Answer:
0.111111…
Step-by-step explanation:
In the problem described, we understand that 1 in 9 friends prefer kiwi.
That's the equivalent of
which is equal to
Please let me know if you have any questions in the comments.
Have fun studying! :)
Answer: PLEASE MARK BRAINLIEST I NEED ONE MORE
Area:113 units squared
Perimeter: 43 units
Step-by-step explanation:
11 times 7 plus 6 times 6 equals
Answer:
(1)
![E(x) = 0.72](https://tex.z-dn.net/?f=E%28x%29%20%3D%200.72)
![Var(x) = 1.1616](https://tex.z-dn.net/?f=Var%28x%29%20%3D%201.1616)
![\sigma = 1.078](https://tex.z-dn.net/?f=%5Csigma%20%3D%201.078)
(2)
![E(x) = 12](https://tex.z-dn.net/?f=E%28x%29%20%3D%2012)
![Var(x) = 1.3](https://tex.z-dn.net/?f=Var%28x%29%20%3D%201.3)
![\sigma = 1.14](https://tex.z-dn.net/?f=%5Csigma%20%3D%201.14)
Step-by-step explanation:
Solving (1):
![\begin{array}{ccccccc}{Days} & {0} & {1} & {2} & {3} & {4}& {5} \ \\ {Probability} & {0.60} & {0.20} & {0.12} & {0.04} & {0.04} & {0.00} \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccccc%7D%7BDays%7D%20%26%20%7B0%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%26%20%7B3%7D%20%26%20%7B4%7D%26%20%7B5%7D%20%5C%20%5C%5C%20%7BProbability%7D%20%26%20%7B0.60%7D%20%26%20%7B0.20%7D%20%26%20%7B0.12%7D%20%26%20%7B0.04%7D%20%26%20%7B0.04%7D%20%26%20%7B0.00%7D%20%5C%20%5Cend%7Barray%7D)
(a): Mean
This is calculated as:
![E(x) = \sum x * P(x)](https://tex.z-dn.net/?f=E%28x%29%20%3D%20%5Csum%20x%20%2A%20P%28x%29)
So, we have:
![E(x) = 0 * 0.60 + 1 * 0.20 + 2 * 0.12 + 3 * 0.04 + 4 * 0.04 + 5 * 0.00](https://tex.z-dn.net/?f=E%28x%29%20%3D%200%20%2A%200.60%20%2B%201%20%2A%200.20%20%2B%202%20%2A%200.12%20%2B%203%20%2A%200.04%20%2B%204%20%2A%200.04%20%2B%205%20%2A%200.00)
![E(x) = 0.72](https://tex.z-dn.net/?f=E%28x%29%20%3D%200.72)
Solving (b): The variance
This is calculated as:
![Var(x) = E(x^2) - (E(x))^2](https://tex.z-dn.net/?f=Var%28x%29%20%3D%20E%28x%5E2%29%20-%20%28E%28x%29%29%5E2)
Where:
![E(x) = 0.72](https://tex.z-dn.net/?f=E%28x%29%20%3D%200.72)
and
So, we have:
![E(x^2) = 0^2 * 0.60 + 1^2 * 0.20 + 2^2 * 0.12 + 3^2 * 0.04 + 4^2 * 0.04 + 5^2 * 0.00](https://tex.z-dn.net/?f=E%28x%5E2%29%20%3D%200%5E2%20%2A%200.60%20%2B%201%5E2%20%2A%200.20%20%2B%202%5E2%20%2A%200.12%20%2B%203%5E2%20%2A%200.04%20%2B%204%5E2%20%2A%200.04%20%2B%205%5E2%20%2A%200.00)
![E(x^2) = 1.68](https://tex.z-dn.net/?f=E%28x%5E2%29%20%3D%201.68)
So, we have:
![Var(x) = E(x^2) - (E(x))^2](https://tex.z-dn.net/?f=Var%28x%29%20%3D%20E%28x%5E2%29%20-%20%28E%28x%29%29%5E2)
![Var(x) = 1.68 - 0.72^2](https://tex.z-dn.net/?f=Var%28x%29%20%3D%201.68%20-%200.72%5E2)
![Var(x) = 1.1616](https://tex.z-dn.net/?f=Var%28x%29%20%3D%201.1616)
Solving (c): The standard deviation.
