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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, = x
The breadth of the 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 ×
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 ×
∴ 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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Answer:
a) 0.2725
b) 0.7275
c) 0.8948
Step-by-step explanation:
This is a binomial distribution probability problem. The formula is:
Where
n is the number of trials [here we are taking 8 person, so n = 8]
x is what we are looking for [in the problem]
p is the probability of success [ 15%, so p = 0.15
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:
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:
and
Thus,
P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2) = 0.2725 + 0.3847 + 0.2376 = 0.8948