Answer:
D
Step-by-step explanation:
When the population standard deviation is unknown while constructing the confidence interval then the estimate of standard deviation calculated from sample is used and due to this the new type of variability arise and then for conducting a confidence interval for mean the t-distribution is used. For calculating confidence interval for mean there are two sampling distributions z distribution and t distribution. When sample size is small and population standard deviation is unknown then t-distribution is used.
Given the expression,

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.
![[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]](https://tex.z-dn.net/?f=%20%5B%288x-56x%5E2%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%5B%28%5Csqrt%7B14x-2%7D%29%28%5Csqrt%7B14x-2%7D%29%5D%20)
If we have
, we will get
by multiplying them. And
.
So here in the problem, we will get,
![[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)](https://tex.z-dn.net/?f=%20%5B%288x-56x%5E2%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%2814x-2%29%20)
Now in the numerator we have
. We can check 8x is common there. we will take out -8x from it, we will get,


And in the denominator we have
. We can check 2 is common there. If we take out 2 from it we will get,

So we can write the expression as
![[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]](https://tex.z-dn.net/?f=%20%5B%28-8x%29%287x-1%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%5B2%287x-1%29%5D%20)
is common to the numerator and denominator both, if we cancel it we will get,

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,


So we have got the required answer here.
The correct option is the last one.
Answer:
921.165 feet
Step-by-step explanation:
Ok we are looking for the length of the base.
Now let's take the question and picture it as a triangle, we will find out that it looks like a right angle triangle.
The height= 645 feet
Angle of elevation= 35°
Base is unknown
To find the base
We recall that tan of angle
= opposite/adjacent
In this case
Angle= 35°
Opposite= height= 645
Adjacent= base
Tan 35 = 645/adj
Adj =645/tan 35
Adj =645/0.7002
Adj = 921.165
The base is 921.165 feet
The answer would be 26 due to the fact that it’s just nearly above the 25 mark
Answer:
Length: 3w-4
Step-by-step explanation:
Length: 3w-4
Width: W
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