Math Questions

13. A cone with a radius of 6 meters has a volume of 542.87 m³. Find the slant height of the cone. height = slant height =

An asteroid is 10^12 miles away from earth, and it is travelling at a speed of 10^5 miles per day. How many days will it take the comet to reach earth? Leave your answer in the form a^b days

f(x)=3600/x+100x+1800 a. what is the domain of f(x)? b. Find the dericative of f(x). c. identify all stationary points of f(x). (if non explain why) d. Identify all singular points of f(x). (if non explain why) e. Identify all endpoints of f(x). (if non explain why)

The slope is 3, and the y-intercept is 9. The slope is 3, and the y-intercept is 12. The slope is 4, and the y-intercept is 9. The slope is 4, and the y-intercept is 12.

Given that x = 15, and y = 60, determine which segments or lines are parallel, and justify your solution. A AB | CD, because alternate interior angles are congruent. B AD | CB, because altemate interior angles are supplementary. C AB CD, because consecutive interior angles are congruent. D AD II CB. because consecutive interior angles are supplementary.

9) Jamal wants to construct a tangent line to circle O that passes through point M. He started by drawing a segment from point O to point M. Next he constructed the midpoint of segment OM. What is the next step in his construction. A) Construct a radius of circle O. B) Set the compass to the width of OP. C) Construct the midpoint of segment OP. D) Draw a diameter passing through point O.

The curve y² = x, the line x = 2, and the x-axis form the sides of the bounded region. Find the volume of the solid generated by revolving about the x-axis. A π/2 B π/4 C 2π D π

17) Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left and 4 units up. Finally, he reflects the image over the line x = 1. Are the original and transformed images congruent? Justify your answer. A) no; Two reflections will change the size of the original image. B) no; Reflections and translations are fluid motions. Fluid motions change the size of the original image. C) yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image. D) yes; Reflections and translations are fluid motions. Fluid motions preserve the size of the original image.

John has a credit card with an APR of 23.95% and a current balance of $12,650.35. He wants to pay it off in 3 years. What will John's monthly payment be? (Remember a credit card is compounded monthly.) Round to the nearest dollar.

A biologist wants to know the width w of a river to properly set instruments for an experiment. From point A, the biologist walks downstream 100 feet and sights to point C (see figure). From this sighting, it is determined that θ = 47°. How wide is the river? (Round your answer to one decimal place.

Write the first five terms of the sequence whose general term, an, is given as an=-5n+ 8.

In Circle O, LAC is a central angle and mzAC = 132°. If Q represents the area of Circle O, write an expression that represents the area of the sector formed by ZAC, in terms of Q. 11/60 Q 6Q 11/30 Q 60/11 Q

Carly wants to invest $1000 in an account that earns 8% interest, compounded quarterly. How many years will it take for he account to have a value of $5000? Round to the nearest whole number.

Carly wants to invest $1000 in an account that earns 6.2% interest, compounded quarterly. How many years will it take for he account to have a value of $5000? Round to the nearest whole number

Lee has collected the cost and sale price of five food items from a supermarket. Cost (in $) 10 25 14 25 Sale Price (in $) 14.5 Yes 32 17 29 21 25 Is there any valid causation among the given data? No Cannot be determined Yes

In past years, the proportion of engineering students at the local college who did not own a calculator was 0.15. Angelina believes the proportion of current population of engineering students who do not own a calculator is lower. She randomly selects 55 students and finds that 0.05 and calculates a p-6 of them do not own a calculator. She uses a significance level of a - value of 0.198. What null and alternative hypothesis did Angelina use for this test, and what conclusion can she make? Note: The item below has been reviewed and is scheduled to be updated. All students will receive full credit for any response to the following. (1 point) H0: p=15 He: p > 15 Angelina fails to reject the null hypothesis because the p-value is greater than the significance level. H0: p=0.15 He: p<0.15 Angelina rejects the null hypothesis because the p-value is greater than the significance level. H0: p=15 He: p<0.15 Angelina fails to reject the null hypothesis because the p-value is greater than the significance level. H0: µ= 0.15 He: µ<0.15

How much would you have to deposit in an account that pays an interest rate of 4.6% compounded monthly, if at the end of 10 years you want $8500 in the account? Use the TMV calculator to fill in the tal N 1% PV PMT 0 FV P/Y 12 CIY

