webcalcman

Are you familiar with the distance formula? \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

You can plug in \(x_2\) as 22 and \(x_1\) as \(x\), and the corresponding values for y (15 or -29 and y) and make three equations

(for context, (x, y) is the center of the circle). Then, you solve the system!

If you have any questions, please contact!

-webcalcman

If we add all three of these expressions together, and find either p or q in terms of the other variable, we can substitute that for each of the angles A, B, and C. Then we can add it up and now it is a single variable equation equal to 180 which should be easy to solve. If you have any questions, just ask.

First, you must bring variables to one side and constants to one side, this makes 2/3m + 14 = 0 the same as 2/3m = -14, then we must divide 2/3m by 2/3 to isolate m, but what we do to one side, we must do to the other, dividing by a fraction is also multiplying by its reciprocal which means 2/3m (3/2) = -14(3/2) which gives us m = -14(3/2), can you solve the rest? If you need any hep, just ask :)

1. This means that the triangle is right and AB and BC are perpendicular, so use the formula 1/2 * b * h to get 1/2 * 6 * 8 = 3 * 8 = 24

2. The three angles of a triangle add up to 180, if we add 135 and 30 we get 165, and if we subtract that from 180 we get an answer of 15 degrees.

If we set up an equation where x is the amount of gallons that the tank can hold, then 1/6x + 2 = 1/2x. Try solving from there, if you need anything, just ask :)

I guess you could just use long division. You could also say that 1/8 is 0.125 so you could multiply 0.125 times 3. If you have any questions, just ask :)

(a): there is a 8/10 probability of pulling a 3 and a 2/10 probability of pulling a 5 so the expected value is \(\frac{8}{10}(3) + \frac{2}{10}(5)\) Expected value for drawing one slip of paper, this is equal to 3.4 or 34/10 or 17/5

(b): well, this would be the exact same idea except the probabilities are different, now the expected value is \(\frac{9}{11}(3) + \frac{2}{11}(5)\) which simplifies to 37/11

(c): Once again, same idea, the expected value would be \(\frac{10}{12}(3) + \frac{2}{12}(5)\) which simplifies to 10/3

If you have any questions, just ask :)

I know, that this answer is a little late, so it may not help if this question was time sensitive, however, I hope this helps. For the product of the rolls to be one, we would need both rolls to be 1 which has a 1/6 * 1/6 = 1/36 probability of occuring, to have a product of 2, we would need a 1 and a 2 on the die rolls, which has a probability of 1/6 * 1/6 = 1/36 and for 3 we would need a 1 and a 3 which has a probability of 1/6 * 1/6 = 1/36. 1/36 + 1/36 + 1/36 = 3/36 = 1/12! If you have any questions, just ask :)

If this was a larger problem, I would have another method, however since this is a smaller variation of this question, you could just check all of the points on the coordinate grid that franklin could be once he takes his step. Also, I'm 90% sure that this is a repost of another problem, if you have any questions, just ask :)