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OleMash [197]
4 years ago
11

Find the volume of each of the following cubes. a. s = 7 kilometers b. s = 11 yards

Mathematics
2 answers:
Karolina [17]4 years ago
7 0

Answer:

a) 343 kilometres³

b) 1331 yards³

Step-by-step explanation:

The volume of a cube is calculated using the following formula, where S is the side length of the cube:

V=S^{3}

a) Cube with side length, s = 7 kilometres

V_{a}=7^{3} \\V_{a}=343

a) Cube with side length, s = 11 yards

V_{a}=11^{3} \\V_{a}=1331

nadya68 [22]4 years ago
6 0

Answer:

Part 1) V=343\ km^{3}

Part 2) V=1,331\ yd^{3}

Step-by-step explanation:

we know that

The volume of a cube is equal to

V=s^{3}

where

s is the length of the cube

Part 1)

we have

s=7\ km

substitute in the formula

V=7^{3}

V=343\ km^{3}

Part 2)

we have

s=11\ yd

substitute in the formula

V=11^{3}

V=1,331\ yd^{3}


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Step-by-step explanation:

The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

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k is the total number of desired outcomes.

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We have that:

6 + 8 = 14 students, which means that N = 14

6 grade 11 students means that k = 6

Teams of 4 members means that n = 4

What is the probability that the team has at least 2 grade 11 students?

This is:

P(X \geq 2) = 1 - P(X < 2)

In which

P(X < 2) = P(X = 0) + P(X = 1)

So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 0) = h(0,14,4,6) = \frac{C_{6,0}*C_{8,4}}{C_{14,4}} = 0.0699

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P(X < 2) = P(X = 0) + P(X = 1) = 0.0699 + 0.3357 = 0.4056

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4056 = 0.5944

0.5944 = 59.44% probability that the team has at least 2 grade 11 students

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