The answer is C because she did write associative instead of distributive in step 2 in which made her work error.
9514 1404 393
Answer:
B. 22 to 26
Step-by-step explanation:
Multiply each value in the ratio by 2/3 to see an equivalent that is among the choices.
33 : 39 = (2/3)(33) : (2/3)(39) = 22 : 26
Length of rectangle = 5 less than 2x width
Perimeter = 146 cm
<u>Equations we will use...</u>
w = width
(2w - 5) = length (l)
perimeter (p) = 2(l + w)
<u>Substitute equation for </u><u>length</u><u> into equation for </u><u>perimeter</u>
p = 2(l + w)
146 = 2((2w - 5) + w) [use distributive prop.]
146 = 4w - 10 + 2w [combine like terms]
146 = 6w -10 [solve for w]
156 = 6w
w = 26 cm
<u>Now substitute width back into the </u><u>equation</u><u> for length...</u>
l = 2w - 5
l = 2(26) - 5
l = 47
Double check to make sure values added up to 146 cm
w + w + l + l = 146
26 + 26 + 47 + 47 = 146
146 = 146
Therefore, the width is 26 cm and the length is 47 cm.
Answer
The scale factor is
Explanation
We have to ways to find the scale factor here:
1. Find the unit fraction from inches to miles; in other words, we need to divide the distance between the cities on the map (in inches) by the actual distance between the cities.
We can conclude that the scale factor is
2. Let be the scale factor.
We know form our problem that 24 miles times the scale factor is equal 4 1/2 inches, so we can set up an equation an solve for :
Just like before, we can conclude that the scale factor is
B.
Answer
6 inches separate the cities on the map
Explanation
We know that our scale factor is 1/4 inch = 1 mile, so we can create a conversion factor to convert 24 miles to inches. Since we need to convert from miles to inches, the denominator of our conversion factor must be 1 mile so we can cancel miles out. Notice that we can also express 1/4 inch as 0.25 inch to simplify our calculations:
We can conclude that if the conversion factor is 1/4 inch = 1 mile, 6 inches separate the cities on the map.
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Answer:
The approximated value of the standard deviation is 0.35.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the distribution of sample means is given by,
And the standard deviation of the distribution of sample means is given by,
The information provided is:
<em>n</em> = 100
<em>σ</em> = 3.5
<em>μ</em> = 66
As the sample size is quite large, i.e. <em>n</em> = 100 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.
Then the approximated value of the standard deviation of sampling distribution of sample mean is:
Thus, the approximated value of the standard deviation is 0.35.
