Answer:
The expression which is equivalent to (k ° h)(x) is
⇒ 2nd answer
Step-by-step explanation:
* Lets explain the meaning of the composition of functions
- Composition of functions is when one function is inside of an another
function
# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside
g(x) and (h ° g)(x) means g(x) is inside h(x)
* Now lets solve the problem
∵ h(x) = 5 + x
∵ k(x) = 1/x
- We need to find (k ° h)(x), that means put h(x) inside k(x)
* Lets replace the x of k by the h(x)
∵ k(x) = ![\frac{1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D)
∵ h(x) = 5 + x
- Replace the x of k by 5 + x
∴ k(5 + x) = ![\frac{1}{5 + x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%20%2B%20x%7D)
∴ The expression which is equivalent to (k ° h)(x) is
Answer:
(a) 0.139258
(b) 0.0064827
Step-by-step explanation:
Let the probability that each member makes a correct decision be
and the probability that each member makes an incorrect decision be
.
From the question, ![p = 0.7](https://tex.z-dn.net/?f=p%20%3D%200.7)
p and q are mutually exclusive. Hence,
![p+q = 1](https://tex.z-dn.net/?f=p%2Bq%20%3D%201)
![q = 1 - p=1-0.7 = 0.3](https://tex.z-dn.net/?f=q%20%3D%201%20-%20p%3D1-0.7%20%3D%200.3)
(a) For majority rule, it means at least 4 members decisions are taken. Taking "C" to mean "correct" and "I" to mean "incorrect", we could have 4C against 3I, 5C against 2I, 6C against 1I and 7C against 0I.
The probability of the correct decision being made is
![P(\ge\text{4C}) = P(\text{4C and 3I}) + P(\text{5C and 2I}) +P(\text{6C and 1I}) +P(\text{7C and 0I})](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20P%28%5Ctext%7B4C%20and%203I%7D%29%20%2B%20P%28%5Ctext%7B5C%20and%202I%7D%29%20%20%20%2BP%28%5Ctext%7B6C%20and%201I%7D%29%20%2BP%28%5Ctext%7B7C%20and%200I%7D%29)
![P(\ge\text{4C}) = (0.7^4\times0.3^3)+(0.7^5\times0.3^2)+(0.7^6\times0.3^1)+(0.7^7\times0.3^0)](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20%280.7%5E4%5Ctimes0.3%5E3%29%2B%280.7%5E5%5Ctimes0.3%5E2%29%2B%280.7%5E6%5Ctimes0.3%5E1%29%2B%280.7%5E7%5Ctimes0.3%5E0%29)
![P(\ge\text{4C}) = 0.0064827 + 0.0151263 + 0.0352947 + 0.0823543 = 0.139258](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20%200.0064827%20%2B%200.0151263%20%2B%200.0352947%20%2B%200.0823543%20%3D%200.139258)
(b) ![P(\text{exactly 4C}) = P(\text{4C and 3I}) = 0.7^4\times0.3^3 = 0.0064827](https://tex.z-dn.net/?f=P%28%5Ctext%7Bexactly%204C%7D%29%20%3D%20P%28%5Ctext%7B4C%20and%203I%7D%29%20%3D%200.7%5E4%5Ctimes0.3%5E3%20%3D%200.0064827)
Answer:
C= 15
Step-by-step explanation:
![\frac{9}{5} C + 32 = 59](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B5%7D%20C%20%20%2B%20%2032%20%3D%20%2059%20%20)
subtracting 32 from both sides
![\frac{9}{5}C = 59 -32](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B5%7DC%20%20%3D%2059%20-32%20)
![\frac{9}{5} C = 27](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B5%7D%20C%20%3D%2027)
Dividing both sides by 9/ 5
![C = 27 \times \frac{5}{9}](https://tex.z-dn.net/?f=C%20%3D%2027%20%5Ctimes%20%20%5Cfrac%7B5%7D%7B9%7D%20)
![C = 3 \times 5](https://tex.z-dn.net/?f=C%20%3D%203%20%5Ctimes%205)
![C = 15](https://tex.z-dn.net/?f=C%20%3D%20%2015)
Answer:
well you should firstcalculate the distance then divide by the primary source and you should be able to get the answer after substituting
Step-by-step explanation:
All the fractions are factors of 30
1/3 X 10, 1/5 X 6, 1/2 X 15.
/\10/30, /\6/30, /\15/30
Add all of them together: 31/30
Then you simplify the total: 1+1/30
1 and 1/30 is the answer