Let {X1, X2, ... } be a sequence of iid Bernoulli random variables with parameter p and let K = X1 +...+Xn, where n is an integer. In addition, let M denote a binomial random variable, independent of {X1, X2,...}, with expected value np. Do the random variables U = X1 + ... + XK and V = X1 + ... + XM have the same expected value? If so, prove it. If not, prove it and compare the two.

The value of {r} is 64 and the value θ is 30°.

A complex number is a number of the form (a + bi), where [a] and [b] are real numbers and [i] is equal to \(\sqrt{-1}\) . The general form of the complex number representation is (a + ib). In this, [a] is called real part and [ib] is called imaginary part.

Given is the complex number -

z = 4√3 - 4i

We can write the value of {r} as -

r = (4√3)² + (- 4)²

r = 16 x 3 + 16

r = 64

θ = tan ⁻¹(4/4√3)

θ = tan ⁻¹(1/√3)

θ = 30°

Therefore, the value of {r} is 64 and the value θ is 30°.

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Answer:

3

Step-by-step explanation:

Answer: 23

Step-by-step explanation:On the scales below, each shape has a different weight. Scale A is balanced, which means that the sum of the weights on the left is equivalent to the sum of the weights on the right. What shape must be added to the right side of Scale B in order to balance it? Explain how you know.

The shape that must be added to the right side of Scale B in order to balance it is a square.

We can see that the scale on the left side of Scale A has a circle and a triangle, while the scale on the right side has a square and a triangle. Since the scale is balanced, we know that the circle and the square weigh the same.

We can also see that the scale on the left side of Scale B has a circle and a square, while the scale on the right side has a triangle. Since the scale is not balanced, we know that the circle and the square do not weigh the same.

The only way to balance Scale B is to add a shape that weighs the same as the circle. Since we know that the circle and the square weigh the same, we can add a square to the right side of Scale B to balance it.

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Answer:

y = 7

Step-by-step explanation:

12-5=7

7+5=12

Answer:

y = 7

Step-by-step explanation:

12 - y = 5

Subtract 12 from both sides.

-y = -7

Multiply both sides by -1.

y = 7

The equation of a line is generally written in the form \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept. So from the parameters we were given, \(m = 2\) and \(c = -3\), thus the equation becomes \(y = 2x + (-3), y = 2x - 3\)

\(y = 2x - 3\)

The equation of the line with a Y-intercept of -3 and a slope of 2 is y = 2x - 3

The slope of the line is represented by m

m = 2

The y-intercept of the line is represented by c

c = -3

The slope-intercept for of the equation of a line is:

y = mx + c

Substitute m = 2 and c = -3 into the equation above

y = 2x - 3

Therefore, the equation of the line with a Y-intercept of -3 and a slope of 2 is:

y = 2x - 3

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a) To test the hypothesis that the population standard deviation σ = 4.1, with a sample size n = 25 and a sample standard deviation s = 3.841, we need to calculate the P-value.

The degrees of freedom (df) for the test is given by (n - 1) = (25 - 1) = 24.

Using the chi-square distribution, we calculate the P-value by comparing the test statistic (χ^2) to the critical value.

the correct conclusion is:

The P-value 0.305 is not significant and so does not strongly suggest that σ < 9.1. The test statistic is calculated as: χ^2 = (n - 1) * (s^2 / σ^2) = 24 * (3.841 / 4.1^2) ≈ 21.972

Using a chi-square distribution table or statistical software, we find that the P-value corresponding to χ^2 = 21.972 and df = 24 is approximately 0.028.

Therefore, the correct conclusion is:

The P-value 0.028 is not significant and so does not strongly suggest that σ < 4.1.

b) To test the hypothesis that the population standard deviation σ = 9.1, with a sample size n = 15 and a sample standard deviation s = 5.506, we follow the same steps as in part (a).

The degrees of freedom (df) for the test is (n - 1) = (15 - 1) = 14.

