Work all of the problems in this self-test without using a calculator. Then check your work by consulting the answers in the back of the book. Where weaknesses show up, use the reference that follows each answer to find the section in the test that provides the necessary review. 1. Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property: (A) Commutative (·): x ( y + z ) = ? (B) Associative (+): 2 + ( x + y ) = ? (C) Distributive: (2 + 3) x = ?

Question

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Answer 1

Textbook Question

Chapter DPT, Problem 1E

Work all of the problems in this self-test without using a calculator. Then check your work by consulting the answers in the back of the book. Where weaknesses show up, use the reference that follows each answer to find the section in the test that provides the necessary review.

1. Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property:

(A) Commutative (·): x(y + z) = ?

(B) Associative (+): 2 + (x + y) = ?

(C) Distributive: (2 + 3)x = ?

(A)

Expert Solution

To determine

To find: The equivalent expression of x(y+z) by using the commutative property.

Answer to Problem 1E

The expression x(y+z) is equivalent to (y+z)x.

Explanation of Solution

Given:

The expression is x(y+z).

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation "⋅", then x⋅y=y⋅x.

Illustration:

The factors of the given expression x(y+z) are x and (y+z).

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, x(y+z) is altered to (y+z)x.

Therefore, the expression x(y+z) is equivalent to (y+z)x.

(B)

Expert Solution

To determine

To find: The equivalent expression of 2+(x+y) by using the associative property.

Answer to Problem 1E

The expression 2+(x+y) is equivalent to (2+x)+y.

Explanation of Solution

Given:

The expression is 2+(x+y).

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “+” operation states that (a+b)+c=a+(b+c).

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, 2+(x+y) is altered to (2+x)+y.

Therefore, the expression of 2+(x+y) is equivalent to (2+x)+y.

(C)

Expert Solution

To determine

To find: The equivalent expression of (2+3)x by using the distributive property.

Answer to Problem 1E

The expression (2+3)x is equivalent to 2x+3x.

Explanation of Solution

Given:

The expression is (2+3)x.

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that (a+b)c=ac+bc.

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, (2+3)x is altered to 2x+3x.

Hence, the expression of (2+3)x equivalent to 2x+3x.

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03:09

Students have asked these similar questions

Let us suppose we have some article reported on a study of potential sources of injury to equine veterinarians conducted at a university veterinary hospital. Forces on the hand were measured for several common activities that veterinarians engage in when examining or treating horses. We will consider the forces on the hands for two tasks, lifting and using ultrasound. Assume that both sample sizes are 6, the sample mean force for lifting was 6.2 pounds with standard deviation 1.5 pounds, and the sample mean force for using ultrasound was 6.4 pounds with standard deviation 0.3 pounds. Assume that the standard deviations are known. Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. Under the null hypothesis, 40 = 0. What level of type II error would you recommend here? Round your answer to four decimal places (e.g. 98.7654). Use a = 0.05. β = i What sample size would be required? Assume the sample sizes are to be equal.…

= Consider the hypothesis test Ho: μ₁ = μ₂ against H₁ μ₁ μ2. Suppose that sample sizes are n₁ = 15 and n₂ = 15, that x1 = 4.7 and X2 = 7.8 and that s² = 4 and s² = 6.26. Assume that o and that the data are drawn from normal distributions. Use απ 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ẞ = 0.05 if the true difference in means is - 2? Assume that α = 0.05. (a) The null hypothesis is 98.7654). rejected. The P-value is 0.0008 (b) The power is 0.94 . Round your answer to four decimal places (e.g. Round your answer to two decimal places (e.g. 98.76). (c) n₁ = n2 = 1 . Round your answer to the nearest integer.

Consider the hypothesis test Ho: = 622 against H₁: 6 > 62. Suppose that the sample sizes are n₁ = 20 and n₂ = 8, and that = 4.5; s=2.3. Use a = 0.01. (a) Test the hypothesis. Round your answers to two decimal places (e.g. 98.76). The test statistic is fo = i The critical value is f = Conclusion: i the null hypothesis at a = 0.01. (b) Construct the confidence interval on 02/022 which can be used to test the hypothesis: (Round your answer to two decimal places (e.g. 98.76).) i

Answer 2

Textbook Question

Chapter DPT, Problem 1E

Work all of the problems in this self-test without using a calculator. Then check your work by consulting the answers in the back of the book. Where weaknesses show up, use the reference that follows each answer to find the section in the test that provides the necessary review.

1. Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property:

(A) Commutative (·): x(y + z) = ?

(B) Associative (+): 2 + (x + y) = ?

(C) Distributive: (2 + 3)x = ?

(A)

Expert Solution

To determine

To find: The equivalent expression of x(y+z) by using the commutative property.

