Math Questions

A bicycle has a listed price of $$31.95 before tax. If the sales tax rate is 6.5 %, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.

For the rational function f(x) =1-x³/x2-x , identify any removable discontinuities. There is a removable discontinuity at x = 3. There are no removable discontinuities for this function. There is a removable discontinuity at x = 1. There are removable discontinuities at x = 0 and x = 1.

A biologist observes a population of birds over a 10 year period. At the beginning of the period, there were 223 thousand birds. By the end of the period, there were 182 thousand birds. Assume the population of birds can be modeled using an exponential function. If P(t) is the population (in thousands), where t is the time since the start of the period, then P(t) ___________(Round your parameters to four decimal places) The population of birds reached 149 thousand ___________ after the start of the observation period (Round your answer to the nearest whole number) What will the population of birds be 17 years after the start of the observation period? ___________ (Round your answer to the nearest thousand)

List the intercepts of the equation y = 3x³ - 81. List 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.) B. There are no intercepts.

Simplify the expression 1+ 3/2y/-5/xy1 and give your answer in the form of A/B

There are five different fish, each of a different species, in a tank that needs to be cleaned. What is the probability that the first two scooped out are a goldfish and a guppy, in that order, assuming both are included among the species in the tank? 1/20 1/60 1/12 1/30

Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid in the first octant bounded by the coordinate planes and the plane z = 5 - x - y

Multiply and simplify your answer. x² - 25/x² 10x + 25.x - 5/x

(ii) How many groups of nine can be chosen that contain at least one man? As in Example 9.5.7b, consider the relationship between the set of groups that consist entirely of women and the set of groups with at least one man. This thinking leads to the conclusion that the number of groups with at least on man is (iii) How many groups of nine can be chosen that contain at most three women? A group of nine that contains at most three women can contain no women, one woman, two women, or three women. So, the number of groups of nine that contain at most three women is

A marble is drawn from a box containing 3 yellow, 2 white, and 14 blue marbles. Find the odds in favor of drawing the following. (a) A yellow marble (b) A blue marble (c) A white marble (a) In reduced form, the odds in favor of drawing a yellow marble are __ to __ (Simplify your answers.) (b) In reduced form, the odds in favor of drawing a blue marble are __ to __ . (Simplify your answers.) (c) In reduced form, the odds in favor of drawing a white marble are __ to __ (Simplify your answers.)

A baseball team had a batting average of 0.245 with a standard deviation of 0.02. What is the probability that a player had a batting average between 0.245 and 0.305? Use the 68-95-99.7 normal distribution curve.

If the market rate of interest is equal to the contract rate of interest, a. the selling price of the bond cannot be determined. b. the bonds will sell for less than their face amount. c. the bonds will sell for more than their face amount. d. the bonds will sell for their face amount.

A gallon of paint will cover 560 square feet of wall space. If I plan to paint a room whose walls measure 2240 square feet, how many gallons of paint will I need? To paint the room, __ gallons of paint will be needed.

Write four equivalent expressions for the given expression. -8v-5/v-2 Choose the expressions that are all equivalent. A.8v-5/v-2,-(8v-5)/v+2,-8v+5/-v+2,8v-5/v+2 B.-(8v-5)/v-2,-8v+5/v-2,-(8v-5)/-v+2,(8v-5)/-v+2 C.-8v-5/v+2,-(8v-5)/v-2,-8v-5/v+2,8v-5/v+2

(1 point) Perform the indicated operation. Note that the denominators are different. Simplify the result, if possible. 2/y-4 6/y-6

One bag contains three white marbles and five black marbles, and a second bag contains four white marbles and six black marbles. A person draws one marble from each bag. Find the probability that both marbles are black. 55/91 25/72 3/8

The amount of time to complete a physical activity in a PE class is normally distributed with a mean of 39.8 seconds and a standard deviation of 6.3 seconds. Round answers to 4 decimal places. a) What is the probability that a randomly chosen student completes the activity in less than 32.3 seconds? b) What is the probability that a randomly chosen student completes the activity in more than 45.3 seconds? c) What proportion of students take between 34.6 and 44.9 seconds to complete the activity? d) 80% of all students finish the activity in less than seconds.

