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3 years ago

What is the midpoint of the segment shown below?

Mathematics

2 answers:

Ilia_Sergeevich [38]3 years ago

7 0

Answer: The correct option is (B) $\left(5,\dfrac{1}{2}\right).$

Step-by-step explanation: We are given to find the midpoint of the line segment shown in the figure.

From the figure, we see

a line segment with co-ordinates of the endpoints (5, 4) and (5, -3).

We know that

the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) is given by

$M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).$

Therefore, the co-ordinates of the line segment shown is given by

$M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right)=\left(\dfrac{5+5}{2},\dfrac{4-3}{2}\right)=\left(5,\dfrac{1}{2}\right).$

Thus, (B) is the correct option.

tatuchka [14]3 years ago

5 0

This is easy to calculate as the line is straight vertical. There are 7 units in between the two end points of the line segment, so dividing this by 2 will give you the units from an end point to the mid point. 7 ÷ 2 = 3.5. Subtracting 3.5 from the higher y-value or adding it to the lower y-value gets you (5, 0.5).

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3 years ago

An elevator has a placard stating that the maximum capacity is 1600 lb�10 passengers. So, 10 adult male passengers can have a m

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Answer:

1. 0.7421 = 74.21% probability the elevator is overloaded.

2. D.No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .