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3 years ago

A triangle has two side lenths of 1 and 16 what is the largest possible whole-number length of the third side?

Mathematics

1 answer:

Afina-wow [57]3 years ago

6 0

Answer:

Step-by-step explanation:

Given that:

Length of two sides of the triangle = 1 and 16 ;

The largest possible whole-number length of the third side would be ;

Recall from triangle inequality theorem; the length of any two sides of a triangle is greater than the third side. Therefore. The largest possible whole number value the third side could have is:

Assume the third side is the largest :

Then, the third side must be less than the sum of the other two sides ;

Third side < (16 + 1)

Third side < 17

Therefore, the closest whole number lesser than the sum of the other two sides is (17 - 1) = 16

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Read 2 more answers

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard

bulgar [2K]

We have been given that the lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years. We are asked to find the probability of a lion living longer than 10.1 years using empirical rule.

First of all, we will find the z-score corresponding to sample score 10.1.

$z=\frac{x-\mu}{\sigma}$ , where,

z = z-score,

x = Random sample score,

$\mu$ = Mean

$\sigma$ = Standard deviation.

$z=\frac{10.1-12.5}{2.4}$

$z=\frac{-2.4}{2.4}$

$z=-1$

Since z-score of 10.1 is $-1$ . Now we need to find area under curve that is below one standard deviation from mean.

We know that approximately 68% of data points lie between one standard deviation from mean.

We also know that 50% of data points are above mean and 50% of data points are below mean.

To find the probability of a data point with z-score $-1$ , we will subtract half of 68% from 50%.

$\frac{68\%}{2}=34\%$

$50\%-34\%=16\%$

Therefore, the probability of a lion living longer than 10.1 years is approximately 16%.

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3 years ago