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OverLord2011 [107]
3 years ago
9

A ladder is inclined at only 23 degrees against the wall what the height of the ladder reaches up the wall

Mathematics
1 answer:
maw [93]3 years ago
7 0

Step-by-step explanation:

To determine what the height of the ladder reaches up the wall we need to know the height of ladder which is not provided in the question.

So if I assume the height of ladder to be 10ft( just a general assumption)

Then, inclined ladder, wall and distance been the bottom of the ladder and wall will form a right angle triangle.

where height of ladder will be hypotenuse, height of the ladder reaches up the wall will be perpendicular and distance been the bottom of the ladder and wall will be base.

Since, A ladder is inclined at 23 degrees against the wall

⇒ height of the ladder reaches up the wall  = Height of ladder×sin23°

= 10ft × sin23° = 3.9073 ft

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The probability that at least two-third of vehicles in the sample turn is 0.4207.

Step-by-step explanation:

Let <em>X</em> = number of vehicles that turn left or right.

The proportion of the vehicles that turn is, <em>p</em> = 2/3.

The nest <em>n</em> = 50 vehicles entering this intersection from the east, is observed.

Any vehicle taking a turn is independent of others.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 50 and <em>p</em> = 2/3.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of <em>X</em> if the following conditions are satisfied:

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np=50\times \frac{2}{3}=33.333>10\\\\n(1-p)=50\times \frac{1}{3}= = 16.667>10

Thus, a Normal approximation to binomial can be applied.

So, X\sim N(np, np(1-p))

Compute the probability that at least two-third of vehicles in the sample turn as follows:

P(X\geq \frac{2}{3}\times 50)=P(X\geq 33.333)=P(X\geq 34)

                        =P(\frac{X-\mu}{\sigma}>\frac{34-33.333}{\sqrt{50\times \frac{2}{3}\times\frac {1}{3}}})

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Thus, the probability that at least two-third of vehicles in the sample turn is 0.4207.

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3 years ago
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