An urn contains 12 white and 8 black marbles. If 9 marbles are to be drawn at random with replacement and X denotes the number of white marbles, find E(X) and V(X).

Approximate solution after 3 iterations: x = -1311.54, y = -15.216, z = 100.219.

To check for diagonal dominance, we compare the absolute value of the coefficient on the diagonal to the sum of the absolute values of the other coefficients in each equation. If the diagonal coefficient is greater in absolute value than the sum of the other coefficients, the system is diagonally dominant.

Let's check the given system of equations for diagonal dominance:

Equation 1: x + 11y - 5z = 14

The diagonal coefficient is 1, and the sum of the absolute values of the other coefficients is 11 + 5 = 16. Diagonal dominance is satisfied for this equation.

Equation 2: 10x - y + 3z = 25

The diagonal coefficient is 10, and the sum of the absolute values of the other coefficients is 1 + 3 = 4. Diagonal dominance is satisfied for this equation.

Equation 3: 2x - y + 13z = 29

The diagonal coefficient is 13, and the sum of the absolute values of the other coefficients is 2 + 1 = 3. Diagonal dominance is satisfied for this equation.

Since diagonal dominance is satisfied for all three equations, we can use the Gauss-Seidel method to solve the system. The Gauss-Seidel method iteratively improves the initial guess of the solution until it converges to an approximate solution.

Given initial guesses x = 0, y = 0, and z = 0, let's apply the Gauss-Seidel method and iterate three times.

Iteration 1:

From Equation 1: x = (14 - 11y + 5z) / 1

Substituting x = 0, y = 0, and z = 0:

x = (14 - 0 + 0) / 1

x = 14

From Equation 2: y = (25 - 10x + 3z) / -1

Substituting x = 14, y = 0, and z = 0:

y = (25 - 10 * 14 + 0) / -1

y = -145

From Equation 3: z = (29 - 2x + y) / 13

Substituting x = 14, y = -145, and z = 0:

z = (29 - 2 * 14 + (-145)) / 13

z = -12.692

Iteration 2:

From Equation 1: x = (14 - 11y + 5z) / 1

Substituting x = 14, y = -145, and z = -12.692:

x = (14 - 11 * (-145) + 5 * (-12.692)) / 1

x = -1311.54

From Equation 2: y = (25 - 10x + 3z) / -1

Substituting x = -1311.54, y = 0, and z = -12.692:

y = (25 - 10 * (-1311.54) + 3 * (-12.692)) / -1

y = -15.216

From Equation 3: z = (29 - 2x + y) / 13

Substituting x = -1311.54, y = -15.216, and z = -12.692:

z = (29 - 2 * (-1311.54) + (-15.216)) / 13

z = 100.219

Iteration 3:

From Equation 1: x = (14 - 11y + 5z) / 1

Sub

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Answer and Step-by-step explanation:

According to the given situation, The r-value associated with the ordered pairs for the linear function is very nearest to zero which does not results in adequate presentation of the outcome.

A quadratic model could properly comprise of a combination of data, as the set of data has a turning point.

This result in data rises and falls which represents the graph of quadratic's graph

A linear representation is not the best way to show the data from the equation as derived from the regression calculator.

Note that when plotted on a graph, it will show an upside down u kind of shape, and it as such look linear is not a good choice.  

Note also that the r-value is linked with the ordered pairs for the linear function as it is said to be closer to zero and thus, it does not show an adequate depiction of the outcome.

Therefore, A linear representation is not the best way to show the data from the equation as derived from the regression calculator.

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Answer:

-2x - 6

Step-by-step explanation:

Answer:

the answer is B

-2X - 6

Step-by-step explanation:

The number of hours that students have to work on homework will be 1/3 hours.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

Mr. K's maths class is 1 and 1/4 hours long.

After working problems on the board for 55 minutes  or 11 / 12 hour.

He gave the students the rest of the class period to work on homework.

