In the diagram, dg = 12, gf = 4, eh = 9, and hf = 3.

to prove that △dfe ~ △gfh by the sas similarity theorem, it can be stated that and
a. ∠dfe is 4 times greater than ∠gfh.
b. ∠fhg is 1/4 the measure of ∠fed.
c. ∠dfe is congruent to ∠gfh.
d. ∠fhg is congruent to ∠efd.

The diagram below shows two separate triangles, DEF and GHF

The corresponding sides FG and FD has the relationship that FD is 4 times FG

The corresponding sides FE and FH has the relationship that FE is 4 times FH

This shows the triangle DEF is 4 times length of triangle GHF

Angles in two triangles that are similar are equals.

With two sides of the same ratio and equal angles, triangle DEF and GFH are similar

The correct statement from above options is angle DFE equals to GFH

79.67% probability that a bulb lasts longer than advertised

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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.

In this problem, we have that:

What is the probability that a bulb lasts longer than advertised?

This is 1 subtracted by the pvalue of Z when X = 4000. So

has a pvalue of 0.2033

1 - 0.2033 = 0.7967

79.67% probability that a bulb lasts longer than advertised