The path of water from a hose on a fire tugboat can be approximated
by the equation y = −0.004×2 + 1.15x + 15,
where y is the height, in feet, of the water above the ocean when the water is x feet from the tugboat. When the water from the hose is 4 feet above the ocean, at what distance from the tugboat is it? Round answer to nearest hundredth
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A model rocket is launched with an initial velocity of 250 ft per
second. The height h, in feet, of the rocket t seconds after the launch is given by h = −16t2 + 250t.
How many seconds after the launch will the rocket be 600 ft above the ground? Round to the nearest hundredth of a second. (Enter your answers as a comma-separated list.)
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A model rocket is launched with an initial velocity of 250 ft per
second. The height h, in feet, of the rocket t seconds after the launch is given by h = −16t2 + 250t.
How many seconds after the launch will the rocket be 500 ft above the ground? Round to the nearest hundredth of a second. (Enter your answers as a comma-separated list.)
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Luis Mahla purchases a Porsche Boxster for $47,900 and finances the
entire amount at an annual interest rate of 5.2% for 4 years. Find the monthly payment. Assume the sales tax is 6% of the purchase price and the license fee is 1% of the purchase price. (Round your answer to the nearest cent.)
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Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers
have shown that the watches have an average life of 36 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 5 months, and the distribution of lifetimes is normal.
(a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.)
%
(b) If Accrotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)?
months
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At Litchfield College of Nursing, 88% of incoming freshmen nursing
students are female and 12% are male. Recent records indicate that 60% of the entering female students will graduate with a BSN degree, while 90% of the male students will obtain a BSN degree. If an incoming freshman nursing student is selected at random, find the following probabilities. (Enter your answers to three decimal places.)
(a) P(student will graduate | student is female)
(b) P(student will graduate and student is female)
(c) P(student will graduate | student is male)
(d) P(student will graduate and student is male)
(e) P(student will graduate). Note that those who will graduate are either males who will graduate or females who will graduate.
(f) The events described the phrases “will graduate and is female” and “will graduate, given female” seem to be describing the same students. Why are the probabilities P(will graduate and is female) and P(will graduate | female) different?
The term given refers to the sample space of all students, while the term and refers to restricting the sample space to females only.
The term and refers to the sample space of all students, while the term given refers to restricting the sample space to females only.
This is by chance. These probabilities are typically the same.
These probabilities are the same.
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John needs 520 wooden boards to build his doghouse. He already has
300 boards and can fit 20 boards in his car at one time. John wonders how many trips to the store he needs to make in order to purchase the remaining boards.
Which equation shows how John could solve his problem?
-a.) 520=20x + 300
-b.) 300= 20x
-c.) 520 + 20x = 300
-d.) 300x + 20 = 520
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A normal distribution has μ = 34 and σ = 5.
(a) Find the z score corresponding to x = 29.
(b) Find the z score corresponding to x = 48.
(c) Find the raw score corresponding to z = −3.
(d) Find the raw score corresponding to z = 1.7.
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
μ = 14.8; σ = 4.1
P(10 ≤ x ≤ 26) =
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Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 52 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 52 tons and standard deviation σ = 1.5 ton.
(a) What is the probability that one car chosen at random will have less than 51.5 tons of coal? (Round your answer to four decimal places.)
(b) What is the probability that 45 cars chosen at random will have a mean load weight x of less than 51.5 tons of coal? (Round your answer to four decimal places.)
(c) Suppose the weight of coal in one car was less than 51.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?
Yes
No
Suppose the weight of coal in 45 cars selected at random had an average x of less than 51.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?
Yes, the probability that this deviation is random is very small.
Yes, the probability that this deviation is random is very large.
No, the probability that this deviation is random is very small.
No, the probability that this deviation is random is very large.
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