Graph on a number line\(x \geqslant 3\)

In the given problem, we are provided with the joint probability density function (pdf) of discrete random variables X and Y. We need to find the constant c, the marginal pdfs of X and Y, and determine whether X and Y are independent.

(a) To find the constant c, we need to ensure that the joint pdf satisfies the properties of a probability distribution. Since the sum of all possible probabilities must equal 1, we can sum the joint pdf over all possible values of X and Y and set it equal to 1. By evaluating the summation, we can determine the value of c.

(b) To find the marginal pdfs of X and Y, we need to calculate the probabilities of each individual variable without considering the other variable. The marginal pdf of X can be found by summing the joint pdf over all possible values of Y, and similarly, the marginal pdf of Y can be found by summing the joint pdf over all possible values of X.
(c) To determine whether X and Y are independent, we need to check if the joint pdf can be expressed as the product of the marginal pdfs. If the joint pdf can be factorized in this way, then X and Y are independent. Otherwise, they are dependent.

By performing the necessary calculations and analysis, we can find the constant c, the marginal pdfs of X and Y, and determine the independence of X and Y based on the properties of the joint pdf.

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Answer:

D)  1.0

Step-by-step explanation:

if y = 1 then x = 1

The given statement, "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is False.

Explanation: Null space is a linear algebra term used to refer to the set of all vectors that are mapped to the null vector. The solution of Ax=0 is also referred to as the null space or kernel of A. Since the matrix is of size 4x4 and non-zero, it must have at least one non-zero eigenvalue. Any non-zero vector multiplied by this non-zero eigenvalue will result in a non-zero vector, even if it is in the nullspace of the matrix. Because of this, a non-zero 4 x 4 matrix's nullspace can have four or fewer linearly independent vectors.

Hence, the statement "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is false.

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Answer:

Value of m = r / [p + z]  

Step-by-step explanation:

Given:

Equation:

mp + mz = r

Find:

Value of m

Computation:

⇒ mp + mz = r

⇒ m [p + z] = r

⇒ m = r / [p + z]

Value of m = r / [p + z]  

Answer:

The formula for measuring the area differs according to shape.

The formula for area of square = a*a

The formula for area of rectangle = l*b

The formula for area of triangle = 1/2*base*height

HOPE IT HELPS :)

PLEASE MARK IT THE BRAINLIEST!

Answer:

Step-by-step explanation:

It depends on the shape

For rectangle it is length x breadth

For triangle it is 1/2 x base x height

For square it is L^2

For circle it is pi x r^2

Etc

Answer:

b = -10

c = 25

Step-by-step explanation:

Since the only solution to x is 5 that mean answer will look something like this:

(x-5) (x-5) = 0

x(x-5) -5(x-5)

x^2 -5x -5x + 25

x^2 -10x + 25

This is same as x^2 + bx + c = 0

where b is -10 and c is 25

My new salary after increasing 2.5% will be $25,625.

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

We have given that :

Salary = $25,000

Percentage increment in salary =2.5%

New salary = 25,000 × (2.5/100 ) + 25,000

                   = 625 + 25,000

New salary = $25,625

Hence the new salary will be $25,625.

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Answer:

Step-by-step explanation:

Step one:

given data

the cost of the laptop= $800

initial payment= $200

monthly payment = $60

let the number of months be x

the expression for the situation is the function for the equation of line

y=mx+c

Step two:

the expression for the situation is

800=200+60x

solve for x

800-200=60x

400=60x

divide both sides by 60

x=400/60

x=6.7

Approximately 7 months

Hey There!!

Your best choice is 76%

Because, 19/25 = x/100

25x = 1900

x = 76

°He got 76% correct!!°

By °Itsbrazts°

Answer:

76%

Step-by-step explanation:

Thomas got 19/25 marks.

** Note: Percents are always out of 100.

We don't know how many marks he got out of 100.

=> 19/25 = x/100

There are two ways to solve it from now.

=> Multiply 19 and 100; 25 and x

=> 25x = 1900

Next, Divide 25 on each side.

=> 25x/25 = 1900/25

=> x = 76

He got 76% on the quiz.

Another way is:

=> 19/25 = x/100

=> We need to divide 25 from 100.

=> We get 4.

So, 25 x 4 = 100

=> 19 x 4 = x

=> x = 76

He got 76% on the quiz.

Both ways are correct.

The number of permutations and combinations possible for the formation is: \(^{31}C_{11} \times ^{12}C_3 \times ^{3}C_1 \times ^{9}C_4 \times ^{7}C_3\)

What are permutations and combinations?

