12) Amusement Parks A thrill ride at an amusement park carries riders 160 feet straight up and then releases them for a free fal
l. The time t in seconds that it takes an object in free fall to reach the ground is t =
where d is the distance in feet that it falls. How long does it take the riders to reach the ground? Give your answer as a radical expression in simplest form. Then estimate the answer to the nearest tenth of a second.
where d is the distance in feet that it falls. How long does it take the riders to reach the ground? Give your answer as a radical expression in simplest form. Then estimate the answer to the nearest tenth of a second.
1 answer:
You might be interested in
Answer:
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of , in which
is mean amount of inches of rain and
is the standard deviation.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
Mean , standard deviation
n days:
This means that
Applying the Central Limit Theorem to the z-score formula.
What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of , in which
is mean amount of inches of rain and
is the standard deviation.
Answer:
53 lies between 7.2² and 7.3²
Step-by-step explanation:
Estimating a root to the nearest tenth can be done a number of ways. The method shown here is to identify the tenths whose squares bracket the value of interest.
You have answered the questions of parts 1 to 3.
__
<h3>4.</h3>You are given that ...
7.2² = 51.84
7.3² = 53.29
This means 53 lies between 7.2² and 7.3², so √53 lies between 7.2 and 7.3.
53 is closer to 7.3², so √53 will be closer to 7.3 than to 7.2.
7.3 is a good estimate of √53 to the tenths place.
_____
<em>Additional comment</em>
For an integer n that is the sum of a perfect square (s²) and a remainder (r), the square root is between ...
s +r/(2s+1) < √n < s +r/(2s)
For n = 53 = 7² +4, this means ...
7 +4/15 < √53 < 7 +4/14
7.267 < √53 < 7.286
Either way, √53 ≈ 7.3.
__
The root is actually equal to the continued fraction ...
Answer:
Step-by-step explanation:
<u>Equation Solving</u>
We are given the equation:
It's required to solve it for a.
Swap sides to have the letter on the left side:
Divide by :