Answer:
dy/dx at x=6 is 0.334
Step-by-step explanation:
The center difference method requires that the values of the function are given in equal intervals which is the case, and allows one to find the value for x = 6 using those of the function for x = 5.5 and for x = 6.5 as follows:

Y = 5/4x + 2
y - (-3) = 5/4 ( x - (-4))
1. Distribute 5/4
y + 3 = 5/4x + 5
2. Subtract three to collect like terms
y = 5/4x + 2
Answer:
a) 
And replacing we got:

b) ![E(80Y^2) =80[ 0^2*0.45 +1^2*0.2 +2^2*0.3 +3^2*0.05]= 148](https://tex.z-dn.net/?f=%20E%2880Y%5E2%29%20%3D80%5B%200%5E2%2A0.45%20%2B1%5E2%2A0.2%20%2B2%5E2%2A0.3%20%2B3%5E2%2A0.05%5D%3D%20148)
Step-by-step explanation:
Previous concepts
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).
And the standard deviation of a random variable X is just the square root of the variance.
Solution to the problem
Part a
We have the following distribution function:
Y 0 1 2 3
P(Y) 0.45 0.2 0.3 0.05
And we can calculate the expected value with the following formula:

And replacing we got:

Part b
For this case the new expected value would be given by:

And replacing we got
![E(80Y^2) =80[ 0^2*0.45 +1^2*0.2 +2^2*0.3 +3^2*0.05]= 148](https://tex.z-dn.net/?f=%20E%2880Y%5E2%29%20%3D80%5B%200%5E2%2A0.45%20%2B1%5E2%2A0.2%20%2B2%5E2%2A0.3%20%2B3%5E2%2A0.05%5D%3D%20148)
Answer:
<h2><em><u>2</u></em></h2>
Step-by-step explanation:

![= \sqrt[5]{32}](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%5B5%5D%7B32%7D%20)
![= \sqrt[5]{2 \times 2 \times 2 \times 2 \times 2}](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%5B5%5D%7B2%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%7D%20)
= <em><u>2</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em>
Answer:
See explanation
Step-by-step explanation:
Polygon WXYZ has vertices W(-1.5, 1.5), X(6, 1.5), Y(6, -4.5), and Z(-1.5, -4.5).
Find the slopes of all sides:
- horizontal line
- slope undefined, so the line is vertical
- horizontal line
- slope undefined, so the line is vertical
Vertical and horizontal lines are perpendicular, so all angles W, X, Y and Z are right angles. Hence, quadrilateral WXYZ is a rectangle