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The triangular region with vertices $(0,-1),(1,0),$ and (0,1) is rotated about the line $x=2 .$ Find the volume of the solid so generated.

Calculus A Complete Course

Applications of Integration

Volumes by Slicing-Solids of Revolution

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Ulises Sosa verified

Numerade educator

What is the polar equation of the parabola y = x² - x?

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Lucas Finney verified

Numerade educator

Let Z be a standard normal random variable. If P(|Z| > zo) = 0.66, where |Z| represents the absolute value of Z, what is the value, zo? A. 0.44 B. 0.52 C. 0.34 D. 0.41

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Qudsiya Anis verified

Numerade educator

An herbal medicine brand contains amounts of the active ingredient (in milligrams, mg) that vary normally from capsule to capsule. A quality control engineer assesses whether capsules of this brand contain larger amounts, on average, than the marketed amount of 10 mg. A simple random sample of 25 capsules finds a mean content of 9.2 mg per capsule. Which of the following options are the appropriate null and alternative hypotheses? A. Ho: µ = 10 versus HA: µ > 10 B. Ho: µ = 9.2 versus HA: µ > 9.2 C. Ho: x-bar = 9.2 versus HA: x-bar > 9.2 D. Ho: x-bar = 10 versus HA: x-bar > 10

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Paul A. verified

Numerade educator

In a bell-shaped symmetric distribution, such as the heights of women, the distance (difference in heights) is greatest between which two percentiles? A. 30th and 40th B. 20th and 30th C. 10th and 20th D. All of these distances are equal.

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Dominador Tan verified

Numerade educator

An automatic dispensing machine dispenses a certain beverage into a 20 ounce cup. Let X be the amount dispensed by the machine where X is Normal with a mean of 19.8, and a standard deviation of 0.9. Let Y be the size of the 20-ounce cup, where Y is Normal with a mean of 20.1 and a standard deviation of 0.7. What is the probability that a randomly selected cup automatically filled by this machine will overflow? We can assume that X and Y are independent. A. 40.9% B. 39.74% C. 60.26% D. 59.1%

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Lucas Finney verified

Numerade educator

What is the probability that a bridge hand (13 cards dealt randomly from a standard deck of 52 cards) contains exactly 2 aces and no spades? A. 0.004 B. 0.003 C. 0.008 D. 0.006

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Qudsiya Anis verified

Numerade educator

A study on the sales of Harry Potter books recently concluded that p% were purchased by readers who were 14 years or older. You just surveyed n people who are Harry Potter book owners and you found that, on average, 18 of them were 14 years or older, with a variance of 7.2. What is the value of n, and what percentage of Harry Potter book sales were purchases by readers who were under the age of 14 (answers are in that order)? A. 30; 40% B. 45; 40% C. 30; 60% D. 45; 60%

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Donna Densmore verified

Numerade educator

Adult salmon have lengths that are normally distributed with a mean of mu = 70 cm and a population standard deviation equal to 5.4 cm. What is the probability that a random sample of n = 10 fish caught will have an average length less than 75 cm? A. 0.17% B. 99.83% C. 2.93% D. 97.07%

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Donna Densmore verified

Numerade educator

Suppose that it is known that Engineering students feel like they’ve done really well on a final exam 20% of the time. If an Engineering student feels like they’ve done really well on a final exam, they will go out to a pub afterwards 30% of the time. If an Engineering student feels like they didn’t do well at all on a final exam, they will go out to a pub 80% of the time. After a final exam, suppose you walk into a pub and see one of your Engineering classmates, what is the chance that they did well on a final exam? A. 49/70 B. 32/35 C. 9/25 D. 3/35 E. 1/7

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James Kiss verified

Numerade educator

Which of these best describes the least squares regression line – that is, the regression line obtained using the method of least squares? A. It is the line which makes the sum of the squared distances perpendicular to the line as small as possible. B. It is the line which best splits the data in half, with 50% of the data points lying above the regression line and 50% of the data points lying below the regression line. C. It is the line which makes the sum of the squared horizontal differences between the observed values and predicted values as small as possible. D. It is the line which makes the sum of the squared distances to the line, in the vertical direction (or y direction) as small as possible. E. More than one of these best describes the least squares regression line.

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