What is the radius of a circle with circumstance 27 in?

The reason why Leslie is wrong is because: D. Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable, with the pair of points having a constant of proportionality.

Mathematically, the rate of change can be calculated by using this formula;

Rate of change = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change = (y₂ - y₁)/(x₂ - x₁)

Rate of change = (-3 - (-4))/(0 - (-1))

Rate of change = 1/1

Rate of change = 1

For the other points chosen, the rate of change is given by:

Rate of change = (5 - (-3))/(2 - (-1))

Rate of change = 8/2

Rate of change = 4.

In conclusion, Leslie is wrong is because the rate of change or constant of proportionality for these data points are not the same.

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Complete Question:

Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (-1, -4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (-1, -4) and (0, -3) to be (-3 - (-4))/(0 - (-1)) = 1 and the rate of change between the points (0, -3) and (2, 5) to be (5 - (-3))/(2 - (-1)) = 8/2 = 4. Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?

Answer:

x = -3

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

You can just do +x on both sides so: 0=3+x and then -3 on both sides: -3=x.

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

(1.75, 3)

Step-by-step explanation:

Let's find L' first: We are reflecting L over the x axis, it means it stays on the same vertical (x=-1.75) and it's y changes sign, going to (-1,75,3).

This new point gets reflected again, over the y-axis. The horizontal coordinate (y=3) remains the same, and  the x coordinate changes sign, going to it's final destination (1,75, 3)

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

We have,

3.

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees.

= 25

We add up all the dots above the numbers between 98.5 and 98.7.

We will not include the dots above 98.5 and 98.7.

4.

The dot plot of the sample mean body temperature for 100 different random samples of size 10 from a population with a mean temperature of 98.6 degrees shows that the majority of the sample means are close to 98.6, and there are very few samples means that exceed 98.6, then it would be surprising to obtain a sample mean of 98.8 or greater from a different random sample.

Thus,

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

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The triangles ΔAEB and ΔCDB are congruent as per SSS criteria. The correct option is (B).

Two triangles are said to be congruent when all of their corresponding sides and angles are equal. For this relation between two triangles, there are many criteria such as SSS, SAS, ASA and RHS.

The relation between the two triangles ΔAEB and ΔCDB as per the given information can be shown as follows,

In ΔAEB and ΔCDB,

AE = CB

AB = CD

EB = BD

Since all the three corresponding sides of the triangles are equal, the triangles  ΔAEB ≅ ΔCDB by SSS criteria.

Hence, the two triangles are congruent by SSS criteria.

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Answer:

20%

Step-by-step explanation:

the question for this problem is basically 32/160*100

32/160=1/5=0.2. We need to make it into a percent so 0.2*100= 20%

Answer:

Step-by-step explanation:

(a) the cost for each person is not always the same

The predicted number for 70$ would be

10

(b) the train appears to go the same distance each minute.

The predicted distance travled for 10 mintues would be

30

Answer:

Step-by-step explanation:

This is a "regular" sin graph that's "taller" than the original. The amplitude is 3; other than that, its period is the same and it has not shifted to the right or left, so the equation, judging from the graph, is

\(y=3sin(x)\)

The gradient vector ∇f(3,2) is (2,3). To find the tangent line to the level curve f(x,y)=6 at the point (3,2), we use the gradient vector. The tangent line at a given point on a level curve is perpendicular to the gradient vector at that point.

The level curve f(x,y)=6 represents all the points (x,y) in the xy-plane where the function f(x,y) takes the value 6. To sketch the level curve, we plot the points that satisfy f(x,y)=6. In this case, the level curve is a hyperbola with equation xy=6.

To find the tangent line at the point (3,2), we use the gradient vector ∇f(3,2) = (2,3). The slope of the tangent line is given by the ratio of the components of the gradient vector, which is 3/2. Using the point-slope form of a line, the equation of the tangent line is y - 2 = (3/2)(x - 3).

To sketch the level curve, the tangent line, and the gradient vector, we plot the hyperbola xy=6, draw the tangent line through the point (3,2) with slope 3/2, and indicate the gradient vector (2,3) at the point (3,2).

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Because the general expression for a quadratic equation is

If you consider the vertical line test (a graph represent a function is a vertical line crosses the curve of the function only once), you can consider that a vertical line at x=5 crosses the curve at two points.

