Give the domain and range. x –3 0 3 y –6 0 6 a. domain {–3, 0, 3}, range: {–6, 0, 6} b. domain {–6, 0, 6}, range {–3, 0, 3} c. domain {3, 0, 3}, range {6, 0, 6} d. domain {6, 0, 6}, range {3, 0, 3} Please select the best answer from the choices provided A B C D

The probability is given as follows:

0.278 = 27.8%.

The event is not mutually exclusive, as the probability is different of zero.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes when two dice are rolled is given as follows:

6² = 36.

The desired outcomes are given as follows:

Hence the probability is given as follows:

(6 + 4)/36 = 5/18 = 0.278 = 27.8%.

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The explicit formula for the sequence 12, 112, 212, 312, 412 is a_n = 100n + 12.

The explicit formula for the given sequence is:

a_n = 100n + 12

In the given sequence, each term is obtained by adding 100 to the previous term. The first term is 12, and each subsequent term is obtained by adding 100 to the previous term.

Using the formula, we can calculate any term in the sequence by substituting the corresponding value of n. For example:

a_1 = 100(1) + 12 = 112

a_2 = 100(2) + 12 = 212

a_3 = 100(3) + 12 = 312

a_4 = 100(4) + 12 = 412

Therefore, the explicit formula for the sequence 12, 112, 212, 312, 412 is a_n = 100n + 12.

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Answer:

The 2nd option is correct, a 90 degree counterclockwise rotation about the origin and then a reflection across the y-axis

Step-by-step explanation:

Answer:

Minimum=60

First Quartile(Q1)=79

Median=86

Third Quartile (Q3)=89

Interquartile range (IQR)=10

Rounding to the nearest whole number, the work required to pump the oil out of the spout is approximately 5,068,032π J.

To find the work required to pump the oil out of the spout, we need to consider the potential energy of the oil. The work done is equal to the change in potential energy.The potential energy of an object is given by the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

Given that the density of the oil is 900 kg/m^3 and the tank is half full, we can determine the mass of the oil. The volume of the tank is calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.

The volume of the tank is (1/2)π(12^2)(4) = 288π m^3.

Since the oil is half full, the volume of the oil is (1/2)(288π) m^3.

The mass of the oil is the density multiplied by the volume:

m = (900 kg/m^3)(1/2)(288π m^3) = 129,600π kg.

The height of the oil is 4 m.

Now, we can calculate the potential energy:

PE = mgh = (129,600π kg)(9.8 m/s^2)(4 m) = 5,068,032π J.

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Potential problems with increasing the minimum wage include job loss, increased cost of living, business closures, regional disparities, and potential skill depreciation. It is important to carefully consider the potential consequences and assess the trade-offs before implementing any changes to the minimum wage.

1. Job Loss: Increasing the minimum wage can lead to job losses, especially for low-skilled workers. Employers may not be able to afford paying higher wages and may choose to reduce their workforce or automate certain tasks. This could result in unemployment and make it harder for individuals to find jobs.
2. Cost of Living: While increasing the minimum wage may help some workers, it could also lead to higher costs of goods and services. Employers may pass on the increased labor costs to consumers, which could result in inflation. This could offset the benefits of higher wages as the cost of living increases.
3. Business Closures: Small businesses, in particular, may struggle to absorb the increased labor costs associated with a higher minimum wage. This could result in business closures, leading to job losses and potentially reducing job opportunities for individuals.
4. Regional Disparities: A nationwide increase in the minimum wage may not account for regional differences in living costs. While a higher minimum wage may be reasonable in some areas with high costs of living, it may be excessive in other regions. This could lead to unintended consequences, such as businesses relocating to areas with lower labor costs.
5. Skill Depreciation: If the minimum wage is increased significantly, there is a risk that it may discourage individuals from pursuing higher education or acquiring additional skills. Some individuals may find it more economically viable to rely on minimum wage jobs rather than investing time and money into further education or training.

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The whole number that has no predecessor is 1.

499 is to the left of 500 on a number line.

The successor of the greatest 5-digit number is 100,000.

The additive identity is 0.

The number of whole numbers is infinite.

1 is called the multiplicative identity.

The result of (77) × 99 is 7,623.

The smallest whole number is 0.

The greatest two-digit number exactly divisible by 18 is 90.

The greatest 7-digit number using the digits 4, 6, and 9 with repetition is 999,9999.

