Can anyone help me with this? I've been stuck on this question for some time-

Angle E is 43 degrees.

Step-by-step explanation:

So we know that AB is parallel to CD.

We also know that Angle CHF is 119 degrees and that Angle B is 18 degrees.

First, let's find Angle DHF. It is the supplementary angle to Angle CHF. Thus, they must total 180:

We already know that Angle CFH is 119. Substitute:

Subtract 119 from both sides:

Therefore, Angle DHF is 61 degrees.

Since Angle DHF is 61 degrees, then angle BGH must also be 61 degrees. This is because they are corresponding angles, and corresponding angles have the same measure.

Also, Angle BGE is the supplementary angle to Angle BGH. In other words:

Find Angle BGE. Substitute 61 for BGH:

Subtract 61:

So, angle BGE is 119 degrees.

Recall that a triangle's interior angles sum to 180. This means that Angle B plus Angle BGE plus Angle E must equal 180. Thus:

Substitute 18 for B and 119 for BGE. Thus:

Add:

Subtract:"

And we're done!

Remarks:

I just realized that you can just use the fact that alternate exterior angles have the same measures to figure out that BGE is equivalent to CHF. Regardless, we will arrive at the same answer :)

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

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