Math Questions

The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 9000 Fun Noodles per day during the summer. Raising the price to $4 will cause the sales to fall to 5000 Fun Noodles per day. a. Assume that the relationship between sales price, x, and number of Fun Noodles sold, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (sales price, number sold). The equation is y=-4000x+21000. (Type your answer in slope-intercept form.) b. Predict the daily sales of Fun Noodles if the price is $3.50. sales

Company XYZ has 34 employees in the Finance Department, 45 technicians, and 32 in the Engineering Department. The HR Department received 20 complaints from the whole company. There were 5 complaints from the technicians and 3 from the Finance Department. There were 7 complaints from the Engineering Department. What percent of complaints came from either the technicians or the Finance Department?

In drawing the slope field for the differential equation dy/dx= x+3y-4, I would draw a short line segment for different points on the x-y plane. What slope should I draw the line segment at the point (0,-2)? Your Answer:

For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. f(x) = 5x² - 2x+5 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The point(s) at which the tangent line is horizontal is (are) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) B. There are no points on the graph where the tangent line is horizontal. C. The tangent line is horizontal at all points of the graph.

A 75 L gas tank has a leak. After t hours, the remaining volume, V, in litres is V(t) = 75 (1 - t/24) ²,0≤ t ≤ 24. Use the product rule to determine how quickly the gas is leaking from the tank when the tank is 60% full of gas.

The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is Multiple Choice O пp≥5. O n(1-P)≥5. O np≤5. O n(1-p)≤5 and np≤5. O np≥5 and n(1-P)≥5.

In a certain weather forecast, the chances of a thunderstorm are stated as "1 in 25." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is____

A manufacturer of personal computers tests competing brands and finds that the amount of energy they require is normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. If the lowest 25 percent and the highest 30 percent are not included in a second round of tests, what are the upper and lower limits for the energy amounts of the remaining computers? Multiple Choice [269.76, 300.24] [278.86, 289.78] [280.22, 289.78] [280.22, 300.24]

Let C be the event that a randomly chosen person has a pet cat. Let D be the event that a randomly chosen person has a pet dog. Identify the answer which expresses the following with correct notation: Of all the people who have a pet cat, the probability that a randomly chosen person has a pet dog. Select the correct answer below: O P(DIC) O P(C AND D) O P(D) AND P(C) O P(CID)

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .3 inches. What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long? Multiple Choice .8413 .6293 .3707 .1587

Use the change of base formula to evaluate log12(1/5) to two decimal places and type your answer in the space below. If your answer is between -1 and 1, be sure to begin your answer with a0. For example if the calculator reads -0.31415 you would type -0.31. log12(1/5)=___

Assume that a rectangle with sides x and y is expanding with time. Let y=2x and x(t)=3t+1. What is the formula for the rate of change of the area with respect to time? dA/dt=12(3t-1) dA/dt=(3t+1) dA/dt=4(3t - 1) dA/dt=12(3t+1)

The time between breakdowns of an alarm system is exponentially distributed with mean 10 days. What is the probability that there is less than 1 breakdown on a given day? .9048 .3679 .0952 .000

What is the solution to this equation? log(2x 100) = 3 A. x= 100 B. x= 550 C. x= 1,000 D. x= 450

Let a = log2 3, b= log2 5 and c=log₂ 7, A. Write the following in terms of a, b and c i. (K:2) log₂ (45): 2a+b-c ii. (K:2) log₂ (52.5): a+b+c-1 B. (1:2) A student write the answer as log₂ (X) = 2a-3b+c-1, find the value of X: (write the number in fraction, if write as 7/8) C. (C:2) Assume that a positive integer Q is between 1 and 20. Find all possible values of Q such that log₂ Q cannot be expressed using a, b and c (such as 1, 2, 3, 4, etc): The reason is because

An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the investment when interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. Then find (e) the doubling time T for the given interest rate. P = $60,000, r=4.8%, t = 5 yr a) The future value of the investment when interest is compounded annually is $ (Type an integer or a decimal. Round to the nearest cent as needed.) b) The future value of the investment when interest is compounded monthly is $ (Type an integer or a decimal. Round to the nearest cent as needed.) c) The future value of the investment when interest is compounded daily is $ (Type an integer or a decimal. Round to the nearest cent as needed.) d) The future value of the investment when interest is compounded continuously is $. (Type an integer or a decimal. Round to the nearest cent as needed.) e) Find the doubling time for the given interest rate. T = yr (Type an integer or decimal rounded to two decimal places as needed.)