Then the number of hours that students have to work on homework will be

⇒ 1 + 1/4 - 11/12

⇒ 5 / 4 - 11/ 12

⇒ (15 - 11) / 12

⇒ 4/12

⇒ 1/3 hours

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Answer:

radius = 7.5 cm

Step-by-step explanation:

Since M is the midpoint of the chord AB then OM is perpendicular to AB

Using Pythagoras' identity in right triangle OMB with hypotenuse OB, the radius of the circle, then

OB² = OM² + MB² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )

OB = radius = \(\sqrt{56.25}\) = 7.5

Answer:  w = 30

Step-by-step explanation: A triangle is 180 degrees, always. One angle is 60 and the other above is 90. We add them together and get 150. Subtract it from 180 and we get 30 degrees.

P.S.: I'm sorry that I put only w, that's the only one I could work out . Also sorry if I'm wrong, maths is not my very strong subject.

The pattern will be attached in the figure attached, in the matrix form.

What is the matrix?

The arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns are known as matrices, which is the plural version of the word matrix. They are rectangular arrays with defined operations for addition, multiplication, and transposition. The constituents of the matrix are its numbers or entries. Vertical entries in matrices are referred to as columns, whereas horizontal entries are known as rows. A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for operations like subtraction, addition, and multiplication. The number of rows and columns in a matrix determines its size, sometimes referred to as its order.

We can arrange it as A = (0 0 0 0 1 1 0 0 1)

We know A*TA = 0

If A has an entry 9 then, the sum of all the diagonal elements.

So the T will be the form of the matrix attached below.

Hence the Pattern will be attached in the figure attached.

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Answer:he equation can be written as y=0x+7 ). Thus, y will always be 7 , creating a horizontal line.

Step-by-step explanation: so it is not c

The graph of y = 7 is a horizontal line. neither is it b so it is a

The unit price of the red ribbon is $0.88 per meter.

What is rate ?

A rate is a measure of the speed of something in relation to another quantity or measurement. It is a ratio that expresses how much of one quantity occurs in a given amount of another quantity. In other words, it is a comparison of two different measurements.

To find the unit price of the red ribbon, we need to divide the total cost by the number of units (in this case, meters) in the roll:

Unit price =  cost / Number of units

In this case, the total cost is $7.92 and the number of units is 9 meters. So, we have:

Unit price = $7.92 / 9 meters

Using a calculator or by performing long division, we can simplify this expression to find the unit price:

Unit price = $0.88 per meter

Therefore, the unit price of the red ribbon is $0.88 per meter.

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If the scale factor is 3/4. Then the perimeter of the original triangle will be 66.67 units.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a scale factor of 3/4.

Then the perimeter of the preimage, the original triangle, before its

dilation will be

Let c be the perimeter of the original triangle.

Then we have

\(\rm \dfrac{3}{4} \times x = 50\\\\x = 66.67\)

Then the perimeter of the original triangle is 66.67 units.

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The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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angle has a measure equal to the sum of the the question is ∠DQS.


According to the problem, we need to find an angle whose measure is equal to the sum of the measures of ∠SQR and ∠QRS. We can use the angle addition postulate which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures.

Let's consider angle ∠DQS. This angle is formed by adjacent angles ∠SQR and ∠QRS. Therefore, according to the angle addition postulate, the measure of angle ∠DQS is equal to the sum of the measures of ∠SQR and ∠QRS.



Thus, we can conclude that the angle ∠DQS has a measure equal to the sum of the measures of ∠SQR and ∠QRS.

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x+1/2x+2/3x+4=30, which has one solution

The test statistic value is approximately 9.69.