Rearranging the numbers using the property of addition:

7326 + 139 + 674 + 861 = (7326 + 861) + 674 + 139 = 8187 + 674 + 139 = 9,000 + 674 + 139 = 9,813.

Finding the product using the distributive property:

798 x 998 = (700 + 90 + 8) x (900 + 90 + 8) = 700 x 900 + 700 x 90 + 700 x 8 + 90 x 900 + 90 x 90 + 90 x 8 + 8 x 900 + 8 x 90 + 8 x 8 = 630,000 + 63,000 + 5,600 + 81,000 + 8,100 + 720 + 7,200 + 720 + 64

= 1,448,504.

The largest 6-digit number exactly divisible by 45 is 999,990.

Simplifying the expression:

75 - [30 + (3 x (18 ÷ 6))] = 75 - [30 + (3 x 3)] = 75 - [30 + 9] = 75 - 39 = 36.

Ramesh buys 15 computers and 15 printers.

Cost of one computer = Rs. 75,326

Cost of one printer = Rs. 8,265

Using the distributive property of multiplication:

Total cost = (Cost of one computer x Number of computers) + (Cost of one printer x Number of printers)

Total cost = (Rs. 75,326 x 15) + (Rs. 8,265 x 15)

Total cost = Rs. 1,129,890 + Rs. 123,975

Total cost = Rs. 1,253,865.

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The equivalent expression of  - 1 / 4 x + 3 / 4  = 12 are as follows:

-1(x / 4) + 3 / 4  = 12

-x + 3/ 4  = 12

(-x / 4) + 3 / 4 = 12

Equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.

In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Therefore, let's find the equivalent expression of - 1 / 4 x + 3 / 4  = 12.

Hence, the equivalent expression are as follows:

-1(x / 4) + 3 / 4  = 12

-x + 3/ 4  = 12

(-x / 4) + 3 / 4 = 12

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Based on the line of best fit in the provided image, it appears that for y = 14, the estimated x-value is approximately 6.

By examining the line of best fit, we can estimate the x-value corresponding to y = 14. In the image provided, the line of best fit appears to be a straight line passing through several data points. Let's assume this line can be approximated by the equation y = mx + b, where m represents the slope and b represents the y-intercept.

To find the x-value when y = 14, we can substitute y = 14 into the equation and solve for x. However, since we don't have the equation explicitly, we will have to estimate the x-value based on the visual representation of the line of best fit.

Looking at the image, we can observe that the line of best fit intersects the y = 14 mark at approximately x ≈ 6. This is an estimation based on the position of the line relative to the given point.

Please note that this estimation is subject to the accuracy of the plotted points and the line of best fit in the image. For a more precise answer, the actual equation of the line of best fit or additional data would be required.

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OD. 9

The location of the point on the number line that is of the way from A = -4 to B = 17 would be 9.

We can calculate it as follows:

Total distance between -4 and 17 is 17 - (-4) = 21

We want the point that is of the way from -4 to 17. Since 4/5 = 0.8, we multiply 21 by 0.8 which gives 16.8.

Rounding 16.8 to the nearest integer gives us 9.

Therefore, the answer is OD: 9

To determine the type of correlation between two variables on a graph, we can examine the pattern or relationship exhibited by the data points.

If the data points on the graph form a roughly linear pattern with a positive slope, it indicates a positive correlation. This means that as one variable increases, the other variable also tends to increase.

Conversely, if the data points on the graph form a roughly linear pattern with a negative slope, it indicates a negative correlation. In this case, as one variable increases, the other variable tends to decrease.

Additionally, the strength of the correlation can be assessed by how closely the data points align with the overall trendline. If the points are tightly clustered around the trendline, it suggests a strong correlation, while scattered points indicate a weaker correlation.

By visually inspecting the graph and observing the direction and pattern of the data points in relation to the trendline, we can determine the type of correlation exhibited by the variables.

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Answer:

B

Step-by-step explanation:

the secant- secant angle LMN is half the difference of the measures of the intercepted arcs , that is

∠ LMN = [tex]\frac{1}{2}[/tex] ( KP - LN)

20° = [tex]\frac{1}{2}[/tex] (96 - LN) ← multiply both sides by 2 to clear the fraction

40° = 96° - LN ( subtract 96° from both sides )

- 56° = - LN ( multiply both sides by - 1 )

56° = LN

Answer:

[tex]\textsf{8.} \quad \textsf{(A)}\;\;\overline{XB}[/tex]

[tex]\textsf{9.} \quad \textsf{(D)}\;\;\overleftrightarrow{BD}[/tex]

Step-by-step explanation:

The radius is the distance from the center of a circle to any point on its circumference.

