(a) To indicate: The elements in the given set S = { n ∈ Z | n = ( − 1 ) k , for some integer k } by using set-roster notation.

Question

Match the division problem on the left with the correct quotient on the left. Note that the denominators of the reminders are omitted and replaced with R. 1) (k3-10k²+k+1) ÷ (k − 1) 2) (k4-4k-28k45k+26)+(k+7) 3) (20k+222-7k+7)+(5k-2) 4) (3+63-15k +32k-25)+(k+4) 5) (317k 13) ÷ (k+4) - 6) (k-k+8k+5)+(k+1) 7) (4-12k+6) + (k-3) 8) (3k+4k3 + 15k + 10) ÷ (3k+4) A) 3k3-6k29k - 4 B) 4k2 + 6 R 7 C)²-9k-8- R D) 4k2+6x+1+ E) 10 Elk³-5-12 R 9 F) k² - 4k R 9 R G) k3-3k2-7k+4 H) k³-k²+8 - 3 R - R 9 R

Answer 1

Question

Chapter 1.2, Problem 7ES

To determine

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

To determine

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

To determine

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

To determine

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

To determine

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

To determine

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

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Match the division problem on the left with the correct quotient on the left. Note that the denominators of the reminders are omitted and replaced with R. 1) (k3-10k²+k+1) ÷ (k − 1) 2) (k4-4k-28k45k+26)+(k+7) 3) (20k+222-7k+7)+(5k-2) 4) (3+63-15k +32k-25)+(k+4) 5) (317k 13) ÷ (k+4) - 6) (k-k+8k+5)+(k+1) 7) (4-12k+6) + (k-3) 8) (3k+4k3 + 15k + 10) ÷ (3k+4) A) 3k3-6k29k - 4 B) 4k2 + 6 R 7 C)²-9k-8- R D) 4k2+6x+1+ E) 10 Elk³-5-12 R 9 F) k² - 4k R 9 R G) k3-3k2-7k+4 H) k³-k²+8 - 3 R - R 9 R

1. Determine whether the following sets are subspaces of $\mathbb{R}^3$ under the operations of addition and scalar multiplication defined on $\mathbb{R}^3$. Justify your answers.(a) $W_1=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=3 a_2\right.$ and $\left.a_3=\mid a_2\right\}$(b) $W_2=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=a_3+2\right\}$(c) $W_3=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 2 a_1-7 a_2+a_3=0\right\}$(d) $W_4=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1-4 a_2-a_3=0\right\}$(e) $W_s=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1+2 a_2-3 a_3=1\right\}$(f) $W_6=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 5 a_1^2-3 a_2^2+6 a_3^2=0\right\}$

The annual aggregate claim amount of an insurer follows a compound Poisson distribution with parameter 1,000. Individual claim amounts follow a Gamma distribution with shape parameter a = 750 and rate parameter λ = 0.25. 1. Generate 20,000 simulated aggregate claim values for the insurer, using a random number generator seed of 955.Display the first five simulated claim values in your answer script using the R function head(). 2. Plot the empirical density function of the simulated aggregate claim values from Question 1, setting the x-axis range from 2,600,000 to 3,300,000 and the y-axis range from 0 to 0.0000045. 3. Suggest a suitable distribution, including its parameters, that approximates the simulated aggregate claim values from Question 1. 4. Generate 20,000 values from your suggested distribution in Question 3 using a random number generator seed of 955. Use the R function head() to display the first five generated values in your answer script. 5. Plot the empirical density…

Answer 2

Question

Chapter 1.2, Problem 7ES

To determine

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

To determine

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

To determine

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

To determine

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

To determine

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

To determine

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

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Answer 3

Question

Chapter 1.2, Problem 7ES

To determine

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

To determine

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

To determine

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

To determine

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

To determine

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

To determine

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

Expert Solution & Answer

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Answer 4

Question

Chapter 1.2, Problem 7ES

To determine

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

To determine

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

To determine

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

To determine

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

To determine

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

To determine

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

Expert Solution & Answer

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Answer 5

Chapter 1.2, Problem 7ES

To determine

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

To determine

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

To determine

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

To determine

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

To determine

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

To determine

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

Answer 6

Chapter 1.2, Problem 7ES

To determine

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

Answer 7

Chapter 1.2, Problem 7ES

To determine

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

Answer 8

To determine

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

Answer 9

To determine

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

Answer 10

To determine

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

Answer 11

To determine

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

Answer 12

To determine

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

Answer 13

To determine

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

Answer 14

To determine

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

Answer 15

To determine

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

Answer 16

To determine

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

Answer 17

To determine

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

Answer 18

Expert Solution & Answer

Answer 19

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Answer 29

Ch. 1.1 - A universal statement asserts that a certain...Ch. 1.1 - A conditional statement asserts that if one...Ch. 1.1 - Given a property that may or may not be true, an...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - Given any real number, there is a number that is...Ch. 1.1 - The reciprocal of any postive real number is...Ch. 1.1 - Prob. 6ES Ch. 1.1 - Rewrite the following statements less formally,...

(a) To indicate: The elements in the given set S = { n ∈ Z | n = ( − 1 ) k , for some integer k } by using set-roster notation.

Solution Summary: The author explains the set-roster notation of the given set: S=leftnin Z|n=

Concept explainers

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

Chapter 1 Solutions

(a) To indicate: The elements in the given set S = { n ∈ Z | n = ( − 1 ) k , for some integer k } by using set-roster notation.

Solution Summary: The author explains the set-roster notation of the given set: S=leftnin Z|n=

Concept explainers

(a) To indicate: The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

(b) To indicate: The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

(c) To indicate: The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

(d) To indicate: The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

(e) To indicate: The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

(f) To indicate: The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.

Chapter 1 Solutions

(a)

To indicate:

The elements in the given set S={n∈Z|n=(−1)k, for some integer k} by using set-roster notation.

(b)

To indicate:

The elements in the given set T={m∈Z|m=1+(−1)i, for some integer i} by using set-roster notation.

(c)

To indicate:

The elements in the given set U={r∈Z|2≤r≤−2} by using set-roster notation.

(d)

To indicate:

The elements in the given set V={s∈Z|s>2 or s<3} by using set-roster notation.

(e)

To indicate:

The elements in the given set W={t∈Z|1<t<−3} by using set-roster notation.

(f)

To indicate:

The elements in the given set X={u∈Z|u≤4 or u≥1} by using set-roster notation.