A tin of paint covers a surface area of 70m².
Each tin costs £5.20.
The entire surface of a solid cylindrical rod with diameter 7m and height 13m needs to be
painted.
Find the minimum cost of painting the rod.

There will be 1, 2, 6, 21 non-isomorphic simple graphs for 2, 3, 4 and 5 vertices.

What are non-isomorphic simple graphs?

A non-isomorphic simple graph is a graph that is distinct from another graph, even if the two graphs have the same number of vertices and edges, and the same connectivity pattern. In other words, two graphs are non-isomorphic if they cannot be transformed into each other by a relabeling of their vertices.

For a small number of vertices, we can enumerate all non-isomorphic simple graphs by hand.

For n = 2, there is only one possible graph, which is the edge connecting the two vertices.

For n = 3, there are only two possible graphs: a triangle (complete graph on 3 vertices) and a single edge with an isolated vertex.

For n = 4, there are six possible graphs:

Complete graph on 4 vertices

Cycle graph on 4 vertices

Complete bipartite graph K2,2

Graph with a central vertex adjacent to all other vertices

Graph with two vertices of degree 3 and two vertices of degree 1

Graph with one vertex of degree 3 and three vertices of degree 1

For n = 5, there are 21 possible graphs, which can be generated by adding edges to the graphs for n = 4.

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SSS - Side - Side - Side

SAS - Side - Angle - Side

ASA - Angle - Side - Angle

AAS - Angle - Angle - Side

The above theorems can be used to compare two triangles.

SSS, which stands for "side, side, side," represents two triangles having identical angles on each of their three sides. Two triangles are said to be congruent if their third sides coincide with those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle match the two sides and included angle of the other triangle. Any angle that may be made by two particular sides is regarded as an included angle.

A triangle is comparable to another if its two matching angles are congruent, according to the AAA postulate of Euclidean geometry. The AAA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.

While in case of ASA the angle - side and another angle of first triangle is equal to the corresponding angle - side - angle of other triangle.

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SSS, SAS, ASA, and AAS are four types of triangle congruence.

SSS (Side-Side-Side) is the congruence of three sides of a triangle. This means that all three sides of the triangle have the same length. To prove SSS congruence, you need to show that the corresponding sides of the two triangles have the same length. This can be done by calculating the length of each side and comparing them.

SAS (Side-Angle-Side) is the congruence of two sides and the included angle of a triangle. This means that the two sides of the triangles must have the same length, and the angles between those two sides must also be the same. To prove SAS congruence, you need to show that the corresponding sides of the two triangles have the same length, and that the angles between those two sides are also the same.

ASA (Angle-Side-Angle) is the congruence of two angles and the included side of a triangle. This means that the two angles of the triangles must have the same measure, and the side between those two angles must also be the same length. To prove ASA congruence, you need to show that the corresponding angles of the two triangles have the same measure and that the side between those two angles is also the same length.

AAS (Angle-Angle-Side) is the congruence of two angles and a non-included side of a triangle. This means that two angles of the triangles must have the same measure, and the side not included between those two angles must also be the same length. To prove AAS congruence, you need to show that the corresponding angles of the two triangles have the same measure, and that the side not included between those two angles is also the same length.

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Answer: 40.6Cm^3

Step-by-step explanation:

The other answer for the most part is correct, except they got the high wrong. The slant height is 8, you can figure out the actual height with the Pythagoras theorem.

a^2+b^2 = c^2

5^2 + b^2=8^2

b = square root 39

b = 6.2

The formula for a cone is: 1/3 pi*r^2*h

Now we plug in our numbers

The diameter is 5 so our radius is 2.5

Our height is 6.2

1/3 * Pi* 2.5^2 * 6.2

12.9 * 3.14

   40.6

There are 12 even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.

What is number of permutation?

Take the number of possibilities for each event and multiply it by itself X times, where X is the total number of events in the sequence, to determine the number of permutations.

For instance, four-digit PINs have 10 possible combinations because each digit can range from 0 to 9.

We see that the last digit of the 3 -digit number must be even to have an even number. Therefore, the last digit must either be 2 or 8.

Case 1 - the last digit is 2. We must have the hundreds digit to be 5 and the tens digit to be any 1 of {1,7,8,9}, thus obtaining 4 numbers total.

Case 2 - the last digit is 8. We now can have 2 or 5 to be the hundreds digit, and any choice still gives us 4 choices for the tens digit. Therefore, we have 2 x 4 = 8 numbers.

Adding up our cases, we have 4 + 8 = 12 numbers.

Hence, there are 12 even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.

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Complete question:

how many even integers are there between 200 and 700 whose digits are all different and come from the set (1, 2, 5, 7, 8, 9}.

Using the vertex of the quadratic function, it is found that his maximum profit is of $75 when he charges $15 for a key-chain.

