just do a c e g and i​

The slope of the line as shown in the diagram attached below = rise/run = 3/5.

The rise of a line over the run of a line would give us the slope of a line on a coordinate plane.

With the given line in the diagram, the image attached below shows the rise as represented by a red line while the run is represented by the blue line.

Therefore, we have:

Run = 10 units

Rise = 6 units

Slope (m) of the line = rise/run = 6/10

Simplify

Slope (m) of the line =  3/5

Therefore, the slope of the line as shown in the diagram attached below = rise/run = 3/5.

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After pouring some water from container A into container B, the new height of the water in both containers will be equal.

When container A is filled with water to the brim, it reaches its maximum capacity. Let's assume the initial height of the water in container A is h.

When some water is poured from container A into container B, the water level in both containers will gradually equalize until they reach the same height. Let's denote this new height as H.

The reason the water levels equalize is due to the principle of fluid equilibrium. When the containers are connected and the water is allowed to flow, the water seeks a common level. This occurs because the pressure at the same height in a fluid is equal.

Therefore, after pouring water from container A to container B, the final height of the water in both containers will be H, which indicates that the water has reached an equilibrium point where the pressure is equal in both containers.

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The dimensions of the page that will minimize the amount of rectangle paper used are 16 inches (height) by 8 inches (width).

Area of the rectangle:

The amount of area occupied by a rectangle within its boundary is known as the area of the rectangle.

The formula to find the area of the rectangle is

A = L x W

where

L refers the length

W refers the width

Given,

A rectangular page is to contain 72 square inches of print. The margins at the top and bottom of the page are to be 2 inches wide. The margins on each side are to be 1 inch wide.

Here we need to find the  dimensions of the page that will minimize the amount of paper used.

Let us consider H and W denote the height and the width of the printed matter area respectively.

Then here we know that the value of HW = 72 and

the area of the sheet of paper is calculated as

A = (H + 4)(W + 2)

Here the value of height of the paper is calculated by H plus the top and bottom margins and

Similarly,  the value of width of the paper is W plus the side margins.

Now, to minimize A, we have to rewrite A in terms of W.

Then we get the value of

A = (72/W + 4) (W + 2)

Which is equal to,

A = 72 + 144/w + 4w + 8

By taking the derivative, then we get,

A' = -144W⁻² + 4

Apply the value of A' = 0, then we get,

144W² = 4

W² = 144/4

W =√36

W = 36.

If the value of W is 6, then the value of H is,

H (6) = 72

H = 72/6

H = 12

Now, we have to add 4 to the height and the 2 to the width in order to find the full paper dimensions.

Then we get the desired dimensions are 16 inches (height) by 8 inches (width).

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Answer:

95 is the sequence

Step-by-step explanation:

The given sequence appears to follow the pattern where each term is obtained by multiplying the previous term by 2 and then adding 1. Using this pattern, we can derive a formula for the nth term of the sequence as a(n) = 3 * 2^(n-1) - 1, where a(n) represents the nth term of the sequence and n is a positive integer.

For example, to find the 6th term of the sequence, we can substitute n = 6 into the formula to get a(6) = 3 * 2^(6-1) - 1 = 3 * 2^5 - 1 = 95. So, the 6th term of the sequence is 95.

Answer:

D.) all of the above

Step-by-step explanation:

Judging from the size of a seed, and the size of how much land you can plant the seeds in you would definitely need more than any of the amounts given.


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Answer:

\(\dfrac{2^3•5^2}{2^5•3•5^4}\)

=\(\dfrac{1}{2^2•3•5^2}\)

Fourth option is the right answer.

Answer:

192

Step-by-step explanation:

According to Euclidian theorem

x^2 = 144*(400-144)

x^2 = 144*256

x^2 = 36864 find the root of both

x = 192

False. Program Evaluation Review Technique (PERT)/Critical Path Method (CPM) and Gantt charts are not mutually exclusive techniques. In fact, they are often used together in project management to plan, schedule, and manage complex projects.