The center of the given circle is point X.

Therefore, the radii in the given circle are line segments XB, XA and XC.

[tex]\hrulefill[/tex]

A tangent is a straight line that touches a circle at only one point.

The line BD touches the circle at point B.

Therefore, the tangent of the given circle is line BD.

Answer:

8. A

9. D

Step-by-step explanation:

The radius is a straight line from the midpoint to the circle's circumference.

A Tangent is a line going through the circumference of the circle.

The sum diverges to negative infinity.

Here we want to find the value of the sum:

[tex]\sum_{m=1}^{ \infty}} (-11/2)*(3/2)^{m + 1}[/tex]

So, that sum goes for infinite values of m, that is bad because you can see that the term with an exponent is larger than 1.

So when m is a really large value, then the term will also be a really large value, which means that the fuction eventually diverges to negative inifnity.

The usual rule that we need to check is that, for large values of m, as m increases, the absolute value of each term decreases.

Here this cleraly does not happen, so the sum diverges.

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The density of Liquid A is equal to the density of Liquid C when they are mixed in the specified ratio.

To determine the density of Liquid C, we need to find the mass and volume of Liquid C and then calculate the density by dividing the mass by the volume.

Given that the density of Liquid A is in a 4:3 ratio with the density of Liquid B, and the mass of Liquid A is in a 5:2 ratio with the mass of Liquid B, we can assume that the ratio of their volumes is also 5:2. This is because density is the ratio of mass to volume.

When 3 cans of Liquid B are mixed with 1 can of Liquid A to make Liquid C, the volume ratio remains the same. So, the volume of Liquid C would be 5 + 3 = 8 units.

Since the density is the mass divided by the volume, the density of Liquid A would remain the same. Therefore, the density of Liquid A is equal to the density of Liquid C.

In conclusion, the density of Liquid A is equal to the density of Liquid C.

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Answer:

(B)  m∠BCD = 108°

Step-by-step explanation:

The measure of an arc is equal to the measure of its corresponding central angle. The corresponding central angle of arc AB is angle ACB.

Therefore, if the measure of arc AB is 72°, then m∠ACB = 72°.

Angles on a straight line sum to 180°.

Assuming that AD is a straight line, then:

m∠BCD + m∠ACB = 180°

m∠BCD + 72° = 180°

m∠BCD + 72° - 72° = 180° - 72°

m∠BCD = 108°

Therefore, the measure of angle BCD is 108°.

Rhe point-slope equation of a line with the labeled point (3, -4) is y + 4 = m(x - 3), where 'm' represents the slope of the line.

To find the point-slope equation of a line using the coordinates of a labeled point, you can use the following formula:
y - y₁ = m(x - x₁)
In this formula, (x₁, y₁) represents the coordinates of the labeled point, and m represents the slope of the line.
Given the coordinates (3, -4) of the labeled point, we can substitute these values into the formula:
y - (-4) = m(x - 3)
Simplifying this equation, we get:
y + 4 = m(x - 3)
This is the point-slope equation of the line.
Now, it's important to note that the problem does not provide information about the slope of the line. Therefore, we cannot determine the exact point-slope equation without knowing the slope. The point-slope equation requires the slope value to be defined.
If you have the slope of the line, let's say it is represented by the variable 'm', you can substitute that value into the equation to get the specific point-slope equation. For example, if the slope is 2, the equation becomes:
y + 4 = 2(x - 3)

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Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

[tex]p(\theta)=\sqrt{11\theta}[/tex]

[tex]\hrulefill[/tex]

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

[tex]f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}[/tex][tex]\hrulefill[/tex]

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

[tex]p(\theta)=\sqrt{11\theta}[/tex]

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

[tex]p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}[/tex]

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

[tex]p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}[/tex]

Now multiply by the conjugate.

[tex]p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\[/tex]

[tex]\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }[/tex]

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

[tex]p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }[/tex]

[tex]\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}[/tex]

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.[tex]\hrulefill[/tex]

Now evaluating the function at the given points.  

