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

Answers

Answer 1

Answer:

Complete Question

The probability that a single radar station will detect an enemy plane is 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?

(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane? (Round your answer to one decimal place.)

Answer:

$n \approx 4$

Step-by-step explanation:

From the question we are told that

The probability that a single radar station will detect an enemy plane is $p =0.65$

Gnerally the probability that an enemy plane flying over will be detected by at least one station is mathematically represented as

$P(X \ge 1 ) = 0.98$

=> $P(X \ge 1 ) = 1 - P(X < 1) = 0.98$

=> $P(X = 0) = 1 - 0.98$ Note $P(X < 1) = P(X = 0)$

=> $P(X = 0) = 1 - 0.98$

=> $P(X = 0) = 0.02$

Generally from binomial probability distribution function

$P(X = 0) = ^nC_0 * p^(0) * (1- p)^(n- 0)$

Here C represents combination hence we will be making use of of combination functionality in our calculators

Generally any number combination 0 is 1

$P(X = 1) = 1 * 1* (1- 0.65)^(n- 0) = 0.02$

=> $(1- 0.65)^(n- 1) = 0.02$

taking log of both sides

$log [(0.35)^(n- 1) ] = log (0.02)$

=> ${n- 1}log[0.35] = -1.699$

=> ${n- 1}* -0.4559 = -1.699$

=> $n= 3.7264 + 1$

=> $n= 4.7264$

=> $n \approx 4$

Gnerally the expected number of stations that will detect an enemy plane is

$E(X) = 7 * 0.65$

=> $E(X) \approx4.5$

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Answers

Answer:

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Step-by-step explanation:

The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?

Answers

the range is the y valuewe can rewrite the given function f(x)=x+5 to y=x+5and our given range are y=7 and y=9so sub in ur y values into the equation to find the x value which are the domain...y=x+5

Which is a simplified form of the expression 2c + 2 + 6c – 4?A. 8c + 2
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Answers

Answer:

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Chad baked 12 cookies with 2 scoops of flour. How many scoops of flour doesChad need in order to bake 42 cookies? Solve using unit rates.

Answers

Answer:

Step-by-step explanation:

Set up a proportion

12 cookies / 2 cups = 42 cookies / x Notice that cookies are on the top and cups are on the bottom of each proportion.

12/2 = 42/x Cross multiply

12x = 84 Divide by 12

x = 84/12

x = 7

He will need 7 cups to make 42 cookies.

Final answer:

Chad needs approximately 7 scoops of flour to bake 42 cookies using the given rate of 2 scoops of flour per 12 cookies.

Explanation:

This problem can be solved using unit rates method. First, we find how much flour is needed for one cookie by dividing the number of scoops of flour used by the number of cookies created. In this case, the unit rate is 2 scoops of flour per 12 cookies, which simplify to about 0.167 scoops/cookie.

To find out how many scoops of flour Chad needs to bake 42 cookies, we will multiply our unit rate by the number of cookies. Here it is: 0.167 scoops/cookie times 42 cookies equals to approximately 7 scoops of flour.

Learn more about unit rates here:

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There are 6 people at a party. if each person must shake hands with other every other person at the party exactly once how many handshakes will there be

Answers

Answer:

If six people all shake hands with each other, how many hand shakes were made in total?

Publish your book. Become an author in 15 days. Get published.

I assume that no two people shake hands if they've already shaken them earlier, irrespective of who initiated it.

In that case Guest 1 will shake hands with 5 others (Guest 2 to 6)

Guest 2 will shake hands with 4 others (Remember she's already shaken hands with Guest 1).

Guest 3 will shake hands with 3 others (having already shaken hands with Guest 1 and 2)

and so on.....

We end up with 5+4+3+2+1 handshakes or 15 handshakes in all!

Step-by-step explanation:

please mark me as a brainlist...

Answer:

15 handshakes

Step-by-step explanation:

the 1st person shakes hands with 5 people

the 2nd person shakes hands with 4 people

the 3rd person shakes hands with 3 people

the 4th person shakes hands with 2 people

the 5th person shakes hands with 1 person

the 6th person shakes hands with no one

5+4+3+2+1=15

A new homeowner needs to put up a fence to make his yard secure. the house itself forms the south boundary and the garage forms the west boundary of the property, so he needs to fence only 2 sides. the area of the yard is 4000 sq ft. he has enough material for 160 ft of fence. find the length and width of the yard.

Answers

Let the width = x feet, then the length = 160 - x feet.

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