Exercise 12. Let X and Y be independent random variables satisfying E|X+Y|^n < [infinity] for some a > 0. Show that E|X|^n < [infinity].

We can use the two-point form to find the equation of the line passing through the two given points:

y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)

where (x1, y1) = (0, 4) and (x2, y2) = (5, 19).

Substituting the values, we get:

y - 4 = ((19 - 4)/(5 - 0))(x - 0)

Simplifying the equation, we get:

y - 4 = (15/5)x

y - 4 = 3x

Adding 4 to both sides, we get:

y = 3x + 4

Therefore, the equation of the line passing through the points (0, 4) and (5, 19) is y = 3x + 4.

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a) find slope

19-4/5-0 = 15/5 = 3

plug into equation

y = 3x + b

plug in coordinate pair to solve for b

4 = 3(0) + b

4 = 0 + b

b = 4

y = 3x + b

The line passes through the x-axis at the point (13/2, 0).

To find where the line passes through the x-axis, we need to find the x-intercept of the line. The x-intercept is the point where the line crosses the x-axis, so the y-coordinate of this point will be 0.

We can use the slope-intercept form of a line, y = mx + b, to find the x-intercept. First, we need to find the slope of the line, m. The slope is given by the formula:
m = (y2 - y1)/(x2 - x1)

Plugging in the given points, we get:

m = (5 - 1)/(-1 - 5)

m = -2/3

Now we can plug in one of the points and the slope into the equation to solve for the y-intercept, b:
1 = -2/3(5) + b
b = -13/3

So the equation of the line is:
y = -2/3x + 13/3

To find the x-intercept, we set y to 0 and solve for x:
0 = -2/3x + 13/3
x = 13/2

So the line passes through the x-axis at the point (13/2, 0).

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The values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.

To find k so that when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2, the remainder is 0, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x-a, the remainder is f(a).

So, if we let f(x) = x^(3)+kx^(2)+k^(2)x+14 and a = -2, we can find the value of k that makes the remainder 0.

f(-2) = (-2)^(3)+k(-2)^(2)+k^(2)(-2)+14 = 0

Simplifying the equation, we get:

-8 + 4k - 2k^(2) + 14 = 0

-2k^(2) + 4k + 6 = 0

Dividing by -2, we get:

k^(2) - 2k - 3 = 0

Factoring the equation, we get:

(k-3)(k+1) = 0

So, k = 3 or k = -1.

Therefore, the values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.

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When x = 4, y = 320/27.

If y varies directly as x, it means that y = kx, where k is a constant. To find k, we can use the given information:

When x = 3, y = 12

12 = k * 3

k = 4

Now that we know k, we can find y when x = 20:

y = k * x

y = 4 * 20

y = 80

Therefore, when x = 20, y = 80.

25. If y varies directly as the square of x, it means that y = k * x^2, where k is a constant. To find k, we can use the given information:

When x = 2, y = 16

16 = k * 2^2

k = 4

Now that we know k, we can find y when x = 8:

y = k * x^2

y = 4 * 8^2

y = 4 * 64

y = 256

Therefore, when x = 8, y = 256.

26. If y varies directly as the cube of x, it means that y = k * x^3, where k is a constant. To find k, we can use the given information:

When x = 3, y = 5

5 = k * 3^3

k = 5/27

Now that we know k, we can find y when x = 4:

y = k * x^3

y = 5/27 * 4^3

y = 5/27 * 64

y = 320/27

Therefore, when x = 4, y = 320/27.

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Answer:

First, subtract 10x on both sides so you get

12=10x-2

Then add 2 odd both sides

14=10x

Then divide both sides by 10

14/10= 10X/10

So you get x=1.4

The 90% confidence interval for the population mean salary is 4650 + 45.24. The correct answer is option f.

To find the 90% confidence interval for the population mean salary, we need to use the formula:

CI = x ± z(s/√n)

Where:
- CI = confidence interval
- x = sample mean
- z = z-score for the desired confidence level
- s = sample standard deviation
- n = sample size

Plugging in the given values, we get:

CI = 4650 ± 1.645(165/√36)

CI = 4650 ± 1.645(165/6)

CI = 4650 ± 1.645(27.5)

CI = 4650 ± 45.2375

CI = 4650 ± 45.24

Therefore, the 90% confidence interval for the population mean salary is 4650 ± 45.24 or (4604.7625, 4695.2375).

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For the given quadratic function the features are:

A parabola, a U-shaped curve, is the shape of a quadratic function's graph.

There are three characteristics that all quadratic functions share:

Thus, for the given quadratic function the features are:

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The simplified rational expression of (5)/(2)-(1)/(2d) is (5d-2)/(2d).

To add rational expressions with different denominators, we first need to find a common denominator. In this case, the common denominator is 2d.

