For the following integral, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges. Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition.

∫(x+5)/x^3+7x+5 dx

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:

21.9 × 0.7

= 153.3

Answer is 153.3

Answer:

15.33

Step-by-step explanation:

21.9 × 0.7 is 15.33 :)

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is 24/36 = 2/3

The two events are mutually exclusive

"Information available from the question"

Stacy rolls a pair of six-sided fair dice.

Now, According to the question:

Let the probability of getting a multiple of 3 is "A"

Let the probability of getting an even number is "B"

Total number of outcomes=36

Total number of favorable outcomes  of either a multiple of 3 or an even number are:-

(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)

Probability = Number of fav. outcomes/ Total no. of outcomes

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number will be given by counting the numbers that are either even or multiples of 3 and then dividing by the number of possible outcomes, 36.

In our case this will be;

24/36 = 2/3

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Answer:

Second answer choice:  

Mean before the change = 84.  Mean after the change = 86

Median before the change =  81.  Median after the change = 85

Step-by-step explanation:

Defining the mean:

Mean before the change:

Thus, we can find the mean before the change by dividing the sum of 75, 78, 81, 90, and 96 by 5:

Mean = (75 + 78 + 81 + 90 + 96) / 5

Mean = (420) / 5

Mean = 84

Thus, the mean before the change is 84.

Mean after the change:

Now we can find the mean after the change by dividing the sum of 78, 81, 85, 90, and 96 by 5:

Mean = (78 + 81 + 85 + 90 + 96) / 5

Mean = (430) /5

Mean = 86

Thus, the mean after the change is 86.

Defining the median:

Median before the change:

Thus, the median before the change is 81.

Median after the change:

Thus, the median after the change is 85.

Takuya will have approximately 234,539.416 yen after conversion from New Zealand dollars.

We are given that: Takuya traded the New Zealand dollars for the Japanese yen.

So, it means that it used conversion to convert one currency into the another.

Now, we have:

1 New Zealand dollar = 62.8792 Japanese yen.

Also, Takuya has a total of $ 3800 dollars.

But $ 70 fee has also to be paid for the exchange.

So, the dollars left will be:

= $ 3800 - $ 70

= $ 3730

Converting them to Japanese yen by multiplication:

$ 3730 = 3730 × 62.8792 yen

= 234,539.416 yen.

Therefore, we get that, Takuya will have approximately 234,539.416 yen after conversion from New Zealand dollars.

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The statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true.

Given, two functions  y = -2f(x) = 1/x

To determine whether the statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true or false, we need to find the value of Y for both functions when x = -2.

Substituting x = -2 in the functions we get:I would ask y = -2(-2) = 4f(-2) = 1/(-2) = -1/2Therefore, the Y value of the function I would ask is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2. Hence, the given statement is true.

Therefore, the statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true.

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The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.

The given function is,

y = 1/2 x + 2.

Also, the domain of the function is {-4, -2, 0}.

Since, the domain of the functions defines the values of x,

And range defines the value of y in function.

The value of y at x = -4

y = 1/2(-4) + 2 = -2 + 2 = 0

At x = -2,

y = 1/2(-2) + 2 = -1 + 2 = 1

At x= 0,

y = 1/2 (0) + 2 = 2

The values of y are 0, 1 and 2.

Hence, the range of the function is {0, 1, 2}.

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The 0.0588 = 5.88% probability of drawing two clubs from a standard deck of 52 cards.

0.0498 = 4.98% probability of drawing two faces from a standard deck of 52 cards.

0.0045 = 0.45% probability of drawing two aces from a standard deck of 52 cards

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

We know standard deck has 52 cards.

And 13 cards are for clubs.

(a).

The probability,

= number of favorable outcomes / number of outcomes

= 13 x 12 / 52 x 51

= 0.0588

0.0588 = 5.88% probability of drawing two clubs from a standard deck of 52 cards.

(b). 12 faces in a deck.

The probability,

= number of favorable outcomes / number of outcomes

= 12 x 11 / 52 x 51

= 0.04977

= 0.0498

0.0498 = 4.98% probability of drawing two faces from a standard deck of 52 cards.

(c). There are 4 aces in the deck.

The probability,

= number of favorable outcomes / number of outcomes

= 4 x 3 / 52 x 51

= 0.0045

0.0045 = 0.45% probability of drawing two aces from a standard deck of 52 cards.

Therefore, the probabilities are 0.0588, 0.0498 and 0.0045.

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Answer:

D. 104

Step-by-step explanation:

\(y \: \alpha \: \frac{1}{ {x}^{2} } \\ \\ y = \frac{k}{ {x}^{2} } \)

when y is 26, x is 4:

\(26 = \frac{k}{ {(4)}^{2} } \\ k = 416\)

when x is 2:

\(y = \frac{416}{ {x}^{2} } \\ \\ y = \frac{416}{ {(2)}^{2} } \\ y = 104\)

Answer:

D; 104

This is the correct answer

The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.

Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.

According to the given information:

The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.

The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.

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Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

Situation which illustrates best the concept of absolute advantage is: Option A - A German factory can build more sports cars than foreign factories.

Absolute advantage is the potential of an individual,  a company, or a  country to produce a higher quantity of output than its competitors while using the same inputs. It means an institution with absolute advantage has more efficiency in producing a particular commodity than its rivals. It utilizes lower marginal cost (materials and labor), making its output much cheaper than others.

A factory in German has an absolute advantage because it can produce more sports car  than foreign countries. Absolute advantage makes the factory more competitive in the market than its rivals.

Therefore, the correct answer is option A.

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Answer:

Angle R is congruent to angle Y; line ZX is congruent to line SQ

Step-by-step explanation:

Order matters when listing sides and angles, as in the question.

R is second listed angle, and so is Y.