To calculate the test statistic for this problem, we will use the following formula:
Test statistic (z) = (p_sample - p_population) / √(p_population * (1 - p_population) / n)
Where:
- p_sample is the proportion of voters who support the taxpayer-funded free college program in the sample (375/610)
- p_population is the proportion of voters who oppose making all U.S public colleges free according to the 2019 Quinnipiac University poll (58% or 0.58)
- n is the sample size (610)
First, let's find p_sample:
p_sample = 375/610 = 0.6148
Now we need to find the proportion of voters who support the program in the population, since we know that 58% oppose it:
p_population = 1 - 0.58 = 0.42
Now we can plug these values into the test statistic formula:
z = (0.6148 - 0.42) / √(0.42 * (1 - 0.42) / 610)
z = 0.1948 / √(0.2436 / 610)
z = 0.1948 / 0.0201
z ≈ 9.69
The test statistic value is approximately 9.69.

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The value of $×$ is 3.14 units

Perimeter is the distance around the edge of a shape. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.

The perimeter of a square is expressed as 4l

The circumference of a circle = 2πr

This means that;

4l = 2πr

4l = 2× 3.142 × 2

4l = 12.57

divide both sides by 4

l = 12.57/4

l = 3.14 units(nearest hundredth)

therefore the value of the side length is 3.14 units

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The survey's reliability and validity depend on the methodology and quality of the sample data.

In the given scenario, a survey aims to investigate whether the proportion of today's high school seniors who own their own cars is higher than it was a decade ago. The survey proposes an alternative hypothesis that suggests a change in the proportion, while the null hypothesis assumes no change. The survey also mentions that the observed result would occur by chance 1.7% of the time if the null hypothesis were true.

To evaluate the reasonability of the survey, we need to consider the concept of statistical significance. Statistical significance is a measure of how likely the observed result would occur due to chance alone, assuming the null hypothesis is true. In hypothesis testing, a common threshold for statistical significance is α (alpha), typically set at 0.05 or 5%.

In this case, the survey suggests that the observed result would occur by chance 1.7% of the time if the null hypothesis were true. This is known as the p-value. The p-value represents the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.

If the p-value is less than the chosen significance level (α), we reject the null hypothesis in favor of the alternative hypothesis. In this scenario, since the p-value is 1.7%, which is less than 5%, we can conclude that the observed result is statistically significant.

Therefore, it is reasonable to conduct the survey and investigate whether the proportion of high school seniors who own their own cars has increased compared to a decade ago. The survey provides evidence to support the alternative hypothesis and suggests that the observed result is unlikely to occur by chance alone, assuming the null hypothesis is true.

However, it's important to note that the survey's reasonability is based on the assumption that the survey methodology and sample data are reliable and representative. The survey should ensure that the sample is randomly selected and sufficiently large to provide accurate results. Additionally, the survey should consider potential confounding variables and sources of bias that could affect the findings.

In summary, the survey investigating the proportion of high school seniors who own their own cars and proposing a higher proportion than a decade ago is reasonable based on the evidence provided, which suggests a statistically significant result. However, the survey's reliability and validity depend on the methodology and quality of the sample data.

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The solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

What is Trigonometric equation?

A trigonometric equation is an equation that involves trigonometric functions such as sine, cosine, tangent, or their inverses. Trigonometric equations arise in a variety of mathematical and scientific contexts, from solving geometric problems involving angles and triangles to modeling periodic phenomena in physics, engineering, and other fields.

Solving a trigonometric equation typically involves finding the values of the unknown variable that satisfy the equation within a certain interval. For example, the equation sin(x) = 0 has infinitely many solutions, but if we restrict the interval to [0, 2π], then the solutions are x = 0, π, 2π, which correspond to the x-intercepts of the sine function in that interval.

Here the equation sin(πx/3) = 0 has solutions whenever πx/3 is an integer multiple of π, since the sine function is zero at these values. Thus, we need to find all integers n such that πx/3 = nπ, or equivalently x = 3n for some integer n.

Since -5 < x < 5, we need to find all integers n such that -5 < 3n < 5. Dividing all sides by 3, we get -5/3 < n < 5/3. The only integers in this range are -1, 0, and 1. Therefore, the solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

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Answer:

14

Step-by-step explanation:

25 percent of 56 is 14

Step-by-step explanation:

100%=56

1%=56÷100=0.56

25%=0.56×25=14

The line which have a steeper slope is Line 1.