Evaluate the series. 5 Σ (71+1) i=1 5 Σ(7i+1)= i=1

A professor sampled 46 students from a large university to obtain a 95% confidence interval for the proportion of students in favor of raising ASB fees. The interval was (.356, .397). If the professor had used a 90% confidence interval instead, the confidence interval would have been A Wider and would have a smaller chance of missing the true proportion. B Wider, but the chance of missing the true proportion cannot be determined. C Wider and would have a larger chance of missing the true proportion. D Narrower and would have a smaller chance of missing the true proportion. E Narrower and would have a larger chance of missing the true proportion.

Write the terms of 4Σi=1 f(xi) Δx., with x₁ = 2, X₂ = 6, x3 = 4, x4 = 0, and Ax=0.2, for the function f(x) =-5/x+1 What is the first term in the series? a₁ = (Simplify your answer. Type an integer or a simplified fraction.) Evaluate the sum.

On Melissa's 6th birthday, she gets a $4000 CD that earns 5% interest, compounded semiannually. If the CD matures on her 12th birthday, how much money will be available? The amount available will be (Simplify your answer. Round to the nearest cent.)

Evaluate the series. 7 Σ(-1)) j=1 7 Σ(-1)= j=1

A recent survey of 18 randomly selected social networking sites has a mean of 11.5 million visitors for a specific month. The standard deviation is 4.58 million. Find the lower bound limit of the 99% confidence interval of the true mean. Round your answer to 3 decimal places.

Data set 14 "Oscar Winner Age " in Appendix B lists ages of actresses when they won Oscars, and the summary statistics are n=87, x= 36.2 years, and s=11.5 years. Use a 0.01 significance level to test the claim that the mean age of actresses when they win Oscars is greater than 30 years.

A random sample of state gasoline taxes (in cents) is shown here for 12 states. Use the data to estimate the lower bound of the true population mean gasoline tax with 99% confidence. 38.4 40.9 67 32.5 51.5 43.4 ... 38 43.4 50.7 35.4 39.3 41.4 Round your answer to 2 decimal places.

Jude walks around a circular path 4 times. The radius of the path is 100 yards. How many yards does he walk in all? Use 3.14 for pl. A. 2512 yards B. 400 yards C. 100 yards

The standard deviation of SAT scores is 126 points. A researcher decides to take a sample of 600 students' scores to estimate the mean score of students in your state. What is the standard deviation of the sample mean?

Which of the following statements is false? A Alpha is the proportion in the tails of the distribution which are outside of the confidence interval. B) There is a different z-value (i.e., critical value) used for each level of alpha. c) In practice, the population means is an unknown quantity that is to be estimated. D) It is possible to construct a 100% confidence interval estimate for the population means.

If the radius of a circle is 162 millimeters, then what is the circumference of the circle? Use pl = 3.14 A. 1,078.96 millimeters B. 1,017.36 millimeters C. 1,000.88 millimeters

A nutritionist found that in a random sample of 59 families, 21% indicated that they ate fruit at least 3 times a week. Find the lower bound limit of the 90% confidence interval of the true proportion of families who said that they ate fruit at least 3 times a week.

In a survey of 1000 U.S. adults, 700 think police officers should be required to wear body cameras while on duty. Construct 99% confidence interval for the population proportion.

The Great Pyramid of Giza, located in Egypt, is one of the Seven Wonders of the Ancient World. The length of one side of its square base is 440 cubits (an ancient unit of length). The Pyramid was 280 cubits tall when it was constructed over 4000 years ago. Which of the following values most closely represents the volume of the Great Pyramid when it was first built? A. 16,800,000 cubic cubits B. 18,100,000 cubic cubits C. 34,500,000 cubic cubits D. 54,200,000 cubic cubits

A factory manufactures a chip used in constructing central processing units for computers. The factory's quality control division has set a limit that no more than 2% of the chips can be defective. They sample 200 computer chips and find that 3 of them are defective. They use this data to calculate the following 90% confidence interval: (0.001, 0.029). Recommend a strategic decision for the factory. A. The factory should continue producing the chips using the same process since the confidence interval shows that the proportion of defective chips could be very close to 0%. B. The factory should continue producing the chips using the same process since 3 defective chips out of 200 is 1.5%, which meets the goal of no more than 2% being defective. C. The factory should consider revising its production process since there is a 90% chance that 2.9% of their chips are defective. D. The factory should consider revising its production process since the confidence interval shows that the proportion of defective chips could exceed 2%.

