Math Questions

You are the manager of an assembly line with machines that fill bags of trail mix. The machines are known to overfill bags 3% of the time. You think one machine is overfilling bags more often than that. A random sample of 65 bags filled by that machine reveals that 4 of the bags are overfilled. After performing a significance test at a significance level of α = 0.05, You calculate a p-value of 0.06811. Make a strategic decision based on this result. Allow the machine to continue operating as it is. Adjust the other machines to match the overfilling rate. Change the size of the bags used for the trail mix for this machine. Pause this machine's operation until it can be adjusted.

Which of the following equations shows "twice a number is eighteen"? 2n=18 2/n = 18 2-n = 18

Use summation notation to write the series. 1/5(1) + 1/5(2) + 1/5(3) +-------=1/5(9) The summation notation for the series is ∑(i=1)

Many students from Europe come to the United States for their college education. From 1980 through 1990, the number S(in thousands), of European students attending a college or university in the U.S. can be modeled by S = 0.05(t^3 – 11t^2+ 45t + 277), where t = 0 corresponds to 1980. In what year were there 31.35 thousand European students attended a U.S. college or university? 1990 2012 2001 2011

The complex number u = a + bi is_____________ of the complex number z if z = u^n = (a + bi)^n.

The hypotenuse of an isosceles right triangle is 18 centimeters longer than either of its legs. Find the exact length of each side. (Hint: An isosceles right triangle is a right triangle whose legs are the same length.) The length of one leg is____ the length of the other leg is______ and the length of the hypotenuse is______

An aquarium reports that guests' mean visit time is 134 minutes. Benjamin, a dolphin trainer at the aquarium, believes the mean visit time is not accurate for guests who visited in the past week. Benjamin randomly surveys guests who visited the aquarium in the past week and receives 28 responses. He calculates a sample mean of 137 minutes with a sample standard deviation of 3.5 minutes. Conduct a significance test using a significance level of α = 0.01 for the mean and make a conclusion. 4.536 > 2.771; Benjamin rejects the null hypothesis. The data suggests that the mean time for guests is mot 134 minutes over the past week. 4.454 > 2.771; Benjamin rejects the pull hypothesis. The data suggests that the mean time for guests is not 134 minutes over the past week. -4.454 <-2.771; Benjamin fails to reject the null hypothesis. The data suggests that the mean time for guests is 134 minutes over the past week. -4.536 <-2.771; Benjamin fails to reject the null hypothesis. The data suggests that the mean time for guests is 134 minutes over the past week.

For the function f(x) = 6x2 + 2x – 4, evaluate and fully simplify each of the following. f(x+h) = f(x+h)-f(x)/h =

A circle in the xy-plane is centered at (3, 0) and has a radius with endpoint (1, 8/3). Which answer choice is an equation of the circle? A) (x – 3)^2 + y^2 = 10/3 B) (x + 3)^2 + y^2 =10/3 C)(x - 3)^2 + y^2 =100/9 D) (x + 3)^2 + y^2 - 100/9

College Clubs. Fourteen freshmen, 10 sophomores, 14 juniors, and 9 seniors belong to a gamers club. If 1 of them is chosen at random to be the club's representative at a national competition, find the probability that an upperclassman is selected, Fraction: _________________Preview Decimal:_________________

The following data table shows the number of wins that teams in a bowling league had in one season. wins frequency 0 2 1 3 2 7 3 8 4 7 5 3 (A) What is the mean number of wins? (B) What is the standard deviation of the number of wins? (Hint: it may help to write the data out as a list) (C) What is the probability that a randomly selected bowling team will have won 3 games this season? wins frequency 0 2 1 3 2 7 3 8 4 7 5 3

The proportion of American adults who own a motorcycle is 2%. Samip believes the proportion of adults who own a motorcycle in his hometown is even lower. He randomly surveys 50 adults from his hometown and finds that 3 of them own a motorcycle. Identify why the sample in this situation does not meet all three conditions to perform a significance test using a Z-statistic The sample is not large enough because (50)(1 -0.02) ≱ 10. The sample was not randomly selected. The sample does not have independence. The sample is not approximately normal because (50 (0.02) ≱ 10.

Jack and Susan bought together 28 books. Susan bought 11 books. Which one of the following equations represents the number of books bought by Jack? Let x be the number of books bought by Jack. x=28 - 11 x=28 + 11 x =11-28

What is the purchase price of a 50 day T-Bill With maturity value of $2,269 that earns an annual interest rate of 4.094%? (Assume a 360-day year). the prushes price is $__ (round to two dimical places.)

