6----->2 1/2
24--->x
x=24*2 1/2/6=4*2 1/2=4*5/2=10 pounds of apples
Answer:
The similar triangle to ABC is DEF
Step-by-step explanation:
0.3x+5 is an expression. If we had an equation, then we would have solved for x. It looks like you need to translate this into a words. You can say
"5 more than 30 percent of a number."
B,13 students prefered math
Answer:
![P(x](https://tex.z-dn.net/?f=P%28x%3C810%29%3D0.5)
![P(x](https://tex.z-dn.net/?f=P%28x%3C800%29%20%3D%200)
![P(x>808.40) = 0.58](https://tex.z-dn.net/?f=P%28x%3E808.40%29%20%3D%200.58)
![P(x\le805.40\ or\ x\ge 808.40) = 0.85](https://tex.z-dn.net/?f=P%28x%5Cle805.40%5C%20or%5C%20x%5Cge%20808.40%29%20%3D%200.85)
Step-by-step explanation:
Given:
![F(x) = \left\{\begin{array}{ll}{0} &; {x](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bll%7D%7B0%7D%20%26%3B%20%7Bx%26lt%3B800%5E%7B%5Ccirc%7D%20%5Cmathrm%7BC%7D%7D%20%5C%5C%20%7B0.05%20x-40%7D%20%26%3B%20%7B800%5E%7B%5Ccirc%7D%20%5Cmathrm%7BC%7D%20%5Cleq%20x%26lt%3B820%5E%7B%5Ccirc%7D%20%5Cmathrm%7BC%7D%7D%20%5C%5C%20%7B1%7D%20%26%3B%20%7Bx%26gt%3B820%5E%7B%5Ccirc%7D%20%5Cmathrm%7BC%7D%7D%5Cend%7Barray%7D)
Solving (a): P(x < 810)
To solve this, we make use of:
![P(x](https://tex.z-dn.net/?f=P%28x%3C810%29%20%3D%20F%28x%29%20%3D%200.05x%20-%2040)
Because
![800^\circ C \le 810 \le 820^\circ C](https://tex.z-dn.net/?f=800%5E%5Ccirc%20C%20%5Cle%20810%20%5Cle%20820%5E%5Ccirc%20C)
So:
![F(x) = 0.05 * 810 -40](https://tex.z-dn.net/?f=F%28x%29%20%3D%200.05%20%2A%20810%20-40)
![F(x) = 40.5 -40](https://tex.z-dn.net/?f=F%28x%29%20%3D%2040.5%20-40)
![F(x) = 0.5](https://tex.z-dn.net/?f=F%28x%29%20%3D%200.5)
Hence:
![P(x](https://tex.z-dn.net/?f=P%28x%3C810%29%3D0.5)
Solving (b): P(x < 800)
To solve this, we make use of:
![P(x](https://tex.z-dn.net/?f=P%28x%3C800%29%20%3D%20F%28x%29%20%3D%20x)
Because:
![x < 800^\circ C](https://tex.z-dn.net/?f=x%20%3C%20800%5E%5Ccirc%20C)
So:
![P(x](https://tex.z-dn.net/?f=P%28x%3C800%29%20%3D%200)
Solving (c): P(x > 808.40)
Here, we make use of complement rule:
![P(x>808.40) = 1 - P(x \le 808.40)](https://tex.z-dn.net/?f=P%28x%3E808.40%29%20%3D%201%20-%20P%28x%20%5Cle%20808.40%29)
Where:
![P(x\le808.40) = 0.05x - 40](https://tex.z-dn.net/?f=P%28x%5Cle808.40%29%20%3D%200.05x%20-%2040)
![P(x\le808.40) = 0.05*808.40 - 40](https://tex.z-dn.net/?f=P%28x%5Cle808.40%29%20%3D%200.05%2A808.40%20-%2040)
![P(x\le808.40) = 0.42](https://tex.z-dn.net/?f=P%28x%5Cle808.40%29%20%3D%200.42)
So:
![P(x>808.40) = 1 - 0.42](https://tex.z-dn.net/?f=P%28x%3E808.40%29%20%3D%201%20-%200.42)
![P(x>808.40) = 0.58](https://tex.z-dn.net/?f=P%28x%3E808.40%29%20%3D%200.58)
Solving (d) The probability that the temperature lies outside 805.60 and 808.40
First, we calculate the probability that it lies within.
This is represented as:
![P(805.40 < x < 808.40)](https://tex.z-dn.net/?f=P%28805.40%20%3C%20x%20%3C%20808.40%29)
This is calculated using:
![P(805.40 < x < 808.40) = F(808.40) - F(805.40)](https://tex.z-dn.net/?f=P%28805.40%20%3C%20x%20%3C%20808.40%29%20%3D%20F%28808.40%29%20-%20F%28805.40%29)
![P(805.40 < x < 808.40) = 0.05*808.40-40 - (0.05*805.40-40)](https://tex.z-dn.net/?f=P%28805.40%20%3C%20x%20%3C%20808.40%29%20%3D%200.05%2A808.40-40%20-%20%280.05%2A805.40-40%29)
![P(805.40 < x < 808.40) = 0.42 - (0.27)](https://tex.z-dn.net/?f=P%28805.40%20%3C%20x%20%3C%20808.40%29%20%3D%200.42%20-%20%280.27%29)
![P(805.40 < x < 808.40) = 0.42 - 0.27](https://tex.z-dn.net/?f=P%28805.40%20%3C%20x%20%3C%20808.40%29%20%3D%200.42%20-%200.27)
![P(805.40 < x < 808.40) = 0.15](https://tex.z-dn.net/?f=P%28805.40%20%3C%20x%20%3C%20808.40%29%20%3D%200.15)
Using complement rule, the required probability is:
![P(x\le805.40\ or\ x\ge 808.40) = 1 - 0.15](https://tex.z-dn.net/?f=P%28x%5Cle805.40%5C%20or%5C%20x%5Cge%20808.40%29%20%3D%201%20-%200.15)
![P(x\le805.40\ or\ x\ge 808.40) = 0.85](https://tex.z-dn.net/?f=P%28x%5Cle805.40%5C%20or%5C%20x%5Cge%20808.40%29%20%3D%200.85)