If JKL is rotated 180 ° clockwise, which describes the location of J’?
(no picture)

The solution for k in the equation given as 20+ 7k = 8k+ 16 is 4

From the question, the algebraic expression is given as

20+ 7k = 8k+ 16

There is no constant to multiply or divide in the expression

So, the equation remains the same

20+ 7k = 8k+ 16

Collect the like term in the above equation

This gives

8k - 7k = 20 - 16

Evaluate the like term in the above equation

So, we have the following representation

k = 4

The above equation cannot be solved further

Hence, the solution is k = 4

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Answer:

47.856

Step-by-step explanation:

We will use

SOH

CAH

TOA

to solve this

we have the adjacent length, but need the hypotonouse

which means that we will use CAH

we have

cos(43)= 35/p

solve for p

47.856

The standard form equation of the ellipse is:

\((x - 4)^2 / 1 + (y + 2)^2 / 64 = 1\)

We have,

To find the standard form equation of an ellipse, we need the coordinates of the center (h, k), the lengths of the major and minor axes (2a and 2b), and the orientation (whether it is horizontally or vertically aligned).

Given the vertices (4, -10) and (4, 6), we can determine that the center of the ellipse is at (4, -2) since the x-coordinate is the same for both vertices.

Given the co-vertices (3, -2) and (5, -2), we can determine that the length of the minor axis is 2 since the y-coordinate is the same for both co-vertices.

The length of the major axis can be found by calculating the distance between the vertices.

In this case, the length of the major axis is 6 - (-10) = 16.

Since the major axis is vertical (the y-coordinate changes), the standard form equation of the ellipse is:

\([(x - h)^2 / b^2] + [(y - k)^2 / a^2] = 1\)

Substituting the values we have:

\([(x - 4)^2 / 1^2] + [(y + 2)^2 / 8^2] = 1\)

Thus,

The standard form equation of the ellipse is:

\((x - 4)^2 / 1 + (y + 2)^2 / 64 = 1\)

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An equation of the parabola that passes through the point (3, 8) and has vertex (9, 5) is y = 1/12(x - 9)² + 5.

In this exercise, you're required to write an equation of the parabola in vertex form by using the completing the square method. Mathematically, the vertex form of a parabola is represented by this mathematical expression:

y = a(x - h)² + k

Where:

h and k represents the vertex of the equation.

Next, we would determine the value of a as follows:

8 = a(3 - 9)² + (5)

8 = a(-6)² + 5

8 = 36a + 5

36a = 8 - 5

36a = 3

a = 3/36

a = 1/12

Substituting the given parameters into the equation, we have;

y = a(x - h)² + k

y = 1/12(x - 9)² + 5

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Answer:

45 students.

Step-by-step explanation:

Answer:

63 students

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the LCM of 30 & 20

30 =  2 * 5 * 3

20 = 2 * 2 * 5

LCM = 2 * 3 * 2 * 5 = 60

60 minutes = 1 hour

So, again at 10am both will leave at the same time

Answer:

11 am.

Step-by-step explanation:

That would be the LCM of 20 and 30 which is 60 minutes.

So the nexrt time will be 10.00 + 60 mins

= 11.00 am.

Situation can be modeled by a linear function, A situation that involves a constant rate of change can be modeled by a linear function.

A linear function is a mathematical representation of a relationship between two variables that forms a straight line when plotted on a graph. It is characterized by a constant rate of change between the variables.

In a linear function, the dependent variable (y) changes at a constant rate for every unit change in the independent variable (x). This means that as x increases or decreases by a fixed amount, y also changes by a consistent amount.

Situations that exhibit a constant rate of change can be effectively modeled by linear functions.

Examples include scenarios such as distance traveled over time at a constant speed, the growth of a bank account with a fixed interest rate, or the cost of an item per unit.

In these cases, the relationship between the variables can be represented accurately using a linear equation or function.

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Situation can be modeled by a linear function, A situation that involves a constant rate of change can be modeled by a linear function.

A linear function is a mathematical representation of a relationship between two variables that forms a straight line when plotted on a graph. It is characterized by a constant rate of change between the variables.

In a linear function, the dependent variable (y) changes at a constant rate for every unit change in the independent variable (x). This means that as x increases or decreases by a fixed amount, y also changes by a consistent amount.

Situations that exhibit a constant rate of change can be effectively modeled by linear functions.