A group of 10 students from elementary school has their height measured. The sample mean is 136 cm and the sample standard deviation is 4.19 cm. What is the lower bound 90% confidence interval about the mean? Round your answer to 3 decimal places.

A person's rectangular dog pen for his dog must have an area of 100 square feet. Also, the length must be 40 feet longer than the width. Find the dimensions of the pen. The width of the pen is and the length of the pen is (Simplify your answers, including any radicals. Use integers or fractions for any numbers in the expressions.)

Azer coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures no Interest payments are made Azero capon bond with a face value of $9000 matures in 20 years. What should the bond be sold for now if its rate of return is to be 2.7%. compounded semiannually? a)A fair price to buy the bond at would be ___Round to the nearest cent as needed)

Scott wants to go on a cruise for his Senior Trip. He needs $2500 for the trip. Scott is currently a freshman. If he invests in a savings account that earns 5.3% interest compounded monthly, how much money does Scott need to invest today $2023.36 $ 2320.63 $382.50 $2000

Check whether the equation 10m - 5+ 7 = 12m + 6 - 2m has solution. 6 = 6, no solution 2 = 6, no solution 3 = 6, no solution

Which of the following represents vector u=RS in linear form, where R (-22, 6) and S(-35, 14)? v= 8i - 13j v= -8i +13j v = 131 + 8j v= -13i + 8j

The sales manager of a company awarded a total of $3000 in bonuses to the most productive salespeople. The bonuses were awarded in amounts of $250 or $750. If at least one $250 bonus and at least one $750 bonus were awarded, what is one possible number of $250 bonuses awarded?

if the radius of the circle is 12 inches, what is the area of sector AOB in terms of it? given; central angle ,AOB= 90 A) 367 π in^2 B) 487 π in^2 (C)721 π in^2 D) 14471 π in^2

If the endpoints of the diameter of a circle are (8,6) and (2.0), what is the standard form equation of the circle? A) (x + 5)^2 + (y + 3)^2 =18 B) (x + 5)^2 + (y + 3)^2 = 3√2 c)(x - 5)^2 + (y - 3)^2 =18 D)(x - 5)^2 + (y - 3)^2 = 3√2

What is the probability that score pulled at random is less than 48.4? Express your answer rounded correctly to the thousandth place. Probability =

The ______of the complex number z = a + bi is z = r(cos(θ) + i sin(θ)), where r is the ______of z.and θ is________

Bentley is deciding between two landscaping companies for his place of business. Company A charges $40 per hour and a $175 equipment fee. Company B charges $50 per hour and a $125 equipment fee. Let A represent the amount Company A would charge for t hours of landscaping, and let B represent the amount Company B would charge for t hours of landscaping. Write an equation for each situation, in terms of t, and determine the interval of hours, t, for which Company A is cheaper than Company B.

The growing seasons for a random sample of 49 U.S. cities were recorded, yielding a sample mean of 184.9 days and the population standard deviation of 54.4 days. Estimate for all U.S. cities the upper bound of the true mean of the growing season with 95% confidence. Round your answer to 2 decimal places.

Graph the following function over a one-period interval. y=3 sec(1/4)x Choose the correct graph below.

The mirror in an automobile headlight has a parabolic cross-section with the light bulb at the focus. On a schematic, the equation of the parabola is given as x^2= 4y. if we want to construct the mirror so that the focus is located at (0,1.25), what is the equation of the parabola?

The cost of a fish dinner to the owner of the Golden Wharf restaurant is $14.75. The fish dinner is sold for $18.75. Determine the percent markup. The markup is %

A small town has two local high schools. High School A currently has 900 students and is projected to grow by 40 students each year. High School B currently has 750 students and is projected to grow by 90 students each year. Let A represent the number of students in High School A in t years, and let B represent the number of students in High School B after t years. Write an equation for each situation, in terms of t, and determine how many students would be in each high school in the year they are projected to have the same number of students.

Rhoda is saving up money for a down payment on a condominium. She currently has $5311, but knows she can get a loan at a lower interest rate if she can put down $6084. If she invests the $5311 in an account that earns 3.6 % annually. compounded quarterly, how long will it take Rhoda to accumulate the $6084? Round your answer to two decimal places, if necessary.

