Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake starts filling it
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<h2>Answer</h2>
After the dilation around the center of dilation (2, -2), our triangle will have coordinates:
First, we are going to translate the center of dilation to the origin. Since the center of dilation is (2, -2) we need to move two units to the left (-2) and two units up (2) to get to the origin. Therefore, our first partial rule will be:
→
Next, we are going to perform our dilation, so we are going to multiply our resulting point by the dilation factor . Therefore our second partial rule will be:
→
→
Now, the only thing left to create our actual rule is going back from the origin to the original center of dilation, so we need to move two units to the right (2) and two units down (-2)
→
→
Now that we have our rule, we just need to apply it to each point of our triangle to perform the required dilation:
Now we can finally draw our triangle:
Assuming that each marble can be picked with equal probability, we notice that there is a total of
marbles, of which 2 are red.
So, the probability of picking a red marble is
In fact, as in any other case of (finite) equidistribution, we used the formula