PERT/CPM is a network-based project management technique that focuses on identifying and sequencing activities, estimating their durations, and determining the critical path—the sequence of activities that determine the project's overall duration. PERT/CPM helps in analyzing the project timeline, identifying dependencies between tasks, and determining the most efficient way to complete the project.

On the other hand, Gantt charts are visual representations of project schedules that use horizontal bars to represent tasks, their durations, and their interdependencies. Gantt charts provide a graphical overview of the project timeline, allowing project managers and team members to see task durations, milestones, and dependencies at a glance. They also facilitate tracking progress and identifying potential scheduling conflicts.

While PERT/CPM focuses on the critical path and task dependencies, Gantt charts provide a broader view of the project schedule and its progress. Both techniques offer valuable insights and are often used in conjunction to effectively plan and manage projects.

Therefore, PERT/CPM and Gantt charts are complementary tools rather than mutually exclusive techniques in project management.

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Answer:

-10

Step-by-step explanation:

Answer:2.561,664¢ or roughly 25.61$.

Step-by-step explanation:

So, the air conditioner will cost 3.5 * 9.53 ¢ = 30.496 ¢ per hour running.

That means 30.496¢ * 12 = 365.952¢ or ≈3.65$ for a day.

Or 365.95¢ * 7 = 2.561,664¢ or ≈25.61$ for a week.

I'm vietanh and have fun studying!

To rotate a coordinate system onto another coordinate system using matrices, you can follow these steps:

1. Determine the angle of rotation: First, determine the angle by which you want to rotate the coordinate system. This angle will be used to create a rotation matrix.

2. Create a rotation matrix: The rotation matrix is a 2x2 or 3x3 matrix that represents the transformation of points in the original coordinate system to points in the rotated coordinate system. The elements of the rotation matrix can be determined based on the angle of rotation.

For a 2D rotation, the rotation matrix is:

 \(\[ \begin{matrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{matrix} \]\)

For a 3D rotation around the x-axis, y-axis, and z-axis, the rotation matrices are:

\(Rx = \left[\begin{array}{ccc}1&0&0\\0&cos\theta&-sin\theta\\0&sin\theta&cos\theta\end{array}\right]\)

\(Ry = \left[\begin{array}{ccc}cos\theta&0&sin\theta\\0&1&0\\-sin\theta&0&cos\theta\end{array}\right]\)

\(Rz = \left[\begin{array}{ccc}cos\theta&-sin\theta&0\\sin\theta&cos\theta&0\\0&0&1\end{array}\right]\)

Note that θ represents the angle of rotation.

3. Apply the rotation matrix: To rotate a point or a set of points, multiply the coordinates of each point by the rotation matrix. This will yield the coordinates of the points in the rotated coordinate system.

For example, if you have a 2D point P(x, y), and you want to rotate it by angle θ, the rotated point P' can be obtained by multiplying the column vector [x, y] by the rotation matrix:

  [ x' ]  =  [ cosθ  -sinθ ]   [ x ]

  [ y' ] =   [ sinθ   cosθ  ] * [ y ]

Similarly, for 3D rotations, you would multiply the column vector [x, y, z] by the appropriate rotation matrix.

Rotating a coordinate system onto another coordinate system using matrices involves the use of rotation matrices. These matrices define how points in the original coordinate system are transformed to points in the rotated coordinate system.

The rotation matrices are constructed based on the desired angle of rotation. The elements of the matrix are determined using trigonometric functions such as cosine and sine. The size of the rotation matrix depends on the dimensionality of the coordinate system (2D or 3D).

To apply the rotation, the coordinates of each point in the original coordinate system are multiplied by the rotation matrix. This matrix multiplication yields the coordinates of the points in the rotated coordinate system.

By performing this transformation, you can effectively rotate the entire coordinate system, including all points and vectors within it, onto the desired orientation defined by the angle of rotation.