Examples include scenarios such as distance traveled over time at a constant speed, the growth of a bank account with a fixed interest rate, or the cost of an item per unit.

In these cases, the relationship between the variables can be represented accurately using a linear equation or function.

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Step-by-step explanation:

the question tells us already what ratio to build : "# of medium sized items / total # of items".

now look at the table. in such a case (different to the one with the soccer vs. basketball preferences) all the specific ratios should be equal. this is like a mixing ratio for a certain substance out of a certain list of ingredients. it does not matter how much you produce, but the mix ratio should always be the same.

10 / 40 = 1/4

15 / 60 = 1/4

20 / 80 = 1/4

perfect.

so, the constant ratio is 1:4

it means one out of 4 ordered items has to be medium sized.

what percentage is 1/4 ?

make the division :

1 : 4 = 0.25

10

20

what is 0.25 ?

it is 0.25 when related to 1 indicating the whole.

and when 100(%) indicates the whole ?

then it is 100 times its value = 0.25×100 = 25%

1/4 corresponds to 25%.

Answer:

a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.

Answer:  first problem 3rd choice  The graph shifts vertically up 5 units

11.) the y intercept is  -5

19.)  f(-8) = -18

last item  third choice  All real numbers such that  are ≥ 0 and ≤ 40

Step-by-step explanation:

19.)  f(x)=2(-8 -3) + 4

              2 (-11)  + 4

                -22 + 4

        f(-8) = -18

The probability of the message being "hi" given the ciphertext "st" is 0.

Consider a shift cipher with three possible messages, with a distribution of probabilities. The three possible messages are as follows:

Pr[M=‘hi’] = 0.3,

Pr[M=‘no’] = 0.2, and

Pr[M=’in’] = 0.5.

To solve this problem, we can use Bayes' theorem. We want to find the probability of the message being "hi" given the ciphertext "st".

Using Bayes' theorem, we have:

Pr[M=‘hi’ | C=‘st’] = Pr[C=‘st’ | M=‘hi’] * Pr[M=‘hi’] / Pr[C=‘st’]

We can break this down into three parts:

Pr[C=‘st’ | M=‘hi’]:

This is the probability that the ciphertext is "st" given that the message is "hi".

To find this probability, we need to encrypt the message "hi" using the shift cipher. If we shift each letter in "hi" by one (i.e., a becomes b, h becomes i, and i becomes j), we get the ciphertext "ij". Since "ij" does not contain the letter "s", we know that Pr[C=‘st’ | M=‘hi’] = 0.Pr[M=‘hi’]:

This is the probability of the message "hi", which is given as 0.3.Pr[C=‘st’]:

This is the probability of the ciphertext "st". We can find this probability by considering all the possible messages that could have been encrypted to produce "st".

There are three possible messages: "hi", "no", and "in". To encrypt "hi" to "st", we need to shift each letter in "hi" by two (i.e., a becomes c, h becomes j, and i becomes k). This gives us the ciphertext "jk".

To encrypt "no" to "st", we need to shift each letter in "no" by five (i.e., n becomes s and o becomes t). This gives us the ciphertext "st". To encrypt "in" to "st", we need to shift each letter in "in" by three (i.e., i becomes l and n becomes q). This does not give us the ciphertext "st", so we can ignore it.

Therefore, Pr[C=‘st’] = Pr[C=‘st’ | M=‘hi’] * Pr[M=‘hi’] + Pr[C=‘st’ | M=‘no’] * Pr[M=‘no’] = 0 + 0.2 * 1 = 0.2

Now we can plug in the values we have found:

Pr[M=‘hi’ | C=‘st’] = 0 * 0.3 / 0.2 = 0

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Answer:

(a)  (3, 0) and (-8, 0)

(b)  (-2.5, 0)

(c) x = -2.5

(d) f(-2.5) = -30.25

Step-by-step explanation:

Given quadratic function:

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

The x-intercepts are when \(f(x)=0\)

\(\implies f(x)=0\)

\(\implies (x-3)(x+8)=0\)

\(\implies (x-3)=0 \implies x=3\)

\(\implies (x+8)=0 \implies x=-8\)

Therefore, the x-intercepts are (3, 0) and (-8, 0)

Midpoint between two points:

\(\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad\)

\(\textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)\)

\(\implies \textsf{Midpoint of the x-intercepts}=\left(\dfrac{-8+3}{2},\dfrac{0+0}{2}\right)=\left(-2.5},0\right)\)

The extreme point of a quadratic function in the form \(f(x)=ax^2+bx+c\) is:

\(x=-\dfrac{b}{2a}\)

Therefore, expand the function so that it is in standard form:

\(\implies f(x)=x^2+5x-24\)

\(\implies a=1, b=5\)

Therefore, the extreme value is:

\(\implies x=-\dfrac{5}{2}=-2.5\)

Alternative method

A quadratic function has an extreme value at its vertex.

