34) Ź (K²-2K) is e (n3) n-2 K+z と3 とー n-2 ヒー」 K²+ 2K ニ n-2 n-2 ニ ヒー」 n(n+)/2n+1) 2n(nti) 5O BU Theore
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1To prove a theorem of the form "If P, then Q" by the indirect method, the first line of the proof should read: Suppose that ___________ is true.Here's a problem that was used as the basis of a television show to illustrate the difference between the way a human mind approaches such a problem and the brute-force approach of a computer that finds the solution by trying all possible 40,320 different arrangements of the digits. Place the digits from 1 though 8 in the eight circles shown in the diagram, but with this restriction: no two digits next to each other in serial order may go in circles that are connected by a direct line. (For example: if 2 is placed in the top circle, neither 1 nor 3 may be placed in any of the three circles in the horizontal row beneath it because each of these circles is connected to the top circle by a direct line.) There is only one solution.
- I. Determine if solving the problem needs permutation or combination.Then, show the working equation. 7. There are four balls of different colors. Two balls are taken at a time. In howmany ways can you do it?8. A certain company will hire 7 men and 4 women. In how many ways can thecompany choose from 9 men and 6 women who qualified for the position?9. In how many ways can you form a four-letter word that can have repeatingconsonant but not vowel?A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second day, he finished 1/n of the job left. On the third day, he finished 1/m of the job left, and on the fourth day,1/n of the job left. On the last day,1/4 of the job was left to be done. If m,n belongs to N and n>m, find m and n.In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, htere is an 8% propability that a nonsmoker will begin smoking a pack or less per day, and a 4% probablility that a nonsmoker will begin smoking more than one pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is an 8% probablity of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in a year? (Round your answers to the nearest whole number.) (a) i) in 1 month; ii) nonsmokers. (. )people iii) 1 pack/day or less (. )people more than 1 pack/day. (. )people (b) i) in 2 months ii) nonsmokers. (. )people iii) 1…
- How would you prove #14 and #15 using either postulate SSS or SAS? And can a problem be proven by both or just one?Suppose you always eat a particular brand of cookes out of the standart sized package, it comes in from the store, which has 4 rows of cookies in equal amounts. You notice that when you eat 3 at a time, there's always one cookie left over. You decide when you purchase the next package, you'll eat 5 at a time, but still, there's always one cookie left over. Since it really is'nt helpfull to always have a leftover cookie, you decide to eat 7 at a time, and there are no cookies leftover, but you notice that in your last grab of 7 cookies, you're one cookie short. A. If you know there are less tha 100 cookies in the package, how many cookies are there? Solve the problem, showing each step of your work, and explain your thinking. B. You decide to space out your cookie eating, and eat one cookie a day, how many weeks will one package of cookies last? C. If you eat 2 cookies a day, how many days will one package of cookies last?Suppose you always eat a particular brand of cookes out of the standart sized package, it comes in from the store, which has 4 rows of cookies in equal amounts. You notice that when you eat 3 at a time, there's always one cookie left over. You decide when you purchase the next package, you'll eat 5 at a time, but still, there's always one cookie left over. Since it really is'nt helpfull to always have a leftover cookie, you decide to eat 7 at a time, and there are no cookies leftover, but you notice that in your last grab of 7 cookies, you're one cookie short. C. If you eat 2 cookies a day, how many days will one package of cookies last?
