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8. (i) How many positive integers not exceeding 200 that are divisible by 3 or 5...
Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7
Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. (b) have distinct digits. (c) are not divisible by either 5 or 7.
an urn contains 12 red How many positive integers between 100 and 500 inclusive, a. are...
an urn contains 12 red
How many positive integers between 100 and 500 inclusive, a. are divisible by 7? b. are odd? c. have the same three decimal digits? (e.g. 333) d. have distinct digits? (e.g. 123, 234, etc.) How many bit strings of length 8 contain a. exactly three 1s? b. at most three 1s? c. at least three 1s? d. an equal number of Os and 1s?
3. Consecutive Sums a. (4 pts) Write 90 as the sum of consecutive positive integers in as many wa...
3. Consecutive Sums a. (4 pts) Write 90 as the sum of consecutive positive integers in as many ways as possible. b. (4 pts) If a number can be written as n (d)(t) where d is an odd number of the form 2k + 1 and d is greater than 1, show symbolically how n can be written as the sum of consecutive numbers. Illustrate this with one example from part a. c. (4 pts) State a conjecture identifying the...
i need a help pleassssse? 5. What is the probability that the sum of the numbers...
i need a help pleassssse?
5. What is the probability that the sum of the numbers on two dice is even when they are rolled? 6. What is the probability that a card selected at random from a standard deck of 52 cards is an ace or a heart? What is the probability that a positive integer not exceed- 100 selected at random is divisible by 5 or 7? nd the probability of winning a lottery by selecting the t...
4. (0) If there are 100 students are in a class room how many of them...
4. (0) If there are 100 students are in a class room how many of them must have their birthday in the same month? (ii) A college teaches 7 different courses. Students from the college are to be randomly selected for a college survey. How many students must be selected to ensure there are at least 5 students from one of the courses?
3. (5 pts) There are currently 100 freshman mathematics majors at Truman State University. It is...
3. (5 pts) There are currently 100 freshman mathematics majors at Truman State University. It is known that 80 are enrolled in the Calculus sequence, 30 are enrolled in Foundations of Mathematics, and 40 are enrolled in Physics. There are 35 who are enrolled in both Calculus and Physics, 20 who are enrolled in both Calculus and Foundations, and 5 who are enrolled in both Foundations and Physics. Only 2 badly-advised students are enrolled in all three of Calculus, Foundations...
discrete mathematics a. 25 identical glass orbs are to be partitioned into 5 groups. How many...
discrete mathematics
a. 25 identical glass orbs are to be partitioned into 5 groups. How many ways are there to do this? b. The orbs are to be partitioned such that each group gets at least one orb. How many ways are there to this? 6 of the orbs are given to the 1 group. How many ways are there to partition the remaining orbs such that the first group has at least the 6 from the beginning of this...
discrete mathematics a. 25 identical glass orbs are to be partitioned into 5 groups. How many ways are there to do t...
discrete mathematics
a. 25 identical glass orbs are to be partitioned into 5 groups. How many ways are there to do this? b. The orbs are to be partitioned such that each group gets at least one orb. How many ways are there to this? 6 of the orbs are given to the 1 group. How many ways are there to partition the remaining orbs such that the first group has at least the 6 from the beginning of this...
*these questions are related to Matlab The number 24 is exactly divisible by eight numbers (i.e. 1, 2, 3, 4, 6, 8, 12 and 24). The number 273 is also exactly divisible by eight numbers (i....
*these questions are related to Matlab
The number 24 is exactly divisible by eight numbers (i.e. 1, 2, 3, 4, 6, 8, 12 and 24). The number 273 is also exactly divisible by eight numbers (i.e. 1, 3, 7, 13,21, 39, 91 and 273) There are 10 numbers in the range of 1:100 that are exactly divisible by eight numbers (i.e. 24, 30, 40, 42, 54, 56, 66, 70, 78 and 88). How many numbers in the range of n-1:20000...
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using t...
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using the inclusion-exclusion principle 3. For the purpose of this problem, a word is an ordered string of 5 lowercase letters from the English alphabet (i.e., the 26 letters from a to z). For example, "alpha" and "zfaxr" are words. A subword of a word is an ordered string that appears as consecutive letters anywhere within the given word. For example, "cat" is...
an urn contains 12 red
How many positive integers between 100 and 500 inclusive, a. are divisible by 7? b. are odd? c. have the same three decimal digits? (e.g. 333) d. have distinct digits? (e.g. 123, 234, etc.) How many bit strings of length 8 contain a. exactly three 1s? b. at most three 1s? c. at least three 1s? d. an equal number of Os and 1s?
3. Consecutive Sums a. (4 pts) Write 90 as the sum of consecutive positive integers in as many ways as possible. b. (4 pts) If a number can be written as n (d)(t) where d is an odd number of the form 2k + 1 and d is greater than 1, show symbolically how n can be written as the sum of consecutive numbers. Illustrate this with one example from part a. c. (4 pts) State a conjecture identifying the...
i need a help pleassssse?
5. What is the probability that the sum of the numbers on two dice is even when they are rolled? 6. What is the probability that a card selected at random from a standard deck of 52 cards is an ace or a heart? What is the probability that a positive integer not exceed- 100 selected at random is divisible by 5 or 7? nd the probability of winning a lottery by selecting the t...
4. (0) If there are 100 students are in a class room how many of them must have their birthday in the same month? (ii) A college teaches 7 different courses. Students from the college are to be randomly selected for a college survey. How many students must be selected to ensure there are at least 5 students from one of the courses?
3. (5 pts) There are currently 100 freshman mathematics majors at Truman State University. It is known that 80 are enrolled in the Calculus sequence, 30 are enrolled in Foundations of Mathematics, and 40 are enrolled in Physics. There are 35 who are enrolled in both Calculus and Physics, 20 who are enrolled in both Calculus and Foundations, and 5 who are enrolled in both Foundations and Physics. Only 2 badly-advised students are enrolled in all three of Calculus, Foundations...
discrete mathematics
a. 25 identical glass orbs are to be partitioned into 5 groups. How many ways are there to do this? b. The orbs are to be partitioned such that each group gets at least one orb. How many ways are there to this? 6 of the orbs are given to the 1 group. How many ways are there to partition the remaining orbs such that the first group has at least the 6 from the beginning of this...
discrete mathematics
a. 25 identical glass orbs are to be partitioned into 5 groups. How many ways are there to do this? b. The orbs are to be partitioned such that each group gets at least one orb. How many ways are there to this? 6 of the orbs are given to the 1 group. How many ways are there to partition the remaining orbs such that the first group has at least the 6 from the beginning of this...
*these questions are related to Matlab
The number 24 is exactly divisible by eight numbers (i.e. 1, 2, 3, 4, 6, 8, 12 and 24). The number 273 is also exactly divisible by eight numbers (i.e. 1, 3, 7, 13,21, 39, 91 and 273) There are 10 numbers in the range of 1:100 that are exactly divisible by eight numbers (i.e. 24, 30, 40, 42, 54, 56, 66, 70, 78 and 88). How many numbers in the range of n-1:20000...
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using the inclusion-exclusion principle 3. For the purpose of this problem, a word is an ordered string of 5 lowercase letters from the English alphabet (i.e., the 26 letters from a to z). For example, "alpha" and "zfaxr" are words. A subword of a word is an ordered string that appears as consecutive letters anywhere within the given word. For example, "cat" is...
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