It is given in the question that the points on the line are given by:-

Line 1: (0,-4) and (2,2)

Line 2:(0,-4) and (4,5)

We have to find which line has a steeper slope.

First we will find the slope of each line.

We know that slope of a line with points (a,b) and (c,d) is given by:-

(d-b)/(c-a)

Slope of Line 1:

(2-(-4))/(2-0) = 6/2 = 3

Slope of Line 2:

(5-(-4))/(4-0) = 9/4 = 9/4 = 2.25

We know that greater the slope of the line means greater the steep of the line.

As,

3 > 2.25

Hence, Line 1 is steeper than Line 2.

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Answer:

6 Meters

Step-by-step explanation:

If the car is driving at a constant velocity of 36 m/s and accelerates at -6.0 m/s ^2 to a stop, then the distance of the car decelerates to a stop in 6 seconds.

a=v/t ->>> 6= 36/t

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Rewriting the expression |3r-15| without using absolute value bars gives

3r < 15 for r < 5

Absolute value do not give negative values it gives only the positive value

The given expression is |3r-15|

|3r - 15| < 0

|3r| < |-15|

3r < 15

If r < 5 then  say 4

|3r - 15|

|3 * 4 - 15|

|12 - 15|

|-3| = 3

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Answer:

Step-by-step explanation:

f^-1(x)=x/2+3

Answer: See explanation

Step-by-step explanation:

The information given in the question can be turned into an equation as:

2u + y = 30 ........ i

5u + y = 42 ........ ii

Subtract i from ii

3u = 12

u = 12/3 = 4

A pair of socks cost $4

Since 2u + y = 30

2(4) + y = 30

8 + y = 30

y = 30 - 8 = 22

A pair of slippers cost $22

bearing in mind that the sum of all interior angles in a polygon is

180(n - 2)    n = number of sides in the polygon

a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.

\(\bold{120+140+160+130+125+140+165+160+140+v=1440}\)

\(\bold{1275+v=1440 \implies v=1440-1275 \implies v=165}\)

The probability that 72% or more of the women in the sample have been on a diet is, 0.1736.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

As given a sample survey interviews an SRS of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months.

p = 0.69

1 - p = 0.31

n = 209

μp = p = 0.69

σp = √(p(1-p))/n = √(0.69*0.31)/209 = 0.03199

= 1 - p(p < 0.72)

= 1 - p((p - μp) / σp < (0.72 - 0.69) / 0.03199)

= 1 - p(z < 0.94)

= 1 - 0.8264

= 0.1736

Hence, the probability is 0.1736.

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Answer:

(9x+2)^2

Step-by-step explanation:

The points A(2, -1, 4), B(3, 1, 2), C(0, 5, 6), and D(-1, 3, 8) form a parallelogram. The area of the given parallelogram is 12 square units.  It is not a rectangle.

To verify if the given points form a parallelogram, we need to check if both pairs of opposite sides are parallel.

The vectors formed by the sides AB and CD are AB = (1, 2, -2) and CD = (-1, -2, 2). The vectors formed by the sides BC and AD are BC = (-3, 4, -4) and AD = (-3, 4, -4).

Comparing these vectors, we can see that AB and CD are parallel, as are BC and AD. This indicates that the given points A, B, C, and D form a parallelogram.

To find the area of the parallelogram, we can use the cross product of the vectors AB and AD (or BC and CD) to find the area of the corresponding parallelogram. The magnitude of the cross product of AB and AD is |AB × AD| = 12.

Since the area of a parallelogram is equal to the magnitude of the cross product of its adjacent sides, the area of the given parallelogram is 12 square units.

To determine if the parallelogram is a rectangle, we can check if any of its angles are right angles. However, since the given points do not have any indication of angles, we cannot determine if the parallelogram is a rectangle based on the information provided.

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