Answer to Problem 1E

The expression x(y+z) is equivalent to (y+z)x.

Explanation of Solution

Given:

The expression is x(y+z).

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation "⋅", then x⋅y=y⋅x.

Illustration:

The factors of the given expression x(y+z) are x and (y+z).

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, x(y+z) is altered to (y+z)x.

Therefore, the expression x(y+z) is equivalent to (y+z)x.

(B)

Expert Solution

To determine

To find: The equivalent expression of 2+(x+y) by using the associative property.

Answer to Problem 1E

The expression 2+(x+y) is equivalent to (2+x)+y.

Explanation of Solution

Given:

The expression is 2+(x+y).

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “+” operation states that (a+b)+c=a+(b+c).

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, 2+(x+y) is altered to (2+x)+y.

Therefore, the expression of 2+(x+y) is equivalent to (2+x)+y.

(C)

Expert Solution

To determine

To find: The equivalent expression of (2+3)x by using the distributive property.

Answer to Problem 1E

The expression (2+3)x is equivalent to 2x+3x.

Explanation of Solution

Given:

The expression is (2+3)x.

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that (a+b)c=ac+bc.

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, (2+3)x is altered to 2x+3x.

Hence, the expression of (2+3)x equivalent to 2x+3x.

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03:09

Answer 3

Textbook Question

Chapter DPT, Problem 1E

Work all of the problems in this self-test without using a calculator. Then check your work by consulting the answers in the back of the book. Where weaknesses show up, use the reference that follows each answer to find the section in the test that provides the necessary review.

1. Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property:

(A) Commutative (·): x(y + z) = ?

(B) Associative (+): 2 + (x + y) = ?

(C) Distributive: (2 + 3)x = ?

(A)

Expert Solution

To determine

To find: The equivalent expression of x(y+z) by using the commutative property.

Answer to Problem 1E

The expression x(y+z) is equivalent to (y+z)x.

Explanation of Solution

Given:

The expression is x(y+z).

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation "⋅", then x⋅y=y⋅x.

Illustration:

The factors of the given expression x(y+z) are x and (y+z).

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, x(y+z) is altered to (y+z)x.

Therefore, the expression x(y+z) is equivalent to (y+z)x.

(B)

Expert Solution

To determine

To find: The equivalent expression of 2+(x+y) by using the associative property.

Answer to Problem 1E

The expression 2+(x+y) is equivalent to (2+x)+y.

Explanation of Solution

Given:

The expression is 2+(x+y).

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “+” operation states that (a+b)+c=a+(b+c).

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, 2+(x+y) is altered to (2+x)+y.

Therefore, the expression of 2+(x+y) is equivalent to (2+x)+y.

(C)

Expert Solution

To determine

To find: The equivalent expression of (2+3)x by using the distributive property.

Answer to Problem 1E

The expression (2+3)x is equivalent to 2x+3x.

Explanation of Solution

Given:

The expression is (2+3)x.

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that (a+b)c=ac+bc.

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, (2+3)x is altered to 2x+3x.

Hence, the expression of (2+3)x equivalent to 2x+3x.

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03:09

Answer 4

Textbook Question

Chapter DPT, Problem 1E

Work all of the problems in this self-test without using a calculator. Then check your work by consulting the answers in the back of the book. Where weaknesses show up, use the reference that follows each answer to find the section in the test that provides the necessary review.

1. Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property:

(A) Commutative (·): x(y + z) = ?

(B) Associative (+): 2 + (x + y) = ?

(C) Distributive: (2 + 3)x = ?

(A)

Expert Solution

To determine

To find: The equivalent expression of x(y+z) by using the commutative property.

Answer to Problem 1E

The expression x(y+z) is equivalent to (y+z)x.

Explanation of Solution

Given:

The expression is x(y+z).

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation "⋅", then x⋅y=y⋅x.

Illustration:

The factors of the given expression x(y+z) are x and (y+z).

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, x(y+z) is altered to (y+z)x.

Therefore, the expression x(y+z) is equivalent to (y+z)x.

(B)

Expert Solution

To determine

To find: The equivalent expression of 2+(x+y) by using the associative property.

Answer to Problem 1E

The expression 2+(x+y) is equivalent to (2+x)+y.

Explanation of Solution

Given:

The expression is 2+(x+y).

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “+” operation states that (a+b)+c=a+(b+c).

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, 2+(x+y) is altered to (2+x)+y.

Therefore, the expression of 2+(x+y) is equivalent to (2+x)+y.

(C)

Expert Solution

To determine

To find: The equivalent expression of (2+3)x by using the distributive property.

Answer to Problem 1E

The expression (2+3)x is equivalent to 2x+3x.