Caleb made a round-trip journey of 160 miles in each direction. Caleb's rate of travel to his destination was 15 mph slower than the rate of travel back home. His whole travel time was 10.4 hours. A) Set up the chart: (Use x as the going rate in the equation.) distance rate time going _______ x ________ returning ________ ________ ________ total ________ ________ _________ B) What is an equation that can be used to solve this problem? ____________ C) What was Caleb's rate of travel going to his destination? _________mph D) What was Caleb's rate of travel on his way home? ____________mph

If an insurance policy covers individual losses up to $10,000 and has a deductible of $500, the insured will be paid how much in the event of a covered loss of $5,000? a)$10,000 b)$4,500 c)$500 d)$9,500 e)$5,500

The density of water is 1 gram per cm^3. An object floats in water if its density is less than water's density, and it sinks if its density is greater than water's. Will a toy in the shape of a rectangular prism that is 1 centimeter by 2 centimeter by 2 centimeter with mass 3 grams sink or float? Explain your reasoning.

2 oz of brand X coffee were mixed with 3 oz of brand Y coffee which costs $4/oz to make Shayna's special coffee blend which costs $12/oz. What is the price per oz of brand X coffee? $21.10/oz $20.60/oz $24/oz $6/oz $26.15/oz

Solve the equation: x2=-1x +132 x = Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and -2/3 as your answers, then enter 4,-2/3 in the box.

Marcia wants to have $2000 in 10 years. Marcia plans on making no deposits or withdrawals. The following are the choices in which she can invest: A savings account earning 2.5% compounding monthly. A checking account earning 1.3% compounded weekly. A money market account earning 3.6% compounded quarterly. Explain which choice Monica should choose.

A random sample of 470 students from a wide geographic area indicated that 73 attended private schools. Estimate the lower bound limit of the true proportion of students attending private schools with 99% confidence.

Given the following vectors, calculate - 9u +7v. u = {-9,-8}, v = {-1, -3}

A small lawn in Los Angeles will be 1/2 acre in size. If 3/4 of the lawn will be filled with bark. What fraction of the lawn will be bark? Math a math drawing to help explain the solution.

The following values represent the height of 6 plants that Leons is growing for her Science project. 18.5 cm, 20 cm, 22.5 cm, 16.5 cm, 25 cm, 30 cm Calculate the IQR. 6.5 cm 9.5 cm 4.5 cm

Solve the system using Cramer's Rule. 4x - 3y = -13 5x – 5y = -15 Find the determinant D (denominator). D = Find the determinant Dₓ associated with x. Dₓ = Find the determinant Dᵧ associated with y. Dᵧ= The solution is (x, y) =( , ).

Doug invests a sum of money in a retirement account with an annual interest rate of 7% compounded quarterly. After 10 years, the balance reached 11,008.79. What was the amount of the initial investment?

Kane's Furniture Store advertised a table at a 16% discount. The original selling price was $116, and the sale price was $100. Was the sale price consistent with the ad? Explain Select the correct choice below and, if necessary, a)A. Yes, the sale price was consistent with the ad, because it represents a 16% discount. B). No, the sale price was $_____ higher than it should have been C). No, the sale price was $______ lower than it should have been

This test contains a total of 7 multiple choice questions, and each multiple choice question features 5 possible answers. (Someone guessing all "a's." for example, would have a string of multiple choice answers that reads "aaaaaaa.") How many total strings of multiple choice answers are possible for our test? (a) 7⁵ (b) 5! (c) (7/5) (d) 5⁷ (e) 1+2⁷ +3⁷ +4⁷ +5⁷

A citizen's delegation to Queen's Park is to be formed by selecting ten names at random from a box. The box contains the names of 20 citizens from Bolton, and 12 citizens from Brampton. What is the probability that the delegation will consist of five citizens from each city? a. 0.1903 b. 0.00312 c. 0.00200 d. 0.01982

Select two items. 1) Determine whether there is a positive, negative, or no correlation. 2) Identify the equation that best fits the data. x y 0 -3 -4 9 3 9 -3 3 4 17 y = -x^2 - 4x + 3 y = x^2 + x - 3 positive corrrelation no correlation negative correlation y = x² + 2x - 1

Given that there exists a surjective function f : S -> T, which of the following substitutions for the sets S and T are possible? Select only one answer. (a) S = {1,2,3}. T= R. (b) S = {x ∈ R : x² - 4 = 0}, T = {5, π, -10} (C) S = {x ∈ R : (x² - 1)(x² - 4)=0}, T = {5,π,-10} (d) S = {1}, T = {x ∈ R : eˣ = 0}. (e) S = {n ∈ N : n ≤ 2022}, T={z ∈ Z : |z| ≤ 202}.

Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for x(t) = 3 - t y(t) = 18 – 4t The Cartesian equation is y =