Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Textbook Question
Chapter 8.2, Problem 12P
* If you multiply a number that has a remainder of 1 when it is divided by 3 with a number that has a remainder of 2 when it is divided by 3, then what is the remainder of the product when you divide it by 3? Investigate this question by working examples. Then explain why your answer is always correct.
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Question
Is the function f(x) shown in the graph below continuous at x = -5?
f(z)
7
6
5
4
2
1
0
-10
-6 -5
-4
1
0
2
3
5
7
10
-1
-2
-3
-4
-5
Select the correct answer below:
The function f(x) is continuous.
The right limit exists. Therefore, the function is continuous.
The left limit exists. Therefore, the function is continuous.
The function f(x) is discontinuous.
We cannot tell if the function is continuous or discontinuous.
Solve this question and check if my answer provided is correct
T1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an
independent set and m(G) = |E(G)|.
(i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The
neighborhood of a vertex in a triangle free graph must be independent; all edges have at least
one end in a vertex cover.
(ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you
may need to use either elementary calculus or the arithmetic-geometric mean inequality.
Chapter 8 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Ch. 8.1 - Johnny says that 3 is a multiple of 6 because you...Ch. 8.1 - Manuela is looking for all the factors of 90. So...Ch. 8.1 - Show how to find all the factors of the following...Ch. 8.1 - a. Write a word problem such that solving your...Ch. 8.1 - a. Write a problem about a realistic situation...Ch. 8.1 - Solve problems (a) and (b), and determine whether...Ch. 8.1 - a. If A and how are answer, B are counting numbers...Ch. 8.1 - * If A, B, and C are counting numbers and both A...Ch. 8.2 - Describe a way that the children in Mrs. Verner’s...Ch. 8.2 - Explain why an odd counting number can always be...
Ch. 8.2 - For each of the two designs in Figure 8.5, explain...Ch. 8.2 - Without determining the number of dots in the...Ch. 8.2 - If you add an even number and an even number, what...Ch. 8.2 - If you multiply an odd number and an odd number,...Ch. 8.2 - * If you multiply an even number by 3 and then add...Ch. 8.2 - * If you multiply an odd number by 3 and then add...Ch. 8.2 - * Suppose that the difference between two counting...Ch. 8.2 - * Suppose that the difference between two counting...Ch. 8.2 - * If you add a number that has a remainder of 1...Ch. 8.2 - * If you multiply a number that has a remainder of...Ch. 8.3 - Use the divisibility test for 3 to determine...Ch. 8.3 - According to the divisibility test for 10, to...Ch. 8.3 - According to the divisibility test for 5, to...Ch. 8.3 - Beth knows the divisibility test for 3. Beth says...Ch. 8.3 - What are all the different ways to choose the ones...Ch. 8.3 - Sam used his calculator to calculate...Ch. 8.3 - Explain how to modify the divisibility test for 3...Ch. 8.3 - For each of the numbers in (a) through (d), verify...Ch. 8.3 - a. Give a clear and complete explanation for why...Ch. 8.3 - a. Find a divisibility test for 25; in other...Ch. 8.3 - a. What are all the different ways to choose the...Ch. 8.3 - a. Find a divisibility test for 8. In other words,...Ch. 8.3 - a. Is it true that a whole number is divisible by...Ch. 8.3 - * Investigate the questions in the following parts...Ch. 8.3 - a. If you add 2 consecutive counting numbers (such...Ch. 8.4 - For which counting numbers, N, greater than 1, is...Ch. 8.4 - Use trial division to determine whether 251 is...Ch. 8.4 - For each of the numbers in (a) through (d),...Ch. 8.4 - Given that 792=23.32.11, find all the factors of...Ch. 8.4 - Without calculating the number 1923+1, explain why...Ch. 8.4 - Following Euclid’s proof that there are infinitely...Ch. 8.5 - Why do we not talk about a greatest common...Ch. 8.5 - Show how to use the definition of GCF to determine...Ch. 8.5 - Show how to use the definition of GCF to determine...Ch. 8.5 - Show how to use the definition of LCM to determine...Ch. 8.5 - Show how to use the definition of LCM to determine...Ch. 8.5 - Show how to use the slide method to determine the...Ch. 8.5 - Show how to use the slide method to determine the...Ch. 8.5 - Show how to use the slide method to determine the...Ch. 8.5 - Find the GCF and LCM of 25.32.5 and 23.34.7...Ch. 8.5 - Find the GCF and LCM of 34.52.75.11 and 37.53.73...Ch. 8.5 - Describe in general how to find the GCF and LCM of...Ch. 8.5 - Show all the details in the following...Ch. 8.5 - Show all the details in the following...Ch. 8.5 - Write a word problem that requires calculating the...Ch. 8.5 - Write a word problem that requires calculating the...Ch. 8.5 - Suppose you are teaching students about least...Ch. 8.5 - Kwan and Clevere are playing drums together,...Ch. 8.5 - At the zoo, the birds must be fed 12 cups of...Ch. 8.5 - There are periodical cicadas with 13-year life...Ch. 8.5 - In a clothing factory, a worker can sew 18 Garment...Ch. 8.5 - Keiko has a rectangular piece of fabric that is 48...Ch. 8.5 - A large gear will be used to turn a smaller gear....Ch. 8.5 - A large gear is used to turn a smaller gear. The...Ch. 8.6 - Use the standard division algorithm to determine...Ch. 8.6 - Use the standard division algorithm to determine...Ch. 8.6 - Use the standard division algorithm to determine...Ch. 8.6 - Write the following decimals as fractions. Explain...Ch. 8.6 - What is the 100th digit to the right of the...Ch. 8.6 - What is another way to write 1.824 as a decimal?...Ch. 8.6 - Without actually determining the decimal...Ch. 8.6 - Give an example of an irrational number, and...Ch. 8.6 - In your own words, prove that the square root of 5...Ch. 8.6 - Carl’s calculator displays only 10 digits. Carl...Ch. 8.6 - Fran has a calculator that shows at most 10...Ch. 8.6 - Tyrone used a calculator to solve a problem. The...Ch. 8.6 - * Show how to find the exact decimal...Ch. 8.6 - Prob. 14PCh. 8.6 - Prob. 15PCh. 8.6 - Prob. 16PCh. 8.6 - Prob. 17PCh. 8.6 - a. Use a calculator to calculate the decimal...Ch. 8.6 - a. Use a calculator to calculate the decimal...Ch. 8.6 - a. Suppose that a fraction AB where A and B are...
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