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what is the GCF of 20c^2 and 12y^3
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Basic Statistics Data Used In Everyday Life
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Discussion E: Hypothesis TestingWeek 9 Post (300+ Words): In hypothesis testing we set alpha, the significance level, which limits the likelihood of making a Type 1 error if the null hypothesis were true. When does a type 2 error occur? Give a real world example of a decision and explain what the null hypothesis, alternative hypothesis, type 1 and type 2 errors would be – which would be worse in this case: Choose two of your classmates’ posts. What could be done to lower the conditional probabilities of making the type 1 error and the type 2 error in their examples? Can both be lowered at the same time?
University of California Los Angeles Conditionally Convergent Exercises
2. Let xn =
n+1
n2+1 .
(a) Prove that (xn) is a decreasing sequence.
(b) Prove that P∞
n=1(−1)n+1xn is a converge ...
University of California Los Angeles Conditionally Convergent Exercises
2. Let xn =
n+1
n2+1 .
(a) Prove that (xn) is a decreasing sequence.
(b) Prove that P∞
n=1(−1)n+1xn is a convergent series.
(c) Find a constant c > 0 such that xn ≥
c
n
for all n ∈ N.
(d) Determine whether the series P∞
n=1(−1)n+1xn is absolutely or conditionally convergent. 3. Let P∞
n=1 xn and P∞
n=1 yn be convergent series. Show that:
(a) P∞
n=1(axn) = a
P∞
n=1 xn for any a ∈ R.
(b) Show that P∞
n=1(xn + yn) = P∞
n=1 xn +
P∞
n=1 yn.
These results are series analogues of the Algebraic limit theorem.
(c) Show that the assumption that both series converge is necessary for part (b).
(d) Is it true that P∞
n=1 xnyn =
P∞
n=1 xn
P∞
n=1 yn
6. Study the convergence of the following series:
(a) X∞
n=1
2
n
n2
(b) X∞
n=1
n
2
2
n
(c) X∞
n=1
(−1)n+1n
2 + 2
n2 + 1
(d) X∞
n=2
n
log n
(log n)
n
(e) X∞
n=1
√
n + 1 −
√
n
n
(f) X∞
n=1
(xn+1 − xn) for any sequence (xn)
Algebra Distributive Property Worksheet
Explain the distributive, inverse, and identity properties in simple language with no formalities.
Select two examples ...
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Explain the distributive, inverse, and identity properties in simple language with no formalities.
Select two examples for each property.
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3. Suppose that the volume of a box is (2p3 + 15p2 + 28p) cubic feet. The height is p feet and the length is (p + 4) feet. Explain the process to find an expression that represents the width. Based on answering this problem, create a new scenario for your classmates to complete.
4. Teach the class how to use the greatest common factor (GCF) to simplify a polynomial expression. Illustrate the concept with examples. Remember that teaching requires detailed explanation, as well as the actual math.
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Most Popular Content
4 pages
Basic Statistics Data Used In Everyday Life
Temperature is a continuous variable that determines the hotness and coldness of something. Its measurements can assume an ...
Basic Statistics Data Used In Everyday Life
Temperature is a continuous variable that determines the hotness and coldness of something. Its measurements can assume any value ranging from real ...
Stratford University Wk 9 Hypothesis Testing Discussion
Discussion E: Hypothesis TestingWeek 9 Post (300+ Words): In hypothesis testing we set alpha, the significance level, whi ...
Stratford University Wk 9 Hypothesis Testing Discussion
Discussion E: Hypothesis TestingWeek 9 Post (300+ Words): In hypothesis testing we set alpha, the significance level, which limits the likelihood of making a Type 1 error if the null hypothesis were true. When does a type 2 error occur? Give a real world example of a decision and explain what the null hypothesis, alternative hypothesis, type 1 and type 2 errors would be – which would be worse in this case: Choose two of your classmates’ posts. What could be done to lower the conditional probabilities of making the type 1 error and the type 2 error in their examples? Can both be lowered at the same time?
University of California Los Angeles Conditionally Convergent Exercises
2. Let xn =
n+1
n2+1 .
(a) Prove that (xn) is a decreasing sequence.
(b) Prove that P∞
n=1(−1)n+1xn is a converge ...
University of California Los Angeles Conditionally Convergent Exercises
2. Let xn =
n+1
n2+1 .
(a) Prove that (xn) is a decreasing sequence.
(b) Prove that P∞
n=1(−1)n+1xn is a convergent series.
(c) Find a constant c > 0 such that xn ≥
c
n
for all n ∈ N.
(d) Determine whether the series P∞
n=1(−1)n+1xn is absolutely or conditionally convergent. 3. Let P∞
n=1 xn and P∞
n=1 yn be convergent series. Show that:
(a) P∞
n=1(axn) = a
P∞
n=1 xn for any a ∈ R.
(b) Show that P∞
n=1(xn + yn) = P∞
n=1 xn +
P∞
n=1 yn.
These results are series analogues of the Algebraic limit theorem.
(c) Show that the assumption that both series converge is necessary for part (b).
(d) Is it true that P∞
n=1 xnyn =
P∞
n=1 xn
P∞
n=1 yn
6. Study the convergence of the following series:
(a) X∞
n=1
2
n
n2
(b) X∞
n=1
n
2
2
n
(c) X∞
n=1
(−1)n+1n
2 + 2
n2 + 1
(d) X∞
n=2
n
log n
(log n)
n
(e) X∞
n=1
√
n + 1 −
√
n
n
(f) X∞
n=1
(xn+1 − xn) for any sequence (xn)
Algebra Distributive Property Worksheet
Explain the distributive, inverse, and identity properties in simple language with no formalities.
Select two examples ...
Algebra Distributive Property Worksheet
Explain the distributive, inverse, and identity properties in simple language with no formalities.
Select two examples for each property.
Explain how each example fits each property.
2. Create your own linear scenario and problem. Have at least two parts to your problem for your classmates to solve. Make sure you know the answer to your own problem!
Here is an example of a linear scenario and problem: A new car costs $21,000, and the car’s value depreciates linearly to $10,500 in three years. Explain the process to write a formula that expresses the car’s value, V, in terms of its age, t, in years. What is the car’s value in 5 years? At what point is the formula useless? Explain. (Do NOT use this example as your linear scenario and problem.)
3. Suppose that the volume of a box is (2p3 + 15p2 + 28p) cubic feet. The height is p feet and the length is (p + 4) feet. Explain the process to find an expression that represents the width. Based on answering this problem, create a new scenario for your classmates to complete.
4. Teach the class how to use the greatest common factor (GCF) to simplify a polynomial expression. Illustrate the concept with examples. Remember that teaching requires detailed explanation, as well as the actual math.
5. Teach your classmates the process to find the domain of a rational function. Illustrate the concept with two examples, one of which requires factoring. Please include both set notation and interval notation as part of your teaching. Remember that teaching requires detailed explanation, as well as the actual math.
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