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Brrunno [24]
1 year ago
14

In rhombus ABCD, the diagonals AC and BDintersect at E. If AE=5 and BE=12, what is thelength of AB?

Mathematics
1 answer:
hram777 [196]1 year ago
8 0

Diagonals that bisect each other are perpendicular and form a right angle.

AEB is a right triangle.

We can apply the Pythagorean theorem:

c^2 = a^2+b^2

Where c is the hypotenuse (longest side) and a and b the other 2 legs.

Replacing:

AB^2 = AE^2+BE^2

AB^2 = 5^2+12^2

AB^2 = 25+144

AB^2 = 169

AB=√169 = 13

Lenght of AB= 13

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Answer:

Yes, we can conclude that the population standard deviation of TV watching times for teenagers is less than 2.66

Step-by-step explanation:

H0 : σ² = 2.66²

H1 : σ² < 2.66²

X²c = (n - 1)*s² ÷ σ²

sample size, n = 40

Sample standard deviation, s = 1.9

X²c = ((40 - 1) * 1.9²) ÷ 2.66²

X²c = 140.79 ÷ 7.0756

X²c = 19.897

Using a confidence level of 95%

Degree of freedom, df = n - 1 ; df = 40 - 1 = 39

The critical value using the chi distribution table is 25.6954

Comparing the test statistic with the critical value :

19.897 < 25.6954

Test statistic < Critical value ; Reject the Null

Hence, we can conclude that the population standard deviation of TV watching times for teenagers is less than 2.66

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