Line ZX is first and third listed, so congruent side is line SQ

Answer:

7x/10

Step-by-step explanation:

Answer:

In y = 3/2x,     x and y are inversely propotional

In -x = y,      x and y are directly propotional

Step-by-step explanation:

In y = 3/2x, the constant of propotionality is 3/2.

In -x = y, the constant of propotionality is -1.

Answer:

with what?

Step-by-step explanation:

The solution is, fraction of Polygon P's area with Q's area is,

=4/1.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

here, we have,

given that,

1 Polygon Q is a scaled copy of Polygon P , using a scale factor of  1/2.

let, area of P = x^2

so, area of Q = x/2^2

                      = x^2/4

fraction of Polygon P's area with Q's area =

x^2 : x^2/4

=1/ 1/4 = 4

Hence,  The solution is, fraction of Polygon P's area with Q's area is,

=4/1.

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Answer:

a) 8 and two thirds

b) 4 and 11/24

c) 8 and 1/12

d)8 and 7/24

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

1. Simplifying the exponent (a⁵a⁹)⁻⁵/a⁻¹⁵ = a⁻⁵⁵

2. Simplifying the exponent  [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = m⁻¹⁰

Exponents are powers to which a number is raised.

1. Given the exponential expression, (a⁵a⁹)⁻⁵/a⁻¹⁵, we desire to simplify the expression. We proceed as follows

Since we have  (a⁵a⁹)⁻⁵/a⁻¹⁵

Using the multiplication law of exponents which is xᵃ x xᵇ = xᵃ⁺ᵇ, the numerator becomes

(a⁵a⁹)⁻⁵/a⁻¹⁵ =  (a⁵⁺⁹)⁻⁵/a⁻¹⁵

=  (a¹⁴)⁻⁵/a⁻¹⁵

Also, using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

 (a¹⁴)⁻⁵/a⁻¹⁵ = (a¹⁴×⁻⁵)/a⁻¹⁵

=  (a⁻⁷⁰)/a⁻¹⁵

Now using the division law of exponents, we have xᵃ/xᵇ = xᵃ⁻ᵇ

So,   (a⁻⁷⁰)/a⁻¹⁵ = a⁻⁷⁰ ⁻⁽⁻¹⁵⁾

= a⁻⁷⁰⁺¹⁵

= a⁻⁵⁵

So, (a⁵a⁹)⁻⁵/a⁻¹⁵ = a⁻⁵⁵

2. Given the exponential expression, [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵, we desire to simplify the expression. We proceed as follows

Since we have [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵

Using the multiplication law of exponents which is xᵃ x xᵇ = xᵃ⁺ᵇ, the numerator becomes

[(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = [(m⁻³⁺⁽⁻⁷⁾)/(m⁻⁴)⁻³]⁵

= [(m⁻³⁻⁷)/(m⁻⁴)⁻³]⁵

= [(m⁻¹⁰)/(m⁻⁴)⁻³]⁵

Also, using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

= [m⁻¹⁰/(m⁻⁴)⁻³]⁵ = [(m⁻¹⁰)/(m⁻⁴×⁽⁻³⁾)]⁵

= [(m⁻¹⁰)/m⁻¹²]⁵

Now using the division law of exponents, we have xᵃ/xᵇ = xᵃ⁻ᵇ

So, [(m⁻¹⁰)/m⁻¹²]⁵ = [m⁻¹⁰ ⁻⁽⁻¹²⁾]⁵

= [m⁻¹⁰⁺¹²]⁵

= [m⁻²]⁵

Using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

[m⁻²]⁵ = m⁻²ˣ⁵

= m⁻¹⁰

So, [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = m⁻¹⁰

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When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include

A. 27, 22, 17, 12, 7

D. 100, 95, 90, 85, 80

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.

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Complete question

Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.

27, 22, 17, 12, 7

5, 10, 15, 20, 25

55, 50, 35, 30, 25

100, 95, 90, 85, 80

75, 65, 55, 45, 35

Option (B) is correct. Thus, percentage of students with scores between 70 and 130 is 95% .

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation.

It reveals the average deviation of each score from the mean. Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that √(5.2/5) = 1.01 will be the standard deviation.

Here:

μ = 100, σ = 15

Thus we have

30 μ - kσ = 70

= 100 – k(15) = 70

= k= 30/15 = 2

Also we have, μ + Ασ: = 130

100+ k(15) = 130

k = 30/15 = 2

Now, the percentage of students with scores between 70 and 130 is same as the percentage of students between μ - 2σ, μ+ 2σ  and by empirical rule the area between μ (+-) 2σ  is 95%. Thus, percentage of students with scores between 70 and 130 is 95%

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The cosine equation of the function shown is f(x) = 4cos(x) + 3

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that the function is shifted up

Next, we enter the points in a graphing calculator to determine the function

From the graph, we have

f(x) = 4cos(x) + 3

Hence, the equation is f(x) = 4cos(x) + 3

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Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

The standard error is 0.0912.

The standard error (SE) is a measure of the precision of the sample mean estimate compared to the true population mean. To calculate the SE, we use the formula SE = standard deviation / square root of sample size.

In this scenario, the population parameter is 0.7, and the sample size is 30. If we assume that the sample mean is an unbiased estimator of the population mean, then the SE can be calculated using the above formula. However, we do not know the standard deviation of the population, so we use the sample standard deviation as an estimate.

Assuming the sample is large enough to assume normality, the formula becomes SE = \(\sqrt{(0.7*0.3)/30}\)   = 0.0912. Therefore, the standard error for a sample size of 30 is 0.0912. This means that if we were to take multiple samples of size 30 from the same population, the standard deviation of the means of those samples would be around 0.0912 away from the population parameter of 0.7 on average.

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To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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