This is calculated as:
![\sigma = \sqrt{Var(x)}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7BVar%28x%29%7D)
![\sigma = \sqrt{1.1616}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B1.1616%7D)
![\sigma = 1.078](https://tex.z-dn.net/?f=%5Csigma%20%3D%201.078)
Solving (2):
![\begin{array}{ccccccc}{x} & {10} & {11} & {12} & {13} & {14}& { } \ \\ {P(x)} & {0.1} & {0.25} & {0.3} & {0.25} & {0.1} & { } \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccccc%7D%7Bx%7D%20%26%20%7B10%7D%20%26%20%7B11%7D%20%26%20%7B12%7D%20%26%20%7B13%7D%20%26%20%7B14%7D%26%20%7B%20%7D%20%5C%20%5C%5C%20%7BP%28x%29%7D%20%26%20%7B0.1%7D%20%26%20%7B0.25%7D%20%26%20%7B0.3%7D%20%26%20%7B0.25%7D%20%26%20%7B0.1%7D%20%26%20%7B%20%7D%20%5C%20%5Cend%7Barray%7D)
(a): Mean
This is calculated as:
![E(x) = \sum x * P(x)](https://tex.z-dn.net/?f=E%28x%29%20%3D%20%5Csum%20x%20%2A%20P%28x%29)
So, we have:
![E(x) = 10 * 0.10 + 11 * 0.25 + 12 * 0.3 + 13 * 0.25 + 14 * 0.1](https://tex.z-dn.net/?f=E%28x%29%20%3D%2010%20%2A%200.10%20%2B%2011%20%2A%200.25%20%2B%2012%20%2A%200.3%20%2B%2013%20%2A%200.25%20%2B%2014%20%2A%200.1)
![E(x) = 12](https://tex.z-dn.net/?f=E%28x%29%20%3D%2012)
Solving (b): The variance
This is calculated as:
![Var(x) = E(x^2) - (E(x))^2](https://tex.z-dn.net/?f=Var%28x%29%20%3D%20E%28x%5E2%29%20-%20%28E%28x%29%29%5E2)
Where:
![E(x) = 12](https://tex.z-dn.net/?f=E%28x%29%20%3D%2012)
and
So, we have:
![E(x^2) = 10^2 * 0.10 + 11^2 * 0.25 + 12^2 * 0.3 + 13^2 * 0.25 + 14^2 * 0.1](https://tex.z-dn.net/?f=E%28x%5E2%29%20%3D%2010%5E2%20%2A%200.10%20%2B%2011%5E2%20%2A%200.25%20%2B%2012%5E2%20%2A%200.3%20%2B%2013%5E2%20%2A%200.25%20%2B%2014%5E2%20%2A%200.1)
![E(x^2) = 145.3](https://tex.z-dn.net/?f=E%28x%5E2%29%20%3D%20145.3)
So, we have:
![Var(x) = E(x^2) - (E(x))^2](https://tex.z-dn.net/?f=Var%28x%29%20%3D%20E%28x%5E2%29%20-%20%28E%28x%29%29%5E2)
![Var(x) = 145.3 - 12^2](https://tex.z-dn.net/?f=Var%28x%29%20%3D%20145.3%20-%2012%5E2)
![Var(x) = 1.3](https://tex.z-dn.net/?f=Var%28x%29%20%3D%201.3)
Solving (c): The standard deviation.
This is calculated as:
![\sigma = \sqrt{Var(x)}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7BVar%28x%29%7D)
![\sigma = \sqrt{1.3}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B1.3%7D)
![\sigma = 1.14](https://tex.z-dn.net/?f=%5Csigma%20%3D%201.14)
Answer:
<em>The shortest possible length for the service road is 2.88 miles.</em>
Step-by-step explanation:
According to the below diagram,
and
are the positions of airport, shopping center and factory respectively.
Given that,
and ![AC= 6.0 miles](https://tex.z-dn.net/?f=AC%3D%206.0%20miles)
In right triangle ![ABC](https://tex.z-dn.net/?f=ABC)
![tan(\angle ACB)=\frac{AB}{BC} \\ \\ tan(\angle ACB)= \frac{3.6}{4.8}=0.75\\ \\ \angle ACB= tan^-^1(0.75)=36.8698.... degree](https://tex.z-dn.net/?f=tan%28%5Cangle%20ACB%29%3D%5Cfrac%7BAB%7D%7BBC%7D%20%5C%5C%20%5C%5C%20tan%28%5Cangle%20ACB%29%3D%20%5Cfrac%7B3.6%7D%7B4.8%7D%3D0.75%5C%5C%20%5C%5C%20%5Cangle%20ACB%3D%20tan%5E-%5E1%280.75%29%3D36.8698....%20degree)
The shortest possible length for the service road from the shopping center to the highway that connects the airport and factory is
.
That means,
is also a right triangle in which
, Hypotenuse
miles and
is the opposite side in respect of
or
.
Now in right triangle ![BCD](https://tex.z-dn.net/?f=BCD)
![Sin(\angle ACB)=\frac{BD}{BC}\\ \\ Sin(36.8698...)=\frac{BD}{4.8}\\ \\ BD=4.8*Sin(36.8698...)=2.88](https://tex.z-dn.net/?f=Sin%28%5Cangle%20ACB%29%3D%5Cfrac%7BBD%7D%7BBC%7D%5C%5C%20%5C%5C%20Sin%2836.8698...%29%3D%5Cfrac%7BBD%7D%7B4.8%7D%5C%5C%20%5C%5C%20BD%3D4.8%2ASin%2836.8698...%29%3D2.88)
So, the shortest possible length for the service road is 2.88 miles.
Answer:
2.34 per pound is unit price
Step-by-step explanation:
14.04 divided by 6 is 2.34