statistics on stepfamilies are difficult to attain, and the statistics we do have are probably underestimates. perfectly accurat
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Answer:
The coordinates of EF are E(5,-4) and F(1,-4).
The line segment EF is in QIV
Step-by-step explanation:
The line segment AB has vertices at: A(-4,5) and B(-4,1).
We apply the rule to reflect AB in the y-axis to obtain CD.
We apply the rule to rotate CD 90 degrees clockwise about the origin to obtain EF.
The coordinates of EF are E(5,-4) and F(1,-4).
See attachment
We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.
Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).
Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.
<h3>Confidence Interval Formula</h3>The formula for constructing a <u>confidence interval for means</u> is as follows:
We are given these variables:
Plug these values into the formula for the confidence interval:
In order to find t*, we can use this formula:
Calculating the z-score associated with "A" will give us t*.
So, let's plug in the confidence interval 95% (.95) into the formula:
Use your calculator or a t-table to find the z-score associated with this area under the curve.. you should get:
Now, let's finish the confidence interval we created:
We can calculate the confidence interval, using this formula, to be:
We are 95% confident that the true population mean μ lies between <u>47.4697 and 52.5303</u>.
Answer:
Segment EF: y = -x + 8
Segment BC: y = -x + 2
Step-by-step explanation:
Given the two similar right triangles, ΔABC and ΔDEF, for which we must determine the slope-intercept form of the side of ΔDEF that is parallel to segment BC.
Upon observing the given diagram, we can infer the following corresponding sides:
We must determine the slope of segment BC from ΔABC, which corresponds to segment EF from ΔDEF.
<h2>Slope of Segment BC:</h2>In order to solve for the slope of segment BC, we can use the following slope formula:
Use the following coordinates from the given diagram:
Point B: (x₁, y₁) = (-2, 4)
Point C: (x₂, y₂) = ( 1, 1 )
Substitute these values into the slope formula:
Similar to how we determined the slope of segment BC, we will use the coordinates of points E and F from ΔDEF to find its slope:
Point E: (x₁, y₁) = (4, 4)
Point F: (x₂, y₂) = (6, 2)
Substitute these values into the slope formula:
Our calculations show that segment BC and EF have the same slope of -1. In geometry, we know that two nonvertical lines are <u>parallel</u> if and only if they have the same slope.
Since segments BC and EF have the same slope, then it means that .
The <u>y-intercept</u> is the point on the graph where it crosses the y-axis. Thus, it is the value of "y" when x = 0.
Using the slope of segment BC, m = -1, and the coordinates of point C, (1, 1), substitute these values into the <u>slope-intercept form</u> (y = mx + b) to solve for the y-intercept, <em>b. </em>
y = mx + b
1 = -1( 1 ) + b
1 = -1 + b
Add 1 to both sides to isolate b:
1 + 1 = -1 + 1 + b
2 = b
Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 2.
Therefore, the linear equation in <u>slope-intercept form of segment BC</u> is:
⇒ y = -x + 2.
<h3><u /></h3><h3><u>Segment EF:</u></h3>Using the slope of segment EF, <em>m</em> = -1, and the coordinates of point E, (4, 4), substitute these values into the <u>slope-intercept form</u> to solve for the y-intercept, <em>b. </em>
y = mx + b
4 = -1( 4 ) + b
4 = -4 + b
Add 4 to both sides to isolate b:
4 + 4 = -4 + 4 + b
8 = b
Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 8.
Therefore, the linear equation in <u>slope-intercept form of segment EF</u> is:
⇒ y = -x + 8.