Mathematics: The failure rate for a guided missile control system is 1 in 1,000. Suppose that a duplicate but completely independent control system is installed in each missile so that, if the first fails, the second can take over. The reliability of a missile is the probability that it does not fail. What is the reliability of the modified missile

The failure rate for a guided missile control system

starr3971

19.01.2022

The reliability is 0.999999.

Step-by-step explanation:

The failure rate for a guided missile control system is 1 in 1,000.

Hence, the probability that the missile will not fail is $\frac{1000 - 1}{1000} = \frac{999}{1000}$ .

According to the new system, if the first fails, the second can take over.

There are two possibilities, either the first one will be fail or not.

If the first one will not fail, then the probability will be $\frac{999}{1000}$ = 0.999.

If the first one will fail, then the probability will be $\frac{999}{1000} \times\frac{1}{1000} = 0.000999$ .

The reliability of the modified missile is 0.999 + 0.000999 = 0.999999.

0,0(0 оценок)

SophieStar15

13.09.2022

The amount deposited in CD is $660

Solution:

Given that , To save for the purchase of a new car, a deposit was made into an account that earns 8% annual simple interest.

Let the amount deposited in new car be $ n

Another deposit, $1700 less than the first deposit, was placed in a certificate of deposit (CD) earning 12% annual simple interest.

Then, amount deposited in CD will be $ (n – 1700)

The total interest earned on both accounts for 1 year was $676

The simple interest is given as:

$\text { Simple interest }=\frac{\text { principal } \times \text {rate} \times \text {time}}{100}$

Simple interest for purchase of new car:

$\text { S. } \mathrm{I}=\frac{n \times 8 \times 1}{100}=\frac{8 n}{100}$

Simple interest for CD:

$\text { S.I } =\frac{(n-1700) \times 12 \times 1}{100}=\frac{12(n-1700)}{100}$

Now, given that S.I for new car + S.I for CD = 676

$\begin{array}{l}{\frac{8 n}{100}+\frac{12(n-1700)}{100}=676} \\\\ {\frac{8 n+12 n-12 \times 1700}{100}=676}\end{array}$

20n = 67600 – 20400

n = 2360

So money deposited in CD = n - 1700 = 2360 – 1700 = 660

Hence, the CD deposit amount is $660

0,0(0 оценок)