Answer:
OPTION B I THINK SOOOO
PLS MAKA ME BRAINIST PLS
Step-by-step explanation:
HOPE YOU HELP
Answer:
x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z
or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z
Step-by-step explanation:
Solve for x:
sin(x) = 1.5
1.5 = 3/2:
sin(x) = 3/2
Take the inverse sine of both sides:
Answer: x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z
or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z
Answer:
P(Y = 0) = 0.09
P(Y = 1) = 0.4
P(Y = 2) = 0.32
P(Y = 3) = 0.19
Step-by-step explanation:
Let the events be:
Wednesday
Thursday
Friday
Saturday
Their corresponding probabilities are
![P(W) = 0.3\\P(T) = 0.4\\P(F) = 0.2\\P(S) = 0.1](https://tex.z-dn.net/?f=P%28W%29%20%3D%200.3%5C%5CP%28T%29%20%3D%200.4%5C%5CP%28F%29%20%3D%200.2%5C%5CP%28S%29%20%3D%200.1)
Since
= number of days beyond Wednesday that it takes for both magazines to arrive(so possible
values are 0, 1, 2 or 3)
The possible number of outcomes are therefore ![4^2 = 16\\(W, W), (W, T), (W, F), (W, S)\\(T, W), (T, T), (T, F), (T, S)\\(F, W), (F, T), (F, F), (F, S)\\(S, W), (S, T), (S, F), (S, S)](https://tex.z-dn.net/?f=4%5E2%20%3D%2016%5C%5C%28W%2C%20W%29%2C%20%28W%2C%20T%29%2C%20%28W%2C%20F%29%2C%20%28W%2C%20S%29%5C%5C%28T%2C%20W%29%2C%20%28T%2C%20T%29%2C%20%28T%2C%20F%29%2C%20%28T%2C%20S%29%5C%5C%28F%2C%20W%29%2C%20%28F%2C%20T%29%2C%20%28F%2C%20F%29%2C%20%28F%2C%20S%29%5C%5C%28S%2C%20W%29%2C%20%28S%2C%20T%29%2C%20%28S%2C%20F%29%2C%20%28S%2C%20S%29)
The values associated for each of the outcomes are as follows:
![Y(W, W) = 0, Y(W, T) = 1, Y(W, F) = 2, Y(W, S) = 3\\Y(T, W) = 1, Y(T, T) = 1, Y(T, F) = 2, Y(T, S) = 3\\Y(F, W) = 2, Y(F, T) = 2, Y(F, F) = 2, Y(F, S) = 3\\Y(S, W) = 3, Y(S, T) = 3, Y(S, F) = 3, Y(S, S) = 3](https://tex.z-dn.net/?f=Y%28W%2C%20W%29%20%3D%200%2C%20Y%28W%2C%20T%29%20%3D%201%2C%20Y%28W%2C%20F%29%20%3D%202%2C%20Y%28W%2C%20S%29%20%3D%203%5C%5CY%28T%2C%20W%29%20%3D%201%2C%20Y%28T%2C%20T%29%20%3D%201%2C%20Y%28T%2C%20F%29%20%3D%202%2C%20Y%28T%2C%20S%29%20%3D%203%5C%5CY%28F%2C%20W%29%20%3D%202%2C%20Y%28F%2C%20T%29%20%3D%202%2C%20Y%28F%2C%20F%29%20%3D%202%2C%20Y%28F%2C%20S%29%20%3D%203%5C%5CY%28S%2C%20W%29%20%3D%203%2C%20Y%28S%2C%20T%29%20%3D%203%2C%20Y%28S%2C%20F%29%20%3D%203%2C%20Y%28S%2C%20S%29%20%3D%203)
The probability mass function of
is,
![P(Y = 0) = 0.3(0.3) = 0.09\\P(Y = 1) = P[(W, T) or (T, W) or (T, T)]\\= [0.3(0.4) + 0.3(0.4) + 0.4(0.4)]\\= 0.4\\\\P(Y = 2) = P[(W, F) or (T, F) or (F, W) or (F, T) or (F, F)]\\= [0.3(0.2) + 0.4(0.2) + 0.2(0.3) + 0.2(0.4) + 0.2(0.2)]\\= 0.32\\\\P(Y = 3) = P[(W, S) or (T, S) or (F, S) or (S, W) or (S, T) or (S, F) or (S, S)]\\= [0.3(0.1) + 0.4(0.1) + 0.2(0.1) + 0.1(0.3) 0.1(0.4) + 0.1(0.2) + 0.1(0.1)]\\= 0.19](https://tex.z-dn.net/?f=P%28Y%20%3D%200%29%20%3D%200.3%280.3%29%20%3D%200.09%5C%5CP%28Y%20%3D%201%29%20%3D%20P%5B%28W%2C%20T%29%20or%20%28T%2C%20W%29%20or%20%28T%2C%20T%29%5D%5C%5C%3D%20%5B0.3%280.4%29%20%2B%200.3%280.4%29%20%2B%200.4%280.4%29%5D%5C%5C%3D%200.4%5C%5C%5C%5CP%28Y%20%3D%202%29%20%3D%20P%5B%28W%2C%20F%29%20or%20%28T%2C%20F%29%20or%20%28F%2C%20W%29%20or%20%28F%2C%20T%29%20or%20%28F%2C%20F%29%5D%5C%5C%3D%20%5B0.3%280.2%29%20%2B%200.4%280.2%29%20%2B%200.2%280.3%29%20%2B%200.2%280.4%29%20%2B%200.2%280.2%29%5D%5C%5C%3D%200.32%5C%5C%5C%5CP%28Y%20%3D%203%29%20%3D%20P%5B%28W%2C%20S%29%20or%20%28T%2C%20S%29%20or%20%28F%2C%20S%29%20or%20%28S%2C%20W%29%20or%20%28S%2C%20T%29%20or%20%28S%2C%20F%29%20or%20%28S%2C%20S%29%5D%5C%5C%3D%20%5B0.3%280.1%29%20%2B%200.4%280.1%29%20%2B%200.2%280.1%29%20%2B%200.1%280.3%29%200.1%280.4%29%20%2B%200.1%280.2%29%20%2B%200.1%280.1%29%5D%5C%5C%3D%200.19)
Answer:
Every 8 minutes, 4 pictures are taken.
Step-by-step explanation:
just trust me
Answer: 3/10
Step-by-step explanation:
Take the derivative of
to get
. Set that equal to 0 to find the critical points of the function. The critical points is when the slope is either 0 or undefined.
Now do:
![20x-6=0\\20x=6\\x=\frac{6}{20} = \frac{3}{10}](https://tex.z-dn.net/?f=20x-6%3D0%5C%5C20x%3D6%5C%5Cx%3D%5Cfrac%7B6%7D%7B20%7D%20%3D%20%5Cfrac%7B3%7D%7B10%7D)
There are quite a few more steps to actually find the minimum, but for this example you can automatically assume its a minimum because it is the only critical point of the function. Ill show you these extra steps tho.
Plug in two numbers into the derivative. One that is less than 3/10 and one that is greater than 3/10. The numbers 0 and 1 are fine. When x = 0, the function is -6. When x = 1, the function is +14. A switch from negative to positive indicates a minimum value