Then, you can conclude that the given relation is not a function.

The domain are the set of x values with points on the curve. In this case:

domain = [2 , oo)

The range are the set of y values with points on the curve. In this case:

range = (-oo , oo)

Answer:

\(y < 85 \div \div 9614 = 88\)

Ты лоххх

Step-by-step explanation:

For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:

The question gives us two points, (-1, 7) (-7, 1), from which we can find the slope and later the equation of the line.

Finding the Slope  

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)  

                                          =  (7 - 1) ÷ (-1 - (-7))

                                         =  6  ÷   6

                                         =   1

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line; where (x₁ , y₁) = (-1, 7):

   we could also transform this into the slope-intercept form ( y = mx + c)

                  since y - 7  =  (x + 1)

                            y =  x + 1 + 7

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

The standard deviation of a probability distribution must be a non-negative value. It represents the measure of the dispersion or spread of the data in the distribution. The standard deviation quantifies how much the values in the distribution deviate from the mean.

Mathematically, the standard deviation (σ) is calculated as the square root of the variance (σ^2) of the probability distribution. The variance is obtained by calculating the average of the squared differences between each data point and the mean, weighted by their respective probabilities.

The standard deviation provides important information about the shape and characteristics of the distribution. A smaller standard deviation indicates that the data points are closer to the mean, resulting in a more concentrated or less dispersed distribution. Conversely, a larger standard deviation indicates that the data points are more spread out from the mean, resulting in a wider or more dispersed distribution.

The standard deviation of a probability distribution must be a non-negative value and is a measure of the dispersion or spread of the data in the distribution.

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Answer:

the length would be 9.6 and the width would be 2.4

Step-by-step explanation:

9.6×2= 19.2

2.4×2= 4.8

19.2+4.8=24

The transformation that took place is a horizontal stretch by a factor of 2

We are given that Polygon ABCD transformed to create polygon A'B'C'D'. Clearly, the polygon is first a translation of the polygon ABCD 1 unit to the right and then it is horizontally stretched by a scale factor of 2.

Since the length of the polygon was earlier 2 units and then the length of the Polygon A'B'C'D' is 4 units. Hence, the transformation that took place in the Polygon ABCD is a horizontal stretch by a factor of 2

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Answer: A Horizontal Stretch by a Factor of 2

Step-by-step explanation:

Answer:

3.5/100*8=.28

Step-by-step explanation:

Answer:

To add fractions, find the LCD and then combine.

3/4 + (1/4−16)= −15

Step-by-step explanation:

To find the powers of a relation, we need to understand the composition of relations. The composition of two relations, denoted as \(R1*R2\), is defined as follows:

Given\(R\)= {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)}

\(R^2\) = {(1, 1), (1, 2), (1, 3), (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}

Therefore,\(R^2\) = {(1, 1), (1, 2), (1, 3), (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}

\(R^2*R\) = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

Therefore, \(R^3\)= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

Hence, \(-R^2\) and\(R^3\)are:

\(-R^2\) = {(-1, -1), (-1, -2), (-1, -3), (-2, -1), (-3, -1), (-3, -2), (-4, -1), (-4, -2), (-4, -3)}

\(R^3\)= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

The relation \(-R^2\) represents the negation of each element in the relation \(R^2\),assuming the set includes negative integers as well.

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r = {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)} on the set {1, 2, 3, 4}, the composition of r with itself, denoted as r^2, and the composition of r with itself three times, denoted as r^3, are calculated.

The composition of relations involves combining the ordered pairs from two relations based on a specific rule. In this case, we are considering the relation r = {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)} on the set {1, 2, 3, 4}.

To find r^2, we need to calculate the composition of r with itself. We multiply the ordered pairs from r in such a way that the second element of each pair matches the first element of another pair. Applying this rule, we have r^2 = {(1, 2), (2, 1), (2, 2), (3, 2), (3, 3), (4, 1)}.

To find r^3, we calculate the composition of r with itself three times. By applying the same rule as before, we have r^3 = {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 3)}.

Therefore, the compositions −r^2 and r^3 of the given relation r can be expressed as −r^2 = {(1, 3), (2, 1), (2, 3), (3, 1), (3, 3), (4, 1)} and r^3 = {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 3)}.

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Answer:

9 and 2

Step-by-step explanation:

...............