The test statistic is calculated as:

χ^2 = (n - 1) * (s^2 / σ^2) = 14 * (5.506 / 9.1^2) ≈ 1.213

Using a chi-square distribution table or statistical software, we find that the P-value corresponding to χ^2 = 1.213 and df = 14 is approximately 0.305.

Therefore, the correct conclusion is:

The P-value 0.305 is not significant and so does not strongly suggest that σ < 9.1.

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Answer:

-0.1

Step-by-step explanation:

-1/100 = -0.01

1/10 = 0.1

-0.01/0.1 = -0.1

Answer:

A. 40°

Step-by-step explanation:

∠Z=∠Y (base ∠ of isosΔ)

    = 60°

∠X=180-60-60(∠ sum of Δ)

    =40°

Answer:

A

Step-by-step explanation:

z = y                                  Both are opposite equal sides

z = 70                                From the first statement.

y = 70                                Given

x = 180 - z - y                    A triangle has 180 degrees

x = 180 - 70 - 70

x = 40

Answer:

5/8 + 7/12

Step-by-step explanation:

Miles to friends house = 5/8

Ditance to the movies = 7 1/2

To find the total distance walked in Wal, we sun the fraction of distance Evans walked to his friend's house and the distance walked from friend's house to the movies ;

That is :

5/8 + 7/12

= 29/24 miles

The probability that the committee has a majority of women is approximately 0.0044.

To calculate the probability that the committee has a majority of women, we need to determine the number of ways we can select a committee with a majority of women and divide it by the total number of possible committees.

First, let's calculate the total number of possible committees. Since there are 63 senators in total (19 women + 44 men), we have 63 options for the first committee member, 62 options for the second, and so on.

Therefore, there are 63*62*61*60*59 = 65,719,040 possible committees.

Next, let's calculate the number of ways we can select a committee with a majority of women. Since there are 19 women in the NY Senate, we have 19 options for the first committee member, 18 options for the second, and so on.

Therefore, there are 19*18*17*16*15 = 28,7280 ways to select a committee with a majority of women.

Finally, let's calculate the probability by dividing the number of committees with a majority of women by the total number of possible committees:

287280/65719040 ≈ 0.0044.

In conclusion, the probability that the committee has a majority of women is approximately 0.0044.

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The quality and credibility of the risk analysis requires a PM to define risk probability and impact, which can then be made into a Probability and Impact Matrix.

The quality and credibility of risk analysis in project management require a comprehensive approach that includes defining risk probability and impact. The probability of a risk event is the likelihood of it occurring, and impact is the magnitude of its consequences on project objectives. Once these factors are defined, they can be used to create a Probability and Impact Matrix, also known as a Risk Matrix, which is a useful tool for assessing and prioritizing risks.

The Probability and Impact Matrix is a grid that lists the probability of an event occurring on one axis and the impact of that event on project objectives on the other axis. The intersection of these two factors represents the level of risk associated with that event. By assigning a probability and impact score to each risk, the PM can prioritize them and allocate resources to mitigate or manage them accordingly.

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Answer:

x = 350 gallons (amt of 60% solution that must be added)

Step-by-step explanation:

Amt of 60% solution = x gallons ; Amt of active ingredient = 0.6x gallons

Amt of 15% solution = 100 gallons ; Amt of active ingredient = 15 gallons

Amt of 50% solution = 100+x gallons ; Amt of active = 50 + 0.5x gallons

EQUATION:

Active ingredient: 0.60x + 15 = 50 + 0.50x

0.10x = 35

x = 350 gallons (amt of 60% solution that must be added)

Answer:

(-2,-2)

Step-by-step explanation:

x^2 + y^2 = 9

A circle has an equation of the form

(x-h)^2 + (y-k)^2 = r^2

where the center is at ( h,k) and the radius is r

The circle is centered at (0,0) and has a radius 3

The only point entirely within the circle must have points less than 3

(-2,-2)

Answer:

a] 5 dogs

b] 16 dogs

Step-by-step explanation:

        The minimum number of dogs that could have a mass of more than 26 kg is 5. This is because dogs with a mass of 30 ≤ x ≤ 40 have a frequency of 5. The dogs in the 20 ≤ x ≤ 30 range could be more than 26 kg, but they could also be less than 26 kg, so these are not included in the minimum.