The total number of public electric charging units available for hybrid vehicles has increased exponentially since 2006. The number of outlets A(t) at these alternative fueling stations t years after 2006 can be approximated by A(t) = 224(2.69), where t= 0 corresponds to 2006. How many outlets were available in 2008, in 2010, in 2011? The number of outlets available in the year 2008 was approximately (Simplify your answer. Round to the nearest integer as needed.)

To further justify the Cofunction Thebrem, use your calculator to find a value for the given pair of trigonometric functions. The trigonometric functions are cofunctions of complementary angles. Round each answer to four places past the decimal point. sin 14°, cos 76⁰ sin 14° = cos 76⁰ =

Assume that 75% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places: a. There are some lefties (≥1) among the 5 people. 0.9990 b. There are exactly 3 lefties in the group. 0.2637 c. There are at least 4 lefties in the group. 0.6328 d. There are no more than 2 lefties in the group. 0.1035 e. How many lefties do you expect? 3.75 f. With what standard deviation?

Ordered: Oxacillin sodium 900 mg in 125 mL D5W IV PB to be infused over 45 min, Drop factor: 20 gtt/mL, Flow rate: gtt / min 5.6 gtt / min 0.56 gtt / min 560 gtt / min 56 gtt / min

Let G be the event that a randomly chosen student is a girl. Let S be the event that a randomly chosen student plays sports. Identify the answer which expresses the following with correct notation: Given that the student is a girl, the probability that a randomly chosen student plays sports. Select the correct answer below: P(SIG) P(G|S) P(G AND S) P(S) AND P(G)

Allison buys a spool of thread for sewing. There are 8 yards of thread on the spool. She uses 2 meters. How much thread is left on the spool in meters? Round your answer to the nearest thousandth, if necessary.

Calculate the scaling factor that will adjust the recipe to produce the desired yield. (Round to 2 decimal places). Recipe Yield 12 6-oz crabs Desired Yield 50 2-oz crab cake).Scaling factor is Maximum number of characters (including HTML tags added by text editor): 32,000

In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan. Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable responses, 15 were males. If one citizen is randomly selected, find the probability that person is male and has a favorable opinion. 0.40 0.65 0.62 0.55 0.25

The function A(x)= x(x + 10) describes the area A of the opening of a rectangular window in which the length is 10 feet more than the width, x. Find the dimensions of the window if the area of the opening is to be 119 square feet by solving A(x) = 119 The width of the window is feet and the length of the window is feet (Simplify your answers.)

Given the final answer in f(x+h)-f(x)/ h (a) 2x + h²-2 (b) 1 (c) 2x +h+2 (d) h

Solve the equation. 5(x+5)=8x+8-3x+17 Select the correct choice below and, if necessary, fill in the answer box that completes your choice. OA. The solution set is { }. (Type an integer or a simplified fraction.) OB. All real numbers are solutions. OC. The equation has no solution.

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models N(t)=0.194³-7.88+2+12.9t+375 and M(t) = 0.031³-0.25t² +6.7t+173 where t represents the year, with t = 0 corresponding to 2000. Find and interpret (N-M)(t). (N-M)(t) = 0.163+³+7.632-6.2t+202, which represents the difference between the number of Navy personnel and the number of Marines personnel. (N-M)(t) = 0.163³-7.632-6.2t-202, which represents the difference between the number of Navy personnel and the number of Marines personnel. (N-M)(t) = 0.163³ +7.632 +6.2t+202, which represents the difference between the number of Navy personnel and the number of Marines personnel. (N-M) (t) = 0.163³-7.63²-6.2t+202, which represents the difference between the number of Navy personnel and the number of Marines personnel. (N-M)(t) = 0.163³-7.632 +6.2t+202, which represents the difference between the number of Navy personnel and the number of Marines personnel.

Let f(x)=2x-5. g(x)=x2, and h(x) = 3x + 4. Perform the indicated composition. f(g(x)) =

Solve the following equation using a graphical method. 12x-16-41-7x x= Type an integer or a simplified fraction.)

A rectangle has a width of x centimeters and a length that is 10 centimeters longer than its width. If the total perimeter is 220 centimeters, what is the measure of the width? 40 centimeters 200 centimeters 50 centimeters 4 centimeters

Consider a function, f(x)=x²-3x, A. determine the average rate of change in the interval [-2, 4] B. determine the instantaneous rate of change at x = 1. You can use the small number approximation, take h = 0.01 for example. C. sketch the curve and the perspective tangent at x=1.

A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find the probability of drawing a yellow chip, not replacing it, and then choosing a blue chip. 3/100 9/625 3/200 18/625

A town has a population of 14000 and grows at 3.5% every year. What will be the population after 14 years, to the nearest whole number?

