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Vlada [557]
3 years ago
12

A window in Michael's room is the shape of a trapezoid. The bases are 30 inches and 40 inches. The height of the window is 24 in

ches. Find the area of the window.
Mathematics
1 answer:
lana [24]3 years ago
3 0

Answer:

The area of the window is of 840 square inches.

Step-by-step explanation:

To find the area of an trapezoid, we need to add the sum of the bases, multiply by the height, and then divide by 2.

Matematically:

A = \frac{(b_{1} + b_{2})*h}{2}

In which b_{1} and b_{2} are the bases and h is the height.

In this question:

b_{1} = 30, b_{2} = 40, h = 24

All the measures in inches, so the area is in square inches.

A = \frac{(30 + 40)*24}{2} = 840

The area of the window is of 840 square inches.

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The television show CSI: Shoboygan has been successful for many years. That show recently had a share of 18, meaning that among
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Answer:

(a) The value of P (None) is 0.062.

(b) The value of P(at least one) is 0.938.

(c) The value of P(at most one) is 0.253.

(d) The event is not unusual.

Step-by-step explanation:

Let <em>X</em> = number of households watching the show.

The probability of the random variable <em>x</em> is, P (X) = <em>p</em> = 0.18.

The sample selected for the survey is of size, <em>n</em> = 14

The random variable <em>X</em> follows a Binomial distribution with parameter <em>n</em> = 14 and <em>p</em> = 0.18.

The probability of a Binomial distribution is computed using the formula:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...

(a)

Compute the probability that none of the households are tuned to CSI: Shoboygan as follows:

P(X=0)={14\choose 0}(0.18)^{0}(1-0.18)^{14-0}=1\times1\times0.06214=0.062

Thus, the value of P (None) is 0.062.

(b)

Compute the probability that at least one household is tuned to CSI: Shoboygan as follows:

P (X ≥ 1) = 1 - P (X < 1)

             = 1 - P (X = 0)

             =1-0.062\\=0.938

Thus, the value of P(at least one) is 0.938.

(c)

Compute the probability that at most one household is tuned to CSI: Shoboygan as follows:

P (X ≤ 1) = P (X = 0) + P (X = 1)

             ={14\choose 0}(0.18)^{0}(1-0.18)^{14-0}+{14\choose 1}(0.18)^{1}(1-0.18)^{14-1}\\=0.062+0.191\\=0.253

Thus, the value of P(at most one) is 0.253.

(d)

An event that has a very low probability of occurrence is known as an unusual event.

The probability of the event "at most one household is tuned to CSI: Shoboygan" is 0.253.

This probability value is not low.

Hence, the event is not unusual.

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