Which of the following statements on the central limit theorem is true? A) if the sample size increases then the sampling distribution much approach an exponential distribution B. if the sample size increases sampling distribution must approach a normal distribution C. if the sample size decreases then the sample distribution must approach a normal distribution D if the sample size decreases then the sampling distribution much approach an exponential distribution

Find the missing terms of the sequence and determine if the sequence is arithmetic, geometric, or neither. 6, 11, 16, 21,_______,______ .

Red Blood Cell Count A simple random sample of 40 adults males is obtained, and the red blood cell count (in cells per microliter) is measured for each of them, with these results: n=40, x= 4.932 million cells per microliter, s=0.504 million cells per microliter ( from Data Set 1 "Body Data" in Appendix B). Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 5.4 million cells per microliter, which is often used as the upper limit of the range of normal values. Does the result suggest that each of the 40 males has red blood cell count below 5.4 million cells pern microliter.

Find the surface area of a square pyramid whose side length of the base is 9 cm and has a slant height of 6 cm. A. 254 cm² B. 142 cm² C. 189 cm²

A recent study of 25 randomly selected employees of a company showed that the mean of the distance they traveled to work was 14.71 miles. The standard deviation of the sample mean was 2.62 miles. Find the upper bound 95% confidence interval of the true mean.

The gas tank of a 2014 Dodge Charger holds 19.1 gallons. How many pounds of carbon dioxide are produced by burning an entire tank of gas? Express your answer rounded to the nearest tenth of a pound.

Find a counterexample to the statement. The sum of two different prime numbers is always prime.

The following problem refers to triangle ABC, find all missing parts. Round degrees to 1 decimal places and sides to the nearest whole number. A = 21.6°, B = 51.4°, a = 130 inches A = B C= a= ___________ inches b= ____________Inches C=______________ inches

Write the terms of 4Σi=1 f(x1) Δx with x₁ = 0, x₂ = 2, x3 = 4, x4= 6, and Δx=1.5, for the function f(x) = 7x². Evaluate the sum. What is the first term in the series? a₁ = (Simplify your answer. Type an integer or a simplified fraction.)

The company has a $150,000 liability at December 31, 2021, of which $30,000 of it is payable in 2022. In its December 31, 2021 balance sheet, the company reports the $150,000 debt as a: $30,000 current liability and a $120.000 long-term liability in the balance sheet. $150,000 current liability in the balance sheet. $150,000 long-term liability in the balance sheet. $120,000 current liability and a $30,000 long-term liability in the balance sheet.

Write the first five terms of the sequence. an=(1/2)n(3n-2) a₁ = (Type an integer or a simplified fraction.)

A pen stand made of wood is in the shape of a cubold with four conical depressions to hold pens. The dimensions of the cubold are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand. Use it = 22/7. 529.68 cm³ 520.48 cm³ 523.53 cm³

According to http://www.thehcf.org/antiidlingprimer.html, Americans waste approximately 3.8 million gallons of gasoline each day by voluntarily idling their cars. How many pounds of carbon dioxide does this produce daily? Express your answer rounded to the nearest tenth of a million pounds of carbon dioxide. million lb of CO₂

Frederick is creating a plan to conduct a randomized survey. He will be asking guests at a baseball stadium to rate their experience. At which location should he take the survey to ensure randomization? the section of seats directly behind home plate the hot dog stand the stadiums front gate the gift shop

The volume produced by revolving about the x-axis the region above the curve y= x³, below the line y = 1 and between x = 0 and x = 1 is ... A π/42 B π/7 C √2/2π D 6π/7

A sample of 15 measurements of the breaking strengths of cotton threads gave a mean of 7.3 oz and a standard deviation of 2.82 oz. Find an upper bound 95% confidence limits for the actual mean breaking strength.

A 95% confidence interval estimate for the difference between two population means, 12000, is determined to be (62.75, 68.52.) If the confidence level is reduced to 90%, the confidence interval (A) insufficient information (B) becomes narrower (C) becomes wider (D) remains the same