There are about 70 math questions, Highschool level.
Jungshik Shin F2021UPG101-093 Asgt 10 is due on Monday, December 06, 2021 at 11:59pm. The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your error, you should consult the textbook, or ask a fellow student, one of the TA’s or your professor for help. There are also other resources at your disposal, such as the Mathematics Continuous Tutorials. Don’t spend a lot of time guessing – it’s not very efficient or effective. Make sure to give lots of significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2, (2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Problem 1. (1 point) a. Evaluate the following: 6P3 = . P(8,4) = . b. Find A and B so that 38!8! = P(A,B). A = and B = . Answer(s) submitted: • • • • (incorrect) Problem 2. (1 point) Ryan has 7 Pokemon figures arranged on his shelf. a. How many different arrangements can he make? He can make arrangements. b. How many different arrangements can he make if he can only fit 6 of the figures? He can make arrangments. Answer(s) submitted: • • (incorrect) Problem 3. (1 point) For this problem, you can receive partial credit for successfully completing any of the answer boxes OR you can leave the first three answer sets answers blank and receive full credit for only completing the final answer. Consider the word CAT NIP. We can define a ”word” to be any arrangement of letters, regard- less if they form an actual English word. We can only use each letter up to as many times they occur in CAT NIP. a) How many different words can be made from re-arranging all of the letters? . b) How many different 4-letter words can be formed? . c) How many different 5-letter words can be made if C is the last letter? . For Full Credit d) How many different 5-letter words can be made if the last letter is either C or N? . Answer(s) submitted: • • • • (incorrect) 1 Problem 4. (1 point) Solve the following equation for n where defined: P(n,2) = 272. n = . Answer(s) submitted: • (incorrect) Problem 5. (1 point) List all “words” that can be formed using all of the letters of TART (including TART itself). Express your answer as a comma-separated list (I recommend al- phatizing it!). Answer(s) submitted: • (incorrect) Problem 6. (1 point) For this problem, you can receive partial credit for successfully completing any of the answer boxes OR you can leave the first two answers blank and receive full credit for only completing the final answer. Find how many ”words” can be made by rearranging all letters of the following: a) OCEAN has words. b) COLLAR has words. For Full Credit c) PRECIPITAT ION has words. Answer(s) submitted: • • • (incorrect) Problem 7. (1 point) a. Evaluate the following: 7C3 = . C(10,4) = .(15 13 ) = . b. Find A and B so that (A B ) = 23×24×···×45×461×2×···23×24 . A = and B = or . (Hint: to get the second answer for B, use some cancella- tion!). Answer(s) submitted: • • • • • • (incorrect) 2 Problem 8. (1 point) For this problem, you can receive partial credit for successfully completing any of the answer boxes OR you can leave the first six answers blank and receive full credit for only completing the final answer. George is planning to spend his day at home watching videos and eating dinner. He has 6 videos to choose from and enough time to watch exactly 3 of them. He can arrange his video-watching in ways. For dinner, George is going to make a casserole by blending all sorts of things together. He has 10 ingredients and will throw 4 of them together for his dish. There are possibilities for his casserole. There are ways that George could live his life on this day. Now, suppose that George’s friend Leonard invites him to attend an all-day Planet-of-the-Apes marathon where he’ll be ordering pizza. There are 5 Planet-of-the-Apes movies and they will choose to watch 4 of them (in the correct order, so we cannot ”re-arrange” them). There are ways they can choose their movies together. They will order a pizza with 6 different toppings from a selection of 9 toppings in total. There are different pizzas they could order. If George goes to Leonard’s, there are different ways that George could live his life today. For Full Credit Given his options, there are ways that George could live his life today. Answer(s) submitted: • • • • • • • (incorrect) Problem 9. (1 point) You have a collection of 11 balls (numbered 1 to 11). a. How many ways can you line up 5 of the balls in row? ways. b. How many ways can you pick 5 of the balls to bring to the beach? ways. c. How many ways can you pick 5 of the balls so that the set contains the 2 ball? ways. d. How many ways can you line up 5 of the balls so that your arrangement includes the 2 ball? ways. Answer(s) submitted: • • • • (incorrect) 3 Problem 10. (1 point) 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 For this problem, you can receive partial credit for successfully completing any of the answer boxes OR you can leave the first two answers blank and receive full credit for only completing the final answer. Recall Pascal’s Triangle, illustrated above. The top row of just 0 is called the 0th row and the left-most entry in each row is called the 0th entry. So, it is drawn to the 4th row above. By either drawing more rows of the triangle or using a convenient formula, find the following: a) The 5th entry of the 7th row: . b) The 5th entry of the 9th row: . For Full Credit c) The 14th entry of the 30th row: . Answer(s) submitted: • • • (incorrect) Problem 11. (1 point) You will only receive credit for completing the final answer; how- ever, you can fill in the other boxes to help you identify any mis- takes along the way. Find the number of paths from A to B. In the first row (across the top) we will have the values: 1 at the point A, , , , , . In the second row we have: , , , , , In the third row we have: , , , , , In the fourth row we have: , , , , , Finally, in the fifth row we have: , , , , , For full credit. There are paths from A to B. Answer(s) submitted: • • • • • • • • • • • • • 4 • • • • • • • • • • • • • • • • • (incorrect) Problem 12. (1 point) Expand and simplify (3x5−2y4)4. Answer: Answer(s) submitted: • (incorrect) Problem 13. (1 point) In the expansion of (2x6 +3)6, find the coefficient of the x24 term. The term is ·x24. Answer(s) submitted: • (incorrect) Generated by c©WeBWorK, http://webwork.maa.org, Mathematical Association of America 5