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kherson [118]
3 years ago
11

6. Find the number of segments (chords) that can be drawn for each of the following:

Mathematics
1 answer:
Gnesinka [82]3 years ago
6 0

Answer:

a) 10

b) 15

c) 190

d) {n \choose 2} = \frac{n!}{(n-2)!2!}

Step-by-step explanation:

Lets start with the generic item (d). In order to draw a chord we need to pick two endpoints from the total of n points of the circle and draw the line between them. The total amount of lines we can draw is equivalent to the total pair of points we can pick to draw them.

In other words, we can draw as many chords as the amount of subsets of 2 elements we can pick from a set of n. That number is the combinatorial number of n with 2 given by

{n \choose 2} = \frac{n!}{(n-2)!2!}

a) If n = 5, the answer is

{5 \choose 2} = \frac{5!}{(5-2)!2!} = \frac{120}{6*2} = 10

there are 10 possibilities

b) for n = 6

{6 \choose 2} = \frac{6!}{(6-2)!2!} = \frac{720}{24*2} = 15

15 possibilities

c) for n = 20, we have

{20 \choose 2} = \frac{20!}{(20-2)!2!} = 190

possibilities.

I hope that works for you!

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Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a variance of 4,000,000 and a mean
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Using the normal distribution, it is found that there is a 0.2776 = 27.76% probability that the life span of the monitor will be more than 20,179 hours.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

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The probability that the life span of the monitor will be more than 20,179 hours is <u>one subtracted by the p-value of Z when X = 20179</u>, hence:

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

Z = \frac{20179 - 19000}{2000}

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Z = 0.59 has a p-value of 0.7224.

1 - 0.7224 = 0.2776.

0.2776 = 27.76% probability that the life span of the monitor will be more than 20,179 hours.

More can be learned about the normal distribution at brainly.com/question/24663213

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