At a raffle, 1000 tickets are sold at $5 each. There are 20 prizes of $25, 5 prizes of $100, and 1 grand prize of $2000. Suppose you buy one ticket. Let the random variable X represent your net gain (remember that the net gain should include the cost of the ticket) after playing the game once. 1. Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities. X (Net Gain) Probability 2. Find the expected value of X, and interpret it in the context of the game. 3. If you play in such a raffle 100 times, what is the expected net gain? 4. What ticket price (rounded to two decimal places) would make it a fair game?

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.

where's the diagram?

step-by-step explanation:

a

step-by-step explanation:

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.