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anygoal [31]
3 years ago
15

Check up 1

Mathematics
1 answer:
zhenek [66]3 years ago
8 0

Answer:

a. The expression for the area of the gym is 15·x

b. The expression for the area of the cafeteria is 15·x + 45

c. The expression for the total area of the gym and the cafeteria is 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria is 36 + 4·x

Step-by-step explanation:

The parameters of the given figures are;

The width of the figure, w = 15

The breadth of the gym, b_{gym} = x

The breadth of the cafeteria, b_{cafeteria} = x + 3

The shape of the area of the gym = A rectangle

The shape of the area of the cafeteria = A rectangle

a. The expression for the area, 'A₁', of the gym is given by the area of a rectangle which is Width × Breadth

The area of the gym, A₁ = The width of the figure × The breadth of the gym

Therefore, we have; The area of the gym, A₁ = w × b_{gym}

A₁ = 15 × x

The area of the gym, A₁ = 15·x

b. The area of the cafeteria, A₂ = The width of the figure × The breadth of the cafeteria

The area of the cafeteria, A₂ = w × b_{cafeteria}

∴ A₂ = 15 × (x + 3) = 15·x + 45

The expression for the area of the cafeteria, A₂ = 15·x + 45

c. The expression for the total area of the gym and the cafeteria, 'A', is given as follows;

A = A₁ + A₂

∴ A = 15·x + 15·x + 45 = 30·x + 45

The expression for the total area of the gym and the cafeteria = 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria, 'P', is given as follows;

P = The perimeter of the rectangular area of the gym plus the area of the cafeteria

∴ P = 2 × 15 + 2 × (x + x + 3)

P = 30 + 4·x + 6

P = 36 + 4·x

The expression for the total perimeter of the gym and the cafeteria P = 36 + 4·x.

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b)  0.7275

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Step-by-step explanation:

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P(x)=\frac{n!}{(n-x)!x!}p^{x}q^{n-x}

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x is what we are looking for [in the problem]

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q is the probability of failure [q = 1-p = 0.85]

Now,

a)

We are looking for "no one" did fling, so x = 0

Let's put into formula and find out the probability:

P(x=0)=\frac{8!}{(8-0)!0!}(0.15)^{0}(0.85)^{8}\\P(x=0)=0.2725

So, the probability that no one has done a one-time fling is 0.2725

b)

Atleast 1 person means P(x ≥ 1).

This can be found by:

P(x ≥ 1) = 1 - P(x=0) = 1 - 0.2725 = 0.7275

THus, Probability that at least one person has done a one-time fling is 0.7275

c)

No more than 2 people means P (x≤2).

This is essentially

P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2)

P ( x = 0 ) is found in part (a), which is 0.2725

P (x = 1 ) and P(x=2) can be found using formula:

P(x=1)=\frac{8!}{(8-1)!1!}(0.15)^{1}(0.85)^{7}\\P(x=1)=0.3847

and

P(x=2)=\frac{8!}{(8-2)!2!}(0.15)^{2}(0.85)^{6}\\P(x=2)=0.2376

Thus,

P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2) = 0.2725 + 0.3847 + 0.2376 = 0.8948

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