[tex]p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??[/tex]

When θ=1:

[tex]p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}[/tex]

When θ=11:

[tex]p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}[/tex]

When θ=3/11:

[tex]p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}[/tex]

Thus, all parts are solved.

The answer, expressed in simplest form, is 9/18.

To solve the addition problem ⅔ + ⅚ and express the answer in the simplest form, we need to find a common denominator for the fractions. The least common multiple (LCM) of 3 and 6 is 6.

Now, let's convert the fractions to have a common denominator of 6:

⅔ = (⅔) * (2/2) = 4/6

⅚ = (⅚) * (3/3) = 5/6

Now we can add the fractions:

4/6 + 5/6 = 9/6

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3:

(9/6) ÷ 3/3 = (9/6) * (1/3) = 9/18

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The correct answer is: d. x → -1 Simplifying further, we get: [tex]\frac{1}{2}+7[/tex] Which equals [tex]\frac{15}{2}[/tex]. d. x → -1

To find the limit of the expression [tex](\frac{x^2}{2} ) - (\frac{7}{x} )[/tex] as x approaches a specific value, we substitute that value into the expression.

a. x → 0:

[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]

Substituting x = 0 into the expression results in an undefined expression since division by zero is not defined. Therefore, the limit in this case is undefined.

b. x → 0:

[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]

Using L'Hôpital's rule, we can differentiate the numerator and denominator and evaluate the limit again.

[tex]lim[/tex]([tex]\frac{2x}{2}[/tex]) - ([tex]\frac{7}{1}[/tex]) as x → 0

Simplifying further, we get:

lim x - 7 as x → 0

Substituting x = 0, we find that the limit is -7.

c. x → 3/14:

lim ([tex](\frac{x^2}{2} ) - (\frac{7}{x} ) x\rightarrow \frac{3}{14}[/tex]

Substituting x = 3/14 into the expression gives:

[tex]\frac{\frac{3}{14}^2 }{2}-\frac{ 7}{\frac{3}{14} }[/tex]

Simplifying this expression, we find that the limit evaluates to [tex]\frac{-77}{6}[/tex]

d. x → -1:

[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]

Substituting x = -1 into the expression gives:

[tex]\frac{-1^2}{2} - (\frac{7}{-1} )[/tex]

Simplifying further, we get:

[tex]\frac{1}{2}+7[/tex]

Which equals [tex]\frac{15}{2}[/tex]

Therefore, the correct answer is:

d. x → -1

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Answer:

To the nearest tenth, we have,

z = 19.9

Step-by-step explanation:

The missing side is the hypotenuse,

And we are given the side adjacent to the angle,

z = hupotenuse = H = ?

Adjacent = A = 15

Angle = α = 41

Since we have to find hypotenuse and we are given adjacent,

Using SOHCAHTOA,

We know the angle and adjcent but need to find Hypotenuse,

So, we use CAH

or,

cos(α) = A/H

cos(α) = 15/z

(since z = hypotenuse)

zcos(α) = A

z = A/(cos(α))

z = 15/cos(41)

z = 19.8752

To the nearest tenth, we get,

z = 19.9

A median is a line segment connecting a vertex of a triangle to the midpoint of the opposite side.

The term that describes a line segment connecting a vertex of a triangle to the midpoint of the opposite side is the "median." In triangle geometry, a median is a line segment that joins a vertex of a triangle to the midpoint of the opposite side.

To understand the concept of a median, let's consider a triangle ABC. The midpoint of side BC is denoted as M, and vertex A is connected to M by a line segment. This line segment AM is referred to as the median from vertex A.

Medians have some interesting properties and play a significant role in triangle geometry. Here are a few key characteristics of medians:

1. Medians Divide the Triangle into Two Equal Areas:

Each median of a triangle divides the triangle into two regions with equal areas. The point where all three medians intersect is called the centroid, which is also the center of mass of the triangle.

2. Medians are Concurrent:

The three medians of a triangle are always concurrent, meaning they intersect at a single point called the centroid. This centroid divides each median in a 2:1 ratio, with the longer segment adjacent to the vertex.

3. Medians Divide the Triangle into Six Congruent Triangles:

The medians of a triangle divide the triangle into six smaller congruent triangles. Each of these triangles shares a common vertex with the original triangle.

4. Medians Determine the Centroid:

The centroid of a triangle is the point of intersection of the three medians. It is the balance point of the triangle, where the triangle would perfectly balance on a needle.