Answer and Step-by-step explanation:

The answer is 9 and 2.

9 times 2 will equals 18.

9 plus 2 equals 11.

#teamtrees #PAW (Plant And Water)

The samples of size n = 2 that can be drawn from this population is 28

From the question, we have the following parameters that can be used in our computation:

Population, N = 8

Sample, n = 2

The samples of size n = 2 that can be drawn from this population is calculated as

Sample = N!/(n! * (N - n)!)

substitute the known values in the above equation, so, we have the following representation

Sample = 8!/(2! * 6!)

Evaluate

Sample = 28

Hence, the number of samples is 28

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Complete question

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

How many samples of size n = 2 can be drawn this population?

The difference quotient for the function is 8.

The function is given by:

f ( x ) = 8 x − 9, where h ≠ 0

To find f(a), substitute a for x in the function. So we have:

f ( a ) = 8 a − 9

To find f(a + h), substitute a + h for x in the function. So we have:

f ( a + h ) = 8 ( a + h ) − 9

The difference quotient can be found using the formula:

(f(a + h) - f(a))/h

Substituting the values found above, we have:

(8 ( a + h ) − 9 - (8 a − 9))/h

Expanding the brackets and simplifying, we have:

((8a + 8h) - 9 - 8a + 9)/h

= 8h/h

= 8

Therefore, the difference quotient for the function is 8.

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Answer:

2

Step-by-step explanation:

Turn 3 2/3 into improper fraction: 11/3

11/3-5/3=6/3=2

The area of the composite shape is 40.57 square m and the perimeter is 34.57 meters

The surface area of composite shapes can be found by breaking the composite shape down into simpler shapes and then finding the surface area of each individual shape.

Here, we have

Area = Area of rectangle + circle

So, we have

Area = 4 * 7 + 22/7 * (4/2)^2

Area = 40.57 square m

So, the area is 40.57 square m

For the perimeter, we have

Perimeter = 2 * (4 + 7) + 2 * 22/7 * (4/2)

Perimeter = 34.57

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Answer:

[B] The probability of Alex picking a red marble is 50%.

[C] They both have the same probability of picking a red marble.

Step-by-step explanation:

Given;

Alex and James both have a bag of marbles.

Alex's bag has 10 red marbles and 10 blue marbles.

James's bag has 15 red marbles, 10 blue marbles and 5 green marbles.

They each take a marble out of their bag without looking.

Solve;

Alex have 10 Blue marbles so 10 out of 20 are Blue.

James has 10 Blue Marbles so 10 out of 30 are Blue.

Hence, [A] They both have the same probability of picking a blue marble.

is False.

Alex have 10 red and 10 blue which 10 = 10

thus, [B] The probability of Alex picking a red marble is 50%.

Alex's have 10 red marbles and James's have 15 red marbles.

10 out of 20 of them are red. Thus, that 50%

15 out of 30 of them are red. Thus, that 50%

50%  = 50%

Hence, [C] They both have the same probability of picking a red marble.

is true.

James have 15 red, 10 Blue, 5 Green marbles.

15 + 10 + 5 =30 [ Total ]

5 out of 30 is Green

5/30 = 0.16666666666

Round = 16.67%

Hence, [D]  The probability of James picking a green marble is 5%.

is False.

15 out of 30 and 10 out of 20

15/30 = 50% and 10/20 = 50%

Thus, [E] James has a higher chance of picking a red marble than Alex.

is False.

~Learn with Lenvy~

Select the statements that are correct:

A - They both have the same probability of picking a blue marble. [ x ]

B - The probability of Alex picking a red marble is 50%. [✓]

C - They both have the same probability of picking a red marble. [✓]

D - The probability of James picking a green marble is 5%. [x]

E - James has a higher chance of picking a red marble than Alex. [x]

We know that ,

\(probability \: \% = \frac{favourable \: outcomes}{total \: outcomes} \times 100 \\ \)

Alex has↷

\( \frac{10}{20} \times 100 = 50\% \\ \)

\( \frac{10}{20} \times 100 = 50\% \\ \)

James has ↷

\( \frac{15}{30} \times 100 = 50\% \\ \)

\( \frac{10}{30} \times 100 = 33.33\% \\ \)

\( \frac{5}{30} \times 100 = 16.66\% \\ \)