Math Questions

Suppose that the total cost (in dollars) of producing x food processors is given by C(x) = 1,800 + 36x -0.6 x². What is the average cos t (in dollars) of producing the 21st food processor? Round your answer to the nearest whole number.

Use a symmetry test to determine which of the following equations demonstrate θ = symmetry. Select all that apply. Select all that apply:

The activity on Denise Hellings' Sears account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is March 1 through March 31, the previous balance was $155.27, and the annual simple interest rate is 21%. (Round your answers to the nearest cent.)

Solve for x. (x + 1)² = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x= (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. The equation has no real solutions.

Ernesto is considering buying a dishwasher for $600. According to a consumer magazine, he can expect to pay $40 per year for the electricity to run the dishwasher. He created the table below to represent the average cost per year, C(t), of owning the dishwasher, including the original price and the cost of electricity, if he keeps it for tyears. What is the average rate of change for the annual cost of owning the dishwasher between 4 years of ownership and 10 years of ownership?

The unknown triangle ABC has angle A = 44° and sides a = 15 and c = 20. How many solutions are there for triangle ABC? Select the correct answer below: 0 triangles 1 triangle 2 triangles Infinitely many triangles

Consider the following points. (-3,7), (6,0) and (6, 7) Determine whether or not the given points form a right triangle. If the triangle is not a right triangle, determine if it is isosceles or scalene

Mia and Vincent are asked to choreograph a dance for the school musical.. Mia can choreograph the dance for the show in 20 hours and Vincent can choreograph the dance by himself in 16 hours. How long would it take to choregraph the dance for the musical if they worked together? Write your answer as a number only. No units. Round your answer to two decimal places, if necessary.

Given that 3 - 2i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x) = x4 - 9x³ - 9x² + 201x - 520

An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 2 IQ points of the true mean. Assume that o = 14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. (Round up to the nearest integer.) The required sample size is Would it be reasonable to sample this number of students? No. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly large number.

Use the formula for nPr, to evaluate the following expression. 9P6

Your itinerary contains a grid map of New York, with each unit on the grid representing 0.5 miles. If the Rockefeller Center is located at (2,-3) and Central Park is located at (6,-3), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? Round your answer to two decimal places, if necessary.

Answer the following. (a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 2.68 × 10-6 meters. Write this number in standard notation. (b) The diameter of Jupiter at its equator is approximately 143,000 kilometers. Write this number in scientific notation.

Given the points C(-3,-1) and D(-1,-6), express the vector CD in terms of i and j. Select the correct answer below: - 2i - 5j 2i - 5j -5i +2j 2i + 5j -2i+ 5j 5i-2j

This exercise uses the radioactive decay model. Radium-221 has a half-life of 30 sec. How long will it take for 96% of a sample to decay? (Round our answer to the nearest whole number.)

Use dimensional analysis: Trent purchases 44 euros worth of souvenirs while on vacation in France. If $1 U.S.= 0.678 euros, find the cost of the souvenirs in United States dollars. Round to the nearest cent.

Connie and Rashim have to survey 2500 homeowners. Connie can do the job alone in 12 hours. If Rashim helps, they can get the job done in 4 hours. How long would it take Rashim to do the job by himself? Write your answer as a number only. No units. Round your answer to two decimal places, if necessary.

Consider the following. e5 - 3x = 15 (a) Find the exact solution of the exponential equation in terms of logarithms. (b) Use a calculator to find an approximation to the solution rounded to six decimal places.

Graph the linear equation by finding and plotting its intercepts. 9x - 4y = 36

Solve the given equation or inequality graphically. (a) x²= 6 - 7x (Enter your answers as a comma-separated list.) (b) -x² ≥ 6-7x (Enter your answer using interval notation.)

What is the converse of the conditional statement, "If two angles are congruent, then they have the same measure"? A. If two angles are not congruent, then they do not have the same measure. B. If two angles have the same measure, then they are congruent. C. If two angles do not have the same measure, then they are not congruent. D. If two angles have the same measure, then they are not congruent.

