Math Questions

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

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 4 to 5. If there were 6417 total votes, how many yes votes were there?

Juli is going to launch a model rocket in her back yard. When she launches the rocket, the function h(t) = -16r2 +681 model the height, h, in feet of the rocket above the ground as a function of time, t, measured in seconds. (a) When will the rocket hit the ground? (b) When will the rocket be 42 feet above the ground?

Permutation and combination: What are your chances of winning the Lucky Millions Lottery if you You pick 4 numbers from 1 to 40 without replacement and 1 number from 1 to 30. Answer format:

Your college is having a housing lottery. The probability that you will get a single room all to yourself next year is 0.2, the probability of getting a double is 0.6, and the probability of getting a triple is 0.2. All of the triples have air conditioning, half of the doubles have air conditioning, and only 10% of the singles have air conditioning. What is the probability that your dorm room next year will have air conditioning?

In 2003, the population of an African country was about 7.6 million people, which is 3 million more than 2 times the population in 1950. Enter and solve an equation to find the approximate population p (in millions) in 1950.

A Food Marketing Institute found that 30% of households spend more than $125 a week on groceries. Assume the population proportion is 0.3 and a simple random sample of 481 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?

Find a, b, c, d such that the cubic function f(x) = ax³ + bx² + cx+d has horizontal tangent lines at (0, -9) and (4,-41). a= b= c= d=

3 days after picking apples, a family had 100 apples left. After 6 days, 76 apples were left. Assuming a linear function, write an equation in the form a(t) = mt + b that shows the number of apples, a(t), left t days after picking them. Be sure to include "a(t) =" in your answer.

Error Analysis Cheryl's math teacher asks, "7 is 50% of what number?" Cheryl incorrectly says, "350." What is the correct answer? What error did Cheryl likely make? 7 is 50% of .... What error did Cheryl likely make? A. She wrote the percent equation as whole = percent part and did not divide by 100. B. She did not divide by 100. C. She wrote the percent equation as percent = whole + part.

There is a line that includes the point (5, 5) and has a slope of 7/5. What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form.

A motorboat travels 180 miles in 6 hours going upstream. It travels 264 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Charlie bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $200 less than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 9% per year, and for the laptop it was 7% per year. The total finance charges for one year were $306. How much did each computer cost before finance charges?

For f(x)=x+4 and g(x) = 4x+4, find the following functions. a. (fog)(x); b. (gof)(x); a. (fog)(1); d. (gof)(1)

Use the figure to the right to find the value of PT. T is the midpoint of PQ. PT=3x+2 and TQ = 5x-8 PT=

Investors buy a studio apartment for $150,000. Of this amount, they have a down payment of $37,500. Their down payment is what percent of the purchase price? What percent of the purchase price would a $60,000 down payment be? Their down payment is% of the purchase price. (Type a whole number.) A. $60,000 down payment would be % of the purchase price. (Type a whole number.)

Find the relative maxima and relative minima, if any, of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = 2x² + 864/x + 8 Relative maximum value(s): Relative minimum value(s):

The drama club is printing t-shirts for its members. The printing company charges a certain amount for each shirt plus a setup fee of $40. There are 21 students in the drama club. Part A: If there are 21 students in the club and the t-shirt order costs a total of $187, how much does each t-shirt cost? Show your reasoning. Part B: The equation 201.50 = f +6.50 (21) represents the cost of printing the shirts at a second printing company. Find the solution to the equation and state what it represents in this situation.

Suppose the newest version of your favorite Smartphone comes out today. Assume that a total of 20 people goes to your local cell phone dealer to purchase this phone today and that each day the total number of people who purchase the Smartphone doubles. How many people have purchased the Smartphone 5 days from today? {your answer just a number}

Use the Zero Product Property and factoring, when necessary, to solve for x. The Math Notes box for Lesson 1.1.4 may be useful, if you need help. Homework Help a. (x+13)(x-7)=0 b. (2x+3)(3x − 7) = 0 c. x(x − 3) = 0 d. x² −5x=0 e. x² - 2x - 35 = 0 f. 3x² +14x − 5 = 0

A box of cereal states that there are 99 calories in a 3/4 cup serving. What is the unit rate for calories per cup? How many calories are there in 3 cups of the cereal? The unit rate is calorie(s) per cup. (Simplify your answer. Type an integer, proper fraction, or mixed number)

z = -1 is what percentile? percentile State your answer to the nearest tenth of a percent. Enter your answer as an integer or decimal number. Examples: 3, -4,

A random variable X can take on three possible values: 0, 8, or 20. Each of these values is associated with the following probabilities: P(X= 0) = 0.25, P (X= 8) = 0.25, and P(X= 20) = 0.5. What is the expected value of X?

Find the number of subsets for the following set. {E,F,G,H} How many subsets does this set have? (Type a whole number.)

Find the initial value a, growth/decay factor b, and growth/decay rate, for the following exponential function: Q(t) = 0.0044(2.34) (a) The initial value is a = (b) The growth factor is b = (Retain at least four decimal places.) (c) The growth rate is r = % help (numbers) (Ensure your answer is accurate to at least the nearest 0.01%) (Note that if r gives a decay rate you should have r < 0.)

Solve each application below using systems. To receive full credit, you must 1) define all variables used, set up a system of 2 equations and 2 variables, 3) solve the system, and 4) write your solution as part of a complete sentence using appropriate units of measure. A Christmas charity party sold tickets for $45 for adults and $25 for children. The total number of tickets sold was 320 and the total for the ticket sales was $13,000. How many adult and how many children's tickets were sold?

A local race for charity has taken place since 1993. Using the actual speeds of the winners from 1993 through 1998, mathematicians obtained the formula y-0.16x+5.5, in which x represents the number of years after 1993 and y represents the winning speed in miles per hour. In what year is the winning speed predicted to be 7.42 mph?

A rectangle's width is one-third its length, and its perimeter is 96 m. Find the dimensions of the rectangle. The length is m and the width is

This problem illustrates the typical approach for creating a model. Use lower case letters. (a) We want to express the area of a circle, A, as a function of its circumference, c. Start with the basic formula we know for the area of a circle in terms of its radius. A= Because we want this area formula in terms of circumference and not radius, we need another formula that will allow us to replace in terms of c. The formula that has both r and c in it is the circumference formula for a circle. c= Solve this equation for r. r= Use this to replace r in terms of c in our area formula. Note the function notation also reminds us that the independent variable should be c when we are done. A(C)= Now try this approach on the following problem. Don't forget, if you need, there is a reference sheet of geometry formulas in the description of this assignment. (b) Express the diagonal of a rectangle, D, in terms of its width, w, if the area of the rectangle is 13 square feet. D(w) =

Stating Parametric Solutions State the standard parametric solutions with parameter k, and for inverse trig values, round your answers to four decimal places. sin(t) = 0.896 if and only if t = (primary solutions) (secondary solutions) t = cos(t) 0.05 if and only if t = (primary solutions) (secondary solutions) t tan(t) t =(primary solutions) (secondary solutions)

Find an equation for the line perpendicular to y=x+5 with y-intercept (0.-13). Write the answer in slope-intercept form. The equation of the line in slope-intercept form is (Simplify your answer. Use integers or fractions for any numbers in the equation. Do not factor)