Explanation of Solution

Given:

The expression is (2+3)x.

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that (a+b)c=ac+bc.

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, (2+3)x is altered to 2x+3x.

Hence, the expression of (2+3)x equivalent to 2x+3x.

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03:09

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(A)

Expert Solution

To determine

To find: The equivalent expression of x(y+z) by using the commutative property.

Answer to Problem 1E

The expression x(y+z) is equivalent to (y+z)x.

Explanation of Solution

Given:

The expression is x(y+z).

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation "⋅", then x⋅y=y⋅x.

Illustration:

The factors of the given expression x(y+z) are x and (y+z).

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, x(y+z) is altered to (y+z)x.

Therefore, the expression x(y+z) is equivalent to (y+z)x.

(B)

Expert Solution

To determine

To find: The equivalent expression of 2+(x+y) by using the associative property.

Answer to Problem 1E

The expression 2+(x+y) is equivalent to (2+x)+y.

Explanation of Solution

Given:

The expression is 2+(x+y).

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “+” operation states that (a+b)+c=a+(b+c).

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, 2+(x+y) is altered to (2+x)+y.

Therefore, the expression of 2+(x+y) is equivalent to (2+x)+y.

(C)

Expert Solution

To determine

To find: The equivalent expression of (2+3)x by using the distributive property.

Answer to Problem 1E

The expression (2+3)x is equivalent to 2x+3x.

Explanation of Solution

Given:

The expression is (2+3)x.

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that (a+b)c=ac+bc.

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, (2+3)x is altered to 2x+3x.

Hence, the expression of (2+3)x equivalent to 2x+3x.

Answer 8

(A)

Expert Solution

To determine

To find: The equivalent expression of x(y+z) by using the commutative property.

Answer to Problem 1E

The expression x(y+z) is equivalent to (y+z)x.

Explanation of Solution

Given:

The expression is x(y+z).

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation "⋅", then x⋅y=y⋅x.

Illustration:

The factors of the given expression x(y+z) are x and (y+z).

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, x(y+z) is altered to (y+z)x.

Therefore, the expression x(y+z) is equivalent to (y+z)x.

Answer 9

(A)

Expert Solution

Answer 10

(A)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

To find: The equivalent expression of x(y+z) by using the commutative property.

Answer 13

Answer to Problem 1E

The expression x(y+z) is equivalent to (y+z)x.

Answer 14

Explanation of Solution

Given:

The expression is x(y+z).

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation "⋅", then x⋅y=y⋅x.

Illustration:

The factors of the given expression x(y+z) are x and (y+z).

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, x(y+z) is altered to (y+z)x.

Therefore, the expression x(y+z) is equivalent to (y+z)x.

Answer 15

(B)

Expert Solution

To determine

To find: The equivalent expression of 2+(x+y) by using the associative property.

Answer to Problem 1E

The expression 2+(x+y) is equivalent to (2+x)+y.

Explanation of Solution

Given:

The expression is 2+(x+y).

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “+” operation states that (a+b)+c=a+(b+c).

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, 2+(x+y) is altered to (2+x)+y.

Therefore, the expression of 2+(x+y) is equivalent to (2+x)+y.

Answer 16

(B)

Expert Solution

Answer 17

(B)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

To find: The equivalent expression of 2+(x+y) by using the associative property.

Answer 20

Answer to Problem 1E

The expression 2+(x+y) is equivalent to (2+x)+y.

Answer 21

Explanation of Solution

Given:

The expression is 2+(x+y).

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “+” operation states that (a+b)+c=a+(b+c).

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, 2+(x+y) is altered to (2+x)+y.

Therefore, the expression of 2+(x+y) is equivalent to (2+x)+y.

Answer 22

(C)

Expert Solution

To determine

To find: The equivalent expression of (2+3)x by using the distributive property.

Answer to Problem 1E

The expression (2+3)x is equivalent to 2x+3x.

Explanation of Solution

Given:

The expression is (2+3)x.

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that (a+b)c=ac+bc.

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, (2+3)x is altered to 2x+3x.

Hence, the expression of (2+3)x equivalent to 2x+3x.

Answer 23

(C)

Expert Solution

Answer 24

(C)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

To find: The equivalent expression of (2+3)x by using the distributive property.

Answer 27

Answer to Problem 1E

The expression (2+3)x is equivalent to 2x+3x.

Answer 28

Explanation of Solution

Given:

The expression is (2+3)x.

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that (a+b)c=ac+bc.

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, (2+3)x is altered to 2x+3x.

Hence, the expression of (2+3)x equivalent to 2x+3x.

Answer 29

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Answer to Problem 1E

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Answer to Problem 1E

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