Once we have the common denominator, we can multiply each fraction by a factor that will give us the common denominator. For the first fraction, we need to multiply by d in the numerator and denominator. For the second fraction, we need to multiply by 2 in the numerator and denominator.

After multiplying, we can combine the numerators and keep the common denominator.

So, the steps to simplify (5)/(2)-(1)/(2d) are as follows:

1. Find the common denominator: 2d
2. Multiply the first fraction by d/d: (5d)/(2d)
3. Multiply the second fraction by 2/2: (2)/(2d)
4. Combine the numerators and keep the common denominator: (5d-2)/(2d)
5. Simplify the numerator: (5d-2)/(2d)

Therefore, the simplified rational expression is (5d-2)/(2d).

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(a) The standard error is 1.17. (b) IT is a two-sided test. (c) If a = 0.05, it can be concluded that we can reject the null hypothesis and accept the alternative hypothesis. (d) A 90% two-sided CI on the difference in means is (0.33, 4.37).

(a) The missing value for the standard error of the difference in sample means can be calculated using the formula:

Standard error = (Difference in sample means) / (Test statistic) = 2.35 / 2.01 = 1.17

(b) This is a two-sided test because the P-value is given for a two-sided test. If it were a one-sided test, the P-value would be half of the given value, or 0.0149.

(c) If a = 0.05, we can conclude that the difference in sample means is statistically significant because the P-value (0.0298) is less than a (0.05). This means that we can reject the null hypothesis and accept the alternative hypothesis that there is a difference in the means.

(d) A 90% two-sided CI on the difference in means can be calculated using the formula:

CI = (Difference in sample means) ± (t-value) × (Standard error)

The t-value for a 90% two-sided CI with 18 degrees of freedom is 1.734. So the CI is:

CI = 2.35 ± 1.734 × 1.17 = (0.33, 4.37)

Therefore, the 90% two-sided CI on the difference in means is (0.33, 4.37).

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This hypothesis test indicates that the team efficiency when working through distance working (e.g. with online meetings) is not generally more efficient than when working with physical presence.

The research question being examined is whether teams that work through distance working (e.g. with online meetings) are generally more efficient than those that work with physical presence. To answer this question, a hypothesis test can be used with a 1% level of significance.

The null hypothesis (H0) is that there is no difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence. The alternative hypothesis (H1) is that there is a difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.

To test this hypothesis, a two-tailed independent t-test was used. The mean score for the team that had used online meetings was 2.63 with a standard deviation of 0.92 and for the team that had worked with physical presence the mean was 2.35 with a standard deviation of 0.81. The t-statistic obtained was 1.71 and the corresponding p-value was 0.093.

Since the p-value (0.093) is not less than the level of significance (0.01), the null hypothesis cannot be rejected. Therefore, the data suggests that there is not a significant difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.

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Answer:

She earns 10 dollars per hour.

Step-by-step explanation:

They substituted h for the amount of hours, since it is unknown. And you can see 10 is multiplied with h. So that is how much she earns an hour.

a) Amount financed is, R164,000

b) Total interest over 60 months is, R98,400

c) The farmer would pay a total of R262,400 after 60 months.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The tractor costs R160 000 excluding VAT

And, He can pay a deposit of R20 000.

Here, He decides to buy the tractor on hire purchase over 60 months at a simple interest rate of 10 %

Hence, We get;

Total price with VAT = R160,000 + 15% of R160,000

                               = R184,000

Hence, We get;

Amount financed = Total price - Deposit

                           = R184,000 - R20,000

                           = R164,000

Thus, Total interest over 60 months = R164,000 x 10% x 5

                                                        = R98,400

Here, Total payment = Amount financed + Total interest

                                = R164,000 + R98,400

                                = R262,400

Therefore, The farmer would pay a total of R262,400 after 60 months.

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AB is indeed the zero matrix, and we have found a 2 x 2 matrix B such that AB is the zero matrix.

When multiplying two matrices, we use the dot product of the rows of the first matrix and the columns of the second matrix to obtain the entries of the resulting matrix. In order for the product of two matrices to be the zero matrix, the dot product of each row of the first matrix with each column of the second matrix must be zero.

