Option 2: Proof
Can you prove using algebra which tray has more pie in?

Answer:

[tex] \sqrt{7y} ( \sqrt{27y} + 5 \sqrt{12y} )[/tex]

[tex] \sqrt{7y} ( \sqrt{9} \sqrt{3y} + 5 \sqrt{4} \sqrt{3y} )[/tex]

[tex] \sqrt{7y} (3 \sqrt{3y} + 10 \sqrt{3y} )[/tex]

[tex]13 \sqrt{7y} \sqrt{3y} [/tex]

[tex]13y \sqrt{21} [/tex]

If a circle graph was constructed from the results, the lake activity has a central angle of 54° is Paddleboarding.

To find the lake activity with a central angle of 54° in the circle graph, we need to determine the percentage of campers who chose that activity.

The total number of campers surveyed is 100, and the number of campers who chose paddleboarding is 54. Therefore, the percentage of campers who chose paddleboarding is:

54/100 x 100% = 54%

To convert this percentage to a central angle in degrees, we can use the formula:

Central angle = Percentage * 360°

So, the central angle for paddleboarding is:

54% x 360° = 194.4°

Therefore, the correct option is d. Paddleboarding.

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the sample space of two-digit numbers using the digits 9, 4, 5, and 8 consists of 16 possible outcomes, and we can list all these outcomes in a table as shown above.

How to solve the question?

To create a sample space of two-digit numbers using the digits 9, 4, 5, and 8, we need to consider all possible combinations of these digits. We can list all possible outcomes in a table where each digit represents a column and each combination represents a row.

The first digit can be any of the four digits, and the second digit can also be any of the four digits, including the same digit as the first. Therefore, the total number of outcomes is 4 x 4 = 16.

Here is the sample space of two-digit numbers using the digits 9, 4, 5, and 8:

         9    4   5     8

9 99 94 95 98

4 49 44 45 48

5 59 54 55 58

8 89 84 85 88

As shown in the table, the first digit can be any of the four digits, and the second digit can also be any of the four digits. For example, the first row shows that the possible two-digit numbers starting with 9 are 99, 94, 95, and 98. Similarly, the second row shows that the possible two-digit numbers starting with 4 are 49, 44, 45, and 48, and so on.

In conclusion, the sample space of two-digit numbers using the digits 9, 4, 5, and 8 consists of 16 possible outcomes, and we can list all these outcomes in a table as shown above.

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The total surface area of all 64 smaller cubes is[tex]486 cm^2[/tex] and the surface area of one small cube is [tex]7.59375 cm^2.[/tex]

The surface region of the beginning 3d shape can be calculated by finding the zone of each confront and including them up.

Since the 3d shape has 6 faces of rise to estimate, we are able to utilize the equation for the region of a square to discover the range of one confront, and after that duplicate by 6:

The surface region of the beginning 3d shape =[tex]6 x (side length)^2[/tex]

=[tex]6 x (4.5 cm)^2[/tex]

= [tex]121.5 cm^2[/tex]

To calculate the overall surface range of all 64 littler 3d shapes, we have to be discover the surface region of each 3d shape and after that include them up.

Each 3d shape has 6 faces, so ready to utilize the equation for the range of a square to discover the zone of one confront, and after that duplicate by 6:

Surface range of one little 3d shape = [tex]6 x (side length of little cube)^2[/tex]

To discover the side length of the littler 3d shapes, we ought to separate the side length of the beginning 3d shape by the number of littler 3d shapes in each measurement.

Since there are 4 littler 3d shapes in each measurement (4 x 4 x 4 = 64), we have:

Side length of little 3d shape = (side length of beginning 3d shape) / 4

= 4.5 cm / 4

= 1.125 cm

In this manner, the surface range of one little 3d shape is:

The surface region of one small cube = [tex]6 x (1.125 cm)^2[/tex]

=[tex]7.59375 cm^2[/tex]

Since there are 64 little 3d shapes, able to discover the full surface region of all the small 3d shapes by duplicating the surface zone of one small cube by 64:

Add up to surface region of all small 3d shapes = Surface zone of one little cube x 64

=[tex]7.59375 cm^2 x 64[/tex]

= [tex]486 cm^2[/tex]

Therefore, the total surface area of all 64 smaller cubes is [tex]486 cm^2.[/tex]

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A. The data does not support the claim that brand A cigarettes contain less than 3 milligrams of tar at the 5% significance level. The p-value is less than 0.05, indicating that the observed mean amount of tar is unlikely to have occurred by chance alone.

