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An identification tag on a school library book consists of two digits in a row (each can be any digit from 0 to 9) followed by two different letters from the set {a, b, w, x, y, z} followed by two more digits that must be different from each other. How many different identification tags can be made? (Type your answer with no commas.)

35 students were asked whether they like Valentine’s Day and whether they like chocolate. 18 students said they like Valentine’s Day, 15 students said they like chocolate, and 8 students don’t like either. How many students said they like both Valentine’s Day and chocolate?

Suppose there is a universal set U where  {x: x is an integer and 

A set X with  is partitioned into three subsets, and . If the number of elements in is twice the number of elements in , and the number of elements in is three times the number of elements in , find the number of elements in each of these subsets of X. (Type in a numerical answer for each) : The number in [X1] = : The number in [X2] = : The number in [X3] =  

Three letters from the set will be arranged in order to make a product code. If letters may be repeated in these codes, then how many codes are possible in which the letter “t” appears exactly once?

An experiment consists of flipping a coin and noting whether the result is a head or a tail. If it is heads, then the coin is flipped three more times and the number of heads in these three flips is noted. If the result of the first flip is a tail, then the coin is flipped one more time and the result (H or T) is noted. Which of the following elements are not in the sample space of the experiment? (select all that apply)

Epicurus distinguishes between different kinds of desires: natural and necessary, natural but not necessary, and neither natural nor necessary (vain/empty). Why does this classification matter for how he thinks we should live? Can you generate a few examples of your own for each category?

Conjugate the verb in parenthesis in the preterit tense for the indicated subject. La bolsa (costar) $28

Fill in the blank with a demonstrative adjective that corresponds to the information given. (That) cinturón de piel (leather) cuesta mucho dinero.

¿Qué ropa usa un turista en la playa? ¿Por qué?