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2 years ago

Algebra 2

Mathematics

2 answers:

kherson [118]2 years ago

8 0

Answer:

Step-by-step explanation:

n=sample size =200

Mean = x bar = 55 hours

Std deviation (Population) = 7 hours

For 99% confidence level

Z critical value = 2.58

Margin of error = ±2.58(std error)

Std error = $\frac{7}{\sqrt{n} } =0.495$

Hence margin of error = ±0.495(258)=1.28

Confidence interval = (55-1.28, 55+1.28) = (53.72, 56.28)

~(53.73, 56.27)

Hence option A

hoa [83]2 years ago

4 0

MOE = +\- 1.27
Confidence Interval is 53.73 to 56.27

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50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

aalyn [17]

Answer:

$EF=4\sqrt{3}$

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

$A_{\text{rect}}=8(6)=48\text{ cm}^2$

The area of the triangle is 1/4 of this. Therefore:

$\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2$

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

$\displaystyle 12=\frac{1}{2}(DE)(DF)$

Since DE = DF:

$24=DF^2$

Thus:

$DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE$

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

$(DE)^2+(DF)^2=(EF)^2$

Therefore:

$(2\sqrt6)^2+(2\sqrt6)^2=EF^2$

Square:

$24+24=EF^2$

Add:

$EF^2=48$

And finally, we can take the square root of both sides:

$EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}$

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2 years ago

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6. Find the area of the triangle below.<br> Be sure to include the correct unit in your answer.

snow_tiger [21]

Answer:

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Step-by-step explanation: area of triangle= 1/2*base*height

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3 years ago

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Step-by-step explanation:

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3 years ago

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inna [77]

Answer:

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Step-by-step explanation:

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3 years ago

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Can you help me from 1 to 8 and tell me how you get the answers for each one of them please

weqwewe [10]

Answer:

See below.

Step-by-step explanation:

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2 years ago