The x-value of the vertex is the midpoint of the x-intercepts.

Therefore, the extreme value is x = -2.5

\(\begin{aligned}\implies f(-2.5) & =(-2.5-3)(-2.5+8)\\& = (-5.5)(5.5)\\& = -30.25\end{aligned}\)

Answer:

r =   4/(x+y)

Step-by-step explanation:

rx + ry = 4

Factor out r

r ( x+y) = 4

Divide each side by (x+y)

r ( x+y) /(x+y) = 4/(x+y)

r =   4/(x+y)

Answer:

a. y = -3

b. x = -3

c. z = - 1

d. y = -7

Step-by-step explanation:

a. 5y - 3 = - 18

5y = -18 +3

5y = -15

y = -15/5

y = - 3

b. -3x - 9 = 0

-3x = 9

x = 9/-3

x = -3

c. 4 + 3(z-8)= -23

4 + 3z-24 = -23

3z - 20 = -23

3z = -23 + 20

3z = -3

z = -3/3

z = - 1

d. 1 - 2(y-4) = 5

1 - 2y + 8 = 5

9 - 2y = 5

-2y = 14

y = 14/-2

y = -7

(a) Forecast: Linear regression  the next year is approx 191.6007.

(b) MSE: Mean Squared Error is approximately 249.1585.

(c) MAPE: Mean Absolute Percent Error is approximately 10.42%.

(a) (a) Forecast using linear regression:
To forecast the number of disk drives for the next year, we can use linear regression to fit a line to the given data points. The linear regression equation is of the form y = mx + b, where y represents the number of disk drives and x represents the year.

Calculating the slope (m):
m = (Σ(xy) - n(Σx)(Σy)) / (Σ(x^2) - n(Σx)^2)

Σ(xy) = (1)(140) + (2)(160) + (3)(190) + (4)(200) + (5)(210) = 2820
Σ(x) = 1 + 2 + 3 + 4 + 5 = 15
Σ(y) = 140 + 160 + 190 + 200 + 210 = 900
Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) + (5^2) = 55

m = (2820 - 5(15)(900)) / (55 - 5(15)^2)
m = (2820 - 6750) / (55 - 1125)
m = -3930 / -1070
m ≈ 3.6729

Calculating the y-intercept (b):
b = (Σy - m(Σx)) / n
b = (900 - 3.6729(15)) / 5
b = (900 - 55.0935) / 5
b ≈ 168.1813

Using the equation y = 3.6729x + 168.1813, where x represents the year, we can predict the number of disk drives for the next year. To do so, we substitute the value of x as the next year in the equation. Let's assume the next year is represented by x = 6:

y = 3.6729(6) + 168.1813
y ≈ 191.6007

Therefore, according to the linear regression model, the predicted number of disk drives for the next year is approximately 191.6007.

(b) Calculation of Mean Squared Error (MSE):

To calculate the Mean Squared Error (MSE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 = 171.8542
Year 2: y = 3.6729(2) + 168.1813 = 175.5271
Year 3: y = 3.6729(3) + 168.1813 = 179.2000
Year 4: y = 3.6729(4) + 168.1813 = 182.8729
Year 5: y = 3.6729(5) + 168.1813 = 186.5458
Next, we calculate the squared difference between the predicted and actual values, and then take the average:

MSE = (Σ(y - ŷ)^2) / n

MSE = ((140 - 171.8542)^2 + (160 - 175.5271)^2 + (190 - 179.2000)^2 + (200 - 182.8729)^2 + (210 - 186.5458)^2) / 5

MSE ≈ 249.1585

The Mean Squared Error (MSE) for the linear regression model is approximately 249.1585.

This value represents the average squared difference between the predicted values and the actual values, providing a measure of the accuracy of the model.

