How many groups of 2/5 are in 4?

−6x + 5y = 16x + 4y = −10

sashaice [31]

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3 0

3 years ago

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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

3 years ago

What is the y-intercept of the line that passes through the points (-3,8) and (1,6)? Convert the answer to a decimal, if necessa

artcher [175]

Answer:

6.5

Step-by-step explanation:

The midpoint of the line is (-1,7). If you draw a line between that and (1.6), you’ll pass through the y-axis at 6.5.

4 0

4 years ago

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Given the following table, what is the quadratic equation?

rusak2 [61]

Answer:

144322221111155554444444333222222

7 0

3 years ago

Jerome found another feather that made the difference between the longest and shortest feather 1 3/4 inches what could be the le

Alchen [17]

Answer:

By assuming that shortest feather has a length of 1/4 inches, the length of the longest feather is 2 inches.

Step-by-step explanation:

A mathematical translation of the statement of the problem is:

$x - y = \frac{7}{4}$

Where x, y represent the lengths of the longest and shortest feathers, respectively. Let assume that length of the shortest feather is 1/4 inches. Then, the length of the longest feather is:

$x = y + \frac{7}{4}$

$x = 2$

By assuming that shortest feather has a length of 1/4 inches, the length of the longest feather is 2 inches.

8 0

4 years ago

How many groups of 2/5 are in 4?​

How many groups of 2/5 are in 4?