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.The act of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the elements of a set if the set is already ordered. Nearly all areas of mathematics involve permutations in some form or another. They frequently appear when various orderings on particular finite sets are taken into account.

In the given question: we have;

Total number of PLayers = 31;

Number of goalkeeper = 3;

Number of Defender = 12;

Number of Midfielders = 9;

Number of Strikers = 7;

We have to select 11 players

and in that we should have 3 defenders; 4 midfielders, 3 strikers, and 1 goalkeeper;

So the permutation and combination possible for choosing a defender from 12 players are: \(^{12}C_3\)

and,

The number of permutations and combinations possible for choosing 1 goalkeeper are: \(^{3}C_1\)

A number of permutations and combinations possible for choosing 4 midfielders are: \(^{9}C_4\)

The number of permutations and combinations possible for choosing 3 strikers are: \(^{7}C_3\)

So, the total number of ways possible is: \(^{31}C_{11} \times ^{12}C_3 \times ^{3}C_1 \times ^{9}C_4 \times ^{7}C_3\)

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Answer:

BOC, since angle B and angle C are bisected, sum of angle OBC and OCB will be half of sum of angles B and C which is 108 degrees.

Answer:

1. x = 67.5

2. x = 2.5

3. x = 35.2

4. x = 2.0

5. x = 17.0

Step-by-step explanation:

Question 1

The proportion is set up in the form x/9 = 15/2. Multiply both sides by two to get rid of the two in the denominator on the right side. After doing so, multiply by 9 on both sides to get rid of the 9 in the denominator on the left:

2x/9 = 15

2x = 9(15)

Next solve for x:

2x = 135

x = 67.5

Question 2

The proportion is set up in the form 20/8.7 = 5.8/x. Multiply both sides by the second denominator, x, and then both sides by the first, 8.7. This will leave you with the work below:

20x/8.7 = 5.8

20x = 8.7(5.8)

Next, solve for x:

20x = 50.46

x = 2.523

Round to the nearest tenth:

x = 2.5

Question 3

The proportion is set up in the form 5/16 = 11/x. Multiply both sides by the second denominator, x, and then both sides by the first, 16. This will leave you with the work below:

5x/16 = 11

5x = 11(16)

Next, solve for x:

5x = 176

x = 35.2

Question 4

The proportion is set up in the form x/0.06 = 17/0.5. Multiply both sides by the second denominator, 0.5, and then both sides by the first, 0.06. This will leave you with the work below:

0.5x/0.06 = 17

0.5x = 17(0.06)

Next, solve for x:

0.5x = 1.02

x = 2.04

Round to the nearest tenth:

x = 2.0

Question 5

The proportion is set up in the form 29/x = 75/44. Multiply both sides by the second denominator, 44, and then both sides by the first, x. This will leave you with the work below:

29(44)/x = 75

29(44) = 75x

Next, solve for x:

1276 = 75x

x = 17.0133

Round to the nearest tenth:

x = 17.0

Answer:

Just choose the first one.

Answer:

FE

FG

AB

EG

AC

BC

step by step explanation:

a = -14

-14+28= 14

14 x 2 = 28

1/2 of -28 --> -14

This means a equals -14.

Esto significa A=-14

(sorry my spanish is not good, hope this helps)

Answer:

Step-by-step explanation:

To solve for x and y, take advantage of the relationships between angles and diagonals in a rhombus. Each diagonal bisects the vertex angle, and the acute angles in each right triangle are complementary.

__

The angles created by the diagonal at the lower left vertex are congruent:

  y° = 21°

__

The angles x° and y° are complementary:

  x° = 90° -21°

  x° = 69°

Answer: X²+2x

Step-by-step explanation:

Use FOIL method

Solve:

 x(x+2)

☽------------❀-------------☾

Hi there!

~

What is \(x(x+2)\) expanded?

\(x(x+2)\) in expanded form is :

\(x^2 + 2x\)

Explanation :

Apply the distributive law: \(a( b + c ) = ab + ac\)

\(x(x+2) = xx + x \times 2\)

\(= xx + x \times 2\)

Then you simplify : \(xx + x \times 2 : x^2 + 2x\)

\(= x^2 + 2x\)

❀Hope this helped you!❀

☽------------❀-------------☾

The next letters in the pattern are 6 and -7.The given pattern alternates between positive and negative numbers. By observing the pattern, we can determine the next numbers in the sequence.

The first number, 2, is positive. The second number is obtained by taking the negative of the previous number and subtracting 1. Therefore, -2 - 1 = -3.The third number is positive and is obtained by taking the absolute value of the previous number and adding 1. Therefore, |-3| + 1 = 4.

