Math Questions

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)

A sequence of transformations is described below: A dilation with a scale factor of 3 A translation left 4 units and down 1 unit Select the statement that describes the resulting image. A. The angle measures are preserved, but the image is a reduction B. The angle measures are preserved, but the image is an enlargement C. The angle measures are not preserved, and the image is a reduction D. The angle measures are not preserved, and the image is an enlargement

A rock is thrown off of a 100 foot cliff with an upward velocity of 50 m/s. As a result its height after t seconds is given by the formula: h(t) = 100+ 50t - 5t² What is its height after 3 seconds? What is its velocity after 3 seconds? (Positive velocity means it is on the way up, negative velocity means it is on the way down.)

A random sample of size n = 616 from a population whose parameter is p = 0.31. a. What is the mean of the distribution of sample proportions? Round the answer accurate to 2 decimal places. b. What is the standard deviation of the distribution of sample proportions? Round the answer accurate to 2 decimal places.

A population of values has a normal distribution with µ=68.9 and σ= 34.3. A random sample of size n = 239 is drawn. Find the probability that a sample of size n = 239 is randomly selected with a mean less than 75.1. Round your answer to four decimal places. P(M<75.1):

Valentina's parents are planning a trip to the Typhoon Towers resort. They plan to get a 6- day Fun Pass, which will give Valentina access to all the slides and pools at the resort during their stay. Her parents also plan to get her a $30 arcade pass. Altogether, Valentina's parents will spend $129 on passes. What is the daily cost of a Fun Pass?

Magnetic resonance imaging (MRI) is a process that pro- duces internal body images using a strong magnetic field. Some patients become claustrophobic and require sedation because they are required to lie within a small, enclosed space during the MRI test. Suppose that 21% of all patients undergoing MRI testing require sedation due to claustrophobia. If 7 patients are selected at random, find the probability that Note: Please keep 4 decimal places in your final answer. a. exactly 2 patients require sedation. b. less than 2 patients require sedation. c. exactly 5 patients require sedation. d. at least 5 patients require sedation.

Javon is in a 26% tax bracket for his federal income tax. If the amount of money that he paid for federal income tax was $19,240, what was his taxable income?

Consider the Quadratic function f(x) = x² - 4x - 21. Its vertex is Its largest x-intercept is x = Its y-intercept is y =

The area of an 19-cm-wide rectangle is 380 cm². What is its length? The length is cm.

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.6 years, and standard deviation of 1.8 years If you randomly purchase one item, what is the probability it will last longer than 10 years? Round answer to three decimal places Enter your answer as an integer or decimal number. Examples: 3, -4, Enter DNE for Does Not Exist, oo for Infinity

Person A deposits $2700 in an account that pays 5% interest compounded once a year. Person B deposits $2550 in an account that pays 6% interest compounded monthly. Complete parts (a) through (c) below. a. Who will have more money in their account after one year? How much more? Select the correct choice below and fill in the answer box within your choice. (Round to the nearest dollar as needed.) A. Person A will have $ more than Person B. B. Person B will have $ more than Person A.

Car Survey In a survey of 1,700 people who owned a certain type of car, 935 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car? % of the people surveyed were satisfied with the car. (Type a whole number.)

At the time of her grandson's birth, a grandmother deposits $15,000 in an account that pays 9% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? Click the icon to view some finance formulas. The value of the account will be $ (Round to the nearest dollar as needed.)

Find the minimum and maximum values of z = 7x + 3y, if possible, for the following set of constraints. x+y≤8 -x+y≤2 2x-y≤ 10

You have a choice between going to an in-state college where you would pay $6500 per year for tuition and an out-of-state college where the tuition is $9000 per year. The cost of living is much higher at the in-state college, where you can expect to pay $700 per month in rent, compared to $450 per month at the other college. Assuming all other factors are equal, which is the less expensive choice on an annual (12-month) basis? The yearly expense of the in-state college is $ college. the and the yearly expense of the out-of-state college is $ Thus, on an annual basis, the less expensive choice is

According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible) a. Compute the probability that a randomly selected peanut M&M is not red. b. Compute the probability that a randomly selected peanut M&M is red or blue. c. Compute the probability that three randomly selected peanut M&M's are all green. d. If you randomly select five peanut M&M's, compute that probability that none of them are brown. e. If you randomly select five peanut M&M's, compute that probability that at least one of them is brown.

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Given this information, find the probability of a pregnancy lasting 308 days or longer. Does that seem likely?

Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 5% each year. In other words, if you have $1 this year, next year it will only buy you $0.95 worth of stuff. How much will $100 buy you in 25 years?

Select the correct answer from each drop-down menu. A square rotated about its center by 360° maps onto itself at _____ different lines of reflection. across _____ different angles of rotation. You can reflect a square onto itself

Find the linear speed v for the following. the tip of a propeller 1 m long, rotating 500 times per min (Hint: r=0.5 m) The linear speed v for the tip of a propeller 1 m long, rotating 500 times per min is min. m per min. m.