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morpeh [17]
3 years ago
6

Find the range for the possible values for x

Mathematics
1 answer:
ziro4ka [17]3 years ago
8 0
I think 6 because 12=3x-6
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The probability that a single radar station will detect an enemy plane is 0.65.
taurus [48]

Answer:

a) We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

b) If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

Step-by-step explanation:

For each station, there are two two possible outcomes. Either they detected the enemy plane, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem, we have that:

The probability that a single radar station will detect an enemy plane is 0.65. This means that n = 0.65.

(a) How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?

This is the value of n for which P(X = 0) \leq 0.02.

n = 1.

P(X = 0) = C_{1,0}.(0.65)^{0}.(0.35)^{1} = 0.35

n = 2

P(X = 0) = C_{2,0}.(0.65)^{0}.(0.35)^{2} = 0.1225

n = 3

P(X = 0) = C_{3,0}.(0.65)^{0}.(0.35)^{3} = 0.0429

n = 4

P(X = 0) = C_{4,0}.(0.65)^{0}.(0.35)^{4} = 0.015

We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?

The expected number of sucesses of a binomial variable is given by:

E(x) = np

So when n = 7

E(x) = 7*(0.65) = 4.55

If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

6 0
2 years ago
PLEASE HELP I NEED THIS TODAY!!​
RideAnS [48]

Answer:

The area is 200.96 in^2

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Mr. lumber got asked his third grade class to name the rule for the following number patterns.
Pie

You always get from one term to the next by adding 6:

573 + 6 = 579

579 + 6 = 585

585 + 6 = 591

591 + 6 = 597

So, the rule is "add 6"

8 0
3 years ago
Read 2 more answers
The numbers of cars (c) in the parking lot increases when the parking fee (f) decrease. Write the correct equation for this scen
vodka [1.7K]
So when one goes up, the other goes down. This is an inverse equation.

An inverse equation looks like this: y = 1/x

In this case, when parking fee (f) decreases, cars (c) increase.
You know which side to put each variable on using the chart they gave you.
f         | c
20.00  15        (20.00 = x/15) x=300
30.00  10        (30.00 = x/10) x=300

So your equation in this case is f = 300/c
Knowing that, plug in the fee of 6.00

6 = 300/c   Multiply both sides by c.
6c = 300    Divide both sides by 6.
c = 50 cars

5 0
3 years ago
Mattis saving to buy a new motorcycle. If he deposits $50 at the end of each month in an account that pays an annual interest ra
liq [111]
In thirty months you should have 5,250.00
4 0
2 years ago
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