The fourth number is negative and is obtained by taking the negative of the previous number and subtracting 1. Therefore, -4 - 1 = -5.

Following this pattern, the next number will be positive and obtained by taking the absolute value of the previous number and adding 1. Therefore, |-5| + 1 = 6.

The next number after 6 will be negative and obtained by taking the negative of the previous number and subtracting 1. Therefore, -6 - 1 = -7.

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The equation of parabola will be x^2 = 20y.

The given focus is (0, 5) and the given directrix is y = -5.

Let (x, y) be any point on the parabola.

The distance from (x, y) to the focus (0, 5) is given by:

sqrt((x-0)^2 + (y-5)^2)

The distance from (x, y) to the directrix y = -5 is simply |y - (-5)| = |y + 5|

By definition of a parabola, these distances are equal. Therefore, we have:

sqrt((x-0)^2 + (y-5)^2) = |y + 5|

Squaring both sides, we get:

\((x-0)^{2} + (y-5)^{2} = (y + 5)^{2}\)

Simplifying and rearranging, we get:

\(x^{2}\) = 4(5)y

Therefore, the equation of the parabola with focus (0, 5) and directrix y = -5 is:

\(x^{2}\) = 20y.

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Answer:

A) r=d/t

B) 221,760 feet per hour

C) 42 miles per hour

D) in this scenario feet per mile makes more sense since the distance is listed in feet.

Step-by-step explanation:

A) you solve for r by divided both sides of the equation by (t)time

B) you take your formula r=d/t and substitute the values of (d) and (t) with 665,280 feet and 3 hours.

C) convert feet to miles by dividing the given amount of feet by 5280 since there are 5,280 feet in 1 mile

D) use feet to make the calculations easier and to avoid making a mistake in converting feet to miles

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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The exponential function for the graph is obtained as Option A : \(y = 6^x\).

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The equation for exponential function is in the form -

\(y = ab^x\)

In the graph it can be seen that the horizontal asymptote is the x-axis.

To find a, look for the coordinate where the curve crosses the y axis.

In the plot, the above scenario happens at 1.

So, the value of a = 1.

To find b, look for the coordinate where the curve crosses the vertical line at x = 1.

In the plot, the above scenario happens at 6.

Then, b is is this number divided by a -

b = 6/1 = 6

So, the equation for the plot is -

\(y = 1(6)^x\)

Therefore, the function is obtained as \(y = 1(6)^x\).

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Answer:

a

Step-by-step explanation:

the unit rate is 10 whcih is higher then everyone elses

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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The mean absolute deviation (MAD) is 12. It represents the average of the absolute deviations of the forecast errors from the mean forecast.

Given forecast errors of 6, 21, and −9, the mean absolute deviation (MAD) is calculated as follows:Step 1: Add all the forecast errors, and find the sum.6 + 21 − 9 = 18Step 2: Find the absolute value of each forecast error.|6| = 6, |21| = 21, |-9| = 9Step 3: Add the absolute values of the forecast errors.6 + 21 + 9 = 36Step 4: Divide the sum by the number of forecast errors (3) to find the mean absolute deviation.36/3 = 12

Therefore, the mean absolute deviation (MAD) is 12. It represents the average of the absolute deviations of the forecast errors from the mean forecast. The absolute deviation is a measure of the distance between the forecast and the actual value. It provides a useful way to evaluate the accuracy of a forecast.

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By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.

An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.

Given,

2x+y=4

x-y=1

By solving above two equations we get,

2x+y=4

x-y=1

3x=5

x=5/3

y=-1+x

y=(5/3)-1

y=2/3

Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

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Answer: 2

Step-by-step explanation:

if you plug in -6 into x, we get

36 - 36 + 2

the 36s will cancel each other out, leaving us with only 2 as our final answer.

Answer: -70

Step-by-step explanation:

-\(6^{2}\) + 6(-6)+2

= -36 - 36 + 2

= - 70

On solving the provided question, we can say that - the slope of the following will be slope, m = \(4-6/4-2 = -2/2 = -1\)

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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On solving the provided question, we can say that - the slope of the following will be slope, m = -1

what is slope?

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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Answer:

105

Step-by-step explanation:

To find area, you have to multiple the width by the height.

15*7=105.

Answer:

Area = 2307.9 cu.cm

Step-by-step explanation:

Height of the cylinder (h) = 15cm

radius (r) = 7 cm

we know ,

\(area \: of \: cyliner = \pi {r}^{2} \times h \\ \: \: \: \: = 3.14 \times {(7cm)}^{2} \times 15cm \\ \: \: = (3.14 \times 49 \times 15) {cm}^{3} \\ = 2307.9 {cm}^{3} \)