Imagine your friend is writing an argument to convince adults that they should allow teens to own and use smartphones. Read her
1 answer:
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Answer:
The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.
Step-by-step explanation:
Assuming that the shortest side of this triangle has a length of "x" feet, then one side is "x + 4" feet and the third is "2*x - 4" feet. Since the perimeter of the deck is 80 feet, then the sum of the length of these sides should be equal to that.
The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.
Answer:
option: b is correct.
( b.Yes, because both figures are rectangles and all rectangles are similar )
Step-by-step explanation:
Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation at the origin.
Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.
The scale factor could be calculated by the ratuio of the sides of the image to the pre-image rectangle.
Rectangle ABCD: Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).
Now consider rectangle EFGH: Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).
Hence the scale factor is:
Hence the scale factor is: 4/3.
Also
∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°
( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).
Hence option: b is correct.
( b.Yes, because both figures are rectangles and all rectangles are similar )
This question is incomplete, the complete question is;
Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and preview ads before the movie starts. Many complain that the time devoted to previews is too long (The Wall Street Journal, October 12, 2012). A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number,
a) If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, what sample size should be used? Assume 95% confidence.
b) If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.
Answer:
a) the required Sample Size is 40
b) the required Sample Size is 62
Step-by-step explanation:
Given the data in the question;
standard deviation σ = 4 minutes
a)
margin of error E = 75 seconds = ( 75 / 60 )minutes = 1.25 minutes
And 95% confidence.
Now, Critical Value of z for 0.95 confidence interval;
∝ = 1 - 0.95 = 0.05
= 1.96
so, sample size n will be;
n = [ × σ/E ]²
we substitute;
n = [ 1.96 × (4/1.25) ]²
n = [ 1.96 × 3.2 ]²
n = [ 6.272 ]²
n = 39.338
Since we referring to a number of sample, its approximately becomes 40
Therefore, the required Sample Size is 40
b)
margin of error E = 1 minutes
And 95% confidence.
Now, Critical Value of z for 0.95 confidence interval;
∝ = 1 - 0.95 = 0.05
= 1.96
so, sample size n will be;
n = [ × σ/E ]²
we substitute;
n = [ 1.96 × (4/1) ]²
n = [ 1.96 × 4 ]²
n = [ 7.84 ]²
n = 61.466
Since we referring to a number of sample, its approximately becomes 62
Therefore, the required Sample Size is 62