Answer:
-24
Step-by-step explanation:
The exponential distribution is:

where

The probability we want is how likely will a dvd player last more than 8 years, given it has already lasted 5 years
To find this, you use conditional probability.

where A is P(x>8) and B is P(x>5)
To find these probabilities, integrate over the distribution:

Sub into conditional probability formula:

Final Answer: Given a dvd player is more than 5 years old, the probability that it will last another 3 more years is about 54.9%
A. -(a+5)
Because the negative sign is outside the parenthesis, multiplying by -1 just removes the negative sign:
-(a+5) * -1 = a+5
B. -(-x+31)
Apply the distributive property:
-(-x+31) becomes (- -x +31) which simplifies to (x+31)
multiply that by -1 to get -x+31
C. -(4x+12)
Because the negative sign is outside the parenthesis, multiplying by -1 just removes the negative sign:
-(4x+12) * -1 = 4x+12
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
Hi there!

To solve, we can use right triangle trigonometry.
Recall that:
sin = O/H, cos = A/H, tan = O/A.
For angle G, HF is its OPPOSITE side, and FG is the hypotenuse.
Therefore, we must use sine to evaluate:
sinG = 14 / 17
sin⁻¹ (14/17) = ∠G. Evaluate using a calculator.
∠G ≈ 55.44°