B. To determine whether the data supports the claim made by the makers of brand A cigarettes, the marketing-research analyst used a one-sample t-test.

The null hypothesis is that the mean amount of tar in brand A cigarettes is 3 milligrams or less. The alternative hypothesis is that the mean amount of tar in brand A cigarettes is greater than 3 milligrams.

The analyst randomly selected 60 cigarettes and found the mean amount of tar to be 2.75 milligrams with a standard deviation of 1.5 milligrams. Using a t-distribution with 59 degrees of freedom (60 - 1), the t-statistic is calculated as follows:

t = (2.75 - 3) / (1.5 / sqrt(60)) = -1.41

The p-value is the probability of observing a t-statistic as extreme as -1.41 or more extreme, given the null hypothesis. Using a t-distribution table or software, the p-value is found to be 0.084.

Since the p-value (0.084) is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, the data does not support the claim that brand A cigarettes contain less than 3 milligrams of tar at the 5% significance level.

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The answer to the given question after considering the two options is true under the condition all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.      

Probability is also known as the estimation of possible changes of a particular event taking place. Furthermore, it is  important while dealing with calculations in the branch of science and mathematics. It is useful in eliminating the total changes of systematic errors, which are hampering the research population.

Some examples of probability

The probability on the event of rolling a 4 with a die is 1/6.

The probability of getting a tails while tossing a coin is 1/2.

The probability of getting  one  joker from a deck of cards is 1/51.

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The complete question is

All probabilities can be expressed as decimal values ranging from 0.00 to 1.00. True or False

Yes, it is true that all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.

This is because probabilities represent the likelihood of an event occurring, and the probability of an event can range from impossible (0.00) to certain (1.00). Therefore, probabilities are expressed as decimal values between these two extremes.
Hi! Yes, all probabilities can be expressed as decimal values ranging from 0.00 to 1.00. A probability of 0.00 represents an impossible event, while a probability of 1.00 represents a certain event. Values between these two extremes indicate varying levels of likelihood for the event to occur.

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If farmer bought a total of 100 sheep and ostriches at an auction and there were 342 legs in total,  the farmer bought 29 ostriches, and the remaining 71 animals were sheep.

Let's assume that the farmer bought x ostriches and y sheep.

Since each ostrich has 2 legs, the total number of legs contributed by the ostriches is 2x. Similarly, each sheep has 4 legs, so the total number of legs contributed by the sheep is 4y.

We know that the total number of animals the farmer bought is 100, so we can write:

x + y = 100

We also know that the total number of legs is 342, so we can write:

2x + 4y = 342

Now we can use the first equation to solve for y:

y = 100 - x

Substituting this into the second equation, we get:

2x + 4(100-x) = 342

Simplifying this equation, we get:

2x + 400 - 4x = 342

-2x = -58

x = 29

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[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank A} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1810)(0.025)(5) \implies I = 226.25 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank B} }{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]A = 1810\left(1+\frac{0.025}{12}\right)^{12\cdot 5} \implies A \approx 2050.73~\hfill \underset{ interest }{\stackrel{2050.73~~ - ~~1810 }{\approx 240.73}} \\\\[-0.35em] ~\dotfill\\\\ 240.73~~ - ~~226.25 ~~ \approx ~~ \text{\LARGE 14.48}[/tex]

Thus, the value of y for the given linear function for the input value of x = 4 , is found as y = 5.

Any function which it graphs as a straight line is said to be linear. Mathematically speaking, this indicates that the function contains one or two variables, but neither exponents nor powers.

Given linear function:

y = 2x - 3 ; with x = 4

To get the value of y ,put x = 4 in the given function:

y = 2(4) - 3

y = 8 - 3

y = 5

Thus, the value of y for the given linear function for the input value of x = 4 , is found as y = 5.

