Karen has 560 friends and family on social media of the friends, 50% are from high school, and 30% are from her after school job. The rest are family
members
How many family members does Karen know on social media?

So the answer is E[X] = 1.2, which is approximately equal to 1.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Let's first consider the probability of a boy being in the front half of the line. There are two possible cases:

The first half of the line contains exactly one boy: There are three boys and seven girls, so the probability of this happening is (3/10)*(7/9) = 7/30. The probability of any one of the three boys being in the front half of the line is therefore 7/30 * 3 = 7/10.

The first half of the line contains exactly two or three boys: There are three boys and seven girls, so the probability of this happening is (3/10)(2/9) + (3/10)(3/9) = 3/10. The probability of any one of the three boys being in the front half of the line is therefore 3/10 * 1 = 3/10.

So, the probability distribution for X is:

X = 0 with probability (7/10)(6/9) = 14/30

X = 1 with probability (7/10)(3/9) + (3/10)(7/9) = 21/30

X = 2 with probability (3/10)(2/9) + (3/10)*(3/9) = 9/30

Now we can calculate the expected value of X:

E[X] = 0*(14/30) + 1*(21/30) + 2*(9/30) = 1.2

So the answer is E[X] = 1.2, which is approximately equal to 1.

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Answer:

12^12

Step-by-step explanation:

12^16/12^4 cancel out to the power of 4 on the bottom and on top for an answer of 12^12

Answer: $25

Step-by-step explanation: 25 times 3(because there are three people) =75 - 45(the amount they spent)=30 the amount they are left with all together.

it took me awhile to answer so sorry for the wait but i hope this helps.

Answer:

Two slabs of rock slide past one another

one slab of rock breaks into two peices

Step-by-step explanation:

The two changes caused by the shear on the earth crust are; A: One slab of rock breaks into two peices. C: Two slabs of rock slide past one another;

Shear stress usually occurs when two plates rub against each other as they move in opposite directions.

Now, when shear stress occurs on the earth's crust, the force generated by the stress tends to push some of the crust in different directions. This would mean that a large part of the crust can break off, which makes the plate size smaller.

Thus, when a shear stress acts on the earths' crust, One slab of rock breaks into two peices. C: Two slabs of rock slide past one another;

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Answer:

$52.50

Step-by-step explanation:

Divide to find the unit rate.

84 / 8 = $10.50 per lawn

Multiply.

10.5 * 5 = $52.50 for 5 lawns

Best of Luck!

Answer:

52.50

Step-by-step explanation:

Answer:

either SAS or not possible, i believe its SAS tho.

Answer:

$6

Step-by-step explanation:

Each pack is $3

So therefore if you multiply 2($3) it is $6 for two packs

In linear equation, The quarts of yellow paint mixed with 6 quarts of red paint should be, 4.

What in mathematics is a linear equation?

the number of quarts of yellow paint should be mixed with 6 quarts of red paint.

According to question

As, 3 quarts of red paint is mixed with 2 quarts of yellow paint

So, 6 quarts of red paint is mixed with

                                6/3  *   2 = 4 quarts of yellow paint

Thus, the quarts of yellow paint mixed with 6 quarts of red paint should be, 4.

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Answer:

False.

Step-by-step explanation:

It's ok to plan future activities for the group, but it's best to plan in the beginning of the group.

The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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Answer: 1125

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The value of g(1) is approximately 0.491, obtained by integrating g'(x) and using the initial condition g(4)=0.325 to determine the constant of integration

the value of g(1) is determined by integrating the given derivative function g'(x) and evaluating it at x=1.

The initial condition g(4)=0.325 is also provided, which can be used to solve for the constant of integration.

integrating the given derivative function g'(x) involves finding the antiderivative of each term separately.

The antiderivative of 1/x is ln(x), the antiderivative of\(e^(-x) -e^(-x),\) and the antiderivative of\(cos(x^100)\) is \(sin(x^100)/100.\)

After integrating each term, we obtain g(x) = ln(x) - e^(-x) \(sin(x^100)/100.\) + C, where C is the constant of integration.

Using the initial condition g(4) = 0.325, we can substitute x=4 and solve for C.

Plugging in the values, 0.325 = \(ln(4) - e^(-4) sin(4^100)/100\) + C. By evaluating this equation, we can find the value of C.

Finally, with the constant of integration C determined, we can substitute x=1 into the function g(x) = \(ln(4) - e^(-4) sin(4^100)/100\) + C to find the value of g(1).

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There are 216 different possible combinations for the lock.

What is linear combinations?