A company makes three sizes of cardboard boxes: small, medium, and large. It costs $3.50 to make a small box, $5.00 for a medium box, and $5.50 for a large box. Fixed costs are $8000. (a) Express the cost of making x small boxes, y medium boxes, and a large boxes as a function of three variables: C= f(x, y, z). f(x, y, z)= (b) Find (6000, 9000, 8000). Interpret your answer. It costs the company $ to make 6000 small boxes, 9000 medium boxes, and 8000 large boxes. (c) What is the domain of f? x≥0, -∞≤y≤∞, z≥0 -∞≤x≤∞, -∞≤y≤∞, x≤0, y ≤0, z≥0 x≥0, y ≥0, z≥0 -∞≤x≤∞, y≥0, z≥0

Which of the following are equivalent forms of the rational expression. 2x² +5x−3/ x²-x-12 (Select all that apply.) (2x - 1)(x-3)/(x-4) (x-3) 2x + 1/x-4 (x+3)(2x - 1)/(x-4) (x+3) 2(x2+5x-3)/x²-x-12 2x - 1/x-4 (2x+1)(x-3)/(x-4)(x-3)

Use the following function to answer parts a through c f(x) = 11x³+127x² +67x+11 a. List all rational zeros that are possible according to the Rational Zero Theorem. +-1, +-1/11+-11 (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) b. Use synthe division to test several possible rational zeros in order to identify one actual zero. One rational zero of the given function is __ (Simplify your answer) c. Use the zero from part (b) to find all real zeros of the polynomial function. The real zeros of the function are

Graph the funtion. f(x) = 3√x-2 Plot five points on the graph of the function, as follows. • Plot the first point using the x-value that satisfies √√x-2 = 0. • Plot two points to the left and two points to the right of the first point. Then click on the graph-a-function button.

Given an hyperbola which passes through point P has vertices V, and V₂, and has foci F, and F₂, which of the following statements is a fact about hyperbolas? Choose the correct statement below. A. If 2a is the length of the conjugate axis, then |d (P,V₁)-d(P,V₂)|= 2a. B. If 2a is the length of the transverse axis, then d (P,F₁)-d(P,F₂)|=2a. C. If 2a is the length of the transverse axis, then |d (P,V₁)-d(P,V₂)|=2a. D. If 2a is the length of the conjugate axis, then |d (P,F₁) -d (P,F₂)|=20.

Cookies are packaged in boxes that measure 18 cm by 20 cm by 6 cm. A larger box is being designed by increasing the length, width and height of the smaller box by the same amount so that the volume is at least 5280 cm³. What are the minimum dimensions of the larger box?

Classify the following events as either independent or dependent. Independent Dependent Add an answer item! Add an answer item!

If n + 1 integers are chosen from the set {1, 2, 3,..., 2n}, where n is a positive integer, must at least one of them be even? To answer this question, let S = {1, 2, 3,..., 2n}, where n is a positive integer, and note that in S there are exactly _____ number of odd integers in T, it is ______ odd integers. Since n + 1 is _____ v for at least one of the elements of T to be even. Thus, the answer to this question is _____

A corporation issues for cash $1,000,000 of 8%, 20-year bonds, interest payable annually, at a time when the market rate of interest is 10%. The straight-line method is adopted for the amortization of a bond discount or premium. Which of the following is true? a. The amount of unamortized premium decreases from its balance at issuance date to a zero balance at maturity. b. The amount of unamortized discount decreases from its balance at issuance date to a zero balance at maturity. c. The amount of the annual interest expense gradually decreases over the life of the bonds. d. The amount of the annual interest expense is computed at 8% of the bond carrying amount at the beginning of the year.

A construction crew has just finished building a road. The crew worked for 43/8 days. If they built 21/7 kilometers of road each day, what is the total length of road they built?

Which great Mosque might have inspired Guarino Guarini for the design of the vaults of S. Lorenzo church in Turin? a. The Friday Mosque, Isfahan b. The Sehzade Mosque in Istanbul c. Taj Mahal, Agra d. Great Mosque of Córdoba

Which of the following statements is true? "Unusual" values of z are those such that |z| < 1 If the confidence level increases then the critical values will move away from 0. If the number of items in a sample is increased, then the margin of error computed within a confidence interval will also increase. A 95% confidence interval for the population mean can be interpreted to say that the population mean has a 95% chance of falling within the limits of the confidence interval

Find the area of the triangle. a=14, b=17, c = 22

At the fair you buy an unlimited ride pass for $28 and plan to play some games costing $1.50 per game. Write a function in x that represents the total amount you spend on rides and games at the fair. Be sure to indicate any domain restrictions. Answer f(x) =______ for x ___

A grocery store buys cereal using the cost function c(n) = { 2n when n < 100 1.9n when 100 ≤ n ≤ 500 1.8n when n > 500 where n is the number of boxes of cereal the grocery store buys and c(n) is the cost of the cereal. The grocery store then sells the cereal using the sales function s(c) = 1.3c. What is the cost of the cereal if the grocery store buys 250 boxes?

There are thirty-six students in your chemistry class, including yourself. You will be in a randomly selected lab group of four people, counting yourself. What is the probability that your three friends Ann, Bob, and Carlos are in your lab group?