        The maximum number of dogs that could have a mass of 26 kg is 16 because both dogs in the 30 ≤ x ≤ 40 range (5) and 20 ≤ x ≤ 30 range (11) could weigh more than 26 kg. 11 + 5 = 16, giving us our answer for the maximum.

Answer:

47

Step-by-step explanation:

Pretty sure it equals 360 degress overall so 360 -313 = ^^^^^^^^^^^^

Answer:

25/7 acres or 3 4/7 acres

Step-by-step explanation:

The sold 2/7 of the land.

1 - 2/7 = 7/7 - 2/7 = 5/7

They have 5/7 of the land left.

5/7 of 5 acres = 5/7 × 5 acres = 25/7 acres = 3 4/7 acres

Answer:

-3x-5 x-4 I this work good luck

Answer:

-(3x-5) (x-4)

Step-by-step explanation:

-3x^2+17x-20

Factor -1 out of -3x^2

-(3x^2)+17x-20

Factor -1 out of 17x

-(3x^2)-(-17x)-20

Rewrite -20 as -1(20)

-(3x^2)-(-17x)-1(20)

Factor -1 out of -(3x^2)-(-17x)

-(3x^2-17x)-1(20)

Factor -1 out of -(3x^2-17x)-1(20)

-(3x^2-17x+20)

Factor.

-((3x-5)(x-4))

Final Anwser:

-(3x-5) (x-4)

Step-by-step explanation:

yes because after the first rotation the triangle formes a parallelogram, because the interior angles are equal, because the parallelogram is basically formed of two identical triangles. after the second rotation the triangle forms yet another parallelogram(the one "glued" to the initial triangle) for the same reason. in conclusion the bases of the final quadrilateral will always be paralel because of the parallelograms=>it will always be a trapezoid

Answer:

10 inches squared.

Step-by-step explanation:

15/2x4/3 -> 60/6 -> 10 inches squared

Answer:

i need help too

Step-by-step explanation:

The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3).

To determine the x-intercept, let y = 0 and solve for x in the equation y = 3x - 1.

Substitute 0 for y in the equation.0 = 3x - 1

Add 1 to both sides1 = 3x

Divide both sides by 3x = 1/3

The x-intercept of the line is (1/3, 0).

To find the y-intercept, let x = 0 and solve for y in the equation y = 3x - 1.

Substitute 0 for x in the equation.y = 3(0) - 1y = -1

The y-intercept of the line is (0, -1).

Therefore, the x-intercept is (1/3, 0), and the y-intercept is (0, -1).

Therefore, The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3). The calculation above supports the conclusion.

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The interest rate your friend is charging you for the $20,000 loan is 20% per year.

The simple interest is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is the interest rate and t is time.

Given that;

The Principal P = $20,000

Accrued amount A = $40,000

Elapsed time t = 5 years

Interest rate r =?

Plug these values into the above formula and solve for the interest rate r:

\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)

Converting r decimal to R a percentage

Rate R = 0.2 × 100%

Rate r = 20% per year

Therefore, the interest rate is 20% per year.

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We choose option B: The P-value gives strong evidence against H_0. The P-value indicates that the null hypothesis is not plausible.

a. To find the test statistic z, we use the formula:

z = (p - P) / sqrt [P(1-P) / n]

where p is the sample proportion, P is the hypothesized proportion under the null hypothesis, and n is the sample size.

Plugging in the values given, we get:

z = (0.43 - 0.5) / sqrt [0.5(1-0.5) / 100] = -1.96

b. To find the P-value for H_a: p < 0.50, we look up the probability of getting a z-score less than -1.96 in a standard normal distribution table. The P-value is the area under the standard normal curve to the left of -1.96.

