Answer:
15% per year
7.5% half year
5000 * 7.5% = $375 every 6 months.
Step-by-step explanation:
Answer:
Step-by-step explanation:
9514 1404 393
Answer:
Step-by-step explanation:
The marked angles form a linear pair, so have a sum of 180°.
(4a +10) +(6a) = 180
10a = 170 . . . . . . . . . . subtract 10
a = 17 . . . . . . . . . . . . . divide by 10
__
Then the measure of angle ABC is ...
∠ABC = 4a +10 = 4(17) +10 = 68 +10 . . . . . substitute 17 for 'a'
∠ABC = 78°
Answer:
458 turns/min ----- 13740/30 min
Step-by-step explanation:
3206/7 (min) = 458
458 x 30 (min) = 13740
The exponential distribution is:
![\lambda e^{- \lambda x}](https://tex.z-dn.net/?f=%5Clambda%20e%5E%7B-%20%5Clambda%20x%7D)
where
![\lambda = \frac{1}{mean}=\frac{1}{5}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B1%7D%7Bmean%7D%3D%5Cfrac%7B1%7D%7B5%7D)
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.
![P(A|B) = \frac{P(A and B)}{P(B)}](https://tex.z-dn.net/?f=P%28A%7CB%29%20%3D%20%5Cfrac%7BP%28A%20and%20B%29%7D%7BP%28B%29%7D%20)
where A is P(x>8) and B is P(x>5)
To find these probabilities, integrate over the distribution:
![P(x \ \textgreater \ N) = \int_N^{\infty} \frac{1}{5} e^{-x/5} dx = e^{-N/5}](https://tex.z-dn.net/?f=P%28x%20%5C%20%5Ctextgreater%20%5C%20N%29%20%3D%20%5Cint_N%5E%7B%5Cinfty%7D%20%5Cfrac%7B1%7D%7B5%7D%20e%5E%7B-x%2F5%7D%20dx%20%3D%20e%5E%7B-N%2F5%7D%20)
Sub into conditional probability formula:
![P(x \ \textgreater \ 8 | x\ \textgreater \ 5) = \frac{P(x\ \textgreater \ 8)}{P(x\ \textgreater \ 5)} = \frac{e^{-8/5}}{e^{-5/5}} = e^{-3/5} = 0.549](https://tex.z-dn.net/?f=P%28x%20%5C%20%5Ctextgreater%20%5C%208%20%7C%20x%5C%20%5Ctextgreater%20%5C%205%29%20%3D%20%5Cfrac%7BP%28x%5C%20%5Ctextgreater%20%5C%208%29%7D%7BP%28x%5C%20%5Ctextgreater%20%5C%205%29%7D%20%3D%20%5Cfrac%7Be%5E%7B-8%2F5%7D%7D%7Be%5E%7B-5%2F5%7D%7D%20%3D%20e%5E%7B-3%2F5%7D%20%3D%200.549)
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%