Math Questions

Molly starts an IRA (Individual Retirement Account) at the age of 32 to save for retirement. She deposits $450 each month. The IRA has an average annual interest rate of 8% compounded monthly. How much money will she have saved when she retires at the age of 65? Round your answer to the nearest cent, if necessary. Answer

Find an and a5 for the following geometric sequence. a1= 162, r=-3

Consider the curve given parametrically by x=4-t², y = t³ - 3t. (a) List all of the points (x, y) where the tangent line is horizontal. (b) List all of the points (x, y) where the tangent line is vertical.

Find the present value of the ordinary annuity. Payments of $40,000 made semiannually for 12 years at 4.2% compounded semiannually A. $674,532.00 B. $741,616.00 C. $751,336.00 D. $748,056.18

A circle has the equation x² + y²-3x+6y + 9 = 0. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is. (Type an ordered pair, using integers or fractions.) The radius of the circle is. (Type an integer or a fraction.) (b) Use the graphing tool to graph the circle. (c) What are the intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed. Type exact answers for

The half-life of radium-223 is approximately 11.43 days. How much of an 8 gram sample of radium-223 would remain after 3 days? Round to three decimal places.

A spinner is divided into 15 identical sectors and labeled 1 through 15. How many spins are expected for a multiple of 4 to be spun 7 times? Select from the drop-down menu to correctly complete the sentence. The spinner is expected to have to spin approximately Choose... times for a multiple of 4 to be spun 7 times.

Where is the function defined by f(x)= In (x) increasing? Where is f(x) decreasing? Where is the tangent line horizontal? Where is f(x) increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your selection. A. The function is increasing on the interval(s) (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never increasing. Where is f(x) decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your selection. A. The function is decreasing on the interval(s). (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never decreasing. Where is the tangent line horizontal? Select the correct choice below and, if necessary, fill in the answer box to complete your selection. A. The tangent line of the function is horizontal at x = (Use a comma to separate answers as needed.)

Two number cubes are rolled for two separate events: Event A is the event that the sum of numbers on both cubes is less than 10. Event B is the event that the sum of numbers on both cubes is a multiple of 3. In terms of a reduced fraction, find the conditional probability of B given that A occurs first.

At the beginning of an experiment, a scientist has 304 grams of radioactive goo. After 180 minutes, her sample has decayed to 19 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) = How many grams of goo will remain after 14 minutes? You may enter the exact value or round to 2 decimal places.

If the alternator-to-engine drive ratio is 2.35 to 1, what rpm will the alternator have when the engine is idling at 500 rpm? Hint: Use a direct proportion. The alternator will have rpm when the engine is idling at 500 rpm. (Type a whole number or a decimal.)

Perform the indicated operation. Note that the denominators are the same. Simplify the result, if possible. (x² 1 / x² - 4x - 5) - (34 -2x / x² - 4x - 5 ) -

A man buys a car for $39,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $600 for 60 months, how much must he put down? (Round your answer to the nearest cent.) $

A random sample of 16 light bulbs has a mean life of 650 hours and a standard deviation of 32 hours. Assume the population has a normal distribution. Construct a 90% confidence interval for the population mean. (Answer in 2 decimal places.)

Complete the sentence below. For the ellipse x²/25 + y²/9 = 1, the value of a is , the value of b is , and the major axis is the -axis. For the ellipse x²/25 + y²/9 = 1, the value of a is , the value of b is , and the major axis is the -axis.

Sandi weighs 145 lb, but she has started a new diet plan that promises she will lose 3 lb per month every month until she reaches her goal weight. Write a linear equation that describes how much Sandi weighs, V, each month, and then use your equation to find out how many months it will take her to get to 115 lb. Use X to denote the number of months since Sandi started her new diet. The linear equation that describes how much Sandi weighs each month is =

Country A has an exponential growth rate of 3.6% per year. The population is currently 4,957,000, and the land area of Country A is 27,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land? This will happen in year(s). (Round to the nearest integer.)

The following diagram is a rough sketch of a storage shed. The owner needs to know the area of the roof so that he knows how many roof shingles to purchase. The angle between the two edges of the roof (the gable) is 110°. The roof panels could be described as the quadrilateral DHKC and DHGE. The front has a width of 12 ft and the width of the side is 28 feet. The triangle CDE is an isosceles triangle. QUESTION: Find the area of the two quadrilaterals that represent the roof AND explain how you were able to determine the area.