In summary, a median is a line segment connecting a vertex of a triangle to the midpoint of the opposite side. Medians have unique properties, including dividing the triangle into equal areas, being concurrent at the centroid, dividing the triangle into congruent triangles, and determining the balance point of the triangle.

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The correct step that comes after constructing a circle when constructing an inscribed square is to use a straightedge to draw a diameter of the circle (option C).

When constructing an inscribed square by hand, the step that comes after constructing a circle is to use a straightedge to draw a diameter of the circle. Therefore, the correct answer is C.

To understand why drawing a diameter comes after constructing a circle, let's review the steps involved in constructing an inscribed square:

1. Start by constructing a circle: To do this, you would use a compass and a fixed point as the center to draw a circle.

2. Draw a diameter of the circle: A diameter is a line segment that passes through the center of the circle and divides it into two equal parts. Using a straightedge, you can draw a straight line that passes through the center of the circle.

3. Find the midpoint of the diameter: The midpoint is the point on the diameter that divides it into two equal parts. You can use a compass or measure the distance from each end of the diameter to find the midpoint.

4. Draw a perpendicular bisector: With the midpoint as the center, use a compass to draw an arc that intersects the diameter on both sides. This arc will create two points on the diameter.

5. Connect the points: Use a straightedge to connect the two points on the diameter. This line segment will be one side of the inscribed square.

6. Repeat the process: Repeat steps 2 to 5 to draw the other three sides of the square, using the circle as a guide.

By drawing a diameter of the circle, you establish a reference line that will be the base for constructing the sides of the inscribed square. It allows you to accurately position the square within the circle and ensure that its vertices lie on the circumference.

Therefore, the correct step that comes after constructing a circle when constructing an inscribed square is to use a straightedge to draw a diameter of the circle (option C).

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The limit of the given expression is -3/4.

To find the limit of the given expression, we can apply the properties of limits and the limit theorem.

Let's break down the expression step by step:

We have the expression [tex](-6x^3 + 7x + 7) / (8x^3 - 8x + 5).[/tex]

First, we notice that both the numerator and denominator are polynomials, and the degree of the denominator is greater than the degree of the numerator.

In such cases, we can use the fact that as x approaches either positive or negative infinity, the highest power term dominates the expression. Therefore, we can simplify the expression by dividing every term by[tex]x^3:(-6x^3/x^3 + 7x/x^3 + 7/x^3) / (8x^3/x^3 - 8x/x^3 + 5/x^3).[/tex]

This simplifies to:

[tex](-6 + 7/x^2 + 7/x^3) / (8 - 8/x^2 + 5/x^3).[/tex]

Now, we can take the limit as x approaches infinity.

As x becomes infinitely large, the terms with x in the denominator tend to zero:

((-6 + 0 + 0) / (8 - 0 + 0)).

Thus, the limit of the given expression as x approaches infinity is:

-6/8 = -3/4.

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Answer:

[tex]r'(1)=\dfrac{1}{16}[/tex]

Step-by-step explanation:

Find the derivative of the following function, then evaluate the function at a point.

[tex]r=\dfrac{1}{\sqrt{5-\theta} } ; \ r'(1)=??[/tex]

[tex]\hrulefill[/tex]

Taking the derivative of the function, r. Start by applying exponent rules.

[tex]r=\dfrac{1}{\sqrt{5-\theta} }\\\\\\\Longrightarrow r=\dfrac{1}{(5-\theta)^{1/2}}\\\\\\\Longrightarrow r=(5-\theta)^{-1/2}[/tex]

Now we can derive the function. Using the chain rule and power rule:

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Chain Rule:}}\\\\\dfrac{d}{dx}\Big[f(g(x))\Big]=f'(g(x))\cdot g'(x) \end{array}\right}[/tex]

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Power Rule:}}\\\\\dfrac{d}{dx}\Big[x^n\Big]=nx^{n-1} \end{array}\right}[/tex]

[tex]r=(5-\theta)^{-1/2}\\\\\\\Longrightarrow r'=-\dfrac{1}{2} (5-\theta)^{-1/2-1} \cdot -1\\\\\\\therefore \boxed{\boxed{r'=\dfrac{1}{2} (5-\theta)^{-3/2}}}[/tex]

Thus, the derivative of the function is found.[tex]\hrulefill[/tex]

Now evaluating the function when θ=1.