Matrix transformations provide a mathematical and systematic approach to rotating coordinate systems, allowing for precise control over the rotation angle and consistent results across different coordinate systems. They are widely used in computer graphics, robotics, and various scientific and engineering fields.

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Answer:

y = -1/3x + 5

Step-by-step explanation:

On solving the provided question, we can say that from equation \(diagonal ^2 = 8^2 + 8^2\), the answer is \(DIAGONAL = 8\sqrt(2) \\\)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

\(diagonal ^2 = 8^2 + 8^2\\diagonal ^2 = 64 + 64\\diagonal ^2 = 128\\diagonal ^2 = 64 * 2\\\)

\(diagonal ^2 = 8 * sq root (2)\\Diagonal of a square = SqrRoot (2 * side^2)\\Diagonal = \sqrt{2 * 8^2} \\Diagonal = \sqrt(128)\\\)

\(\sqrt(128) = \sqrt(2 * 64) = \sqrt(2) * 8\\DIAGONAL = 8\sqrt(2) \\\)

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Answer:

A

Step-by-step explanation:

By using this method, each person has an equal chance of getting to sit in the front seat.

Put each person's name on a separate price of paper in a bag. Randomly draw the winning name.

Roll a number cube, If it lands on 1 or 2, Peter wins. If it lands on 3 or 4, Roddy wins, If it lands on 5 or 6, Scott wins.

A fair decision is one in which all three studnets have an equal chance of winnning. If each person's name is put in a bag, each person has a 1/3 chance of sitting in the front. If a number cube is rolled, the probability of each person sitting in the front is 1/3.

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Expression is a combination of numbers, operators and variables. the value of the expression −51 − 17 − (−37) is -31.

Expression is a combination of numbers, operators and variables.

The given expression is minus fifty one minus seventeen minus of minus thirty seven.

−51 − 17 − (−37)

We have to use BODMAS rule to solve this expression

-51-17+37

Now add  minus fifty one and minus seventeen

We get minus 68

-68+37

Now subtract 37 from 68 and put minus sign in the answer.

We get answer as minus thirty one.

-31

Hence option C is correct. the value of the expression −51 − 17 − (−37) is -31.

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The absolute value inequality given is |3x - 1| ≥ 4. We will solve this inequality and express the answer using interval notation. Additionally, we will graph the solution set.

To solve the absolute value inequality |3x - 1| ≥ 4, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: (3x - 1) ≥ 4

In this case, we have 3x - 1 ≥ 4. Solving this inequality, we find 3x ≥ 5, which gives x ≥ 5/3.

Case 2: -(3x - 1) ≥ 4

Here, we have -(3x - 1) ≥ 4. Solving for x, we get -3x + 1 ≥ 4, which leads to -3x ≥ 3 and x ≤ -1.

Therefore, the solution set is x ≤ -1 or x ≥ 5/3. In interval notation, the solution set can be expressed as (-∞, -1] ∪ [5/3, +∞).

To graph the solution set on a number line, we mark -1 with a closed circle (inclusive) and 5/3 with an open circle (exclusive), then shade the regions to the left of -1 and to the right of 5/3. This represents the solution set on the number line.

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The total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d. To calculate the total amount to be paid, we need to consider the compounded interest on the borrowed amount.

The nominal interest rate of 12% compounded quarterly means that interest is added to the principal four times a year. Using the formula for compound interest, we can calculate the future value of the loan. The formula is given as:

Future Value = Principal * (1 + (Nominal Interest Rate / Number of Compounding Periods))^Number of Compounding Periods * Number of Years

In this case, the principal is $7,500, the nominal interest rate is 12% (or 0.12), the number of compounding periods per year is 4 (quarterly), and the number of years is 10.

Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + (0.12 / 4))^(4 * 10) = $24,465

Therefore, the total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d.

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The probability of event A or B occurring (P(A or B)) is 0.5680, which corresponds to option c. To solve this problem, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Since events A and B are independent, we know that P(A and B) = P(A) * P(B)

Substituting the given probabilities, we get:

P(A or B) = 0.40 + 0.28 - (0.40 * 0.28)
P(A or B) = 0.68 - 0.112
P(A or B) = 0.568

Therefore, the answer is c. 0.5680.