The following equations define x = = f(t) and y = g(t) implicitly as functions of t. x³ - 2²2² = -17, 5y³ + 3t² = 67, Find the slope of this curve at the point on the curve associated with t = 3. Slope = Σ

Use properties of logarithms to rewrite the given expression as the logarithm of a single quantity, then enter that single quantity in the answer box to complete the expression. 2 logb (x) + 2logb (y) logb( )

Find the equation in x and y for the line tangent to the curve given parametrically by x = sint, y = cost, at the point on the curve associated with t=π/4 y =

The pulse rates of 174 randomly selected adult males vary from a low of 35 bpm to a high of 115 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 99% confidence that the sample mean is within 4 bpm of the population mean. Complete parts (a) through (c) bela a. Find the sample size using the range rule of thumb to estimate σ. n= (Round up to the nearest whole number as needed.)

In the first part of the video, Freddie was posed the problem of having 400 baseball cards and selling 150 cards, and asked how many cards he had left. He used a standard algorithm to set up the problem and solve. Freddie explained his work in the following steps. (i) zero minus zero is zero (ii) zero minus five is five (iii) four minus one is three Which step is incorrect in Freddie's work? (iii) (ii) (i) None, the solution is correct

Find the prime factorization of 96 using a factor tree. Enter the prime factors you find from smallest to largest separated by the multiplication symbol, e.g. 2x2x3 x 5.

In Exercises 5-12, let P = (-2, 2), Q = (3, 4), R = (-2, 5), and S = (2, -8). Find the component form and magnitude of the vector. 9. 2QS 10. (√2) PR 11. 3QR + PS 12. PS - 3PQ

The distribution of NBA scores follows approximately a normal distribution with a mean of 102 and a variance of 81. What is the probability that a team from a randomly chosen game will score between 93 and 111 points in a given game? 0.317 0.500 0.683 0.954

Write the negation of the statement. There is at least one person in this class who won't pass. Choose the correct negation for the given statement. All people in this class won't pass. Some people in this class will pass. No one in this class will pass. All people in this class will pass.

Compute the ordinary interest, the exact interest, and their difference. Round answers to the nearest cent. Ordinary Exact Principal, Rate, and Time Interest Interest Difference $3,650 at 8% for 75 days $294.10, $292.00, $2.10 $73.00, $60.00, $13.00 $60.83, $60.00, $0.83 $60.83, $59.00, $1.83

An ordered pair (x, ß) for which the system of linear equations (1 + a)x+By+ z = 2 ax + (1+B)y+z=3 ax+By+ 2z = 2 has a unique solution, is (a) (2, 4) (b) (-4, 2) (c) (1, -3) (d) (-3, 1)

Based on the following data, what is the quick ratio, rounded to one decimal point? Accounts payable $ 30,000 Accounts receivable 60,000 Accrued liabilities 5,000 Cash 40,000 Fixed assets 670,000 Intangible assets 50,000 Inventory 69,000 Long-term investments 80,000 Long-term liabilities 100,000 Prepaid expenses 1,000 Temporary investments 30,000 a. 3.7 b. 2.9 c. 4.3 d. 5.1

Bonds Payable has a balance of $1,000,000 and Discount on Bonds Payable has a balance of $12,500. If the issuing corporation redeems the bonds at 99, what is the amount of gain or loss on redemption? a. $2,500 gain b. $22,500 gain c. $22,500 loss d. $2,500 loss

Water is dropped at the rate of 2cm³/sec into a cone of semivertical angle 45°. The rate at which periphery of water surface changes when height of the water in the cone is 2 cm, is :- 1 cm/sec 2 cm/sec 3 cm/sec 4 cm/sec

Solve the following logarithmic equation. Use a calculator if appropriate. log (4x+3)+ log 2 = log (7x+8) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { }. (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is the empty set, Ø.

