For this type of problem, it is best to use Venn diagrams as shown in the picture. The areas where the circles intersect are the mutual events that occur together. The area where all circles intersect is denoted as x. These are the students who play all sports. Assuming all of the students play sports in the school, all of the numbers in the circles should add up to 405. The remaining area would be the difference. The solution is as follows:
Students who play tennis and hockey: 45 - x
Students who play hockey and softball: 60 - x
Students who play only tennis and softball: 39 - x
Students who only play tennis:
251 - 45 + x - 39 +x -x = x + 167
Students who only play hockey:
157 - x - 45 + x - 60 + x = x + 52
Students who only play softball:
111 - x - 60 + x - 39 + x = x + 12
The sum of all of these should be 405:
45-x+60-x+39-x+x+167+x+52+x+12 = 405
Solving for x,
x = 30
Therefore, there are 30 pupils who play all sports; 15 pupils who play tennis and hockey; 30 pupils who play hockey and softball; 9 pupils who play tennis and softball; 197 pupil who only play tennis; 82 pupils who only play hockey; and 42 pupils who only play softball.
The answers of the product is 1.8 * 0.63 = 1.134
Financial Market, as it’s to do with them getting the money.
write it how would you respect to x or respect to y
Answer:
(a) Horizontal line test
Step-by-step explanation:
A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.
<h3>Inverse relation</h3>
The inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.
<h3>Inverse function</h3>
If the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to <em>pass</em>.
A function will have an inverse function if it passes the Horizontal Line Test.
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<em>Additional comment</em>
The attached graph shows a function (red curve) that <em>does not pass the horizontal line test</em>. Its inverse relation is the green curve, which you can see is <em>not a function</em>. It does not pass the vertical line test.
The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.