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kkurt [141]
3 years ago
13

A sequence of two transformations that can be used to show that polygon ABCDE is congruent to polygon GFJIH

Mathematics
1 answer:
Ket [755]3 years ago
4 0

Answer:

Yes,they are congruent.

Step-by-step explanation:

We are required to make two transformations  and prove that they are congruent.

First Transformation:Now rotate the polygon FGHIJ by 90° about the axis parallel to x-axis and passinfg through the vertex I.You can observe that the sides are of same length AB=GF=2 units.

Second Transformation: Keeping the polygon ABCDE constant shift the centre of polygon FGHIJ to the centre of polygon ABCDE you will observe thta they exactly overlap on each other hence they are congruent with each other.

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A university planner wants to determine the proportion of spring semester students who will attend summer school. Suppose the un
ss7ja [257]

Answer:

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have prior estimation for the population proportion we can use the value \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.112}{1.64})^2}=53.60  

And rounded up we have that n=54

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.90=0.1 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.112 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have prior estimation for the population proportion we can use the value \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.112}{1.64})^2}=53.60  

And rounded up we have that n=54

3 0
2 years ago
When I am finding the surface area, do I cube or square it? Or does it depend on the shape/object?
LUCKY_DIMON [66]

Answer:

it depends on shape and object or how wide or tall the figure is.

Step-by-step explanation:

5 0
3 years ago
I need help with this!
sertanlavr [38]

Answer:

67 degrees

Step-by-step explanation:

first find angle abc by subtracting 68 from 101 == 33

then add it to half of 68 (34) to get angle abe

we know it is half because if there is a bisector, both angles cbe and ebd are equal

8 0
3 years ago
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I’m having trouble with this
lara [203]

Answer:

24 or 25, because of the max height it can reach on the graph, its reaching the maximum height it can go

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8 0
2 years ago
8. Is the following statement true or false? Justify your conclusion. If a and b are nonnegative real numbers and a + b =0, then
atroni [7]

Answer:

If a + b = 0 then a = 0 and b =0

a  | b | a + b (answer)

0 | 0 | 0

0 | 1  | 1

0 | 2 | 2

1  | 0 | 1

2 | 0 | 2

1  | 1  | 2

2 | 1  | 3

 

Step-by-step explanation:

Considering the following conditions for the real numbers:

a\geq 0\\b\geq 0

Following the rules of these in-equations, it is possible to deduce:

a + b \geq 0

Then, if the proposed statement is:

a + b = 0

The conditions above shall comply the requirements established, but first, analyzing the statement:

If a \geq 0 and b \geq 0 then a + b \geq a, a + b \geq b and a + b \geq 0.

If a = 0 and b a non negative real number, then a + b \geq b, but because to a = 0, then a + b = b. Due to the commutative property of sums, the same behavior will be presented if b = 0 and a a non negative real number.

According to that, if  a + b = 0, then a = 0 and b = 0.

7 0
3 years ago
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