Can anyone tell me what the answer please

Mathematics

1 answer:

Tasya [4]3 years ago

3 0

What you're looking at in this image are two alternate exterior angles.

Alternate exterior angles, are, essentially, exterior angles of a transversal that runs through two parallel lines. These angles are on alternating sides. These angles, assuming the lines are parallel, must be equal.

There's a proof behind why these angles are equal, but I won't bore you with the specifics as the question doesn't require it.

So - we know that these two angles must be equal to prove that the lines A and B are parallel. Knowing this, we can write an equation:

5x + 20 = 3x + 60

<u>Subtract 20 from both sides:</u>

5x + 20 - 20 = 3x + 60 - 20

5x = 3x + 40

<u>Subtract 3x from both sides:</u>

5x - 3x = 3x - 3x + 40

2x = 40

x = 20

If you have any questions on how I got to the answer, just ask!

- breezyツ

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3 years ago

The following data gives the speeds (in mph), as measured by radar, of 10 cars traveling north on I-15. 76 72 80 68 76 74 71 78

____ [38]

Answer:

71.123 mph ≤ μ ≤ 77.277 mph

Step-by-step explanation:

Taking into account that the speed of all cars traveling on this highway have a normal distribution and we can only know the mean and the standard deviation of the sample, the confidence interval for the mean is calculated as:

$m-t_{a/2,n-1}\frac{s}{\sqrt{n} }$ ≤ μ ≤ $m+t_{a/2,n-1}\frac{s}{\sqrt{n} }$

Where m is the mean of the sample, s is the standard deviation of the sample, n is the size of the sample, μ is the mean speed of all cars, and $t_{a/2,n-1}$ is the number for t-student distribution where a/2 is the amount of area in one tail and n-1 are the degrees of freedom.

the mean and the standard deviation of the sample are equal to 74.2 and 5.3083 respectively, the size of the sample is 10, the distribution t- student has 9 degrees of freedom and the value of a is 10%.

So, if we replace m by 74.2, s by 5.3083, n by 10 and $t_{0.05,9}$ by 1.8331, we get that the 90% confidence interval for the mean speed is: