What is the probability that a hand of 5 cards chosen randomly and without replacement from a standard deck of 52 cards (which has 4 kings and 4 queens) contains the king of spades, exactly 1 other king, and exactly 2 queens

e - 3,4 = 18,7

e = 18,7 + 3,4

e = 22,1

Answer: b

Step-by-step explanation: 123212p1233213,12,3l12n321

3,2132333333333333333331321m3

The complex partial fraction for the rational functions are: 16/(z⁴+4) = (-4i/√2)/(z² + 2i) + (4i/√2)/(z² - 2i)

To find the complex partial fractions, we first factor the denominator as follows:

z⁴ + 4 = (z² + 2i)(z² - 2i)

Then we can write the rational function as:

16/(z⁴ + 4) = A/(z² + 2i) + B/(z² - 2i)

where A and B are constants to be determined.

We now need to find the values of A and B. To do this, we multiply both sides of the equation by the common denominator (z⁴ + 4), which gives:

16 = A(z² - 2i) + B(z² + 2i)

We can now substitute z = i√2 into this equation, which gives:

16 = A(-2) + B(2i√2)

Solving for A, we get:

A = -4i/√2

Similarly, substituting z = -i√2 gives:

A = 4i/√2

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a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).

(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.

Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.

Now, let's find the expected value of X:

E[X] = E[Y/n] = E[Y]/n = np/n = p.

Therefore, X is an unbiased estimator of p.

(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.

Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.

(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:

E[X(1-X)] = E[X - X²] = E[X] - E[X²].

We already know that E[X] = p from part (a).

Now, let's find E[X²]:

E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².

Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:

E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.

Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].

(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.

E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].

For unbiasedness, we want this to be equal to p(1-p)/n:

c[(n-1)[p(1-p)/n]] = p(1-p)/n.

Simplifying, we have:

c(n-1)p(1-p) = p(1-p).

Since this should hold for all values of p, (n-1)c = 1.

Therefore, the value of c is c = 1/(n-1).

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STEP 1

Interpret question to make sense geometrically.

We have circular shapes, thus, we are dealing with circles and these circles have their area, however, we seek the angle with which when used to cut the circle will give us an area of 220 sq cm.

Note that this is a fraction of the total area of the circle.

This will be illustrated diagrammatically below

Area of a sector is given as:

STEP 2

Find unknown

The ci

Answer:

180

Step-by-step explanation:

36, 72, 108, 144, 180

90, 180

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The value of x as an int variable is 0

An int(integer) variable is a variable containing only whole numbers.

Given the expression;

x = - 3 + 4 % 6/ 5

Let's make into proper fraction, we have

x = - 3 + {}4/ 100 × 6/ 5

Multiply through

x = -3 + 6/ 5/ 4/ 100

x = -3 + {6/ 5 ÷ 0. 4}

x = -3 + {3}

expand the bracket

x = -3 + 3

Add like terms

x = 0

Thus, the value of x as an int variable is 0

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Complete question;

Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 + 4 % 6/ 5;

The inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.

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According to the question, to graph the linear inequality expressions then the given expressions should be equal to the respective number.

In the first equation that is: x<-2 or x = -2

The given expression can be drawn in the second quadrant when the value of the x-axis is negative and it is a straight line which tends to infinity.

In the second equation that is: y ≤ x+2 or y = x+2

The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive  and it is a straight line which tends to infinity.

Similarly, in the third equation that is: y ≤ x-3 or y = x-3

The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive  and it is a straight line which tends to infinity.

What is linear inequality?

Linear inequalities are those expressions in which comparison between the variables is performed. And the comparison can be done between two values or between the two expressions. It uses the symbols of the inequality like greater than, equal to, etc.

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9514 1404 393

Answer:

  400; building and equipment fixed cost

Step-by-step explanation:

The cost equation has two terms. The constant term (400) is the daily fixed cost of building and equipment. The variable term (175p) represents the cost of producing p phones.

The y-intercept is 400. It is the daily fixed cost of the building and equipment.

Answer:

The y-intercept of the function is 400 which represents the fixed cost for rent and equipment.

Step-by-step explanation:

Since Parker must pay $400 even to make 0 phones, that means $400 is the fixed cost that Parker must pay for rent and equipment regardless of the number of phones produced.

Have a good day :)

Answer:

The larger angle is;

Explanation:

Given that the two woods are cut to form complementary angles.

Recall that complementary angles add up to 90 degrees.

Given the two angles as;

Solving the equation for x;

Since we have the value of x, we can the substitute to find the values of each angle;

Therefore, form the values of the two angles, the larger angle is;

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer:

a is 3,2 b is 1,-2 and c is -2,1

Step-by-step explanation:

u take the first number then you just put em together

Answer:

The second choice is correct:

.. Q - P

_____

The constant term is all you really need to look at to figure this.

