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raketka [301]
3 years ago
7

I know they are similar because of equivalent angles but im not sure how to explain

Mathematics
1 answer:
o-na [289]3 years ago
6 0
In ΔDCE + ΔGFH,
∠C = ∠F (given)
∠D = ∠C (angle sum of a triangle)
∠H = ∠E (angle sum of a triangle)
∴ ΔDCE is similar to ΔGFH
Hope this helps!
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Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and
balu736 [363]

Answer:

(a) The sample size required is 43.

(b) The sample size required is 62.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean is:

 CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}

The margin of error for this interval is:

 MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}

(a)

The information provided is:

<em>σ</em> = 4 minutes

MOE = 72 seconds = 1.2 minutes

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

 z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use a z-table.

Compute the sample size required as follows:

 MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}

       n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}

          =[\frac{1.96\times 4}{1.2}]^{2}\\\\=42.684\\\\\approx 43

Thus, the sample size required is 43.

(b)

The information provided is:

<em>σ</em> = 4 minutes

MOE = 1 minute

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

 z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use a z-table.

Compute the sample size required as follows:

 MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}

       n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}

          =[\frac{1.96\times 4}{1}]^{2}\\\\=61.4656\\\\\approx 62

Thus, the sample size required is 62.

3 0
3 years ago
120 is what percent of 90? Lo in
allsm [11]

Answer:

133.33%

Step-by-step explanation:

120= 120/90

the word OF = multiplication

120/90 x 100/100=133.33/100

133.33/100=133.33%

7 0
3 years ago
A person who is 68in tall casts a shadow that is 54in long. At the same moment, a tree casts a shadow that is 18ft long. What is
34kurt

Answer:

<u>22.67 ft</u> is the height of tree.

Step-by-step explanation:

Given:

Height of a person is 68 in and casts a shadow that is 54 in long.

At the same point, a tree casts a shadow that is 18 ft long.

Now, to find the height of tree.

Let the height of tree be x.

If height of a person is 68 in he casts a shadow of 54 in.

So, 68 in is equivalent to 54 in.

Thus, x is equivalent to 18 ft.

Now, to get the height of tree by using cross multiplication method:

\frac{68}{54} =\frac{x}{18}

<em>By cross multiplying we get:</em>

<em />1224=54x<em />

<em>Dividing both sides by 54 we get:</em>

22.67=x

x=22.67\ ft.

Therefore, the height of the tree is 22.67 ft.

6 0
3 years ago
Simplify these expressions:<br> 1) 8y + 5 - 10y - 2
yKpoI14uk [10]

Answer:

here I think

Step-by-step explanation:

8y + 5 - 10y - 2 = (8y-10y)+(5-2)=-2y+3

4 0
3 years ago
14 mm<br> 29 mm<br> Calculate the surface area.
tino4ka555 [31]

Answer:

14x29=406 2hich would be the area

Step-by-step explanation:

4 0
3 years ago
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