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
Answer:
x = 10 units
Explanation:
First, let's consider the smaller triangle.:
It is a right-angled triangle, therefore, we can use the special trig functions.
tan θ = opposite / adjacent
tan 45 = opposite / 5
opposite = 5
Now, for the larger triangle:
It is also a right angled triangle which means that we can use the special trig functions.
sin θ = opposite / hypotenuse
sin (30) = 5 / x
x = 10 units
Hope this helps :)
You can do 25 divide by 5 and you get 5. Then you multiply 5 times 10 and your answer will be of 50. The mole digs 50 holes in 25 minutes.
I have a link from a really good video i had his problem but i couldnt solve it so i watched this video
<span>
</span>https://www.youtube.com/watch?v=iGeajxe0W50
Answer:
10
Step-by-step explanation:
100% = 40 teams
1% = 40 ÷ 100 = 0.40
25% = 0.40 x 25 = 10