[tex]r'=\dfrac{1}{2} (5-\theta)^{-3/2}\\\\\\\Longrightarrow r'(1)=\dfrac{1}{2} (5-1)^{-3/2}\\\\\\\Longrightarrow r'(1)=\dfrac{1}{2} (4)^{-3/2}\\\\\\\Longrightarrow r'(1)=\dfrac{1}{2}\Big(\dfrac{1}{8} \Big)\\\\\\\therefore \boxed{\boxed{r'(1)=\frac{1}{16} }}[/tex]

Thus, the problem is solved.

The relationship shown in the diagram can be described as follows: For each input value, there is a corresponding output value. The output value is obtained by performing certain operations on the input value according to the rules specified in the diagram.

2.2.1: The relationship shown in the diagram represents a function where each input value corresponds to a specific output value. The diagram may include various operations or rules to transform the input values into their respective output values.

2.2.2: Using the information provided in the flow diagram, we can complete the table as follows:

  - For input 0, the output is 1.

  - For input 1, the output is 2.

  - For input 2, the output is 4.

  - For input 4, the output is LO.

  - For input 5, the output is 182.

  - For input 182, the output is 2.

  - For input 2, the output is 4.

  - For input -1, the output is 12-10.

  - For input 12-10, the output is 2.

2.2.3: To calculate the input value for the given output value of -21, we follow these steps:

  - Start with the output value -21.

  - Reverse the operations or rules specified in the diagram to transform the output back into the input.

  - Apply the reverse operations in the opposite order to obtain the input value.

Please note that without a specific diagram or additional information, it is challenging to provide precise steps for reversing the operations or rules. The steps may vary depending on the complexity and specifics of the diagram.

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The apparent midpoint of AB is (3, 3) (option b).

To find the apparent midpoint of AB, we need to determine the coordinates that represent the midpoint of the line segment AB.

The given triangle ABC is placed on a grid. Since the coordinates are not provided for points A and B, we cannot directly calculate the midpoint using their coordinates. Therefore, we'll have to rely on the visual representation provided.

Looking at the grid, we can see that the line segment AB is a diagonal of the square formed by the grid lines. The square has sides of length 3 units, as it extends from (1, 1) to (4, 4).

The midpoint of a line segment is the point that divides the segment into two equal parts. Since the square has sides of length 3, the midpoint of AB should be at the halfway point between (1, 1) and (4, 4).

To calculate the coordinates of the midpoint, we take the average of the x-coordinates and the average of the y-coordinates.

The x-coordinate of the midpoint is (1 + 4) / 2 = 5 / 2 = 2.5.

The y-coordinate of the midpoint is (1 + 4) / 2 = 5 / 2 = 2.5.

Therefore, the apparent midpoint of AB is (2.5, 2.5).

However, none of the given options match the calculated midpoint. It's possible that there is an error or discrepancy in the given options. Based on the calculations, the correct apparent midpoint of AB should be (2.5, 2.5). Thus, the correct option is a.

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Answer:

-2,1,6,13,22

Step-by-step explanation:

cn = n^2 -3

Let n=1

c1 = 1^2 -3 = 1-3 = -2

Let n=2

c2 = 2^2 -3 = 4-3 = 1

Let n=3

c3 = 3^2 -3 = 9-3 = 6

Let n=4

c4 = 4^2 -3 = 16-3 = 13

Let n=5

c5 = 5^2 -3 = 25-3 = 22

The amount of air required to fill the hemisphere is 9408284.599 mm³

The quantity of paint required is 2023 cm³

4. For a hemisphere, the volume is calculated using the formula

2/3 π r³

The radius is 165 mm. plugging the value results to

= 2/3 π 165³

= 9408284.599 mm³

5. The volume of the prism is solved using the formula

= length * width * depth

= 17 * 17 * 7

= 2023 cm³

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Tom's percentage score is above 75%, which is the passing threshold, we can conclude that Tom has indeed passed the assessment.

To determine if Tom has passed the assessment, we need to calculate his percentage score out of the total marks.

Percentage Score = (Tom's Score / Total Marks) * 100

Given that Tom's score is 98 marks and the total marks are 128:

Percentage Score = (98 / 128) * 100 ≈ 76.5625%

Since Tom's percentage score is above 75%, which is the passing threshold, we can conclude that Tom has indeed passed the assessment.

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