If

and

are mutually independent, then

and

.
If

and

are independent, then

. Ditto for

and

.
The inclusion/exclusion principle says that

Since

and

are mutually exclusive, their intersection is the empty set. It then follows that

also is the empty set, so the last probability is also 0.
Plug in what we know:

Answer:
x = -21
Step-by-step explanation:
62 + 2x - 20 = 0.
Combine like terms
42 +2x =0
Subtract 42 from each side
42-42 +2x = 0-42
2x = -42
Divide each side by 2
2x/2 = -42/2
x = -21
Answer:
X product of powers
Quotient of powers
Power of a power
X power of a product
Negative exponent
X zero exponent
Hope this helps ʕ•ᴥ•ʔ
Invested at 3% = x
invested at 4% = 2x
invested at 5% = x+500
0.03x + 0.04(2x) + 0.05(x+500) = 2025
0.03x + 0.08x +0.05x +25 = 2025
0.16x = 2000
x= 12,500
4% = 2x = 12,500 * 2 = $25,000
Answer:

--- Variance
Step-by-step explanation:
Given

Solving (a): Calculate the mean.
The given data is a grouped data. So, first we calculate the class midpoint (x)
For 51 - 58.

For 59 - 66

For 67 - 74

For 75 - 82

For 83 - 90

So, the table becomes:

The mean is then calculated as:



-- approximated
Solving (b): The sample variance:
This is calculated as:

So, we have:


-- approximated