(c) Calculation of Mean Absolute Percent Error (MAPE):

To calculate the Mean Absolute Percent Error (MAPE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 ≈ 171.8542
Year 2: y = 3.6729(2) + 168.1813 ≈ 175.5271
Year 3: y = 3.6729(3) + 168.1813 ≈ 179.2000
Year 4: y = 3.6729(4) + 168.1813 ≈ 182.8729
Year 5: y = 3.6729(5) + 168.1813 ≈ 186.5458

Next, we calculate the absolute percent error for each year, which is the absolute difference between the predicted and actual values divided by the actual value, multiplied by 100:

Absolute Percent Error (APE):

Year 1: |(140 - 171.8542) / 140| * 100 ≈ 18.467
Year 2: |(160 - 175.5271) / 160| * 100 ≈ 9.704
Year 3: |(190 - 179.2000) / 190| * 100 ≈ 5.684
Year 4: |(200 - 182.8729) / 200| * 100 ≈ 8.563
Year 5: |(210 - 186.5458) / 210| * 100 ≈ 11.682
Finally, we calculate the average of the absolute percent errors:

MAPE = (APE₁ + APE₂ + APE₃ + APE₄ + APE₅) / n

MAPE ≈ (18.467 + 9.704 + 5.684 + 8.563 + 11.682) / 5 ≈ 10.42

The Mean Absolute Percent Error (MAPE) for the linear regression model is approximately 10.42%.

This value represents the average percentage difference between the predicted values and the actual values, providing a measure of the relative accuracy of the model.

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The events A and B are dependent events. Option C is answer.

The probability of the union of events A and B, denoted as P(AUB), is calculated as the sum of their probabilities minus the probability of their intersection, denoted as P(AB). So, using the given information, we can find:

P(AB) = P(A) + P(B) - P(AUB)

= 0.2 + 0.3 - 0.44

= 0.06

If A and B were independent events, then we would have P(AB) = P(A)P(B), which is not the case here since P(AB) ≠ P(A)P(B). Thus, A and B are dependent events.

Option C is answer.

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The answer is , the volume of the rectangular piece of iron is 6.96 × 10⁻⁷ m³.

The formula for the volume of a rectangular prism is given by V = l × b × h,

where "l" is the length of the rectangular piece of iron, "b" is the breadth of the rectangular piece of iron, and "h" is the height of the rectangular piece of iron.

Here are the given measurements for the rectangular piece of iron:

Length (l) = 7.08 × 10⁻³ m,

Breadth (b) = 2.18 × 10⁻² m,

Height (h) = 4.51 × 10⁻³ m,

Now, let us substitute the given values in the formula for the volume of a rectangular prism.

V = l × b × h

V = 7.08 × 10⁻³ m × 2.18 × 10⁻² m × 4.51 × 10⁻³ m

V= 6.96 × 10⁻⁷ m³

Therefore, the volume of the rectangular piece of iron is 6.96 × 10⁻⁷ m³.

Therefore, the correct answer is 6.96 × 10⁻⁷ m³.

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Therefore ,the probability that the number of heads will exceed 60 is 0.0176

The number of outcomes that could occur is the basis for the response is known as probability .To this question  the outcome in this case might be either head or tail. Therefore, there is a 50% chance that the result will be a head.

Here,

The  fair coin is tossed at random 100 times.

So we have to find probability that the number of heads will exceed 60

Thus,

=> P(number of heads will exceed 60) = \(\frac{C^{100} _{1} }{C^{2} _{60}}\)

=> P(number of heads will exceed 60) =   0.01760010010885238

=> P(number of heads will exceed 60) =  0.0176

Therefore ,the probability that the number of heads will exceed 60 is 0.0176

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Answer:  b = 45 inches

Work Shown:

\(a^2+b^2 = c^2\\\\b^2 = c^2-a^2\\\\b = \sqrt{c^2-a^2}\\\\b = \sqrt{51^2-24^2}\\\\b = \sqrt{2025}\\\\b = 45\\\\\)

For more information and examples, check out the pythagorean theorem.

The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.

The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.

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Answer:

3x-2

Step-by-step explanation:

(-7x+6)-(-10x+8)

open the parenthesis

-7x+6+10x-8

combine like terms

3x-2

To find the general solution of the system x' = 10 −5 8 −12 x, we first need to find the eigenvalues and eigenvectors of the coefficient matrix.

