Adding up all 6 probabilities gives a total of 1, which means that this is a valid distribution function. Observing that P(0) = P(5), P(1) = P(4), and P(2) = P(3), this is a symmetric distribution.
Its mean will be in the middle, which is at x = 2.5.
The standard deviation is calculated by multiplying each P(x) by the square of deviation (x - average)^2: (0.032)(0 - 2.5)^2 + (0.152)(1 - 2.5)^2 + (0.316)(2 - 2.5)^2 + (0.316)(3 - 2.5)^2 + (0.152)(4 - 2.5)^2 + (0.032)(5 - 2.5)^2 = 1.242, then taking the square root: sqrt(1.242) = 1.1145.
Answer:
146 whistles
Step-by-step explanation:
First, convert 122 feet to inches, by multiplying it by 12
122(12)
= 1464
Divide this by 10 to find how many whistles he can make
1464/10
= 146.4
Since we can only have a whole number of whistles, we have to round down to 146.
So, he can make 146 whistles
Put the same variable on the same side first than solve
For any quadratic functions, ax² + bx + c, we can easily find the x-coordinate of its vertex through the use of the formula below.

where a and b are the coefficients of the function. For f(x), we have a = -1 and b = -16. Thus, we have


Since we now have the x-coordinate of the vertex, we can just easily substitute 8 into f(x) as shown below.


Thus, the
vertex of f(x) is (8, 60). The vertex of the function shows the maximum value that the function can reach. For this particular case, the vertex represents the
maximum profit that the shop owner could earn.The x-intercepts of the function are the values of x when f(x) is zero. By equation f(x) with zero, we can solve the quadratic equation to find the x-intercepts as shown below.





From this, we can see that the x-intercepts are
(6, 0) and (10, 0). We just discussed that the x-intercepts are the values of x when y is zero. So, for this case it means that the shop does not earn a profit if they sell 6 or 10 candles. Basically, the x-intercepts represent the
number candles sold if the shop wants to break even.
Answer:
Switch x and y.

Step-by-step explanation:
Switch the x and y, so the equation would read as:
![x = \sqrt[3]{8y} +4](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B8y%7D%20%2B4)
Then solve for y.
![x = \sqrt[3]{8y} + 4\\\\\\x - 4 = \sqrt[3]{8y} \\\\\\(x-4)^{3} = 8y\\\\\\\\\\\frac{1}{8} (x-4)^{3}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B8y%7D%20%2B%204%5C%5C%5C%5C%5C%5Cx%20-%204%20%3D%20%5Csqrt%5B3%5D%7B8y%7D%20%5C%5C%5C%5C%5C%5C%28x-4%29%5E%7B3%7D%20%3D%208y%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5Cfrac%7B1%7D%7B8%7D%20%28x-4%29%5E%7B3%7D)
#teamtrees #WAP (Water And Plant)