In mathematics, a linear combination is a sum of scalar multiples of one or more variables. More formally, given a set of variables x1, x2, ..., xn and a set of constants a1, a2, ..., an, their linear combination is given by the expression:

a1x1 + a2x2 + ... + anxn

Since there are three dials on the combination lock and each dial can be set to one of six numbers, the total number of possible combinations is the product of the number of options for each dial.

Therefore, the total number of combinations is: 6 x 6 x 6 = 216

So there are 216 different possible combinations for the lock.

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The question asks for the 13-period Exponential Moving Average (EMA) in Period 13 based on the given closing prices. The closing prices for each period are provided, and we need to calculate the EMA for the 13th period.

The Exponential Moving Average (EMA) is a type of moving average that assigns more weight to recent prices, resulting in a smoother trend line. It is calculated using a formula that incorporates a smoothing factor, which determines the weight given to each period's closing price. To calculate the EMA, we first need to determine the smoothing factor (alpha). The formula for alpha is alpha = 2 / (n + 1), where n is the number of periods. In this case, n is 13, so alpha = 2 / (13 + 1) = 0.1538.

To calculate the EMA for each period, we start with the simple moving average (SMA) for the first period (which is the same as the closing price). For the subsequent periods, we use the formula: EMA = (Closing Price - Previous EMA) x alpha + Previous EMA.

Based on the given closing prices, we can calculate the 13-period EMA as follows:

For Period 1, the EMA is the same as the closing price, which is 20.

For Period 2, the EMA is (223 - 20) x 0.1538 + 20 = 45.3054.

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The differential equation y'' + 2y' + 2y = cos(2x) can be solved using Laplace transform. The Laplace transform of y'' is s²Y(s) - sy(0) - y'(0), the Laplace transform of y' is sY(s) - y(0), and the Laplace transform of y is Y(s).

The Laplace transform of cos(2x) is s/(s² + 4). Solving for Y(s) gives Y(s) = (s/(s² + 4)) / (s² + 2s + 2). Taking the inverse Laplace transform of Y(s) gives y(t) = (1/2)sin(2x) - (1/2)cos(2x).

The Laplace transform of a differential equation is a way of converting the differential equation into an algebraic equation. This can be done by taking the Laplace transform of both sides of the differential equation. The Laplace transform of a derivative is s times the Laplace transform of the function, and the Laplace transform of a function is simply the function evaluated at s.

Once the differential equation has been converted into an algebraic equation, it can be solved for the Laplace transform of the solution. The Laplace transform of the solution is then converted back into the time domain using the inverse Laplace transform.

In this case, the Laplace transform of the differential equation y'' + 2y' + 2y = cos(2x) is:

s²Y(s) - sy(0) - y'(0) + 2sY(s) - 2y(0) + 2Y(s) = s/(s² + 4)

Solving for Y(s) gives:

Y(s) = (s/(s² + 4)) / (s² + 2s + 2)

Taking the inverse Laplace transform of Y(s) gives:

y(t) = (1/2)sin(2x) - (1/2)cos(2x).

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The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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Answer:

(z+7)*(z+4)

Step-by-step explanation:

The first term is,  z2  its coefficient is  1 .

The middle term is,  +11z  its coefficient is  11 .

The last term, "the constant", is  +28

Step-1 : Multiply the coefficient of the first term by the constant   1 • 28 = 28

Step-2 : Find two factors of  28  whose sum equals the coefficient of the middle term, which is   11 .

     -28    +    -1    =    -29

     -14    +    -2    =    -16

     -7    +    -4    =    -11

     -4    +    -7    =    -11

     -2    +    -14    =    -16

     -1    +    -28    =    -29

     1    +    28    =    29

     2    +    14    =    16

     4    +    7    =    11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  4  and  7

                    z2 + 4z + 7z + 28

Step-4 : Add up the first 2 terms, pulling out like factors :

                   z • (z+4)

             Add up the last 2 terms, pulling out common factors :

                   7 • (z+4)

Step-5 : Add up the four terms of step 4 :

                   (z+7)  •  (z+4)

            Which is the desired factorization

Answer:

option 4

Step-by-step explanation:

g(x) = x² + 4x + 4

      = x² + 2 * x * 2 + 2²   {Compare with identity a²+ 2ab +b² = (a +b)²}

      = (x + 2)²

\((\dfrac{f}{g})(x) = \dfrac{(x +2)}{(x+2)*(x+2)}\\\\\\= \dfrac{1}{x+2}\)

Answer:

\(a_{62}=-107\)

Step-by-step explanation:

This is an arithmetic sequence:

\(a_n=a_1+(n-1)d\)

where d is the common difference and n is the index of any given term.