Find the indefinite integral using the substitution x = 10 sin(θ). (Use C for the constant of integration.) ∫1/(100 - x²)3/2dx

Amy and Chuck each buy a house in the same neighborhood for $250,000. Amy's monthly mortgage payment is $400 more per month than Chuck's. Which one of the following statements could explain this difference? Amy chose a shorter term for her mortgage, so her monthly payments are higher. Chuck has a lower credit score, so his interest payments are also lower. Amy made a larger down payment, so her monthly payments are also larger. Chuck made a larger down payment, so his monthly payments are larger.

Find the intervals where the graph is concave up or concave down. Also find all inflection points and critical points. Do not graph. (V.A. -vertical asymptote, I.P.= inflection point, C.U. = concave up, C.D. = concave down) f(x) = (x - 5)4/3 C.D. x < 5, C.D. x > 5, I.P. x = 5 C.D. x < 5, C.U. x > 5, I.P. x = 5 C.U. x < 5, C.D. x > 5, stationary point x = 5 C.U. x < 5, C.U. > 5, LP. x=5 C.U. x < 5, C.U. x > 5, V.A. x = 5

Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by parts. Use C for the constant of integration.) ∫ xe4x dx

Explain how you know when a scenario describes a permutation situation versus a combination situation. Give an example of a permutation scenario not mentioned in this lesson.

Find the compound interest and future value. Round your answers to the nearest cent. Do not round intermediate steps. Principal Rate Compounded Time $530 4.35% Quarterly 5 years The future value is $ and the compound interest is $

Write the exponential function y= 500e-0.07t in the form y =abt (a) Once you have rewritten the formula, give b accurate to at least four decimal places. b= _______ help (numbers) If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual growth/decay rate. The rate you determine should be positive in either the case of growth or the case of decay (by choosing decay, the negative rate is implied). (b) The annual ? rate is % per year (round to the nearest 0.01%).

For the polynomial below, 1 is a zero. f(x) = x³ - 7x² + 8x - 2 Express f(x) as a product of linear factors.

If a building contractor hires 6 day laborers and 1 concrete finisher, his payroll for the day is $1110. If he hires 1 day laborer and 4 concrete finishers, his daily cost is $875. Find the daily wage for each type of worker. Solve the problem using matrices. The daily wage for the laborer is $. The daily wage for the concrete finisher is

In the Ohio lottery Classic Lotto game 6 numbers are drawn at random from 49 possible numbers. What is the probability of your lottery ticket matching all six numbers? Hint: Order is not important.

In 2012, there were about 313 million people in the United States, and just under 9 million of them had assets of $1 million or more. At the same time, there were 8,336,697 people in New York City, and 727,100 of them had assets of $1 million or more. Compute the density of millionaires in the general population for New York City and the whole United States. Based on those numbers, select any of the choices below which are true. New York has a density of millionaires more than twice that of the country as a whole. The density of millionaires is about the same for New York City as for the United States. Millionaires seem to prefer New York City to much of the rest of the United States. There is something in the water of New York City that encourages millionaires.

Which of the following is true for Walter Gropius? (Select all that apply) □ a. Gropius envisioned that workshop projects would attract commissions or production licenses □ b. Gropius arranged painters such as Paul Klee and Wassily Kandinsky to teach principles of form □ c. In Staatliches Bauhaus he created a new type of institution dedicated to training students in all aspects of de □ d. He firmly believed that fine art came through mastery of craft □ e. Gropius believed that students do not need to be given manual instructions in craft workshops □ f. He saw the curriculum of the Bauhaus as a continuation of the Beaux-Arts training

David has available 400 yards of fencing and wishes to enclose a rectangular area. Express the area A of the rectangle a a function of the width w of the rectangle. For what value of w is the area largest? What is the maximum area? Sketch the graph of A(w).

A restaurant packed lunches for an event. Each lunch had a sandwich, a side, and a cookie. •Sandwich choices: ham, turkey, cheese • Sides: chips, apple, carrot sticks, celery, orange • Cookie choices: chocolate chip, oatmeal, sugar, snickerdoodle Assuming the probabilities of each selection are the same for all options in a category, what is the probability of randomly choosing a lunch containing a cheese sandwich, chips, and a chocolate chip cookie? 1/60 60 1/1.320 1,320

Estacia wants to learn more about excluded values. a. Explain to Estacia why x cannot be 4 in the expression x+2/x-4 b. Find the excluded values of x in each of the expressions of problem 3-99. c. Create an expression that has the excluded values of x = -6 and x≠1/3 . Be prepared to share your expression to the class.

In ΔHIJ, ∠H ≈ ∠J, JH = 10 and IJ = 14. Find the length of HI. ?

The cost of reserving a particular domain name is $22 up front plus $4.89 per month. Find the cost of reserving that domain name for the following: (a). 2 months The cost of reserving a particular domain name for 2 months is