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2 years ago

14

Suppose Birmingham, Huntsville, and Gadsden, Alabama, form a right triangle. What is the distance from Huntsville to Gadsden? Th

anks for answering!

1 answer:

olga_2 [115]2 years ago

7 0

Answer:

76.7 miles

Step-by-step explanation:

Use the Pythagorean Theorem:

$a^2+b^2=c^2\\\\61^2+d^2=98^2\\\\3721+d^2=9604\\\\d^2=5883\\\\d\approx76.7$

Therefore, the distance from Huntsville to Gadsden is about 76.7 miles

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Lena [83]

Step-by-step explanation:

Let the painting's width be w inches and length be l inches.

w + 6 = 2l

w = 2l - 6 --(1)

2w + 2l = 84 --(2)

sub (1) into (2):

2(2l - 6) + 2l = 84

2l - 6 + l = 42

3l = 48

l = 16

when l = 16, w = 2(16) - 6 = 26

area of painting = lw = 16 x 26 = 416square inches

Therefore, only statements 1, 3 and 5 are true

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3 years ago

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The heights of baby giraffe are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 b

ANEK [815]

Answer:

$P(\bar X$

And we can solve this using the following z score formula:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we use this formula we got:

$z = \frac{63-63.6}{\frac{2.5}{\sqrt{100}}}= -2.4$

So we can find this probability equivalently like this:

$P( Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(63.6,2.5)$

Where $\mu=63.6$ and $\sigma=2.5$

We select n =100. Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We want this probability:

$P(\bar X$

And we can solve this using the following z score formula:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we use this formula we got:

$z = \frac{63-63.6}{\frac{2.5}{\sqrt{100}}}= -2.4$

So we can find this probability equivalently like this:

$P( Z$

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3 years ago