For the 250 students asked, 96 enjoy Korean Dramas, 125 adore Western TV Series, and 148 love Anime Shows. Also, 52 enjoy both K-Dramas and Western TV Series, 56 adore both Anime and Western TV Series, and 64 love both K-Dramas and Anime Shows. Moreover, 45 loves to watch all three types of shows. How many students do not watch Anime or K- Dramas? a. 62 students b. 70 students c. 81 students d. 83 students

Plot the given graph by finding the values of y that correspond to the values of x of 0, 1, 2, 3, 4, 5, 6, and 7 on a calculator. (Remember, the numbers 0, 1, 2, and so on represent radian measure.) y = 6 sin x

This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Imme of the surroundings is 70°F. (a) Find a function T(t) that models the temperature t hours after death. (b) If the temperature of the body is now 72°F, how long ago was the time of death? (Round your answer to the nearest whole number

A boat leaves the marina and sails 5 miles west, then 10 miles southeast. How far, in miles, from the marina is the boat? (Round your answer to the nearest hundredth if necessary.)

Contestants A, B, C, D, E, and F are in a 10K race. How many different ways can a race with 6 runners be completed? (Assume there is no tie.) In how many ways can A finish first and D finish second? What is the probability that A finishes first and D finishes second? Enter a reduced fraction or decimal.

Write this statement as a conditional in if-then form: A triangle is a polygon with three sides. A. If a polygon is a triangle, then it has three sides. B. If a triangle has three sides, then it is a polygon. C. If a triangle is a polygon, then it has three sides. D. If a triangle has three sides, then all polygons have three sides.

Given u = (-6, -2) and 7 = (-3, 4), find the dot product u · v. Give just a number for your answer. For example, if you found u = 4, you would enter 4.

Match the definitions in Column A with the correct words/terms in Column B. Write your answers on a separate sheet of paper. Column A 1. Statement that can either be written "If..., then form 2. Part of a conditional statement that follows it 3. Part of a conditional statement that follows "then" 4. Denial of a statement formed by adding or removing the word NOT from a statement 5. To add or remove the word NOT from a statement to change its truth value from true to faise or from false to true 6. Statement formed from a conditional statement 7. by switching the hypothesis and conclusion Statement formed from a conditional statement by negating the hypothesis and conclusion 8. Statement formed from a conditional statement by switching and negating the hypothesis and conclusion 9. Statement combining a conditional statement and its converse, using the phrase "if and only if Column B A. hypothesis B. conclusion C. Inverse D. contrapositive E. negation F. negate G. biconditional H. converse 1. conditional

A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in the figure (a) Find a function that models the cross-sectional area of the gutter in terms of x. (b) Find the value of x that maximizes the cross-sectional area of the gutter. (c) What is the maximum cross-sectional area for the gutter?

Fill in the table using this function rule. f(x)=2√x Simplify your answers as much as possible. Click "Not a real number" if applicable.

Your credit card has a balance of $1,200. Its interest rate is 20.5%. You have stopped using the card, because you don't want to go any deeper into debt. Each month, you make the minimum required payment. Your credit card issuer recently changed their minimum required payment policy, in response to the Bankruptcy Abuse Prevention and Consumer Protection Act of 2005. As a result, your minimum required payment is $48. (Round your answers to the nearest cent.) (a) During the September 10 through October 9 billing period, you pay the minimum required payment on September 25th. Find the average daily balance, the finance charge and the new balance. (The new balance includes the finance charge.)

A group of first ten shoppers in Town Mall have the following body temperature in Degree Celsius: 36.0, 36.2, 37, 35.9, 37, 36.2, 37.2, 36.0, 36.2 and 36.4. What is the percentile rank of the shopper with a body temperature of 36.4 Degree Celsius?

