Evaluate the expression if r = 12 and t = -6. (t-r)/3
2 answers:
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See the attached image for the answers in figure 2 and figure 3. Figure 1 will be used to generate figure 2 and figure 3.
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Use the given table to compute the row and column totals. We simply add up values to get these totals.
Boys: 108+23 = 131 meaning that there are 131 boys total so this value will go in row 1 of the "total" column attached to the right side of the given table. See figure 1.
Girls: 99+16 = 115 will go right under 131.
Right-Handed: 108+99 = 207 will go under 99 in the "right handed" column in the "total" row.
Left-handed: 23+16 = 39 will go next to the 207 in the same total row as before
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We have the row and column totals computed. Now onto the next step.
Copy the entire table (with row and column totals) to another sheet of paper or just below the table you just wrote out. This new second table will be built upon and altered. First, erase the bottom "total" row. Now divide everything in row 1 by the total
108/131 = 0.82442748091603 which rounds to 0.82
23/131 = 0.17557251908397 which rounds to 0.18
So we'll have 0.82 and 0.18 fill in for the first row of the "Boys" row. See figure 2.
Do the same for the second row. Divide everything in this row by the total 115
99/115 = 0.8608695652174 which rounds to 0.86
16/115 = 0.1391304347826 which rounds to 0.14
The values 0.86 and 0.14 will go in the first two columns of row 2.
The totals will divide by each other to lead to 1
131/131 = 1
115/115 = 1
which explains why we have two '1's in the very right column. They represent 100%
Again, see figure 2 to see how the values are placed.
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We'll follow similar steps as before in the previous section. Copy the table from figure 1 but now erase the entire right-hand column marked "total".
Divide everything in column 1 by the total 207
108/207 = 0.52173913043479 which rounds to 0.52
99/207 = 0.47826086956521 which rounds to 0.48
207/207 = 1
Divide everything in column 2 by the total 39
23/39 = 0.58974358974359 which rounds to 0.59
16/39 = 0.41025641025641 which rounds to 0.41
39/39 = 1
See figure 3 to see how the values are filled in. The values in red are the results we got in this section. The '1's have already been filled in by your teacher.
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Side Note: In figure 2, the red values in the "Boys" row add up to 1
0.82+0.18 = 1
The same can be said for the "girls" row too
0.86+0.14 = 1
In figure 3, the red values in the "right handed column" add to 1
0.52+0.48 = 1
And similarly for the "left-handed" column
0.59+0.41 = 1
These four facts are not coincidences. For instance, 82% of the boys are right-handed so that leaves 18% left-handed boys (see row1 of figure 2). So 82% + 18% = 100% which is represented by 0.82+0.18 = 1
--------------------------------------------
Use the given table to compute the row and column totals. We simply add up values to get these totals.
Boys: 108+23 = 131 meaning that there are 131 boys total so this value will go in row 1 of the "total" column attached to the right side of the given table. See figure 1.
Girls: 99+16 = 115 will go right under 131.
Right-Handed: 108+99 = 207 will go under 99 in the "right handed" column in the "total" row.
Left-handed: 23+16 = 39 will go next to the 207 in the same total row as before
--------------------------------------------
We have the row and column totals computed. Now onto the next step.
Copy the entire table (with row and column totals) to another sheet of paper or just below the table you just wrote out. This new second table will be built upon and altered. First, erase the bottom "total" row. Now divide everything in row 1 by the total
108/131 = 0.82442748091603 which rounds to 0.82
23/131 = 0.17557251908397 which rounds to 0.18
So we'll have 0.82 and 0.18 fill in for the first row of the "Boys" row. See figure 2.
Do the same for the second row. Divide everything in this row by the total 115
99/115 = 0.8608695652174 which rounds to 0.86
16/115 = 0.1391304347826 which rounds to 0.14
The values 0.86 and 0.14 will go in the first two columns of row 2.
The totals will divide by each other to lead to 1
131/131 = 1
115/115 = 1
which explains why we have two '1's in the very right column. They represent 100%
Again, see figure 2 to see how the values are placed.
--------------------------------------------
We'll follow similar steps as before in the previous section. Copy the table from figure 1 but now erase the entire right-hand column marked "total".
Divide everything in column 1 by the total 207
108/207 = 0.52173913043479 which rounds to 0.52
99/207 = 0.47826086956521 which rounds to 0.48
207/207 = 1
Divide everything in column 2 by the total 39
23/39 = 0.58974358974359 which rounds to 0.59
16/39 = 0.41025641025641 which rounds to 0.41
39/39 = 1
See figure 3 to see how the values are filled in. The values in red are the results we got in this section. The '1's have already been filled in by your teacher.
--------------------------------------------
Side Note: In figure 2, the red values in the "Boys" row add up to 1
0.82+0.18 = 1
The same can be said for the "girls" row too
0.86+0.14 = 1
In figure 3, the red values in the "right handed column" add to 1
0.52+0.48 = 1
And similarly for the "left-handed" column
0.59+0.41 = 1
These four facts are not coincidences. For instance, 82% of the boys are right-handed so that leaves 18% left-handed boys (see row1 of figure 2). So 82% + 18% = 100% which is represented by 0.82+0.18 = 1
An easy way to do this is to parameterize the directed line segment from B to A by the function
with 0 ≤ t ≤ 1.
The point P₂ splits up AB so that BP₂ = 3/8 AB and AP₂ = 5/8 AB. Then we reach the point P₂ when t = 3/8, so its coordinates are