In a group of 100 people, 27 speak German, 30 speak Mandarin, 40 speak Spanish, 3 speak all three languages. 12 speak only German, 15 speak only Mandarin and 8 speak Spanish and Mandarin but not German.
a.) Draw a Venn diagram showing this information, and fill in the missing regions.
b.) Find the probability that a randomly selected person speaks only Spanish.
c.) Given that a person speaks Spanish, find the probability that they also speak Mandarin.

What is the reflection image of (5,-3) across the line y = -x?

Clara schumann is buying bagels for her coworkers, she buys a dozen bagels priced at $5.49 a dozen. the bakery's cost for making the bagels is $2.25 per dozen. what is the markup rate based on selling price on a dozen bagels?

You were told that the amount of time lapsed between consecutive trades on the new york stock exchange followed a normal distribution with a mean of 15 seconds. you were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. the probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. what is the probability that the time lapsed between two consecutive trades will be between 14 and 15 seconds?