Math Questions

1. (5 pts) Graph one continuous function f(x) such that all of the following hold: a. f(x) is increasing on (-∞, -4) b. f(x) is constant on (-4,2) c. f(x) is decreasing on (2,5) d. f(x) is increasing on (5,0)

Marcus needs to bike at least 80 miles this week for his training. If he has already biked 23 miles this week, then how many miles should he bike on each of the 5 remaining days this week?

Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each. y = 7.5x y = 5.5x + 10 1. Substitute: 7.5x= 5.5x + 10 How many classes could Anna take so that the total cost for the month would be the same? What is the total monthly cost when it is the same for both gyms?

Tamika finds some nickels and quarters in her change purse. How many coins does she have if she has 10 nickels and 11 quarters? How many coins does she have if she has a nickels and y quarters?

Consider the parabola given by the equation: f(x) = - 4x² - 14x - 3 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two intercepts of the parabola and write them as a list, separated by commas: It is OK to round your value(s) to to two decimal places.

Suppose that $100,000 from a retirement account is invested in a large cap stock fund. After 25 yr, the value is $183,777.11. (a) Use the model A=Pez^rt to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent.

Victor and his sister have both been saving money to help pay for college. Victor deposited $750 at a local bank 3 years ago, earning a simple interest rate of 4% paid upon withdrawal. His sister deposited $800 at a local bank 3 years ago, earning a simple interest rate of 3% paid upon withdrawal. Compare the interest Victor earned after 3 years to how much interest his sister earned after 3 years?

Catherine earns a yearly salary of $75,000. Lola earns a yearly salary of $80,000. Catherine will receive a salary increase of $4,800 per year, and Lola will receive a salary increase of $3,900 per year. Which equation can be used to find n, the number of years it will take Catherine to earn the same salary as Lola? 75,000+ 4,800n = 80,000+ 3,900n 75,000n +4,800 = 80,000n + 3,900 75,000n + 4,800 = 80,000+ 3,900n 75,000n +4,800n = 80,000n + 3,900n

The equation c = 2.5t represents the cost, c, for t tickets to the school play. Does a value of 3.5 for t make sense in this situation? Explain your reasoning.

Use Hooke's Law to determine the work done by the variable force in the spring problem. Four joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.40 meter.

On separate sets of axes, graph each of the following equations. If you do not remember any shortcuts for graphing, you can always make an x→y table. a. y=-2x +7 b. y = 3/5x + 1 c. 3x + 2y = 6 d. y = x²

A hospital has 5 doctors (Dr. A, Dr. B, Dr. C, Dr. D and Dr. E). An administrator is going to randomly choose 2 of them to be on a committee. Write out the sample space (all the possible outcomes) for this random phenomenon.

Two lines are cut by a transversal. If you want to show that the lines are parallel, which of the following angle pairs would you show to be congruent? I. Alternate interior II. Vertical III. Consecutive interior IV. Alternate exterior V. Corresponding A I, IV, and V only B I and IV only C I, II, and V only D I, III, and V only

Solve the equation. 3x+6/3 - 4x / X-2 =X Select the correct choice below and, if necessary, fill in the answer box to complete your A. The solution set is (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is the empty set.

What will a $150,000 house cost 10 years from now if the price appreciation for homes over that period averages 6% compounded annually? The future cost of the house will be $ (Do not round until the final answer. Then round to the nearest cent as needed.).

Use your calculator to find the value of y for the system of equations using matrices. 2x - 3y + 2z = 13 3x+y=z=2 3x - 4y - 3z = 1

A radio station claims that the amount of advertising per hour of broadcast time has an average of 12 minutes and a standard deviation equal to 1.2 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 15 minutes. Calculate the z-score for this amount of advertising time. z = 1.15 z = -2.50 Z=-1.15 z = 2.50

Select the correct answer below: x-intercepts: (7,0), (-5,0), and (-6,0). y-intercept: (0,0) x-intercepts: (-7,0), (5,0), and (6,0). y-intercept: (0,0) x-intercepts: (7,0), (-5,0), and (-6,0). y-intercept: (0, -210) x-intercepts: (-7,0), (5,0), and (6,0). y-intercept: (0,210) x-intercepts: (7,0), (-5,0), and (-6,0). y-intercept: (0,210) x-intercepts: (-7,0), (5,0), and (6,0). y-intercept: (0, -210)

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $90 and you pay 70% of the manufacturer's recommended list price. Plan B offers an annual membership fee of $30 and you pay 90% of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? (Assume that the distributions being compared have approximately the same shape.) A score of 92 A score of 688 Both scores have the same relative position.

An investment company pays 8% compounded semiannually. You want to have $17,000 in the future. (A) How much should you deposit now to have that amount 5 years from now? (Round to the nearest cent.) (B) How much should you deposit now to have that amount 10 years from now? (Round to the nearest cent.)

In a state's Pick 3 lottery game, you pay $1.48 to select a sequence of three digits (from 0 to 9), such as 600. If you select the same sequence of three digits that are drawn, you win and collect $354.12. Complete parts (a) through (e). a. How many different selections are possible?

What is -9.2(8x-4) +0.7(2+6.3x) simplified? -69.19x-32.39 -69.19x + 38.2 72.2x + 41.21 75x-338.2

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = x, y = 0, X = 6 (a) the x-axis (b) the y-axis (c) the line x = 6 (d) the line x = = 9

A city's population in the year x = 1959 was y = 1,775,650. In 1953 the population was 1,774,750. Compute the slope of the population growth (or decline) and choose the most accurate statement from the following: The population is increasing at a rate of 150 people per year. The population is increasing at a rate of 50 people per year. The population is decreasing at a rate of 250 people per year. The population is decreasing at a rate of 150 people per year. The population is decreasing at a rate of 50 people per year. The population is increasing at a rate of 250 people per year.

