka selects a retriever. The probability is (Type an integer or a simplified fraction.)

Three friends split the cost of a pizza and a salad. The pizza costs $15 and the salad costs $6. Which expression can you use to find how much each person owes? (15+6)÷3 15+(6x3) (15+3)+6

If AC has length 13 and BC has length 18, find: • The length of AB: • The measure of angle B (in degrees): • The measure of angle C (in degrees): If you use a calculator to find a decimal approximation, your answer must be accurate to at least 3 decimal places. If you're using a calculator, be sure that your calculator is set to degrees, not radians. You are also allowed to use the inverse trig functions in your answer instead of using a calculator. sin ¹(z) can be entered as arcsin(x) or asin(x).

4. As you've heard, the smallest pair of amicable numbers, 220 and 284, were known to the ancient Greeks, the next pair of amicable numbers, 17296 and 18416, were discovered by the Islamic mathematician Ibn al-Banna in the 14th century (and rediscovered by Fermat). Thousands more have been found since. In Italy in 1866, however, 16-year-old Nicolo Paganini discovered a small pair of amicable numbers, 1184 and 1210, that had been overlooked for centuries. Verify that 1184 and 1210 are an amicable pair.

The mean weight of male nurses working at a local hospital is less than 172 lbs. Express the null and alternative hypotheses in symbolic form for this claim. Ho: µ H₁: µ Use the following codes to enter the following symbols: > enter >= <enter <= enter !=

There was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 3.1% each year. Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between y and f.

Hurricane damage: In August and September 2005, Hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed, and of those that survived, many required extensive cleaning. It was thought that cleaning of flood-damaged homes might present a health hazard due to the large amounts of mold present in many of the homes. In a sample of 362 residents of Orleans Parish who had participated in cleaning of one or more homes, 74 had experienced symptoms of wheezing, and in a sample of 182 residents who had not participated in cleaning, 21 reported wheezing symptoms (numbers read from a graph). Can you conclude that the proportion of residents with wheezing symptoms is greater among those who participated in the cleaning of flood-damaged homes? Let P1 denote the proportion of residents with wheezing symptoms who had cleaned flood-damaged. homes, and let P2 be the population proportion with wheezing symptoms who did not participate in the cleaning of flood-damaged homes. Use the a= 0.05 level of significance and the critical value method. State the null and alternate hypotheses. Ho: H₁: This hypothesis test is a

Use identities to find values of the sine and cosine functions for the angle measure. θ, given that cos2θ= and 90° < θ < 180 sinθ = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) cosθ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Solve equation by using the quadratic formula. List the solutions, separated by commas. 4w²+3w6=0 W=

Considering only the values of β for which csc² βcos (2β) is defined, which of the following expressions is equivalent to csc² βcos (2β)? Select the correct answer below: 2 2 - sec² β 2sin²β - tan² β 2sin β cot²β - 1

Select the correct answer from each drop-down menu. ΔABC has vertices at A(11, 6), B(5, 6), and (5, 17). ΔXYZ has vertices at X-10, 5), -12, -2), and Z-4, 15). ΔMNO has vertices at M-9, -4), M-3, -4), and O(-3, -15). ΔJKL has vertices at 17, -2), K12, -2), and L(12, 7). ΔPQR has vertices at P(12, 3), Q(12, -2), and A(3,-2). Triangle ABC and triangle XYZ Triangle ABC and triangle MNO Triangle JKL and triangle ABC Triangle PQR and triangle XYZ can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.