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correct question:

Find the value of y for the given value of 'x'.

y = 2x - 3 ; x = 4

Answer:

  -3

Step-by-step explanation:

You want the graphical solution to x² +6x +9 = 0.

The graph of the expression on the left shows it has a value of 0 when x = -3.

The solution is x = -3.

__

Additional comment

A graphing calculator is very helpful when you want a graphical solution.

If you want to graph this by hand, you can rewrite it as ...

  (x +3)² = 0

The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.

There are 49,152 possible ways to pick teams for a basketball game in a PE class with 13 students if the two best players cannot be on the same team.

If we denote the two best players as A and B, then we can split the problem into two cases

A is on the red team: In this case, B can be on any of the remaining 12 students, and the other 11 students can be split between the red and blue teams in any way. Therefore, there are 12 × 2^11 = 24,576 possible team combinations.

A is on the blue team: This case is identical to case 1, so there are also 24,576 possible team combinations.

Therefore, the total number of possible team combinations where A and B are not on the same team is

24,576 + 24,576 = 49,152.

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Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar

(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:

Therefore, the blank spaces should be filled as follows:

Translate the solid circle 2 units to the left and 2 units down.

Dilate the solid circle by a scale factor of 2.

(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.

This is because all circles are similar

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If the measure of angle RST is 60°, and RS=4 units, then the area of sector RST is 8.374 square units.

In geometry, a "Sector" of a circle is defined as the portion of circle enclosed by two radii and the arc between them. It can be thought of as a slice or a wedge cut out of a circle.

To find the area of the "sector-RST" in circle centered at "S", we use the formula for area of a sector of a circle, which is :

⇒ Area of sector = (θ/360) × π × r²,

where θ = central angle of sector in degrees, π = 3.14159, and r = radius of circle,

In this case, we are given that m∠RST = 60 degrees and RS = 4 units. Since RS is the radius of the circle centered at "S", we use RS = r,

Substituting the values, θ = 60 degrees, r = RS = 4 units,

We get,

⇒ Area of sector RST = (60/360) × 3.14 × (4)²,

= (1/6) × 3.14 × 16,

= 8.374 square units,

Therefore, the required area of sector is 8.374 square units.

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The given question is incomplete, the complete question is

In circle centered at "S", R and T are the points on the circumference with m∠RST = 60 and RS=4 units .Find area of sector RST.

The greatest common factor of 90 and 315 when divided by the least common multiple of 5 and 15 is 45.

When we multiply all the common prime factors, we get the greatest common factor of the numbers.

These prime factors should come from the prime factorization of the numbers given. These should be in all the unique combinations possible.

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The fewest number of trips needed to get everything across the river without anything being eaten is 5 trips.

The problem requires Fanny to figure out a sequence of steps that will enable her to transport the fox, chicken, and bag of corn across the river without anything being eaten.

To solve this problem she must come up with a plan that allows her to transport all three items without putting any of them at risk.

Here we have

The named Fanny bought a specially-trained fox named Federico and a chicken and a bag of corn seeds

To safely transport the fox, the chicken, and the bag of corn across the river, Fanny must follow a specific sequence of steps to ensure that nothing is eaten. Here is one possible solution:

Therefore,

The fewest number of trips needed to get everything across the river without anything being eaten is 5 trips.

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The feasible solution is known as a locally optimal solution.

It may not be the best possible solution for the entire optimization problem.

If there are no other feasible solutions with a larger objective function value.

The immediate neighborhood, then the feasible solution is known as a locally optimal solution.

This means that the solution is optimal within a particular region of the feasible space but may not necessarily be the globally optimal solution. Bhe best possible solution over the entire feasible space.

In other words, a locally optimal solution is the best possible solution. Among all feasible solutions in its immediate neighborhood or region.

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The total length of the beads on one braid is 8.11 centimeters

Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.

To find the total length of the beads on one braid, we need to evaluate the expression:

7 x 1.03 + 0.9

Multiplying 7 by 1.03 gives us:

7 x 1.03 = 7.21

Then, adding 0.9 gives us:

7.21 + 0.9 = 8.11

Therefore, the total length of the beads on one braid is 8.11 centimeters.