Let's construct a 2 x 2 matrix B such that AB is the zero matrix. We can use two different nonzero columns for B to obtain the zero matrix. Let's start with the first column of B:

B = [b1 b3]
   [b2 b4]

We need to find values for b1, b2, b3, and b4 such that the dot product of each row of A with each column of B is zero. Let's start with the first row of A and the first column of B:

-12b1 + 4b2 = 0

We can rearrange this equation to solve for b2 in terms of b1:

b2 = 3b1

Now let's look at the second row of A and the first column of B:

15b1 - 5b2 = 0

Substituting the value of b2 from the first equation gives us:

15b1 - 5(3b1) = 0

Simplifying gives us:

0 = 0

This equation is always true, so we can choose any value for b1 and find the corresponding value for b2. Let's choose b1 = 1:

b2 = 3(1) = 3

Now let's look at the first row of A and the second column of B:

-12b3 + 4b4 = 0

We can rearrange this equation to solve for b4 in terms of b3:

b4 = 3b3

Now let's look at the second row of A and the second column of B:

15b3 - 5b4 = 0

Substituting the value of b4 from the first equation gives us:

15b3 - 5(3b3) = 0

Simplifying gives us:

0 = 0

This equation is always true, so we can choose any value for b3 and find the corresponding value for b4. Let's choose b3 = 2:

b4 = 3(2) = 6

Now we have the values for all of the entries of B:

B = [1 2]
   [3 6]

Let's check our work by multiplying A and B:

AB = [-12 4] [1 2]
    [ 15 -5] [3 6]

 = [(-12)(1) + (4)(3)  (-12)(2) + (4)(6)]
    [(15)(1) + (-5)(3)  (15)(2) + (-5)(6)]

 = [0 0]
    [0 0]

So AB is indeed the zero matrix, and we have found a 2 x 2 matrix B such that AB is the zero matrix.

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Answer:

The initial price of the store item would be the price before any price adjustments were made, which corresponds to when x=0.

Plugging x=0 into the given function, we get:

f(0) = 320(0.90)^0 = 320(1) = 320

Therefore, the initial price of the store item was $320.

Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).

To use synthetic division to find the result of the given polynomial division, we need to follow these steps:

1. Write the coefficients of the dividend polynomial in a row: 2 10 8 1 24
2. Write the constant term of the divisor with the opposite sign in front of the row: -2 | 2 10 8 1 24
3. Bring down the first coefficient: -2 | 2 10 8 1 24
         -----------
            2
4. Multiply the first coefficient by the divisor's constant term and write the result under the second coefficient: -2 | 2 10 8 1 24
         -----------
            2 -4
5. Add the second coefficient and the result from step 4: -2 | 2 10 8 1 24
         -----------
            2  6
6. Repeat steps 4 and 5 for the remaining coefficients: -2 | 2 10 8 1 24
         -----------
            2  6  4 -6
7. The last number in the row is the remainder. If it is 0, the division is exact. If not, we need to express the result in the form: quotient + (remainder)/(divisor)

In this case, the quotient is 2x^(3)+6x^(2)+4x-6 and the remainder is 36. So the result of the division is:
2x^(3)+6x^(2)+4x-6+(36)/(x+2)

Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).

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The slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.

To find the y-intercept and slope of the linear equation x  +y=-6 1/2, we

need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's isolate y by subtracting x from both sides of the equation:

x + y = -6 1/2

y = -x - 6 1/2

Now we can see that the equation is in slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is -6 1/2.

Therefore, the slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.

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Answer: the first quadrant : 12° i the second quadrant : 168° i

the third quadrant : -168° i the forth quadrant : 348°.

Step-by-step explanation:

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Determinant of the given triangular matrix  is 105.

The determinant of a matrix is a number that represents the volume or area of the matrix. It is calculated by using a formula that involves the entries of the matrix, and is used in solving linear equations and in proving theorems in linear algebra.

The determinant of a triangular matrix can be found by multiplying the elements on the main diagonal. In this case, the main diagonal elements are -3, 5, and -7.

So, the determinant of the triangular matrix is:
-3 * 5 * -7 = 105

Therefore, the determinant of the triangular matrix is 105.

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The required, value of x in the rational equation x⁵=618 is approximately 4.951.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
To solve for x in the rational equation x^5 = 618, we need to isolate x on one side of the equation.

Taking the fifth root of both sides, we get:

[tex]x = 618^{1/5}[/tex]

The approximate value of the fifth root of 618 is approximately 4.951.

Therefore, the value of x is approximately 4.951.

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Answer:

Option B.

Step-by-step explanation:

Let r represent right questions and w represent wrong questions

Total number of questions can be written as:
r + w = 30

We can multiply the question type by the number of points and set it to equal to the total points:

4r - 1w = 20

Thus, our two equations match with Option B best.

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The area of the trapezoid is 335 square inches.

What is Trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The distance between the bases is called the height or altitude of the trapezoid.

First, we need to convert the lengths of the bases and the perpendicular distance to the same units. Let's convert 6 feet to inches:

6 feet = 6 x 12 inches = 72 inches

Now we can calculate the area of the trapezoid using the formula:

Area = (a + b) * h / 2

where a and b are the lengths of the bases and h is the perpendicular distance between them.

Substituting the given values, we get:

Area = (62 + 72) * 5 / 2

Area = 134 * 5 / 2

Area = 670 / 2

Area = 335 square inches

Therefore, the area of the trapezoid is 335 square inches.