A quadratic equation is modeled by:

\(y = ax^2 + bx + c\)

The vertex is given by:

\((x_v, y_v)\)

In which:

\(x_v = -\frac{b}{2a}\)

\(y_v = -\frac{b^2 - 4ac}{4a}\)

Considering the coefficient a, we have that:

In this problem, the function is:

\(f(x) = (x - 10)(60 - 3x)\)

In standard format, it is given by:

\(f(x) = -3x^2 + 90x - 600\)

Which means that it's coefficients are a = -3, b = 90, c = -600.

Hence:

\(x_v = -\frac{90}{2(-3)} = 15\)

\(y_v = -\frac{90^2 - 4(-3)(-600)}{4(-3)} = 75\)

Hence, his maximum profit is of $75 when he charges $15 for a key-chain.

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Answer:

1. M={Mon,Tues, Wed, Thurs...Sunday }

2. A={Jan to Dec}

3. T={9,18}

4. H={42, 1, 2, 3, 6, 7, 14, 21}

5. S={1,3,5,7}

6. H={X;X Multiples of 12}

7. O={x:x is a vowel}

8. P={x;x is a factor of 12}

9. E={x;x symbols of card of deck}

10.S= {x;x of the year with 30 days}

The correct expression to represent the similarity of these two triangles is,

21/35 = x/30.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know two triangles are similar if the ratio of their corresponding sides is equal.

Therefore, The correct way to represent the similarity is,

21/35 = x/30.

We can solve for x here,

35x = 21×30.

5x = 3×30.

x = 3×6.

x = 18.

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The sample is not approximately normal because (50) (0.02) is not equal to or greater than 10.

The conditions for performing a significance test using a z-statistic require a sample size large enough to satisfy the Central Limit Theorem, which means that the sample should be approximately normal. In this case, the expected number of adults who own a motorcycle in the sample is only 1, which is less than the threshold of 10 needed for approximate normality. Therefore, the sample distribution is not normal, and a z-statistic cannot be used for hypothesis testing. The other conditions, such as random sampling and independence, are not relevant to this particular issue.

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Complete question:

The proportion of American adults who own a motorcycle is 2%. Samip believes the proportion of adults who own a motorcycle in his hometown is even lower. He randomly surveys 50 adults from his hometown and finds that 3 of them own a motorcycle. Identify why the sample in this situation does not meet all three conditions to perform a significance test using a z-statistic

The sample is not large enough because (50) (1-0.02) is not equal to or greater than 10.

The sample was not randomly selected.

The sample does not have independence.

The sample is not approximately normal because (50) (0.02) is not equal to or greater than 10.

The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y=-5/3x-2.

Given that the line passes through the point (-6,8) and has a slope of -5/3.

We are required to find the equation of the line whose description is given.

Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation, quadratic equation or cubic equation. Slope intercept form in the equation be y=mx+c.

We have been given slope be -5/3.

y=mx+c--------------1

Put m=-5/3 in equation 1.

y=-5/3x+c------------2

Put (-6,8) in equation 2.

8=-5/3 *(-6)+c

8=-5*(-2)+c

8=10+c

c=-2

Use the value of c in equation 2.

y=-5/3x-2

Hence the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y=-5/3x-2.

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Answer:

The correct option is (C).

Step-by-step explanation:

The claim made by the golf analyst is:

Claim: The standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes.

A standard deviation test is to be performed.

The hypothesis for the test will be defined as follows:

H₀: The standard deviation of the 18-hole scores for a golfer is 3.5 strokes, i.e. σ = 3.5.

Hₐ: The standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes, i.e. σ ≤ 3.5.

Thus, the correct option is (C).

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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Answer:

2100.29164641

Answer: y=-25

Step-by-step explanation:

Plug in -8 for x

3(-8)-1

-24-1

-25

Answer:

x= -25

Step-by-step explanation:

-8(3)-1=

-24-1=

-25

Rewrite the expression using the definition of base of a log:

Answer:

a = 27

The associated z score for filling to 10.98 oz. is -1.16.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

where x is the raw score, μ is the mean and σ is the standard deviation.

Given that μ = 12.01, σ = 0.89, hence:

For x = 10.98:

z = (10.98 - 12.01)/0.89 = -1.16

The associated z score for filling to 10.98 oz. is -1.16.

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The sine of the angle -2π/3 is -√3/2. When we draw an angle in standard position with a measure of -2π/3, we rotate the terminal side 2π/3 radians clockwise from the positive x-axis. The cosine of this angle is -1/2, and the sine is -√3/2.

To draw an angle in standard position with a measure of -2π/3, we start by placing the initial side of the angle on the positive x-axis (rightward direction). Then, we rotate the terminal side of the angle in the counterclockwise direction.

The angle -2π/3 corresponds to a rotation of 2π/3 radians in the clockwise direction from the positive x-axis.

Next, let's determine the values of cosine and sine for this angle:

Cosine: The cosine of an angle is the x-coordinate of the point where the terminal side intersects the unit circle. For the angle -2π/3, the cosine can be found by evaluating cos(-2π/3).

Cos(-2π/3) = cos(4π/3) = -1/2

Therefore, the cosine of the angle -2π/3 is -1/2.

Sine: The sine of an angle is the y-coordinate of the point where the terminal side intersects the unit circle. For the angle -2π/3, the sine can be found by evaluating sin(-2π/3).

