Show how to subdivide and recombine the parallelogram below to form a B by H rectangle thereby explaining why the area of the pa
rallelogram is B times H.
1 answer:
Below is the proof why the area of a parallelogram is B times H
<h3>How to form a rectangle from the parallelogram</h3>The following steps would create a rectangle from the parallelogram
- Step 1: Cut out the triangular part of the parallelogram
- Step 2: Attach the triangular part to the other end of the parallelogram
See attachment for the steps.
When the rectangle has been created, we have the following dimensions:
Length = h
Width = B
The area of a rectangle is:
Area = Length * Width
This gives
Area = h * B
Evaluate
Area = Bh
Hence, the area of a parallelogram is B times H
Read more about parallelograms at:
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Answer:
We conclude that the sodium content is same as what the nutrition label states.
Step-by-step explanation:
We are given that the nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium.
The FDA randomly selects 40 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1088.64 milligrams of sodium per package with a sample standard deviation of 234.12 milligrams.
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<u><em>Let </em></u><u><em> = average sodium content.</em></u>
So, Null Hypothesis, :
= 1100 milligrams {means that the sodium content is same as what the nutrition label states}
Alternate Hypothesis, :
1100 milligrams {means that the sodium content is different from what the nutrition label states}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about population standard deviation;
T.S. = ~
where, = sample average sodium content = 1088.64 milligrams
s = sample standard deviation = 234.12 milligrams
n = sample of packages of Oriental Spice Sauce = 40
So, <u><em>test statistics</em></u> = ~
= -0.307
The value of z test statistics is -0.307.
<em>Since, in the question we are not given the level of significance so we assume it to be 5%. </em><em>Now, at 0.05 significance level the t table gives critical values of -2.0225 and 2.0225 at 39 degree of freedom for two-tailed test.</em><em> </em>
<em>Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><em><u>we fail to reject our null hypothesis</u></em><em>.</em>
Therefore, we conclude that the sodium content is same as what the nutrition label states.