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The composite functions and their domains are:
(a) (fog)(x) = 30x + 8, domain: all real numbers
(b) (gof)(x) = 30x + 40, domain: all real numbers
(c) (fof)(x) = 36x + 56, domain: all real numbers
(d) (gog)(x) = 25x, domain: all real numbers

The composite functions are formed by substituting one function into another. We can find the composite functions for f(x)=6x+8 and g(x)=5x by following these steps:

(a) (fog)(x) = f(g(x)) = f(5x) = 6(5x) + 8 = 30x + 8

The domain of (fog)(x) is the set of all real numbers, since there are no restrictions on the values of x.

(b) (gof)(x) = g(f(x)) = g(6x+8) = 5(6x+8) = 30x + 40

The domain of (gof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.

(c) (fof)(x) = f(f(x)) = f(6x+8) = 6(6x+8) + 8 = 36x + 56

The domain of (fof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.

(d) (gog)(x) = g(g(x)) = g(5x) = 5(5x) = 25x

The domain of (gog)(x) is also the set of all real numbers, since there are no restrictions on the values of x.

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Answer: 1,068 and wil

Step-by-step explanation:

The solution set of inequality " for 9t+27 <4t-18" in interval notation is (-∞, -9).

To solve the inequality 9t + 27 < 4t - 18, we need to isolate the variable t on one side of the inequality. Here are the steps:

1. Subtract 4t from both sides: 9t - 4t + 27 < -18
2. Simplify: 5t + 27 < -18
3. Subtract 27 from both sides: 5t < -45
4. Divide both sides by 5: t < -9

Now we can write the solution set in interval notation: (-∞, -9)

So the solution set is all values of t that are less than -9.

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Answer:

So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.

Step-by-step explanation:

Assuming that the tape diagram shows the ratio of adult tickets to child tickets as 3:2, we can represent this as follows:

  AAA

  AAA

  AAA

  CCC

  CCC

In this diagram, each square represents a certain number of tickets. To determine how many tickets each square represents, we need to know the total number of squares in the diagram.

There are a total of 3 + 3 + 3 + 2 + 2 = 13 squares in the diagram. Since the theater sold 126 tickets in total, we can divide 126 by 13 to find out how many tickets each square represents:

126 ÷ 13 ≈ 9.69

So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.

The probability of the spinner not landing on A is 0.47.

To find the probability that the spinner does not land on A, we need to add up the frequencies of the outcomes where A does not appear, which are (B,B), (B,C), (C,B), and (C,C):

Frequency of not landing on A = Frequency(B,B) + Frequency(B,C) +  Frequency(C,B) + Frequency(C,C)

Frequency of not landing on A = 15 + 17 + 13 + 14 = 59

The total number of outcomes is 125, so the probability of not landing on A is:

P(not A) = Frequency of not landing on A / Total number of outcomes

P(not A) = 59 / 125 = 0.47

Therefore, the probability of the spinner not landing on A is 0.47.

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a)0

b)0.09

c)0.09

d)0

e)P(3x6) = 0.09  P(3 < x < 6) = 0

A) P(x = 4) = 0

B) P(x4) = 0.09

C) P(at most 5 courses) = 0.09

D) P(at least 5 courses) = 0  P(more than 5 courses) = 0

E) P(3x6) = 0.09  P(3 < x < 6) = 0

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An equation in slope-intercept form is y = -7x + 12.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (2, -2), an equation of this line can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (-9 - (-2))/(3 - 2)(x - 2)

y + 2 = (-9 + 2)/(3 - 2)(x - 2)

y = -7x + 14 - 2

y = -7x + 12

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Binomial and Normal distributions are two different types of probability distributions that are commonly used in statistics. Both distributions involve a set of possible outcomes, and the probability associated with each outcome.

The Binomial Distribution is used for discrete data such as coin flips, the number of defective items in a production run, and the number of wins and losses in a series of games. It is used with the formula P(x;n,p) and the techniques of probability, permutations, and combinations.

The Normal Distribution is used for continuous data such as height, weight, IQ scores, and test scores. It is used with the formula P(x;μ,σ) and the techniques of statistics, standardization, and z-scores.

Both distributions have the same basic shape and the same basic idea of a probability of a certain outcome. The main difference between them is that the Binomial Distribution is discrete and the Normal Distribution is continuous.

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After 21 minutes the location of BO in the wheel is EO

The location of BO after 21 minutes is solved using the data:

It takes 4 minutes for the wheel to make one complete rotation

hence in 21 minutes the rotation covered is

= 21 / 4

= 5.25

This is 5 complete rotations and 0.25 (a quarter rotation).

0.25 rotation is

=0.25 * 360

= 90

Each gap in the wheel is

360 / 12 = 30 degrees

hence three steps from B which is EO

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