Sin(-2π/3) = sin(4π/3) = -√3/2

Therefore, the sine of the angle -2π/3 is -√3/2.

In summary, when we draw an angle in standard position with a measure of -2π/3, we rotate the terminal side 2π/3 radians clockwise from the positive x-axis. The cosine of this angle is -1/2, and the sine is -√3/2.

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Answer:

Vertex = (5,0)

Axis of symmetry = x = 5

Explanation:

Y = 3(x-5)^2

Equal 3(x-5) to 0

y = 3 = 0

x-5 = 0

x = 5

Vertex = (5,0)

Formula for Axis of symmetry: x = -b/2a

Write 3(x-5)^2 in standard form

Y = 3x^2 - 30x + 75

x = -b/2a

x = -(-30)/2(3)

x = 30/6

x = 5

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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The cost of one computer is £600 and the cost of one printer is £800.

Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.

Let the cost of a computer be x and the cost of a printer be y.

Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)

4x + 5y = 6000 ---------------------- (2)

Solving equations (1) and (2) simultaneously:x = 600y = 800

Therefore, the cost of a computer is £600 and the cost of a printer is £800..

:Therefore, the cost of one computer is £600 and the cost of one printer is £800.

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Mutually exclusive events are two events that cannot occur at the same time. The conditional probability of B given A is also equal to zero, since P(B|A)=P(A and B)/P(A)=0.

This means that their intersection is empty, or P(A and B)=0.This also means that their union is the sum of individual probabilities, P(A)+P(B). This is because the intersection of two mutually exclusive events is equal to the product of their probabilities, or P(A and B)=P(A)P(B). Therefore, the probability of either event occurring is the sum of the probability of each event since the intersection of both events is zero. As a result, the conditional probability of B given A is also equal to zero, since P(B|A)=P(A and B)/P(A)=0.

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Answer: it is 1 :)

also i took the quiz and got it right! hope this helps!!

The expected time for completion of Activity "X" on a PERT chart is 9 hours.

PERT analysis is a project management technique that is used to evaluate and analyze the tasks involved in finishing a project. It makes use of 3 duration estimates: optimistic, pessimistic, and most likely times to calculate the expected duration of each activity. These estimates are used to analyze the critical path, slack time, and schedule of the project.

Let's calculate the expected time for completion of Activity "X" on a PERT chart using the given estimates:

Optimistic time (O) = 6 hours

Most likely time (M) = 9 hours

Pessimistic time (P) = 12 hours

Expected time (TE) = [O + 4M + P] ÷ 6= [6 + 4(9) + 12] ÷ 6= [6 + 36 + 12] ÷ 6= 54 ÷ 6= 9

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Answer:

A)median score = 116

b)lower quartile= 102

Answer:

y=1/2x-3

Step-by-step explanation:

I hope you meant slope of the line...

You can find the slope like this-

1/2x= how you move (so m for move)

-3 =where you begin (so b for begin)

So next time you find the slope, just ask yourself where you "begin" (where the line starts) and how you "move" (how the line moves)

Answer:

8 inches is the height

Step-by-step explanation:

\(12*10=120\)

\(960/120=8\)

Answer:

The height is 8 inches

Step-by-step explanation:

We have 12in as our length and 10in as our width.

12 × 10 = 120

960 ÷ 120 = 8in

To double check: 12 × 10 × 8 = 960

hopefully this helped :3

15 candy bars must be bought at the cost of $0.72 per piece to bring the average down to $0.80.

To find the number of candy bars needed to bring the average cost down to $0.80, we can use the formula for average:

(sum of costs)/(number of candy bars).

Let's denote the number of candy bars needed as x. We know that the sum of costs for the group of ten candy bars is 10 * $0.89 = $8.90.

To bring the average down to $0.80, the sum of costs for the x candy bars must be (10 * $0.89 + x * $0.72).

Now we can set up the equation:

(10 * $0.89 + x * $0.72)/(10 + x) = $0.80.

Simplifying this equation, we get:

8.9 + 0.72x = 0.8(10 + x).

Solving for x, we find that x = 15.

Therefore, 15 candy bars must be bought at the cost of $0.72 per piece to bring the average down to $0.80.

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complete question:

A group of ten candy bars has an average cost of $0.89 per candy bar. How many bars must be bought at the cost of $0.72 a piece to bring the average down to $0.80?

this line does not pass through the origin (0, 0), since the vector x = [0, 0] does not satisfy the equation Ax = b.

One possible example is:

A = [[1, 2], [2, 4]]

b = [3, 6]

The solution set of Ax = b is the set of all vectors of the form x = [x1, x2] such that:

x1 + 2x2 = 3

2x1 + 4x2 = 6

Solving this system of equations, we get:

x1 = 3 - 2x2

x2 = x2

So the solution set is the set of all vectors of the form x = [3 - 2x2, x2]. This is a line in R² with slope -2 and y-intercept (3, 0)

Note that this line does not pass through the origin (0, 0), since the vector x = [0, 0] does not satisfy the equation Ax = b.

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