Find the center of mass of the given system of point masses lying on the x-axis. m₁ = 0.2, m₂ = 0.3, m3 = 0.4, m4 = 0.1 X₁ = 1, X₂ = 2, X3 = 3, x4 = 4 x̄ =

Which of the following is a prime number? Enter a, b, c, d, or e. a. 211 b. 187 C. 219 d. 183 e. 177

A rectangular piece of cardboard, 100 cm by 40 cm, is going to be used to make a rectangular box with an open top by cutting congruent squares from the corners. Calculate the dimensions (to one decimal place) for a box with the largest volume.

Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs. The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $68,600 for sales and $49,000 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole number.) sales department $ service department $ X X

In July 2005, the internet was linked by a global network of about 352.8 million host computers. The number of host computers has been growing approximately exponentially and was about 36.9 million in July 1998. (a) Find a formula for the number, N, of internet host computers (in millions of computers) as an exponential function of t, the number of years since July 1998, using exponential function of the form N(t) = aet. What are the values of a and k in your model? help (numbers) a = k= (Either enter the answer in exact form, or a numerical approximation accurate to four decimal places.) (b) Based on your equation above, what is the annual percentage growth rate of N? (Enter your answer in exact form, or a numerical approximation that is accurate to 0.01 %. Do not use approximations before the final answer.) % By (c) What is the doubling time of N? years (round your answer to the nearest 0.001 years)

Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.3, 0.2, and 0.5, respectively. What is the expected number of books a customer will purchase The expected number of books that the customer will purchase is (Type an integer or a decimal.)

(1 point) Sylvia is running a marathon. Let D(1) represent the total distance in kilometers she has runt hours after starting. Find a formula for each of the following functions in terms of the function D. Note: Be careful with your input variables. a) M (h), the total distance in meters she has run after h hours. M(h) = b) K(m), the total distance K(m) = kilometers she has run after m minutes. c) C(s), the total distance in centimeters she has run after s seconds C(s) =

Dani had $200 in her savings account. When she turned 18, the bank began charging her a $5.00/month fee. Write a function in terms of a for the balance of her savings account if she doesn't notice the monthly fee. Complete the following. Use standard slope-intercept form. B(a)=

The numbers of seats in the first 12 rows of a high-school auditorium form an arithmetic sequence. The first row has 9 seats. The second row has 11 seats. a. Write a recursive formula to represent the sequence. b. Write an explicit formula to represent the sequence. c. How many seats are in the 12th row?

39.9% of consumers believe that cash will be obsolete in the next 20 years. Assume that 6 consumers are randomly selected Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years. The probability is

Which of the following statements are equivalent to the statement "Not all cats do not like having their belly rubbed"? Select the correct answer below: Some cats do not like having their belly rubbed. Some cats like having their belly rubbed. All cats do not like having their belly rubbed. All cats like having their belly rubbed.

Green plants absorb sunlight to power photosynthesis, the chemical synthesis of food from water and carbon dioxide. The compound responsible for light absorption and the color of plants, chlorophyll, strongly absorbs light with a wavelength of 642.nm. Calculate the frequency of this light. Round your answer to 3 significant digits.

Which of the following is a composite number? Enter a, b, c, d, or e. a. 29 b. 37 c. 57 d. 41 e. 31

There is a formula that estimates how much your puppy will weigh when it reaches adulthood. The method we present applies to medium-sized breeds. First find your puppy's weight w at an age of a weeks, where a is 16 weeks or less. Then the predicted adult weight W = W(a, w), in pounds, is given by the formula W = 52w/a In this exercise we consider puppies that weigh w = 2 pounds at age a. (a) Write a formula for W as a function of the age a. W =

Decide if you are given enough information to prove that the quadrilateral is a parallelogram for each description below. One pair of opposite sides are congruent. All angles are congruent. One angle is a right angle. Diagonals are perpendicular. One pair of consecutive angles are congruent. Diagonals are perpendicular and congruent Two pairs of opposite angles are congruent. One pair of opposite sides are both parallel and cc

Let fix) be defined such that f(-1) = 1 and f'(x) = cos(-1/x2+x), where -2<x<1. Part A: Find the tangent line approximation for f(-0.9). Part B: If f(-0.9) has an actual value of 1.3, use the shape of the graph to determine if this is an overestimate or underestimate. Justify your answer.

Find the critical value z necessary to form a confidence interval at the level of confidence shown below. c=0.83 Z0=0