Math Questions

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

Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below. 60, 58, 64, 64, 68, 50, 57 On the eighth day, she drinks 82 ounces of water. Select all the true statements about the effect of the eighth day's amount on Joanna's daily amount distribution. The average daily amount of water is the same with or without the inclusion of the eighth day's amount. The interquartile range of the data decreases when the eighth day's amount is included in the data. The median amount of water is the same with or without the inclusion of the eighth day's amount. The median amount of water is higher when the eighth day's amount is included in the data. The interquartile range of the data increases when the eighth day's amount is included in the data.

Solve the equation using the quadratic equation. x² = 2-6x

Fill in the blanks: The goal of an optimization problem is to find the maximum or minimum value of the__ function subject to the__ The goal of an optimization problem is to find the maximum or minimum value of the function subject to the

The equation V = 17.8 +3.8x gives the value (in thousands of dollars) of an investment after a months. Interpret the Slope in this situation. The value of this investment is

A right circular cone is inscribed inside a larger right circular cone with a volume of 200 cm³. The axes of the cones coincide, and the vertex of the inner cone touc the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the volume of the inner cone. The ratio of the height of the inner cone to the height of the outer cone is

The point P(2, -1) lies on the curve y = 1/(1-x). (a) If Q is the point (x, 1/(1-x)), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x: (ii) 1.9 (iii) 1.99 (vi) 2.1 (vii) 2.01 (i) 1.5 (v) 2.5 (iv) 1.999 (viii) 2.001 (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2, -1). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(2, -1).

Justify whether x³ + y2 = 3xy has a horizontal tangent at (2, 4). No, because 3y-3x²/2y-3x≠0 at (2,4) Yes, because 3y-3x²/2y-3x=0 at (2,4) Yes, because 3y-3x²/2y-3x=0 at (2,4) No, because 3y-3x²/2y-3x≠0 at (2,4)

Find the distance between the points using the following methods. (2,7), (9, 9) (a) the Distance Formula (b) integration

Calculate the derivative of the following function. y = sin (4 cos x)

What is the polynomial function in factored form? f(x) = x³ + 2x² - 5x - 6 Enter your answer by filling in the boxes. f(x)=

Suppose a student wishes to minimize the objective function on a closed interval, but finds that it has only a single local maximum. Where should the student look for the solution to the problem? Choose the correct answer below. A. Determine the value of each endpoint for the objective function. B. Determine the value where the objective function is equal to 0. C. Determine the value where the first derivative of the objective function is equal to D. Determine the value where the second derivative of the objective function is equal to

Let Z be a standard normal random variable. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) P(Z > -1.25) = (b) P(Z ≤ 1.70) = (c) P(-0.66 <2<2.15) = 0

Find the quotient and simplify your answer. If the quotient is undefined, indicate "undefined". 0 ÷23/24

x = -5 : Determine if the relation is a function. If it is not, identify two ordered pairs as proof.

Solve the following system of equations. Provide your answer below: x² - y²= 11 -3x² + 2y²= -3

Determine whether the following statements are true and give an explanation or counterexample. a. The zeroes of f' are - 3, 1, and 4, so the local extrema are located at these points. Choose the correct answer below. A. False. The zeros of f' are the inflection points of f. B. True. The zeros of f' are the local extrema of f. C. True. The zeros of f' are local extrema so long as the denominator is nonzero at those points. D. False. A zero of f' is a critical point and is a local extremum so long as it is in the domain of f(x) and f'(x) changes sign. Take, for example, the function f(x) = (x+3)³(x - 1)³(x-4)³.

A 10-ft-tall fence runs parallel to the wall of a house at a distance of 9 ft. Find the length of the shortest ladder that extends from the ground to the house without touching the fence. Assume the vertical wall of the house is 20 ft high and the horizontal ground extends 25 ft from the fence. The length of the shortest ladder is

The label on a 20 mL aminophylline vial indicates a strength of 500 mg/20 mL. (a) How many mL of aminophylline would contain 200 mg of this drug? (b) How many mg of aminophylline would be contained in 1 mL of this solution?

A company's profit in dollars has a function of the number of widgets sold, w, is given by this function: -2w² + 120w - 30= P. How many widgets were sold if the profit was $970? 0 50 60 120 30

A theorem states that one local extremum implies absolute extremum. Verify that the following function satisfies the conditions of this theorem on its domain. Then find the location and value of the absolute extrema guaranteed by the theorem. f(x) = -3x² + 4x-6 The function has one local__ on its domain __ because f' changes sign from __to __ as x increases through the critical point, c.