Answer:
![P(z> \frac{(69.3-64)-0}{\sqrt{2.74^2 +2.7^2}}) =P(z>1.38)](https://tex.z-dn.net/?f=%20P%28z%3E%20%5Cfrac%7B%2869.3-64%29-0%7D%7B%5Csqrt%7B2.74%5E2%20%2B2.7%5E2%7D%7D%29%20%3DP%28z%3E1.38%29)
and we can find this probability using the complement rule and we got:
![P(z>1.38)=1-P(z](https://tex.z-dn.net/?f=%20P%28z%3E1.38%29%3D1-P%28z%3C1.38%29%20%3D%201-0.9162%3D%200.0838)
So then we can conclude that approximately 8.38% of the men are taller than women
Step-by-step explanation:
Let X the random variable who represent the heights of women aged 20 to 29 and the distribution is given by:
![X \sim N(64, 2.74)](https://tex.z-dn.net/?f=%20X%20%5Csim%20N%2864%2C%202.74%29)
And let Y the heights of men aged 20 to 29 and the distribution for Y is given by:
![Y \sim N(69.3, 2.7)](https://tex.z-dn.net/?f=%20Y%20%5Csim%20N%2869.3%2C%202.7%29)
And for this case we want to find the following probability:
![P(Y>X) = P(Y-X >0)](https://tex.z-dn.net/?f=%20P%28Y%3EX%29%20%3D%20P%28Y-X%20%3E0%29)
The distribution for Y-X is given by:
![Y-X \sim N (\mu_Y -\mu_X , \sqrt{\sigma^2_Y +\sigma^2_X})](https://tex.z-dn.net/?f=%20Y-X%20%5Csim%20N%20%28%5Cmu_Y%20-%5Cmu_X%20%2C%20%5Csqrt%7B%5Csigma%5E2_Y%20%2B%5Csigma%5E2_X%7D%29)
We can define the random variable Z= Y-X and the we can use the z score formula given by:
![z =\frac{z -\mu_z}{\sigma_z}](https://tex.z-dn.net/?f=%20z%20%3D%5Cfrac%7Bz%20-%5Cmu_z%7D%7B%5Csigma_z%7D)
And using the z score formula we got:
![P(z> \frac{(69.3-64)-0}{\sqrt{2.74^2 +2.7^2}}) =P(z>1.38)](https://tex.z-dn.net/?f=%20P%28z%3E%20%5Cfrac%7B%2869.3-64%29-0%7D%7B%5Csqrt%7B2.74%5E2%20%2B2.7%5E2%7D%7D%29%20%3DP%28z%3E1.38%29)
and we can find this probability using the complement rule and we got:
![P(z>1.38)=1-P(z](https://tex.z-dn.net/?f=%20P%28z%3E1.38%29%3D1-P%28z%3C1.38%29%20%3D%201-0.9162%3D%200.0838)
So then we can conclude that approximately 8.38% of the men are taller than women
Volume of a cone = πr<span><span>^2 x </span><span>h/<span>3
Volume = 81</span></span></span>π x (14/3)
Volume = 378π = 1187.52 in^3
Let x be for unknown number. Let x be first number .
X+1 To be second number .x+2be third number. X+(x+1)+(x+2)=312.
Simplify to get 3x+3=312 . Subtract 3 from both sides 3x-3=312-3. Once you subtract get 3x=109.then divide 3 both sides . 3x/3=309/3. To get x= 103.
Now once you have that First number 103. Second number 103+1=104 . And third number 103+2=105. To check add them 103+104+105=312
Answer:
sphere (see the explanation)
Step-by-step explanation:
we know that
When you will rotate a circle about its diameter, you will obtain a sphere.
The radius of the sphere will the same as that of the circle.
In this problem
The circle is rotated about the line y=1
The line y=1 passes through a diameter of the circle
The equation of the circle is
![(x-1)^2+(y-1)^2=1](https://tex.z-dn.net/?f=%28x-1%29%5E2%2B%28y-1%29%5E2%3D1)
see the attached figure to better understand the problem
so
The circle is rotated about its diameter
therefore
The resulting three-dimensional object will be a sphere with radius of 1