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Ksenya-84 [330]
3 years ago
5

Rectangle ABCD is congruent to rectangle. Which sequence of transformations could have been used to transform rectangle ABCD to

produce rectangle? A. Rectangle ABCD was rotated 90° clockwise around the origin and then translated 7 units left. B. Rectangle ABCD was rotated 90°counterclockwise around the origin and then reflected across the x-axis. C. Rectangle ABCD was rotated 90° counterclockwise around the origin and then translated 8 units down. D. Rectangle ABCD was rotated 90° clockwise around the origin and then reflected across the y-axis.
Mathematics
1 answer:
il63 [147K]3 years ago
7 0
Rectangle ABCD was rotated 90° counterclockwise around the origin and then translated 8 units down.
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Here are summary statistics for randomly selected weights of newborn​ girls: nequals=174174​, x overbarxequals=30.930.9 ​hg, seq
MaRussiya [10]

Answer:

The 95% confidence interval would be given by (29.780;32.020)  

Step-by-step explanation:

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".

\bar X=30.9 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size  

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=174-1=173

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that t_{\alpha/2}=1.97, this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.  

Now we have everything in order to replace into formula (1):

30.9-1.97\frac{7.5}{\sqrt{174}}=29.780    

30.9+1.97\frac{7.5}{\sqrt{174}}=32.020

So on this case the 95% confidence interval would be given by (29.780;32.020)    

The value 29.6 is not contained on the interval calculated.

5 0
3 years ago
Given: ΔABC is a right triangle.
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Pythagorean Theorum since that is what you are trying to prove.
6 0
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If a triangle is a right triangle then the other two angles must be acute true or false ?
kolezko [41]

Answer:

The sum of the angles in any triangle is 180 degrees. If one of the three angles is 90 degrees (a right angle) the the sum of the other two angles is 90 degrees. Therefore each of the other two angles must be acute.

The statement is TRUE.

Step-by-step explanation:


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A person stands 10 feet away from the base of a 300-foot office building.
snow_tiger [21]

Answer:

The answer will be A.

Step-by-step explanation:

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a coin bank holds nickels, dimes, and quarters. there are 54 coins in the bank and the value of the coins is $4.75. if there are
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