If events A and B are independent, we can find the probability of A or B occurring (P(A or B)) by using the formula: P(A or B) = P(A) + P(B) - P(A) * P(B).

Given the probability of event A (P(A)) is 0.40 and the probability of event B (P(B)) is 0.28, we can plug these values into the formula:

P(A or B) = 0.40 + 0.28 - (0.40 * 0.28) = 0.40 + 0.28 - 0.112 = 0.568.

So, the probability of event A or B occurring (P(A or B)) is 0.5680, which corresponds to option c.

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Answer:

3 divided by 4 will equal 0.75 which is equivalent to 0.75. or you can do 6/8 which will also equal 0.75. and 6/8 is equivalent to 3/4. so therefore it's confirmed that 3/4 is equivalent to 0.75

The sequence {cos(n/3)} does not converge. In order to see this, note that cos(n/3) oscillates between -1 and 1. Therefore, the sequence cannot have a limit.

In fact, the sequence {cos(n/3)} is unbounded. It should be noted that cos(n/3) is always positive for n > 0. Therefore, the sequence must grow without bound.

The sequence oscillates between -1 and 1. This is because cos(n/3) is a periodic function with period 2pi. Therefore, for any given value of n, there is another value of n such that cos(n/3) = -cos(n/3).

A sequence with oscillating terms cannot have a limit. This is because a limit is a single number that all the terms of the sequence approach as n goes to infinity.

The sequence {cos(n/3)} is unbounded.

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The Taylor series for the function f centered at 7 can be determined using the given information about the derivatives of f at 7. Additionally, we can find the radius of convergence of the Taylor series.

To find the Taylor series for f centered at 7 and determine the radius of convergence R, we can follow these steps:

The general form of the Taylor series expansion of a function f(x) centered at a is given by:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...

We are given the derivative of f at 7, f^(n)(7), which can be written as:

f^(n)(7) = (-1)^n * n! / 6^n * (n + 4).

We need to find the coefficients of the Taylor series. To do that, we substitute a = 7 into the derivative expression:

f^(n)(7) = (-1)^n * n! / 6^n * (n + 4) = f^(n)(a) / n!.

Simplifying the expression, we have:

f^(n)(a) = (-1)^n / 6^n * (n + 4).

Now, we can substitute the coefficients into the general form of the Taylor series:

f(x) = f(7) + f'(7)(x - 7)/1! + f''(7)(x - 7)^2/2! + f'''(7)(x - 7)^3/3! + ...

To find the radius of convergence R, we use the formula:

R = 1 / lim sup |a_n / a_(n+1)|,

where a_n is the nth coefficient of the series.

Substituting the coefficients, we have:

R = 1 / lim sup |(-1)^n / 6^n * (n + 4) / (-1)^(n+1) / 6^(n+1) * (n + 5)|,

R = 1 / lim sup |6(n + 4) / (n + 5)|,

R = 1 / lim sup |6(n + 4) / (n + 5)|,

R = 1 / lim sup |6(n + 4) / (n + 5)|,

R = 1 / 6.

Therefore, the radius of convergence R of the Taylor series is 1/6.

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Answer:

the base = 7 in

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area = 1/2 base * height

Area = 28

height = 8

base = ?

28 = 1/2 * 8 * base

28 = 4 * base

28/4 = base

base = 7

The ordering of the volume o the cylinders will be B, C and A.

Radius of 4 units, the area of the circle is 16π

Radius of 10 units is 100π

Radius of 16 units is 256π

Volume is the measure of the amount of space that an object occupies, often expressed in cubic units such as cubic meters, cubic feet, or liters. It is a physical quantity that describes how much three-dimensional space an object or substance occupies.