A freight company has shipping orders for two products. The first product has a unit volume of 10 cu ft and weighs 50 lb. The second product's unit volume is 3 cu ft, and it weighs 40 lb. If the company's trucks have 2,320 cu ft of space and can carry 21,100 lb, how many units of each product can be transported in a single shipment with one truck using the entire volume and weight capacity? first product second product

The height above ground (in feet) of a ball dropped from the top of a tall building after t seconds is given by the polynomial h=-16t^2 +53. What is the height after 1 second? After 5/4 What is the height after 1 second?

Lola needs to rent a ballroom for a formal event. Ballroom S charges $52.50 per hour and one-time rental fee of $500. Ballroom T charges $62.50 per hour and a one-time rental fee of $300. Which inequality can be used to find x, the minimum number of hours rented so that the total cost at Ballroom S is less than the total cost at Ballroom 7? 52.5r+ 500 > 62.5r + 300 52.5 +500x> 62.5 +300x 52.5 +500x < 62.5 +300x 52.5x + 500 < 62. 5x + 300

A parabola that passes through the point (3, 52) has vertex (-7, 12). Its line of symmetry is parallel to the y-axis. Find equation of the parabola: y = When x = 13, what is the value of y: What is the average rate of change between x = -7 and x = 13:

Given a polynomial that has zeros of -5, 3i, and -3i and has a value of 432 when x = 3. Write the polynomial in standard form ax^n + bx^n-1 +....

A ladybug crawls around the outside of a rectangle that measures 12 cm by 15 cm. The ladybug stays exactly 1 cm from the rectangle at all times to form a larger figure. How far does the ladybug crawl in one trip around the figure? ? What is the area of the new rectangle bound by the path of the bug? ?

Convert the measurement 2710 g= kg

Taxes: The Internal Revenue Service reports that the mean federal income tax paid in the year 2010 was $8040. Assume that the standard deviation is $4900, The IRS plans to draw a sample of 1000 tax returns to study the effect of a new tax law. (a) What is the probability that the sample mean tax is less than $7800? Round the answer to at least four decimal places.

A cartographer used a scale of 1 inch:300 meters for the heights of different mountains. If the actual height of one of those mountains is 3,600 meters, what is its height on the map? 100 inches 1,080 inches 12 inches 108 inches

Solve equation by the quadratic formula. List the solutions, separated by commas. 2r² - 3r+13= 8

Suppose the number of prisoners held in a certain type of prison, measured in thousands, can be described by the quadratic equation P = -1.94x²+76.35x+737. The variable x represents the number of years since 1990. According to the equation, how many prisoners were there in the year 2001 (x = 11) and 2006 (x = 16)? There were approximately thousand prisoners in 2001. (Simplify your answer. Round to two decimal places as needed.) There were approximately thousand prisoners in 2006. (Simplify your answer. Round to two decimal places as needed.) *****

A Kite 50 feet above the ground moves horizontally at a speed of 9 ft/sec. At what rate is the angle between the string and the ground decreasing when 140 feet of string is out?

Convert the measurement. 3 yd = inches

Bert is going to claim a depreciation tax credit for his business car. The car costs $28,000 when new, and Bert anticipates it will be worth $16,000 three years later. (d) How long does it take for the car to lose all of its value? (c) Express the value V of the car as linear function of time t, the number of years after the car was purchased. (e) In the context of this problem, what is the range of the linear function?

The projected worldwide spending for a certain type of service, in millions of dollars, for the years 2006-2011 can be estimated by the polynomial s= -35.4x² +924.6x +493, where x is the number of years after 2006. Find the projected worldwide spending for x=0, x=2, and x = 5. Use the polynomial to estimate the projected worldwide spending for this service, in millions of dollars, for the year 2006 (x = 0). $million (Type an integer or a decimal.)

Graph the following quadratic function. f(x) = 2x² + 4x + 5 Find the vertex of the function.

For what values of x does the graph of f(x) = x³ + 2x² + x + 16 have a horizontal tangent?

Leo invested $1900 in an account with annually compounded interest. After 3 years, he had $2275 in the account. What was the interest rate of the account? Round your answer to one decimal place. Do not write the percent sign. Provide your answer below:

Determine whether the ordered pair is a solution to the inequality. y≥(x-1)² (a) (-4, 31) (b) (3, 0) (c) (-3,-15) (a) Is the ordered pair (-4, 31) a solution to the inequality?

Darryl made a deposit into an account that earns 7% annual compound interest. After 36 months, the value of his account was $1,041.29. What was the approximate amount of Darryl's initial deposit?

Hunter makes shoelaces for the cleats to earn money for the football team. Each shoelace needs to measure 50 3/4 inches long. He needs to make 4 shoelaces. How many inches does he need to make the 4 shoelaces?

Solve the following equation. Be sure to check your proposed solution by substituting it for the variable in the given equation. 7x-19=-124 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is ) (Type an integer or a simplified fraction) B. The solution set is (x] x is a real number). C. The solution set is.

The position function of a particle is given by s = 2t³ - 15t²-81t, t> 0. where s is measured in meters and t in seconds. Find all values of t> 0 for which the particle is moving at a velocity of 3 m/s t=

A pumpkin is launched 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is s (t)=-4.92t2 +19.6t+58.8, where s is in meters. When does the pumpkin strike the ground?

The ages of 10 grooms at their first marriage are listed below. Find the midquartile. 35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9 34.2 43.7 34.1 34.5