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Alenkinab [10]
3 years ago
10

Find the volume of the prism below. ​

Mathematics
2 answers:
prohojiy [21]3 years ago
8 0

Answer:

72 units³

Step-by-step explanation:

length = 12 units

height = 4 units

width = 3 units (8 - 5 = 3)

12 x 3 x 4 = 144

144 / 2 = 72

MArishka [77]3 years ago
7 0
These are the steps good luck have a great day

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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
Solve and show your work for each question. What is 0.(24) ̅ ̅ expressed as a fraction in simplest form? What is 0.24 ̅ expresse
Elden [556K]
The answer to this question is 24/99. 0.24 with 24 repeating in fractional form is 24/99. You put a 9 in the denominator for every repeating digit.
8 0
3 years ago
I need help on this questions #4 and #5
11Alexandr11 [23.1K]
4) 5x+8= -27
5) a÷4+1.5=b
3 0
3 years ago
Plz help and thank you
Nastasia [14]

Answer:

60%

Also known as 330 students

Step-by-step explanation:

Plz mark brainliest!!!

6 0
3 years ago
Read 2 more answers
Simplify 6(x + 2) + 7.
Elina [12.6K]

Answer:

6x+19

Step-by-step explanation:

First thing first, we need to multiply the 6 into the equation. We do this by multiplying the x and 2 by 6.

6(x+2)+7

Multiply

6x+12+7

Now we need to combine like terms by adding the 12 and 7

6x+19

There it is simplified.

8 0
2 years ago
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