For P(x), the constant is +2.

For Q(x), the constant is -6.

For P+Q, the constant is -4 . . . . not correct

For Q-P, the constant is -8 . . . . correct

For PQ, the constant is -12 . . . . not correct

For P-Q, the constant is 8 . . . . .not correct

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

The solution is Option A.

The value of the 13th number from the equation A = ( -2/3 ) ( n - 1 ) is A = -8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( -2/3 ) ( n - 1 )   be equation (1)

On simplifying the equation , we get

The thirteenth number in the list is n = 13

So , when n = 13

A = ( -2/3 ) ( n - 1 )

A = ( -2/3 ) ( 13 - 1 )

On further simplification , we get

A = ( -2/3 ) ( 12 )

A = ( -2 ) x 4

So , the value of A = -8

Hence , the thirteenth number in the list is A = -8

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To show the formation of a sulfide ion from a neutral sulfur atom, we need to add two electrons to the sulfur atom, as sulfide ion has a charge of -2. Therefore, the equation for this process is: S + 2e- → S2-

In this equation, S represents the neutral sulfur atom, while S2- represents the sulfide ion that is formed after the addition of two electrons. This reaction is a reduction reaction, as sulfur is gaining two electrons to form a negatively charged ion.
In summary, the equation S + 2e- → S2- shows the formation of the sulfide ion from a neutral sulfur atom by adding two electrons to it. This equation highlights the importance of electron transfer in chemical reactions and how it can lead to the formation of new compounds.

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Answer:

sorry I don't know.....

Condition: A pair of alternate exterior angles are complementary.

Co-planar lines are those lines which are in single plane. For example

if there are two lines AB and CD so for co-planar lines both lines must be in a single plane. Such that it can be in XY or YZ or ZX, any one of the plane.

Also,

Complementary Angles: If the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

Supplementary Angles: Supplementary angles are those angles that sum up to 180 degrees.

Congruent Angles: Congruent angles are the angles that have equal measure.

Refer the figure attached to the answer:

In figure, Angles D, B, E and F are interior angles. Angles A, C, H and G are exterior angles. Angles (D, F) and (B, E) are alternate interior angles.

Now, Looking up the options:

A) A pair of alternate interior angles are congruent.

that means Angle B and E are congruent.

B) A pair of co-interior angles are supplementary.

that means Angle B + F = 180 degree.

C) A pair of corresponding angles are congruent.

that means Angle C and E are congruent.

D) A pair of alternate exterior angles are complementary.

that means Angle A+H=90 degree

After looking all the option A), B) and C) all represents that the lines can be parallel but D) does not indicate that the lines can be parallel.

Hence, A pair of alternate exterior angles are complementary condition does not satisfy that the two lines are parallel.

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Disclaimer: The question given was incomplete on the portal. Here is the complete question.

Question: Two coplanar lines are cut by a transversal. Which condition does NOT guarantee that the two lines are parallel.

A) A pair of alternate interior angles are congruent.

B) A pair of co-interior angles are supplementary.

C) A pair of corresponding angles are congruent.

D) A pair of alternate exterior angles are complementary.

Yes, any sentence written using addition has its own subtraction equivalent. This is done using the example below.

This can be done using Linear Algebra. Linear Algebra is a branch of mathematics that deals with linear combinations. It includes transformation properties and deals with vectors, planes, mappings, and other spaces.

We can use linear algebra to write equations as discussed in the problem. For example, let's take an unknown variable whose quantity we have to find, which will be x. If we add 13.5 to this variable we get 67.89 as the result.

⇒ x + 13.5 = 67.89    (i)

According to the properties of linear algebra, we can bring the 13.5 on the LHS to the RHS to solve this equation. The 13.5 will become negative in this process -

⇒ 67.89 - 13.5 = x  (ii)

Hence, here we have equation (ii) which is the subtraction equivalent of equation (I). We can solve the equation for the value of x as well and the equations would still be the same.

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The first point to plot on the mean control chart would be at 1.9 at control chart with both limits.

1. There are four measurements in each sample, as shown in the table.

2. To plot the first point on the mean control chart, we need to calculate the mean of the first sample. Adding up the four measurements from the 10:00 am sample (2.0 + 1.8 + 2.0 + 1.8) gives a total of 7.6. Dividing by the number of measurements in the sample (4) gives a mean of 1.9. Since the mean is within the control limits of 1.8 and 2.2, the first point on the chart would be plotted at 1.9.
1. To determine how many measurements are in each sample, we simply count the number of measurements provided for each time.

10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)

Each sample contains 4 measurements.

2. To plot the first point on a mean control chart, we need to calculate the mean of the first sample (10:00 am).

Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4
Mean = 7.6 / 4
Mean = 1.9

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1. There are 4 measurements in each sample.

