Answer:
1.967 × 10⁻¹¹
Step-by-step explanation:
This is a conditional probability problem
Probability that a 12 year old leaf blower works for 5 more years = Probabilty that a leaf blower works for 17 years, given that it has worked for 12 years = P(17|12)
P(17|12) = P(17 n 12)/P(12)
P(17 n 12) = P(17)
Exponential random variable is given as
f(x) = λ e^(-λ.x)
λ = rate parameter = 5 years per blower
x = variable whose probability is required = 17
f(17) = 17 e^(-5×17)
f(17) = 17 e⁻⁸⁵ = 2.067 × 10⁻³⁶
f(12) = 12 e^(-5×12)
f(12) = 12 e⁻⁶⁰ = 1.051 × 10⁻²⁵
P(17|12) = (2.067 × 10⁻³⁶)/(1.051 × 10⁻²⁵)
P(17|12) = 1.967 × 10⁻¹¹
Answer:
Step-by-step explanation:
Area of square=L^2
A=4cm ×4cm
A=16cm^2
Let's use Gaussian elimination. Consider the augmented matrix,
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C-1%20%26%202%20%26%203%20%26%200%20%26%201%20%26%200%5C%5C1%20%26%201%20%26%204%20%26%200%20%26%200%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add row 1 to row 2, and add -1 (row 1) to row 3:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%202%20%26%201%20%26%201%20%26%200%5C%5C0%20%26%202%20%26%205%20%26%20-1%20%26%200%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add -2 (row 2) to row 3:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%202%20%26%201%20%26%201%20%26%200%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add -2 (row 3) to row 2:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%200%20%26%207%20%26%205%20%26%20-2%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add row 2 and row 3 to row 1:
![\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%200%20%26%200%20%26%205%20%26%203%20%26%20-1%5C%5C0%20%26%201%20%26%200%20%26%207%20%26%205%20%26%20-2%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
So the inverse is

One reason would be if you did not know the answer so you could do
4-5=x
another reason would be if the problem gave you the answer but not one of the things to get the answer
4-x=-1
not sure if that is what you want but I hope this helped
35.98 million miles from the sun