Consider flipping a weighted coin with the property that the coin comes up heads with probability p and tails with probability 1 − p. suppose that you flip the coin repeatedly until it comes up tails. let x be the random variable for the number of flips completed. find e[x] and var(x). you may use wolfram alpha or another tool to compute the value of any infinite sums.

Julia chooses a card at random from her set of cards. what is the probability that the card is labeled cat or hamster?

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.

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