The P-value is approximately 0.025.

c. Since the P-value is less than the significance level of 0.05, we can reject the null hypothesis at the 5% level of significance. The P-value gives strong evidence against H_0. Therefore, we choose option B: The P-value gives strong evidence against H_0. The P-value indicates that the null hypothesis is not plausible.

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(i) The pdf of random variable X is:

\(fx(x) = {2bx e^{(-bx^2)}\), x > 0

0, x < 0

(ii) The pdf of Y is:

\(fy(y) = b\sqrt y / e^{(by)} , y > 0\)

0, y ≤ 0

(i) To find the probability density function (pdf) of X, we need to take the derivative of the cumulative distribution function (cdf) with respect to x.

For x > 0, we have:

\(Fx(x) = 1 - e^{(-bx^2)}\)

Differentiating both sides with respect to x gives:

fx(x) = d/dx Fx(x) = \(d/dx [1 - e^{(-bx^2)}] = 2bx e^{(-bx^2)}\)

For x < 0, we have:

Fx(x) = 0

Differentiating both sides with respect to x gives:

fx(x) = d/dx Fx(x) = d/dx [0] = 0

Therefore, the pdf of X is:

\(fx(x) = {2bx e^{(-bx^2)}\), x > 0

{0, x < 0

(ii) To find the pdf of \(Y = X^2\), we can use the transformation method. The transformation function is \(g(x) = x^2\).

We have:

Fy(y) = P(Y ≤ y) = P(\(X^2\) ≤ y) = P(-√y ≤ X ≤ √y) = Fx(√y) - Fx(-√y)

Differentiating both sides with respect to y gives:

fy(y) = d/dy Fy(y) = d/dy [Fx(√y) - Fx(-√y)]

= (1/2y) fx(√y) - (-1/2y) fx(-√y)

\(= (1/2y) 2b\sqrt y e^{(-by)}\)

= \(b\sqrt y / e^{(by)}\)

Therefore, the pdf of Y is:

\(fy(y) = b\sqrt y / e^{(by)} , y > 0\)

0, y ≤ 0

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Answer:

12

Step-by-step explanation:

(5×6)-½(3×6 + 2×4 + 2×5)

=30 - ½(18+8+10)

= 30 - ½(36)

=30-18= 12

Answer:

A= -40

B= 16

C= 40

D= 50

Step-by-step explanation:

The values of the matrix is a = -40, b = 16, c = 40, d = 50.

A matrix is an arrangement of numbers, expressions or symbols arranged in rows and columns as a rectangular array. These rows and columns define the size or dimension of a matrix.

For the given situation,

The matrix is

\(\left[\begin{array}{ccc}4&-1&-4\\0&5&-2\\0&8&10\end{array}\right] = \left[\begin{array}{c}-7&-11&22\end{array}\right]\)

The operation on matrix is

\(-8R2- > R2\) and

\(5R3- > R3\)

⇒ \(\left[\begin{array}{ccc}4&-1&-4\\0&-40&16\\0&40&50\end{array}\right] = \left[\begin{array}{c}-7&88&110\end{array}\right]\)

On comparing this equation with the given equation,

\(a=-40, b=16, c=40, d=50\)

Hence we can conclude that the values of the matrix is a = -40, b = 16,     c = 40, d = 50.

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In the given proof shown below, the idea of tangents and perpendicularity is used to set up a relationship between two lines, AR and BS.

The tangent is a term that is used to tell more or described as the  point of contact between a circle or an ellipse and a single line.

Based on the fact  that the tangent line is perpendicular to radius of the circle.

Hence, AR ⊥ RS and BS ⊥ RS

Therefore, AR and BS ⊥ similar to line RS.

So,  the line AR or BS are said to be either in same line or parallel. because , they are the radius of different circles.

Therefore, AR ║BS.

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Answer: Answer: The answer should be f = 1.

Answer:

f=1

Step-by-step explanation:

3f+2=8-3f

6f=6

f=1

checking answer:

-1+2+4=8-3

5=5