What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?
2 answers:
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Answer:
95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].
Step-by-step explanation:
We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample mean time = 5.15 years
= sample standard deviation = 1.68 years
n = sample of college graduates = 4400
= population mean time
<em>Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.</em>
<u>So, 95% confidence interval for the population mean, </u><u> is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%
level of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> = [
,
]
= [ ,
]
= [5.10 , 5.20]
Therefore, 95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].
Answer:
third side = 9
Step-by-step explanation:
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let the third side be x, then
x² + 40² = 41², that is
x² + 1600 = 1681 ( subtract 1600 from both sides )
x² = 81 ( take the square root of both sides )
x = = 9
The third side is 9