So, the correct answer is B.8.11 centimeters.

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Based on the data provided in the table, the valid inferences are A, B and C, while inference D cannot be confirmed.

A conclusion that is logical, rational, and backed by solid reasoning, statistical analysis, or scientific principles is considered to be a valid inference when it is derived from the available facts or evidence. It should be founded on trustworthy and pertinent data and adhere to accepted rules of statistical or scientific reasoning.

In addition to being compatible with accepted theories, guiding principles, or previous research findings, a valid inference should take into account any constraints and potential sources of mistake in the data or evidence. In other terms, a valid inference is a plausible and convincing conclusion that may be reached using acceptable statistical or scientific techniques from the relevant information or evidence.

A. Valid: There are more students who spend at least 4 hours per week on homework than students who spend less than 4 hours per week on homework.

B. Valid: Approximately 11% of students in the school district spend at least 6 hours per week on homework, based on the "At least 6" category which has 28 students out of the total 250 students surveyed.

C. Valid: About 50% of students who spend less than 4 hours per week on homework spend less than 2 hours per week, based on the total number of students in the "Less than 2" and "2 to less than 4" categories compared to the total number of students in the "Less than 4" category.

D. Not valid: The table does not provide data specifically about students who spend at least 4 hours per week on homework and their hours of homework beyond 4 hours, so this inference cannot be made.

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Both functions have the same axis of symmetry equation, which is x = -3.

Given that, Maxine graphs a function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8).

Ricardo graphs p(x) = (x+3)² + 4

We need to check if both the function axis of symmetry equation.

So,

Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.

Axis of symmetry = The axis of symmetry is an imaginary straight line that divides the shape into two identical parts or that makes the shape symmetrical.

For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.

For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.

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(a) The linear programming model to maximize the profit is written as,

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

(b) The optimal solution is x1 = 0, x2 = 8/3, x3 = 8, x4 = 0, and the maximum profit is $40.

(a) Linear programming model:

Let x1, x2, and x3 be the number of acres allocated to lemon, peach, and cherry trees, respectively. Then, the objective function we want to maximize is:

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

The first term represents the revenue from selling lemons, the second term represents the revenue from selling peaches, the third term represents the revenue from selling cherries, the fourth term represents the cost of fertilizer, and the last term represents the cost of labor.

The constraints are:

x1 + x2 + x3 ≤ 200 (total available land)

10x1 + 12x2 + 10x3 ≤ 20000 (total available labor hours)

x1, x2, x3 ≥ 0 (non-negativity constraints)

(b) Simplex algorithm:

Convert the linear programming model into standard form by introducing slack variables and expressing all variables in terms of these variables.

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

Subject to:

x1 + x2 + x3 + x4 = 200

10x1 + 12x2 + 10x3 + x5 = 20000

x1, x2, x3, x4, x5 ≥ 0

In this case, the entering variable is x1, as it has the highest coefficient in the objective function.

Step 5 (continued):

1.6 0.1 0 1 -48 32 <- Z

0.4 0.9 1 1/10 0 40 <- x1

8.4 3.3 0 -1/10 1 1840 <- x5

The entering variable is x3, as it has the highest coefficient in the objective function.

The leaving variable is x1, as it has the smallest ratio of RHS to its coefficient in the x3 column.

x2 x1/12 x3 x5/120 x4 RHS

2.5 1/5 0 -1/60 0 40 <- Z

0.5 -1/5 1 1/60 0 8 <- x3

0.5 2/15 0 1/60 1/10 8/3 <- x2

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Answer:

40-m=21

40-40-m=21-40

m=21-40

m=-19

Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Answer:

Jaxon made 11 free throws over the season.

Step-by-step explanation:

If he made 5% of his free throws, we know that he will make 5% of the total number of free throws he took, which is 220:

We multiply 220 by 0.05, or 5% to find out how many free throws he made:

220*0.05 = 11

After that, we now know that Jaxon made 11 of his free throws out of 220 over the course of the season, or 5%.

The range of a data set is the difference between the highest and lowest numbers in the set. To find the range for the given set of data, we first need to find the highest and lowest values in the set. From the given set of data, we can see that the minimum value is 3 and the maximum value is 12. Therefore, the range of the given set of data is 12 - 3 = 9.