Use a calculator to solve the following equation for on the interval [-90°, 90°]. csc (θ) = -1.761 Round to one decimal place. Provide your answer below:

Some medicines can wear off in the body exponentially. In this case, assume the rate decays hourly for a starting amount of 250 mg of medication according to the equation: M = 300(0.84)t Solve this equation to determine the number of hours, t, that it will take for the initial 300 mg of medicine to decrease to 10 mg. Round to two decimal places.

A rocket is fired upward with a velocity (v) of 680 feet per second. Find how many seconds pass before the rocket reaches the ground (S=0) again. Use the quadratic equation S = - 16t² +680t. It will take seconds until the rocket reaches the ground again. (Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed.)

Fill in the table using this function rule. f(x)=√x+2 Simplify your answers as much as possible. Click "Not a real number" if applicable.

From her camp, a hiker walks 550 meters north, then 425 meters southeast. How far, in meters, from the camp is the hiker? Select the correct answer below: 390.58 550.00 695.07 975.00 STION

If f(x) = 3x² + 2x, find each of the following. (a) f(0) (b) f(-3) (c) f(2) (a) f(0) = (Simplify your answer.) (b) f(-3)= (Simplify your answer.) (c) f(2)= (Simplify your answer.)

Obtain an approximate value for the logarithm using natural logarithms. log 5313 log 5313 (Round to three decimal places as needed.)

Ice Cream: An ice-cream cone has a radius of 2.3 cm and a height of 6.7 cm. The cone is filled with ice-cream and one additional scoop in the shape of a sphere with the same radius as the cone is placed on top. What is the amount of ice cream in cubic cm? Round to the nearest hundredth.

Marco has joined a bowling league, and is trying to raise his average to 170. On his last four games he scored 164, 170, 165, and 171. How much will he need to score on the next game to raise his mean to 170?

Consider the polynomial below. x3 + x2 - 14x - 22 Use the remainder theorem to determine which binomial expression divides the polynomial so that the remainder is 2. A. x-2 B. x-1 C. x + 3 D. x + 4

Express the confidence interval using the indicated format. Express the confidence interval 0.469 ± 0.077 in the form of - E<p <+E. 0.4305< p <0.5075 0.392 < p < 0.469 0.469 <p <0.546 0.392<p <0.546

An ice-cream cone has a radius of 2.8 cm and a height of 6.7 cm. The cone is filled with ice-cream and one additional scoop in the shape of a sphere with the same radius as the cone is placed on top. What is the amount of ice cream in cubic cm? Round to the nearest hundredth.

Find the exact value of the following, without using a calculator. sin (sin-¹(2) + tan -1(-5) sin sin -¹+tan ¹(-5)- -0

The density of gold is 19.3 g/cm³. A weight of 1 ounce is equivalent to a mass of about 28.35 g. Which of these is closest to the side length of a cube-shaped block of gold that has a weight of 8 ounces? A. 2.27 cm B. 3.43 cm C. 9.09 cm

A graphing calculator is recommended. A function is given. f(x) = 9+ x + x² - x³ (a) Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer rounded to two decimal places. (b) Find the intervals on which the function is increasing and on which the function is decreasing. State each answer rounded to two decimal places.

If an object is dropped, the relationship between the distance it falls and the time that it has been falling is given by: d = 1/2 gt2 where: d is the distance the object falls, in feet t is the time the object falls, in seconds g is a constant due to gravity, 32.2 ft/sec² While standing on a bridge overlooking a river, you drop a rock and time how long it takes to hit the water. If the time is 1.5 seconds, how high is the bridge above the water, to the nearest whole foot? feet

A rocket is fired upward with an initial velocity v of 70 meters per second. The quadratic function h(t) = -5t² + 70t can be used to find the height h(t) of the rocket, in meters, at any time t in seconds. Find the time it takes for the rocket to reach its maximum height. What is the maximum height reached by the rocket? The rocket reaches the maximum height at The maximum height that the rocket will reach is meters.