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1 year ago

Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)

Mathematics

1 answer:

3241004551 [841]1 year ago

5 0

First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

$\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ =\sqrt{(8--5)^2+(-3-4)^2} \\ \\ =\sqrt{(13)^2+(-7)^2} \\ \\ =\sqrt{169+49} \\ \\ =\sqrt{218} \\ \\ \approx14.7648... \end{gathered}$

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.

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3 years ago

A mass club has 40 members the number of girls is five less than two times the number of boys how many members are boys how many

Lorico [155]

Answer:

15 boys and 25 girls

Step-by-step explanation:

The sum of boys (b) and girls (g) is given as 40:

g + b = 40

The number of girls is 2 times the number of boys minus 5:

2b - 5 = g

First formula can be rewritten as g = 40 - b

Then you can substitute this for g in the second, and you get:

2b-5 = 40-b

Which simplifies to:

2b + b = 40 + 5

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b = 15

g = 40-15 = 25

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3 years ago

Explain if 12.1 is rational or irrational

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3 years ago

Each contestant in the Hunger Games must be trained to compete. Suppose that the time it takes to train a contestant has mean 5

LiRa [457]

Answer:

11.51% probability that it will take less than 450 days to train all the contestants.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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 $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n variables, the mean is $\mu*n$ and the standard deviation is $s = \sigma\sqrt{n}$

In this question:

$n = 100, \mu = 100*5 = 500, s = 4\sqrt{100} = 40$

Approximate the probability that it will take less than 450 days to train all the contestants.

This is the pvalue of Z when X = 450.

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

By the Central Limit Theorem

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

$Z = \frac{450 - 500}{40}$

$Z = -1.2$

$Z = -1.2$ has a pvalue of 0.1151

11.51% probability that it will take less than 450 days to train all the contestants.

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3 years ago

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Answer:

1. 1.6x has a variable which means an unknown number

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Step-by-step explanation:

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5 + 0.10x means 5 more than 0.10 times an unknown number. A real world example here would be "10% off a sale plus $5 coupon". We don't know the price of the item but we do know it is 10% off and we get $5 off. Once we know the price we input it int for x and find the total discount.

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