Math Questions

The lines L₁, L2, L3,... L2₂0 are distinct. All the lines L4, L8, L12, L16 and L20 are parallel. All the lines L₁,L5, L9, L13, L17 pass through a given point A. The maximum number of points of intersection of these 20 lines is

Two stores sell the same refrigerator for the same original price. Store A advertises that the refrigerator is on sale for 15% off the original price. Store B advertises that it is reducing the refrigerator's price by $150. When Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal. Let p represent the refrigerator's original price. Which equation models this situation?

A store advertises that during its Labor Day sale, $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars at 8 a.m. and x > 100, what, in terms of x, is the cost c of Hakeem's purchase?

Discuss the validity of the following statement. If the statement is true, explain why. If not, give a counter example. Every polynomial function is one-to-one. Choose the correct choice below.

The distribution of heights of both five-year old boys and seven-year old boys is approximately Normal. The mean height of a five-year old boy is 43 inches and the standard deviation is 1.8 inches. The mean height of a seven-year old boy is 48 inches and the standard deviation is 2.1 inches. John's height was 44 inches on his fifth birthday, and today, on his seventh birthday, he measures 49 inches tall. What can you conclude about the rate of John's growth when compared to other boys his age?

f(x) = (x+7)²(x+9)(x-12)² List each zero of faccording to its multiplicity in the categories below.

At lunch a waiter had eleven customers and five of them didn't leave a tip. If he got Ssix each from the ones who did tip, how much money did he earn?

The profit for a product can be described by the function P(x)=202x-5000-x² dollars, where x is the number of units produced and sold. To maximize profit, how many units must be produced and sold? What is the maximum possible profit?

A 1.000-g sample of chromium metal reacted with oxygen gas to give 1.462 g of product. Calculate the empirical formula of the chromium oxide.

In a random sample of 200 cars of a particular model, 3 have a manufacturing deficit. At this rate, how many of 10,000 cars of the same model will have a manufacturing deficit? (A) 150 (B) 200 (C) 250 (D) 300

An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are worth five points. How many two point questions are on the test? How many five point questions are on the test?

Caleb bought 3 orders of cheese dip to share with his friends. How much did he spend on cheese dip?

Angela Montery has a five-year car loan for a Jeep Wrangler at an annual interest rate of 5.9% and a monthly payment of $595.50. After 3 years, Angela decides to purchase a new car. What is the payoff on Angela's loan? (Round your answer to two decimal places.)

What percentage of the general U.S. population are high-school dropouts? The Statistical Abstract of the United States, 120th Edition, gives the percentage of high- school dropouts by state. For convenience, the data are sorted in increasing order.

Assume you intend to create a stratified sample of 250 from a population of 920 trucks, 1540 subcompact cars, 1320 sedans, 450 motorcycles, 110 R.V.'s, 550 luxury cars, and 780 sports cars. How many subcompacts should you have in your sample? a 65 b 60 C 68 d 70

A small business sells custom oak moldings in 12-foot lengths. One molding type has the revenue function R(x) = 59x and the cost function C(x) = 2800+ 45x. Find the number of 12-foot lengths of this molding that must be sold to break even. X = lengths

A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 10 in /min, how fast is the thickness of the ice decreasing when it is 3 in. thick? How fast is the outer surface area of ice decreasing?

The speed of light is approximately 6.71 a 10 miles per hour. Which of the following options shows this number correctly written in standard notation?

College students average 7.1 hours of sleep per night with a standard deviation of 45 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 8.1 hours?

A hiker is walking down a mountain. She walked 5,978 feet in 17 minutes. In that time, she descended 1,024 feet from the top of the mountain. She then walked 3,972 feet in 7 minutes. In that time, she descended 500 more feet. Express the average rate of change in altitude of the hiker from her starting point to her ending point as a unit rate.

Combine like terms to simplify the expression below. -6y + 7y = 1y 32 + y - 2y² Now, re-write the equation with the variable with the highest exponent first.

A ball is thrown upward from the top of a 48-foot-high building. The ball is 64 feet above ground level after 1 second, and it reaches ground level in 3 seconds. The height above ground is a quadratic function of the time after the ball is thrown. Write the equation of this function.

Two cities have nearly the same north-south line of 101° W. The latitude of the first city is 23° N, and the latitude of the second city is 36° N. Approximate the distance between the cities if the average radius of Earth is 6400 km.

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53 inches, and standard deviation of 6.8 inches. What is the probability that the height of a randomly chosen child is between 39.9 and 54.9 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

Sadie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5 hours and charged her $77 for parts. The total was $302. Which equation could be used to determine x, the cost of labor per hour? r

Junior is saving money in his piggy bank. He starts with 10 cents and adds two pennies each day. Create an x → y table and a graph for the function for which x represents the number of days since Junior started saving money and y represents the total money he has saved.

A pennant is shaped like a right triangle with hypotenuse 10 feet. The length of one side of the pennant is 2 feet longer than the length of the other side. Find the length of the two sides (legs) of the pennant. Enter your answers as a comma separated list.

