For each of the situations described, state whether the sampling procedure is simple random sampling, stratified random sampling
1 answer:
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Answer:
=
Step-by-step explanation:
In order to add fractions, the denominators must all be the same value (the lowest common denominator). The <em>lowest common denominator</em> is the smallest value that all of the given denominators (in this case, the denominators are 4, 14, and 7) can divide into.
Here, the smallest number that all three of the given denominators can perfectly divide into is 28:
28 ÷ 4 = 7
28 ÷ 14 = 2
28 ÷ 7 = 4
<em>Therefore, our lowest common denominator is 28.</em>
<em />
The next step is to change our numerators to match our lowest common denominator. To do this, we have to multiply the numerator by the same value that we would need to multiple the denominator by in order to get our lowest common denominator.
For our first term of 1/4, we need to multiply our denominator (4) by 7 in order to get our lowest common denominator of 28. So, we need to also multiply our numerator by 7:
×
=
<em>Therefore, our first term becomes </em><em>.</em>
For our second term of 5/14, we need to multiply our denominator (14) by 2. So, we need to also multiply our numerator by 2:
×
=
<em>Therefore, our second term becomes </em><em>.</em>
For our third term of 6/7, we need to multiply our denominator (7) by 4. So, we need to also multiply our numerator by 4:
×
=
<em>Therefore, our third term becomes </em><em>.</em>
Now that they all have the same denominator, we simply have to add all three together:
+
<em> </em>+<em> </em>
<em> </em>=
When we simplify this into a mixed number, we get:
=
<em />
<em>Options:</em>
<em>Rotation of 180° about point B </em>
<em>Rotation of 90° about point b </em>
<em>Reflection over the x-axis </em>
<em>Translation down 2 units</em>
<em></em>
Answer:
Rotation of 180° about point B
<em></em>
Step-by-step explanation:
Considering coordinates of point B
Assume the coordinates of the line at point B is (x,y)
i.e.
First, we need to determine the slope at point B
Taking coordinates about the origin.
The slope of B is:
Where
--- origin
becomes
Taking the options one after the other:
Option A.
When rotated by 180°, the resulting coordinates of B would be
Taking the slope of B'
The slope of B is:
Where
--- origin
becomes
Notice that the slope of B and B' is the same;
<em>Hence:</em>
<em>Rotation of 180° about point B answers the question</em>
<em></em>
<em>There's no need to check for other options</em>