Answer the following questions. be sure to include your bar model, calculations and final answer in your submissions.
#1 there were an equal number of boys and girls in a school auditorium. after 24 boys left the auditorium, there were 3 times as many girls as boys. how many children were there in the beginning?
#2 sarah spent 4/9 of her paycheck on food, 1/3 of her remaining money on rent, $180 on shopping, $270 on clothing, and saved the remaining $50. what fraction of her paycheck did she save?
#3 meera paid $240 for 4 pairs of shoes and 4 pairs of shorts. each pair of shoes cost 4 times as much as a pair of shorts. find the difference in price between a pair of shoes and a pair of shorts.
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What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)

Find the cube roots of 8i. write the answer in a + bi

You are in a room of 22 people (including yourself). each of you has their own deck of 52 cards — assume each deck is well-shuffled, and can be assumed to be fair and independent of each other.1. each you draws the top card of your deck.what is the probability that at least one other person has drawn the same card as you? 2. let x be the number of people who drew a card that was also drawn by at least one other person. for example, if you all drew the same card, x=22, but if you all drew different cards, x=0. what is the expected value of x? 3. consider the same situation as the last question, but this time with 29 people: all 29 of you are in a room with your own decks of cards, and you draw one of them.what is the probability that at least one person draws the ace of spades? 4. let x be the number of the types of card drawn. for example, if everyone draws the same card, x=1, but if everyone draws a different card, x=29. what is the expected value of x?