2. The first point to plot on the mean control chart would be 1.9, corresponding to the 10:00 am sample.

To determine the number of measurements in each sample, simply count the number of values for each time point.
10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)
There are 4 measurements in each sample.
To plot the first point on the mean control chart, calculate the mean of the first sample (10:00 am).
Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4 = 7.6 / 4 = 1.9.

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Answer:

A person's age and height

Step-by-step explanation:

Required

Select which do not represent proportionality

Proportionality exists when a unit rate can be calculated.

For instance:

- If 2 litres of gas is $2, then the unit rate is $1 per litre

- If an employee is paid $100 for 5 days, then the unit rate is $20 daily

- If 5 movie tickets cost $50, then the unit rate is $10 per movie

The above scenario are used to describe options (2 - 4) because they can be expressed in unit rates.

However, this is not the same for age and height because age is not a function of height and height is not a function of age. In other words, they can not be expressed in proportions.

So, option (a) is not a situation of proportionality.

Answer:

x=2

Step-by-step explanation:

Area of a triangle = 1/2(b*h)

Plug in what you have

5=1/2(x*5)- Multiply by the reciprocal

10=5x- Divide by 5

x=2

Answer:

Step-by-step explanation:

the slope-International cept frome y= mx + b was where m is the slope and b y-intercept

y=mx +b

m= -2/5

b=2

slope is :2/5

y-intercept is :2

x.   y  

0.  2

1    8/5

Answer:

Step-by-step explanation:

perp. -5/2

y + 2 = -5/2(x - 2)

y + 2 = -5/2x + 5

y = -5/2x + 3

Ignatius of Loyola, the Spanish priest and theologian who founded the Society of Jesus (Jesuits) in the 16th century, focused on several key issues during the period of the Counter-Reformation.

These issues can be broadly categorized into spiritual, educational, and institutional reforms.

Spiritual Reforms: Ignatius emphasized the importance of personal piety and spiritual discipline. He promoted the practice of spiritual exercises, including meditation, prayer, and self-examination, to cultivate a deep and intimate relationship with God. Ignatius encouraged individuals to reflect on their sins and seek forgiveness through confession and penance.

Educational Reforms: Ignatius recognized the power of education in shaping individuals and society. He established schools and universities to provide a comprehensive education that combined intellectual rigor with spiritual formation. The Jesuits placed great emphasis on academic excellence, encouraging critical thinking, the pursuit of knowledge, and the integration of faith and reason.

Pastoral Reforms: Ignatius focused on improving the quality of pastoral care and religious instruction. He trained his followers to be skilled preachers and spiritual directors, equipping them to guide and support individuals in their spiritual journey. Ignatius also emphasized the importance of catechesis, ensuring that people received proper religious education and understood the teachings of the Catholic Church.

Missionary Work: Ignatius and the Jesuits had a strong missionary zeal. They undertook extensive missionary endeavors, particularly in newly discovered territories during the Age of Exploration. They sought to bring Christianity to non-Christian lands and convert indigenous populations to Catholicism. The Jesuits established missions, schools, and hospitals in various parts of the world, playing a significant role in spreading Catholicism.

Overall, Ignatius of Loyola's reforms aimed to strengthen and revitalize the Catholic Church in response to the challenges posed by the Protestant Reformation. His focus on personal spirituality, education, pastoral care, and missionary work contributed to the renewal and expansion of the Catholic Church during the Counter-Reformation.

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Answer:

\(f(x)=x^3+x^2-8x-8\)

Step-by-step explanation:

The mean of the data set is equal to 13.

The median of the data set is equal to 14.

Mathematically, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data, we have;

Total, F(x) = 9 + 16 + 14 + 11 + 9 + 15 + 14 + 16

Total, F(x) = 104

Mean = 104/8

Mean = 13.

First of all, we would sort the observations (data set) from the least to greatest as follows:

Data set = 9, 9, 11, 14, 14, 15, 16, 16

Median = (14 + 14)/2.

Median = 14

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Answer:

the answer d x234 +485eedyu874rr

Answer:

Step-by-step explanation:

x^3+x^2-17x+15  replace x with 3

3^3+3^2-17(3)+15 =0

27+9-51+15  combine

=0

Answer:

The rate of change, or the slope is \(-\frac{1}{4}\) or -0.25

Using the formula \(\frac{y2-y1}{x2-x1}\) we get:

\(\frac{8-12}{16-0} = \frac{-4}{16} = \frac{-1}{4}\)

Answer:

-1/4

Step-by-step explanation:

Rate of change formula (slope)

\(\frac{y^2-y^1}{x^2-x^1}\)

Plug in.

\(\frac{12-8}{0-16}\)

Combine like terms.

\(\frac{4}{-16}\)

\(\frac{-1}{4}\)

Slope means rise over run. Find the change in the y value and the change in the x value to calculate slope.