The common difference of the given sequence is -2:

\(13-15=-2\\11-13=-2\)

Using the first term and the common difference, you can write the equation for this sequence:

\(a_n=15+(n-1)(-2)\)

And using that equation, you can find the 62nd term:

\(a_{62}=15+(62-1)(-2)\\a_{62}=15+(61)(-2)\\a_{62}=15-122\\a_{62}=-107\)

The equivalence of the remainder following the division of 17 and 30 by N indicates that the largest value N can have is 30

The remainder term in a division of one value by a second value is the value which is less than the divisor, remaining after the divisor divides the dividend by a number of times indicated by the quotient.

The remainder following the division of 17 and 30 by the number N are the same.

Let R represent the remainder following the division of the integers 17 and 30 and let b represent the number of times N divides 30 than 17. Using the long division formula, we get;

17/N = Q + R/17

30/N = b·Q + R/17

30/N - 17/N = 13/N

The substitution property indicates that we get the following equation;

30/N - 17/N = b·Q + R/17 - (Q + R/17) = b·Q - Q

30/N - 17/N = b·Q - Q

13/N = b·Q - Q = (b - 1)·Q

13/N = (b - 1)·Q

The fraction 13/N which is equivalent to the product of (b - 1) and Q indicates that N is a factor of 13

13 is a prime number, therefore, the factors of 13 are 13 and N

Therefore, the possible values of N are 13 and 1

The largest value N can have is therefore, 13

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Answeriits the one in the forth box

Step-by-step explanation:

The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The perimeter of a rectangle is 40 cm. The length is 14 cm.

Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.

Fran says she can find the width using the equation 2x + 28 = 40.

now, we get,

1. Divide both sides by 2

 2(x+14) = 40

 x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

 2x + 28 = 40

 2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

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Answer:

26

Step-by-step explanation:

 decimal form 5.09901951

Answer: Side length E D corresponds to Side length B A because they are in the same position.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

bottom left: -6 + (-1/3)

Step-by-step explanation:

hope this helps :)

An equation in slope-intercept form to represent this linear function is y = 65x + 40.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Let the fee per month = x.

Given that, A membership at Rocky Heights Climbing Gym costs $65 per month plus a $40 initial fee.

y = 65x + 40.

Hence, an equation in slope-intercept form to represent this linear function is y = 65x + 40.

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To find the matrices A1 and A2, we first need to determine the size of each matrix. Since the orderings of x, y, and z are given, we know that the size of each matrix will be 4x4.

a) Matrix A1:

The relation r1 is from x to y, where x divides y. So, for each pair (x, y) that satisfies this condition, we put a 1 in the corresponding entry of the matrix. Otherwise, we put a 0. Using the ordering of x and y given, we get:

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A1 =  1 1 0 0

     0 1 1 0

     0 0 1 1

     0 0 0 1

b) Matrix A2:

The relation r2 is from y to z, where y > z. So, for each pair (y, z) that satisfies this condition, we put a 1 in the corresponding entry of the matrix. Otherwise, we put a 0. Using the ordering of y and z given, we get:

makefile

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A2 =  0 0 0 0

     1 0 0 0

     1 1 0 0

     1 1 1 0

c) Matrix product A1A2:

To compute the matrix product A1A2, we multiply each row of A1 by each column of A2 and add the products. The (i,j)-entry of the product matrix is obtained by taking the dot product of the ith row of A1 and the jth column of A2. We get:

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A1A2 =  1 1 0 0   0 0 0 0   0 1 1 1 0 0 0 0

       0 1 1 0 * 1 0 0 0 = 0 0 1 1 0 0 0 0

       0 0 1 1   1 1 0 0   0 0 0 1 0 0 0 0

       0 0 0 1   1 1 1 0   0 0 0 0 0 0 0 0

d) Matrix for relation R2∘R1:

To find the matrix for the composition R2∘R1, we multiply the matrices A2 and A1 in that order, i.e., A2A1. We get:

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A2A1 =  0 1 1 1

       0 0 1 1

       0 0 0 1

       0 0 0 0

e) Relation R2∘R1:

The matrix A2A1 has a 1 in position (i,j) if and only if there exists a k such that R1(i,k) = 1 and R2(k,j) = 1. Using the ordering of x, y, and z given, we can write the pairs corresponding to each 1 in the matrix:

R2∘R1 = {(2,3), (2,4), (2,5), (3,4), (3,5), (4,5)}

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