7. (ASV, Exercise 2.20 ) - 3 points. A fair die is rolled repeatedly. Use precise notation of probabilities of events and random variables for the solutions to the questions below. (a) Write down a precise sum expression for the probability that the first five rolls give a three at most two times. (b) Calculate the probability that the first three does not appear before the fifth roll. (c) Calculate the probability that the first three appears before the twentieth roll but not before the fifth roll.

The decibel level of sound is 50 db greater on a busy street than in a quiet room where the intensity of sound is watt/m2. the level of sound in the quiet room is db, and the intensity of sound in the busy street is watt/m2. use the formula , where is the sound level in decibels, i is the intensity of sound, and is the smallest sound intensity that can be heard by the human ear (roughly equal to watts/m2).

Evaluate 8j -k+148j−k+14 when j=0.25j=0.25 and k=1k=1.

Urgent! 20 points! here is a you are the new manager at trusty goods wholesale produce. you need to figure out how to adjust the amount of produce in your notes after the events of the day: you got 5 more crates of bananas someone returned 2 crates of apples a worker dropped a crate of grapes (oh no! , you had to throw them out) you sold a crate of bananas you sold 5 crates of apples can you write an expression to describe your day using: "a" for crates of apples "b" for crates of bananas and "g" for crates of grapes? make sure the expression is in simplest form question 2 (3 points) explain your steps using sentences.