Answer:
A. Actute triangle
Step-by-step explanation:
Is A because an acute triangle is a triangle where all the angles are the same.
Can not be B. because isosceles triangles have two sides that are the same which doesn't relate to angles.
Can not be C. because equilatiral triangles are triangles with sides that are all the same.
Can not be D. because for a triangle to be obtuse one of the angles needs to be greater that 90 degrees.
So it has to be A.
(1+x^2)^8
=(1+8x^2+8*7/(1*2)x^4+8*7*6/(1*2*3)x^6+8*7*6*5/(1*2*3*4)x^8+....)
=1+8x^2+28x^4+56x^6+70x^8+....)
For x<1, higher power terms diminish in value, hence we can approximate powers of numbers.
1.01=(1+0.1^2) => x=0.1 in the above expansion
(1.01)^8
=1+8(0.1^2)+28(0.1^4)+56(0.1^6) [ limited to four terms, as requested]
=1+0.08+0.0028+0.000056 (+0.00000070)
=1.082856 (approximately)
Answer:
Which One ?
Step-by-step explanation:
<h2><u>
Answer with explanation:</u></h2>
The confidence interval for population mean (when population standard deviation is unknown) is given by :-
![\overline{x}-t^*\dfrac{s}{\sqrt{n}}< \mu](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D-t%5E%2A%5Cdfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%3C%20%5Cmu%3C%5Coverline%7Bx%7D%2Bz%5E%2A%5Cdfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
, where n= sample size
= Sample mean
s= sample size
t* = Critical value.
Given : n= 25
Degree of freedom : ![df=n-1=24](https://tex.z-dn.net/?f=df%3Dn-1%3D24)
![s=\ $19.95](https://tex.z-dn.net/?f=s%3D%5C%20%2419.95)
Significance level for 98% confidence interval : ![\alpha=1-0.98=0.02](https://tex.z-dn.net/?f=%5Calpha%3D1-0.98%3D0.02)
Using t-distribution table ,
Two-tailed critical value for 98% confidence interval :
![t^*=t_{\alpha/2,\ df}=t_{0.01,\ 24}=2.4922](https://tex.z-dn.net/?f=t%5E%2A%3Dt_%7B%5Calpha%2F2%2C%5C%20df%7D%3Dt_%7B0.01%2C%5C%2024%7D%3D2.4922)
⇒ The critical value that should be used in constructing the confidence interval = 2.4922
Then, the 95% confidence interval would be :-
![93.36-(2.4922)\dfrac{19.95}{\sqrt{25}}< \mu](https://tex.z-dn.net/?f=93.36-%282.4922%29%5Cdfrac%7B19.95%7D%7B%5Csqrt%7B25%7D%7D%3C%20%5Cmu%3C93.36%2B%282.4922%29%5Cdfrac%7B19.95%7D%7B%5Csqrt%7B25%7D%7D)
![=93.36-9.943878< \mu](https://tex.z-dn.net/?f=%3D93.36-9.943878%3C%20%5Cmu%3C93.36%2B9.943878)
![=93.36-9.943878< \mu](https://tex.z-dn.net/?f=%3D93.36-9.943878%3C%20%5Cmu%3C93.36%2B9.943878)
![=83.416122< \mu](https://tex.z-dn.net/?f=%3D83.416122%3C%20%5Cmu%3C103.303878%5Capprox83.4161%3C%5Cmu%3C103.3039)
Hence, the 98% confidence interval for the mean repair cost for the dryers. = ![83.4161](https://tex.z-dn.net/?f=83.4161%3C%5Cmu%3C103.3039)