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DaniilM [7]
3 years ago
6

The height of one story of a building is about 10 feet. The bottom of the ladder on the fire truck must be at least 24 feet away

from the building. How many stories can the ladder reach?
Mathematics
2 answers:
DENIUS [597]3 years ago
5 0
The most possible answer is 2 stories 
Anni [7]3 years ago
3 0

Answer: There are atleast 2 stories that the ladder can reach.

Step-by-step explanation:

Since we have given that

Height of one story of a building  = 10 feet

Length between the bottom of the ladder and the building = 24 feet

So, we need to find the number of stories that the ladder can reach.

So, Number of stories is given by

\dfrac{\text{Length b/w ladder and building}}{\text{Height of one story}}\\\\=\dfrac{24}{10}\\\\=2.4

Hence, there are atleast 2 stories that the ladder can reach.

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Answer:

(a) The mean or expected value of <em>X </em>is 2.2.

(b) The standard deviation of <em>X</em> is 1.3.

Step-by-step explanation:

Let <em>X</em> = number of times the traffic light is red when a commuter passes through the traffic lights.

The probability distribution of <em>X</em> id provided.

The formula to compute the mean or expected value of <em>X </em>is:

\mu=E(X)=\sum x.P(X=x)

The formula to compute the standard deviation of <em>X </em>is:

\sigma=\sqrt{E(X^{2})-(E(X))^{2}}

The formula of E (X²) is:

E(X^{2})=\sum x^{2}.P(X=x)

(a)

Compute the expected value of <em>X</em> as follows:

E(X)=\sum x.P(X=x)\\=(0\times0.06)+(1\times0.25)+(2\times0.35)+(3\times0.15)+(4\times0.13)+(5\times0.06)\\=2.22\\\approx2.2

Thus, the mean or expected value of <em>X </em>is 2.2.

(b)

Compute the value of E (X²) as follows:

E(X^{2})=\sum x^{2}.P(X=x)\\=(0^{2}\times0.06)+(1^{2}\times0.25)+(2^{2}\times0.35)+(3^{2}\times0.15)+(4^{2}\times0.13)+(5^{2}\times0.06)\\=6.58

Compute the standard deviation of <em>X</em> as follows:

\sigma=\sqrt{E(X^{2})-(E(X))^{2}}\\=\sqrt{6.58-(2.22)^{2}}\\=\sqrt{1.6516}\\=1.285\\\approx1.3

Thus, the standard deviation of <em>X</em> is 1.3.

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