Of the 42 students in a certain Spring 2010 Math 147 class, 19 passed both the mid-term and the final examinations. A total of 25 students passed the mid-term examination and a total of 30 students passed the final exam.

(a) Represent this information on a Venn diagram. (Take the set of the 52 students to be the universal set.)

(b) How many students failed both examinations?

You are designing a rectangular pet pen for your new baby puppy. you have 30 feet of fencing you would like the fencing to be 6 1/3 feet longer than the width

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?

Aright triangle has an area of 21 m2. the dimensions of the triangle are increased by a scale factor of 4. what is the area of the new triangle