Use a calculator to find the following natural logarithm. In 67 In 67= (Round to four decimal places as needed.)

The amount of money (in trillions of dollars) that is invested in passively managed mutual funds can be approximated by the function A(x) = 0.35(1.14)*, where x = 1 corresponds to the year 2001. (a) What was the amount of money in passively managed mutual funds in 2012 and 2016? (b) If the trend continues, what is the first full year when the amount of passively managed mutual funds exceeds $7.1 trillion? (a) Which of the following describes how to find amount of money in passively managed mutual funds in 2012 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the amount of money in passively managed mutual funds in 2012, substitute for x and evaluate to find f(x). B. To find the amount of money in passively managed mutual funds in 2012, find the intersection point of the graphs y = 0.35(1.14) and y = of money in passively managed mutual funds in 2012 is represented by the y-coordinate In 2012, the amount of money in passively managed mutual funds was about $ (Type an integer or decimal rounded to the nearest hundredth as needed.) trillion. Which of the following describes how to find the amount of money in passively managed mutual funds in 2016 using the given information? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal.) A. To find the amount of money in passively managed mutual funds in 2016, find the intersection point of the graphs y = 0.35(1.14)* and y= of money in passively managed mutual funds in 2016 is represented by the y-coordinate. B. To find the amount of money in passively managed mutual funds in 2016, substitute for x and evaluate to find f(x).

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a graphing utility. y = cos 3x y = 0 X = 0 X =π/6

Given the functiony = -2x² -5x - 4, give the number and type of solutions. Then use the quadratic formula to find the zeros. Show all work to receive full credit. Please upload a photo of your work.

Suppose an investor deposits $26,000 into a savings account for 6 years at 6.25% interest. Find the total amount of money in the account if the interest is: 1. Compounded annually, then the investment is worth __ after 6 years. 2. Compounded quarterly, then the investment is worth __ after 6 years. 3. Compounded monthly, then the investment is worth __ after 6 years. 4. Compounded weekly, then the investment is worth __ after 6 years. 5. Compounded daily, then the investment is worth __ after 6 years. • Round your answers to the nearest cent. • Use a dollar sign to indicate that your answer is a monetary value.

Recall that profit equals revenue minus cost. For the revenue and cost functions shown, answer parts (a) through (e) below. R(x) = 420x-2x² and C(x) = 100x + 10,880, with 0≤x≤ 150 (a) Find the break-even point. The break-even point(s) is (are) x = (Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as needed.)

The 1999 article about the CA lottery in the paper San Luis Obispo Tribune gave the following information on the age distribution of adults: 35% are between the ages of 18 and 34; 51% are between the ages of 35 and 64; and 14% are 65 and older. The article also gave information on the age distribution of those who purchase lottery tickets: People ages 18-34 purchase 36 tickets; people 35-64 purchase 130 tickets; and people 65 and older purchase 34 tickets. Suppose the data resulted from a random sample of 200 lottery ticket purchasers. Based on this sample, is it reasonable to conclude that the proportions stated in the article are accurate at 5% level of significance? Please be sure to give the value of the test statistic, P- value, and null rejection region.

Match the items. a. 8√2 b. 71 c. -15 d. 2i√12 1. √-49 2.√-48 3. √128 4. √-25 x √-9

The solution of differential equation y1y3 = 3y2² is (where a, b, c are arbitrary constants & yn denotes nth derivative of y w rt'x O x = ay² + by + c O y = ax² + bx + c O y = ae^x + be-^x +c O x = ae^y + be^-y+c

a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. f(x) = -1/x, a=1 approximate -1/1.05 a. p₁ (x) =

What is the asymptote of f(x) = -2(3)^x+4? y = 4 y=-2 y=0 y=3

Consider the set of real numbers: {x| -1 < x ≤0}. Graph the set of numbers on the real number line.

During the 2005 football season, Team Tackle beat Team Sack by 15 points. If their combined scores totaled 39, find the individual team scores. Team Tackle's score was points.

Let z₁ and z₂ be two complex numbers satisfying (z-w)²+(z-w²)² = 0, where w is non real cube root of unity. Also let 'a' be a variable point on the circle |z+1/2|=√3/2 and a₁, a2 are values of a such that lal is maximum and minimum respectively. On the basis of above information, answer the following questions : Number of complex numbers a such that la - a₁l +|a -a₂l= √6 is

12.Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular. a.Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right angles. b.Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular. c.Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right angles. d.Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not perpendicular. A B C D

Each baseball team has nine players and each football team has eleven players. Five schools have both baseball and football teams. Three schools have only a baseball team. How many players are there for all eight schools?