Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Chapter 8.5, Problem 13P
Show all the details in the following calculations:
a. Add
b. Add
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#7 Using implicit differentiation, find the equation of the tangent line to the given curve at the given point:
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An investigator analyzed the leading digits from 797 checks issued by seven suspect companies. The frequencies were found to be 0, 19, 2, 50, 361, 309, 10, 22, and 24, and those digits correspond to the
leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result
from fraud. Use a 0.10 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud?
Leading Digit
Actual Frequency
Benford's Law: Distribution of Leading Digits
1
2
3
4
5
6
7
8
9
0
19
2
50
361
309
10
22
24
30.1%
17.6%
12.5%
9.7%
7.9%
6.7%
5.8%
5.1%
4.6%
Determine the null and alternative hypotheses.
Ho The leading digits are from a population that conforms to Benford's law.
H₁: At least one leading digit has a frequency that does not conform to Benford's law.
Calculate the test statistic, x².
x²
=
(Round to three…
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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- Q3: Define the linear functional J: H₁(2) R by ¡(v) = a(v, v) - L(v) Л Let u be the unique weak solution to a(u,v) = L(v) in H(2) and suppose that a(...) is a symmetric bilinear form on H(2) prove that 1- u is minimizer. 2- u is unique. 3- The minimizer J(u) can be rewritten under 1(u) = u Au-ub, algebraic form 1 2 Where A, b are repictively the stiffence matrix and the load vector Q4: A) Answer 1- show that the solution to -Au = f in A, u = 0 on a satisfies the stability Vullfll and show that ||V(u u)||||||2 - ||vu||2 2- Prove that Where lu-ul Chuz - !ull = a(u, u) = Vu. Vu dx + fu. uds B) Consider the bilinea forta Л a(u, v) = (Au, Av) (Vu, Vv + (Vu, v) + (u,v) Show that a(u, v) continues and V- elliptic on H(2)arrow_forward2. Classify the Stability of Fixed Points in a Dynamical System The dynamical system problem is located on page 60 of the file. Identify the fixed points and classify their stability using linearization and eigenvalues. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide a detailed explanation of your analysis.arrow_forwardEvaluate the Z-Transform of the Sequence The Z-transform problem is provided on page 70. Compute the Z-transform of the given sequence and determine the region of convergence. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show all steps and provide detailed reasoning.arrow_forward
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