Hence, the answer is 9.

The center-radius form of the circle is:

(x + 3)² + (y - 5)² = 25

What is a circle?

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Given the equation (x - 11)² + (y + 4)² = 15, we can see that the equation is in standard form:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle, and r is the radius. Comparing the given equation with the standard form, we can see that:

h = 11, k = -4, and r² = 15

Taking the square root on both sides, we get:

r = √15

Therefore, the center of the circle is (11, -4) and the radius is √15.

The center-radius form of the circle with center (-3, 5) that passes through the point (0, 1) can be found using the formula:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius. We are given that the center of the circle is (-3, 5), so we can substitute these values into the formula:

(x - (-3))² + (y - 5)² = r²

Simplifying the expression on the left-hand side, we get:

(x + 3)² + (y - 5)² = r²

Now, we need to find the value of r. Since the circle passes through the point (0, 1), we can substitute these values into the equation above:

(0 + 3)² + (1 - 5)² = r²

Simplifying the expression on the left-hand side, we get:

9 + 16 = r²

25 = r²

Taking the square root on both sides, we get:

r = 5

Therefore, the center-radius form of the circle is:

(x + 3)² + (y - 5)² = 25

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Answer: E

Step-by-step explanation: The line going up has a slope of one and the y intercept is 2. The first equation should be y=x+2. The next one has a downwards slope with a y intercept of -4. y=-x-4. Ths means it would be E

Rounding to the nearest hundredth, we get an expected count of 128.06 for that cell.

One of the four fundamental mathematical processes, along with addition, subtraction, multiplication, and division, is addition.

To find the expected count for the cell corresponding to navigation from social media before Mabel made the change, we need to calculate the total number of observations in that category (before the change), and the total number of observations in the entire sample (before and after the change). Then we can use those values to calculate the expected count.

Total number of observations in the social media category before the change:

57 + 71 = 128

Total number of observations in the entire sample before the change:

170

Expected count for the cell corresponding to navigation from social media before the change:

(expected proportion of social media visitors) x (total number of observations in the entire sample before the change)

We can estimate the expected proportion of social media visitors by calculating the overall proportion of social media visitors in the entire sample before the change:

128 / 170 = 0.7529

So the expected count for the cell corresponding to navigation from social media before the change is approximately:

0.7529 x 170 = 128.06

Rounding to the nearest hundredth, we get an expected count of 128.06 for that cell.

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Answer:

64 the expected count for the cell corresponding to navigation from social media before Mabel made the change

The two tangent theorem can be used to find the required equations and  the lengths of the of the segments and tangents as follows;

4. 6x - 16 = 4x - 10

5. x = 13

6. 10y - 3 = 7y + 21

7. y = 8

8. GK = 139
9. GZ = 77

10. ZL = 62

The two tangent theorem states that intersecting tangent segments from the point of the intersection to the circle are congruent.

The two tangent theorem indicates;

PZ = GZ, and ZK = ZL

Therefore;

4. An equation that can be used to solve for x can be obtained from the equation formed using the two tangent theorem and plugging in the value of ZK and ZL in the equation; ZK = ZL

The equation is therefore; 6·x - 16 = 4·x + 10

5. 6·x - 16 = 4·x + 10

6·x - 4·x = 10 + 16 = 26

2·x = 26

x = 13

6. The equation that can be used to solve for y can be obtained from the equation PZ = GZ, by plugging in the values of PZ and GZ in the equation as follows;

10·y - 3 = 7·y + 21

7. 10·y - 3 = 7·y + 21

10·y - 7·y = 21 + 3 = 24

3·y = 24

y = 24/3 = 8

y = 8

8. GK = GZ + ZK

Therefore; GK = 7·y + 21 + 6·x - 16

GK = 7 × 8 + 21 + 6 × 13 - 16 = 139

GK = 139

9. GZ = 7·y + 21 = 7 × 8 + 21 = 77

GZ = 77

10. ZL = 4·x + 10

Therefore; ZL = 4 × 13 + 10 = 62

ZL = 62

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