In the case of a solid object, volume can be calculated by measuring its dimensions (such as length, width, and height) and using a formula to calculate the amount of space it occupies. For example, the volume of a rectangular box can be calculated by multiplying its length, width, and height.

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The Tennesseean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on current issues. In a recent poll, 762 readers responded to a question. To answer this question, we need more information about the question itself. However, I can provide a general format for an answer that includes the terms you mentioned.

The Tennesseean, an online newspaper, uses daily polls to gather opinions from readers. These polls allow the newspaper to gauge public sentiment on a variety of current issues. The recent poll in question received 762 responses, indicating a level of engagement from the readership.

The Tennesseean, an online newspaper located in Nashville, Tennessee, values reader input and conducts daily polls to gather opinions on a wide range of current issues. In a recent poll, a total of 762 readers responded to the question at hand. This high number of responses indicates that the readership is actively participating in the poll and shows a strong interest in expressing their opinions.

The Tennesseean's decision to conduct daily polls is a strategic approach to engage its audience and involve them in the newspaper's content creation process. By seeking reader opinions, the newspaper ensures that its reporting and coverage align with the interests and preferences of its audience. The high response rate of 762 readers suggests that the poll question was relevant and engaging to the readership.

The Tennesseean's use of daily polls to obtain reader opinions is a commendable effort to involve its audience in the news-making process. The substantial number of responses received in a recent poll, with 762 readers participating, demonstrates a strong level of engagement from the newspaper's readership. This feedback helps the newspaper to better understand the interests and perspectives of its audience, allowing it to deliver more relevant and informative content.

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The number 56 when compared to 10 is the same as 28 compared to 5.

Option- C(56)

Let x be the number when compared to 10 is same as 28 compared to 5.

So, finding the value of x by comparing the ratios of the above stated values.

Therefore,

                    \(\frac{x}{10} = \frac{28}{5}\)

So, Cross multiplying the above equation,

                      x × 5 = 28 × 10

                       5x = 280

                        x = \(\frac{280}{5}\)

                        x = 56

So, 56 when compared to 10 bears the same ratio as 28 compared to 5.

Option number - C

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To find the mass of the thin bars, we need to integrate the density function over the given interval. The density function is given as p(x) = 1 + sin x, for 0 ≤ x ≤ π.

We know that density is defined as mass per unit volume. In this case, the density function represents the mass per unit length. So, to find the mass of the thin bars, we need to integrate the density function over the given length.

The formula for mass is given as:

m = ∫ρ(x)dx

where m is the mass, ρ(x) is the density function, and dx is the infinitesimal length element.

So, in this case, we have:

m = ∫(1 + sin x)dx

Integrating this expression, we get:

m = x - cos x + C

where C is the constant of integration.

Now, we need to evaluate this expression for x = π and x = 0 and subtract the two to get the mass of the thin bars.

m = π - cos π - (0 - cos 0)

m = π + 1

Therefore, the mass of the thin bars with the given density function is π + 1.

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Answer:

i think that the answer 90 degrees

Step-by-step explanation:

i really hope this helped

Answer:

34 degrees C

Step-by-step explanation:

30+30+30+35+35+35+34=229

229/7=32.714

and when you round up you get 33

To prove that at any party of 31 people, there's always a person who knows an even number of others, we can use the pigeonhole principle.

The pigeonhole principle states that if we distribute more than "n" objects into "n" boxes, then at least one box must contain more than one object. In this case, the "objects" represent the people at the party, and the "boxes" represent the number of people each person knows.

Let's assume, for the sake of contradiction, that every person at the party knows an odd number of others. This means that each person has an odd number of acquaintances.

Now, let's consider the sum of the number of acquaintances for all 31 people. Since each person knows an odd number of others, the sum of odd numbers is also an odd number.

However, if we count the total number of acquaintances in a group, it must be even since each acquaintance involves two people. This creates a contradiction because we cannot have both an odd and an even sum for the total number of acquaintances.

Therefore, our assumption that every person knows an odd number of others must be false. Hence, there must be at least one person at the party who knows an even number of others.

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