The characteristic equation is det(A - λI) = 0, where A is the coefficient matrix, λ is the eigenvalue, and I is the identity matrix. So, we have:

det(10-λ -5 8 -12-λ) = 0
(10-λ)(-12-λ) - (-5)(8) = 0
λ\(^2\) - 2λ - 64 = 0
(λ - 8)(λ + 8) = 0
λ1 = 8, λ2 = -8

Next, we need to find the eigenvectors corresponding to each eigenvalue. For λ1 = 8, we have:

(10-8)x1 - 5y1 + 8z1 = 0
-5x1 + (8-8)y1 + 8z1 = 0
8x1 + 8y1 + (-12-8)z1 = 0

Simplifying the system, we get:

2x1 - y1 + 4z1 = 0
-5x1 = 0
8x1 + 8y1 - 20z1 = 0

Solving for x1, y1, and z1, we get:

x1 = 0
y1 = 0
z1 = t

So, the eigenvector corresponding to λ1 = 8 is [0, 0, t].

For λ2 = -8, we have:

(10+8)x2 - 5y2 + 8z2 = 0
-5x2 + (8+8)y2 + 8z2 = 0
8x2 + 8y2 + (-12+8)z2 = 0

Simplifying the system, we get:

18x2 - 5y2 + 8z2 = 0
-5x2 + 16y2 + 8z2 = 0
8x2 + 8y2 - 4z2 = 0

Solving for x2, y2, and z2, we get:

x2 = 2t
y2 = 5t
z2 = -2t

So, the eigenvector corresponding to λ2 = -8 is [2t, 5t, -2t].

Now that we have the eigenvalues and eigenvectors, we can write the general solution as:

\(x(t) = c1[0, 0, t]e^{(8t)} + c2[2t, 5t, -2t]e^{(-8t)}\)
where c1 and c2 are constants determined by initial conditions.

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Answer:

Step-by-step explanation:

-7x-2y=-13

x-2y=11

(subtract the first inequality from the second)

-7x-x = -8x

-2y-(-2y) = 0

-13-11= -24

-8x=-24

x=3

(now place the x value into the second inequality)

3-2y=11

-2y=11-3

-2y=8

y=-4

x=3

y=-4

Answer: x=3, y= -4

Steps: The two equations are," -7x-2y=-13 " and " x - 2y = 11 "

Let's take the 2nd equation and find for x

x - 2y = 11

x= 11 + 2y

Now place the value of x in the first equation:

-7(11+2y) - 2y = -13

-77 - 14y - 2y = -13

- 16y= -13 + 77

y= 64/-16

y= -4

Now that you found the value of y, place it again on the 2nd equation:

x - 2(-4) =11

x + 8= 11

x=11-8

x= 3

Brainliest pls if i am correct!

Answer:

38

Step-by-step explanation:

Find the values of each function.

f(-9)= 4

g(6)=6

Then plug them in.

-1 x 4 + 7 x 6

-4+42

38!

Answer:

I think its 13

Please mark brainliest if its correct and want further answers :)

We are asked to convert the repeating decimal to fraction

Step 1: Multiply both sides by 100 because there are two repeating digits

Step 2: Subtract the first equation from the second one

Therefore, the fractional form of the repeating decimal 4.7277272... is 52/11

Answer:

answer is 1 metre

Step-by-step explanation:

We can assume the width be 'x'

Now we would get the equation

(2x+10)(2x+14)=192

on solving we get x=1

Answer:

this is just a system of equations

x+y=4

2x+3y=12

x=-y+4

plug in

2(-y+4)+3y=12

-2y+8+3y=12

y+8=12

y=4

plug in

x+4=4

x=0

(0,4)

Hope This Helps!!!

Answer:

(0,4)

Step-by-step explanation:

find x by subtracting y from both sides

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

In a parallelogram, opposite sides are equal. Therefore, AB = CD.

5x * 3 = 15 * x

15x = 15

x = 1

Therefore, the value of x is 1.

To find the area of parallelogram ABCD, we can use the formula A = base x height, where the base is the length of side AB and the height is the perpendicular distance between side AB and the opposite side CD. Since the height of parallelogram ABCD is given as 6, we need to find the length of side AB.

From the given information, we know that AB = 5x * 3, where x = 1. Therefore, AB = 15. Now we can calculate the area of parallelogram ABCD as:

A = base x height

A = 15 x 6

A = 90 square units

Therefore, the area of parallelogram ABCD is 90 square units.

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