When Harper commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 24 minutes and a
1 answer:
Answer:
So then we can conclude that we expect the middle 95% of the values within 18 and 30 minutes for this case
Step-by-step explanation:
For this case we can define the random variable X as the amount of time it takes her to arrive to work and we know that the distribution for X is given by:
And we want to use the empirical rule to estimate the middle 95% of her commute times. And the empirical rule states that we have 68% of the values within one deviation from the mean, 95% of the values within two deviations from the mean and 99.7 % of the values within 3 deviations from the mean. And we can find the limits on this way:
So then we can conclude that we expect the middle 95% of the values within 18 and 30 minutes for this case
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First, you need to know that the total (degrees) of the interior angles is 360 because this is a quadrilateral.
The unnumbered angle is 109 degrees. We know this because the angle labeled 71 degrees and the unnumbered angle are supplementary. So you subtract 180 from 71 to get 109.
To solve for x, we need to realize the other numbers playing into the angles' values. To make solving this easier, I'm gonna assign letters to the angles.
(10x+6) is angle A.
(13x-2) is angle B.
(8x-1) is angle C.
and 109 (the one we solved) is angle D.
We know that the total of the interior angles is 360, so we can add the 2 from angle B and the 1 from angle C to 360. This is because these numbers are subtracted from the other values.
Now, we have to subtract the 6 from angle A from 363, because the 6 is added to the other values.
Now we have to subtract 109 from 357 because you want to get the x's by themselves. Since you're solving for x.
That leaves you with 248. Now you add all the x's up to get the total number of x's. You have 10x from angle A, 13x from angle B, and 8x from angle C.
You get 31x. To get what x is, you divide 248 by 31.
That equals 8. So now that you know that x equals 8, if you need to find the values of the angles, you just plug in the numbers into the formulas.
Check your work by plugging your answers in and seeing if they add up to 360.
Which they should:)
So...
angle A= 86
angle B=102
angle C=63
angle D=109
and x=8
Hope this helped!!!
The unnumbered angle is 109 degrees. We know this because the angle labeled 71 degrees and the unnumbered angle are supplementary. So you subtract 180 from 71 to get 109.
To solve for x, we need to realize the other numbers playing into the angles' values. To make solving this easier, I'm gonna assign letters to the angles.
(10x+6) is angle A.
(13x-2) is angle B.
(8x-1) is angle C.
and 109 (the one we solved) is angle D.
We know that the total of the interior angles is 360, so we can add the 2 from angle B and the 1 from angle C to 360. This is because these numbers are subtracted from the other values.
Now, we have to subtract the 6 from angle A from 363, because the 6 is added to the other values.
Now we have to subtract 109 from 357 because you want to get the x's by themselves. Since you're solving for x.
That leaves you with 248. Now you add all the x's up to get the total number of x's. You have 10x from angle A, 13x from angle B, and 8x from angle C.
You get 31x. To get what x is, you divide 248 by 31.
That equals 8. So now that you know that x equals 8, if you need to find the values of the angles, you just plug in the numbers into the formulas.
Check your work by plugging your answers in and seeing if they add up to 360.
Which they should:)
So...
angle A= 86
angle B=102
angle C=63
angle D=109
and x=8
Hope this helped!!!