Given nt+1= = nt + 3.6 and n4 = 12.6: a) Make a table for the first five terms. b) Find n20 and n_22. c) Find the t for which n 102.6 and nt = -70.2. d) Write an algebraic representation for this sequence.

It is given to you that an equation of the tangent line to the graph of y = g(x) at x = 16 is 6x + 9y = 15 It follows that y = ___ and that y is the equation of the tangent line to y = g(x²) at x = 4 iand that y = ____ the equation of the tangent line to y = (g(x))² at x = 16.

Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function? Select all correct answers. Select all that apply: {(2, 10), (8,8), (-4,7), (3, 10)} {(8,6), (-2,-1), (-4,-2), (-2, 8)} ((-3,4), (7,6), (0, 1), (0,8)} ((9,6), (6,0), (1,-5), (0,6)} {(2,1), (2,0), (9, 14), (-3,8)}

You have tablets with a strength of 2.37 mg, and you must give 0.16 g. How many tablets will you need? Less than 1 Exactly 1 More than 1

What is the slope of a line perpendicular to the line whose equation is x - 3y = 12. Fully simplify your answer.

- A boat leaves port A and travels 40 knots for 2 hours on a bearing of N 62° W then travels at the same speed for 3 hours on a bearing of N 28° E to port B. Find the distance and bearing from port B to A.

The parabola y = x² +4 has two tangents which pass through the point (0, -4). One is tangent to the parabola at (A, A²+4) and the other at (-A, A² + 4). Find (the positive number) A.

The city of Raleigh has 11,900 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 600 randomly selected registered voters was conducted. 353 said they'd vote for Brown, 219 said they'd vote for Feliz, and 28 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Round your answer to four decimal places. This sample statistic suggests that we might expect of the 11,900 registered voters to vote for Brown. Round to the nearest whole number.

In 2012, the population of a city was 5.62 million. The exponential growth rate was 2.48% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 9 million? d) Find the doubling time. of the number of years since 2012

Alexis de Tocqueville observed American society during the beginning of industrialization. Which of the following best characterizes his observations? a) Americans are insufficiently focused on their careers and miss opportunities to advance in the job market. b) Americans need to be more like people who live in the Old World and lighten their spirits. c) Americans regularly participate in government elections but cannot agree on which path is the best one to follow. d) Americans have become so obsessed with accumulation that they have no time left to enjoy life and participate in their free political system.

Calculate dcos(u)/dx for the following choices of u(x) : u(x) = 6 — x², dcos(u(x))/dx u(x) = 1/x, dcos(u(x))/dx u(x) = tan(x), dcos(u(x))/dx

Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the y-axis. (Round your answer to three decimal places.) y = x²/2 +6₁ 0≤x≤5

Let y = (x+sin(x))⁴. Find g(x) and f(x) so that y = (fog)(x), and compute the derivative using the Chain Rule. f(x) = g(x) = (fog)' =

In a recent survey of college-educated adults, 102 indicated that they regularly work more than 45 hr a week. If this represents 34% of those surveyed, how many people were in the survey? There were people in the survey.

For what values of x does the graph of f(x) = 2x³ - 12x² + 0x + 12 have a horizontal tangent? Enter the x values in order, smallest first, to 4 places of accuracy: x1 = ≤ x₂ =

Your patient is to receive a dosage of 15 mg and you have only 1 tablet labeled 5 mg. How many more mg are needed?

LB. Johnson Middle School held a track and field event during the school year. The chess club sold various drink and snack items for the participants and the audience. Altogether, they sold 486 items that totaled $2,673.

A rope is 60 in in length and must be cut into two pieces. If one piece must be three times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary. The length of the smaller piece is in. The length of the larger piece is in.

Complete the proof of the statement, "If a figure is a rectangle, then it must me a parallelogram". Use the diagram provided to help you. Angles A and D are supplementary [Select] transversal AD, so lines DC and AB are parallel by the [Select] Similarly, angles A and B are [Select] same side interior angles formed by transversal AB which makes lines AD and BC also parallel. Finally, ABCD must be a parallelogram because we have just proven both pairs of opposite sides are [Select]

The equation y = 1/2 x - 12 represents a function where x is the input and y is the output. Which of the following statements correctly describes the function? The graph is nonlinear because it is always increasing. The graph is nonlinear because it increases at a constant rate. The graph is linear because it is always increasing. The graph is linear because it increases at a constant rate.

Edna is fouled hard in an exciting basketball game. It is ruled a flagrant foul, and the opponent is tossed from the game. As a result, Edna is allowed to shoot two free throws. She is a good shooter and, on average, makes 82% of her free throws. Assuming independence between the 2 free throws, what is the probability that Edna will miss both free throws?

Find the angular speed w for the following. a wind turbine with blades turning at a rate of 15 revolutions per minute The angular speed for a wind turbine with blades turning at a rate of 15 revolutions per minute is minutes. radians. radians per minute.

(a) Find the domain of the following function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. x², if 0<x≤2 f(x)= x+2, if 2<x<5 7, if x ≥ 5