Math Questions

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.

Solve the following logarithmic equation. Express your answer as either an exact expression or a decimal approximation rounded to four decimal places. If there is no solution, indicate "No Solution (Ø)." In(x-3) - In(x) = 5

Compute the area of the region R bounded by the curve r = 1- cosθ. This curve was sketched in the previous homework (and you can refer to that sketch). Use the double integral method (polar integrals; section 14.3), that is, integrate function 1 over the region.

In the last lesson, you came up with a formula for the tax a couple owed based on their wage income. A similar formula for a single person with taxable income more than $9,075 but not over $36,900 is T 0.15w-1976.25, where T is the tax owed, and w is the wage income. This formula is an example of a linear equation, and equation where every term is a constant or a single variable not raised to a power. This particular linear equation involves two variables. In this equation w would be considered the input or independent variable since it is the value typically provided to the equation, and T is the output or dependent variable since its value depends on the input, and its value is the output of the expression on the right side of the equation.

Suppose that a random sample of 9 adults has a mean score of 80 on a standardized personality test, with a standard deviation of 8. (A higher score indicates a more personable participant.) If we assume that scores on this test are normally distributed, find a 99% confidence interval for the mean score of all takers of this test. Then find the lower limit and upper limit of the 99% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers one decimal place. (If necessary, consult a list of formulas.)

A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $75 per hour. a. Write a linear model that represents the total cost of recording an album as a function of studio time (in hours). Use the variablet to represent the number is used. C= b. Is it less expensive to purchase 12 hours of recording time at the studio or a $750 music software program that you can use to record on your own com It is less expensive to purchase Explain your reasoning. The cost for 12 hours of recording time is $

If a simple random sample is taken, and a 90% confidence interval of 1.53 <o< 2.08 is constructed from the sample statistic, s, the following is the correct interpretation: "We are 90 % confident that the interval from 1.53 to 2.08 actually does contain

Select the correct answer from the drop-down menu. Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75° with the ground. The height of the kite from the ground is meters.

Locate the critical points of the following function. Then use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither. f(x) = 2x³-6x² +2 What is (are) the critical point(s) of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) is (are) x = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. There are no critical points for f.

Sam and Jen had a tax liability of $5,115 last year. They were entitled to tax credits of $119 and withholding amounted to $110 per month. Sam and Jen owed other taxes of $678. Calculate the amount of the refund or the amount of taxes due (as the case may be). $4,354 refund $4,886 refund $4,208 due $4,354 due

Complete the table of values for f(x) = 6x . Complete the table of coordinates.

Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. f(x) = 6(x + 2)5/2 (2x-7), on [-2,00)

Sandy and Bill put 2,870 coins into rolls of 50 coins each. How many complete rolls did they make? How many coins were left over?

The mean SAT score in mathematics is 519. The founders of a nationwide SAT preparation course claim that graduates of the course score higher, on average, than the national mean. Suppose that the founders of the course want to carry out a hypothesis test to see if their claim has merit. State the null hypothesis Ho and the alternative hypothesis H, that they would use.

Condense the following expressions into a single logarithm by applying the properties of logarithms. Make sure your final answer is written as a single logarithm. a. 2 log(x) - 5 log(y) + 9 log(z) = b. -2 log(z) + 5log(x) - 9 log(y) =

- If initial velocity of a particle is 40 m/s and it is moving in a straight line under constant retardation 5 m/s². The ratio of displacement in 4 second and 4th second will be

There are 125 passengers in the first carriage, 150 passengers in the second carriage and 175 passengers in the third carriage, and so on in an arithmetic sequence. What's the total number of passengers in the first 7 carriages? 2800 875 1750 700 1400

Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 25 liters per minute. There are 700 liters in the pond to start. Let W represent the amount of water in the pond (in liters), and let T' represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below.

Given the ellipse below, determine the coordinates of the two foci. Enter your answers as ordered pairs (x, y) and leave in radical form. (x-1)2/36 + (y+2)2/16 = 1

Find all solutions by factoring. 3w² - 13w=10

Jaquan hopes to earn $1500 in interest in 2.9 years time from $120,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds semi-annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

A quadratic equation can be written in vertex form or in standard form. Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why. a. Factor the equation. b. Graph the parabola. c. Identify the vertex, minimum, or maximum of the parabola. d. Solve the equation using the quadratic formula.

Janine has 12 cookies. Mark has three more than half the number of cookies that Janine has. Angelo has twice the number of cookies that Mark has. What is the ratio of the number of Angelo's cookies to the number of Janine's cookies? 3:4 3:2 1:1 4:3 2:3

A bank loaned out $31,000, part of it at the rate of 8% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $2,710.00. How much was loaned at each rate?

The revenue function is given by R(x) = x p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x) = 49(2), find the revenue if 14 units are sold. Round to two decimal places.

Estimate 25% of $98.50. Do not give the exact answer use estimation.

Find the intervals on which p is increasing and decreasing. p(z)=z² cosz - 2 cos z - 2z sin z on ( π/2, 5π/2) Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function p is increasing on the open interval(s) and decreasing on the open interval(s). (Simplify your answer. Type an exact answer, using it as needed. Type your answer in interval notation. Use a comma to separate answers needed.) B. The function p is decreasing on the open interval(s). The function p is never increasing. (Simplify your answer. Type an exact answer, using C. The function p is increasing on the open interval(s) (Simplify your answer. Type an exact answer, using D. The function p is never increasing or decreasing.

Solve the inequality: -2x+5<8 The answer as an inequality: The answer in interval notation:

The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $250 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function. C(n) = 250n+6500 Answer the following questions. (a) If the total cost is $12,250, how many tons is the company transporting? (b) What is the total cost of transporting 14 tons?

Tessa has recently inherited $5600, which she wants to deposit into a CD account. She has determined that her two best bets are an account that compounds monthly at an annual rate of 4.7% (Account 1) and an account that compounds semi-annually at an annual rate of 5.1% Which account would pay Tessa more interest?

Jenny buys a dining table costing $795.95. The store charges $55 for delivery. State taxes are 5.5% and local sales taxes are 1.5%. What is the total purchase price? (Round your answer to the nearest cent.) $905.67 $906.67 $909.67 $910.52