Answer:
The probability that a randomly chosen widget weighs more then 19 grams is 0.468.
Step-by-step explanation:
<em>X</em> = Widget weights produced at Acme Widget Works
It is provided that <em>X</em> is normally distributed with mean 17.46 grams and variance 375.67 grams.
Compute the probability that a randomly chosen widget weighs more then 19 grams as follows:
![P(X>19)=P(\frac{X-\mu}{\sqrt{\sigma^{2}}}>\frac{19-17.46}{\sqrt{375.67}})](https://tex.z-dn.net/?f=P%28X%3E19%29%3DP%28%5Cfrac%7BX-%5Cmu%7D%7B%5Csqrt%7B%5Csigma%5E%7B2%7D%7D%7D%3E%5Cfrac%7B19-17.46%7D%7B%5Csqrt%7B375.67%7D%7D%29)
![=P(Z>0.08)\\\\=1-P(Z](https://tex.z-dn.net/?f=%3DP%28Z%3E0.08%29%5C%5C%5C%5C%3D1-P%28Z%3C0.08%29%5C%5C%5C%5C%3D1-0.53188%5C%5C%5C%5C%3D0.46812%5C%5C%5C%5C%5Capprox%200.468)
Thus, the probability that a randomly chosen widget weighs more then 19 grams is 0.468.
We have been given that there are 8 different types of chips at Subway. We are asked to find the number of different ways to choose 2 of them.
We will use combinations to solve our given problem.
Number of combinations of r objects chosen from n objects is given by ![C(n,r)=\frac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=C%28n%2Cr%29%3D%5Cfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
![C(8,2)=\frac{8!}{2!(8-2)!}](https://tex.z-dn.net/?f=C%288%2C2%29%3D%5Cfrac%7B8%21%7D%7B2%21%288-2%29%21%7D)
![C(8,2)=\frac{8\cdot 7\cdot 6!}{2\cdot 1\cdot 6!}](https://tex.z-dn.net/?f=C%288%2C2%29%3D%5Cfrac%7B8%5Ccdot%207%5Ccdot%206%21%7D%7B2%5Ccdot%201%5Ccdot%206%21%7D)
![C(8,2)=\frac{8\cdot 7}{2}](https://tex.z-dn.net/?f=C%288%2C2%29%3D%5Cfrac%7B8%5Ccdot%207%7D%7B2%7D)
![C(8,2)=4\cdot 7](https://tex.z-dn.net/?f=C%288%2C2%29%3D4%5Ccdot%207)
![C(8,2)=28](https://tex.z-dn.net/?f=C%288%2C2%29%3D28)
Therefore, you can choose 2 of them in 28 different ways.
The surface area of a shape is the area of each face added together.
Triangles
The area of a triangle is 1/2*w*h. So 1/2*6*8 = 24. We have two of these faces, so we'll add this twice.
Outer Rectangles
The area of a rectangle is w*h, so for these we'll do 9*20 = 180. These shapes are again duplicates, so we'll add them twice.
Center Rectangle
Again, we know the area of a rectangle is w*h, so 6*20 = 120. This is the only shape that isn't repeated.
Finally, we need to add the areas of the shapes up.
24 + 24 + 180 + 180 + 120 = 528
Therefore the surface area of the net is 528 cm^2.
The approximate value of
is 1.52832 or 1.53.
What is the logarithmic Expression?
A logarithmic expression is an function that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.
Here
= ![log_{2^{3} }24](https://tex.z-dn.net/?f=log_%7B2%5E%7B3%7D%20%7D24)
= ![\frac{1}{3} log_{2}24](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20log_%7B2%7D24)
= ![\frac{1}{3} log_{2}{8.3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20log_%7B2%7D%7B8.3%7D)
= ![\frac{1}{3} log_{2}8 + \frac{1}{3} log_{2}3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20log_%7B2%7D8%20%2B%20%5Cfrac%7B1%7D%7B3%7D%20log_%7B2%7D3)
= ![\frac{1}{3} log_{2}2^3 + \frac{1}{3} log_{2}3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20log_%7B2%7D2%5E3%20%2B%20%5Cfrac%7B1%7D%7B3%7D%20log_%7B2%7D3)
= ![\frac{3}{3} log_{2}2 +\frac{1}{3} log_{2}3](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B3%7D%20log_%7B2%7D2%20%2B%5Cfrac%7B1%7D%7B3%7D%20log_%7B2%7D3)
= ![1 + \frac{1}{3} log_{2}3](https://tex.z-dn.net/?f=1%20%2B%20%5Cfrac%7B1%7D%7B3%7D%20log_%7B2%7D3)
= 1 + 0.5283
l
≈ 1.53
The approximate value of
is 1.52832 or 1.53.
Learn more about Logarithmic expression from :
brainly.com/question/20785664
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