First integral:
Use the rational exponent to represent roots. You have
And from here you can use the rule
to derive
Second integral:
Simply split the fraction:
So, the integral of the sum becomes the sum of three immediate integrals:
So, the answer is the sum of the three pieces:
Third integral:
Again, you can split the integral of the sum in the sum of the integrals. The antiderivative of the cosine is the sine, because . So, you have
Answer:
a) The probability that a hobbit picked at random is no more than 36.7 in tall is P= 0.56631.
b) The probability that a random sample of 16 hobbits have a mean height of no more than 36.7 in tall is P=0.74857.
c) The probability that a random sample of 100 hobbits have a mean height of no more than 36.7 in tall is P=0.95254.
Step-by-step explanation:
We have this parameters for the population: normally distributed with mean 36 in. and standard deviation 4.2 in.
a) The probability can be computed calculating z and looking up in a table.
The probability that a hobbit picked at random is no more than 36.7 in tall is P= 0.56631.
b) In this case, the sample standard deviation change to
.
We can calculate z with the sample standard deviation
The probability that a random sample of 16 hobbits have a mean height of no more than 36.7 in tall is P=0.74857.
c) We apply the same principle as in pont b.
We can calculate z with the sample standard deviation
The probability that a random sample of 100 hobbits have a mean height of no more than 36.7 in tall is P=0.95254.
Answer: -3
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You fill in the formula with the info they give you and solve for v:
5 = -16(3.5)^2 + 3.5v + 6.5 That simplifies to 5 = -196 + 3.5v + 6.5 Now simplify further by combining like terms and getting the v term by itself on one side. 194.5 = 3.5v Now divide both sides by 3.5 to get a velocity of 55.57 feet per second.