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Keith_Richards [23]
3 years ago
15

10 POINTS!! HELP ASAP!! What is the length of AC?

Mathematics
2 answers:
il63 [147K]3 years ago
8 0

Answer:

D.  144

Step-by-step explanation:

Triangle BAC is similar to triangle DEC, so you can set up a ratio:

\frac{84}{156-x} = \frac{7}{x}

Then cross multiply

84x = 7 (156 - x)

84x = 1092 - 7x

Add 7x to both sides.

91x = 1092

Divide both sides by 91.

x = 12

AC = 156 - x

AC = 156 - 12

AC = 144

My name is Ann [436]3 years ago
4 0

Answer:

D

Step-by-step explanation:

Δ CED and Δ CAB are similar thus the ratios of corresponding sides are equal, that is

\frac{CE}{CA} = \frac{ED}{AB} , substitute values

\frac{x}{156-x} = \frac{7}{84} = \frac{1}{12} ( cross- multiply )

12x = 156 - x ( add x to both sides )

13x = 156 ( divide both sides by 13 )

x = 12

Thus

AC = 156 - x = 156 - 12 = 144 → D

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Comment
(my edit) it is not that 2/15 is wrong (although it is not entirely right).
1/3 is the correct answer if you assume that what happened during the first draw has nothing to do with what will happen on the second. It is like saying if you throw 11 heads in a row with a fair coin, what are the chances of throwing a heads on the 12th throw? The answer is 1/2. That is the same kind of question you have asked.

The two of us who have responded have really responded to what are the chances of drawing 2 white chips. The question really does not restrict us in a way that prevents us from saying that. I'll stick with
B <<<< answer
but I think it would be nice if the writer of the question made it clear that 1/3 should be the proper answer. I am glad you came back and posted the right answer. It makes me think. 

The semi right answer is B <<<<---- 

If my reasoning bothers anybody, I'll reedit again. I'm only leaving it because sometimes a mistake is more instructive than a given answer.
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Answer:

1. The chi-squared statistic = 10.36

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2. The range of the p-value from the Chi squared table = 0.75 < p-value < 0.90

Step-by-step explanation:

1. The Chi squared test is given as follows;

\chi ^{2} = \sum \dfrac{\left (Observed - Expected  \right )^{2}}{Expected  }

Therefore,

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The chi-squared statistic is given as follows;

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The chi-squared statistic = 10.36

The degrees of freedom, df = 18 - 1 = 17 since the all of the expected count have a minimum value of 18

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2. The range of the p-value from the Chi squared table is given as follows;

0.75 < p-value < 0.90.

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