Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Combinations and sequences are widely used in mathematics to explain and assess situations in which the order or selection of components might influence the final result.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

A combination is a grouping of things from a bigger set in which the order of the components is irrelevant. A sequence is a collection of elements that are ordered in a precise order. Combinations and sequences are frequently used in mathematics to describe and evaluate situations where the order or selection of components might impact the final outcome, such as in combinatorics, probability, and statistics.

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Complete question:

A combination of values that, when arranged correctly, result in a final value. true/false

In order from x - y = 3 ... to y = 4 - 5x, the number of solutions of each system of equations is given as follows:

There are three possible number of solutions for each system of equations, and the cases are presented as follows:

We look at these coefficients, and then obtain the number of solutions for each system in this problem.

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Answer:

What equation

Step-by-step explanation:

When converted from active voice to passive voice, the sentences read as follows:

Active Voice refers to a sentence construction where the subject is performing the action described by the verb. It emphasizes the doer of the action.

On the other hand, Passive Voice refers to a sentence construction where the action is performed on the subject, rather than the subject performing the action. It emphasizes the action or the object affected by the action.

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Answer: The slope between the points (0,-5) and (-2,3) is (-3 - (-5)) / (-2 - 0) = -8 / -2 = 4.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

This is a classic example of a system of equations with two variables. We can set up two equations to represent the given information:

x = number of ducks

y = number of sheep

heads: x + y = 15

legs: 2x + 4y = 38

To solve for the number of ducks, we can use substitution. We can solve one of the equations for one of the variables and substitute it into the other equation.

For example, solving the first equation for y: y = 15 - x. Then substitute it into the second equation:

2x + 4(15 - x) = 38

Solving this equation will give you the value of x, which is the number of ducks.

x = 5

So, there are 5 ducks in the meadow.

Answer:

ofc 15 heads 15 ducks bro comman sense no logic in there

Answer:

27.6 is a rational number

Step-by-step explanation:

A rational number is any number that can be expressed as a fraction. Since 27.6 Since 27.6 can be expressed as 276/10 or 138/3, 27.6 is a rational number.

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The value of the function when evaluated is 3

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

g(x) = 2x ^ 2 - 3x + 5

Express properly

So, we have the following representation

g(x) = 2x^2 - 3x + 5

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

g(-2) = 2(-2)^2 - 3(-2) + 5

Evaluate the like terms

g(-2) = -8 + 6 + 5

So, we have

g(-2) =

Hence, the function value is 3

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The function h(x) represents the cost of the jeans if you first use the coupon and then apply the store discount.

The function h(x) can be computed using the composition of functions f(x) and g(x). The function j(x) represents the cost of the jeans if you first apply the store discount and then use the coupon.

The function g(x) can be computed using the composition of functions g(x) and f(x).

If you use the composition h(x), you will pay $27 for the jeans. If you use the composition j(x), you will pay $30 for the jeans.

Therefore, the composition h(x) will give you a better discount since it is cheaper.

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The function that represents how much you would pay if you use the store discount first and then mall coupon is:

j(x) = 0.75*x - 5

Wewant to write a function that represents how much you would pay if you use the store discount and then tha mall coupon.

We know that:

So if first we apply the discount, then we need to do the composition:

f(g(x)) = g(x) - 5

Replacing g(x) there we will get:

f(g(x)) = g(x) - 5 = 0.75*x - 5

j(x) = 0.75*x - 5

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one may determine how much fence is necessary for a playground with a 256 square yard area is P = 1024 / x.

What is quadrilateral?

Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

P = 4x

Area = x²

Px = 4x²

x² = Px/4

Area = Px/4

The fencing will be equal to the perimeter, with an area 256 sq yd

256 = Px/4

P = 1024 / x

Thus, using a straightforward equation, one may determine how much fence is necessary for a playground with a 256 square yard area is P = 1024 / x.

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The integral is evaluated and the value of the integral is found to be 3/2.

Given that,

The integral is ∫∫(5+10y) dy dx

To find : To evaluate the iterated integral,

= ∫(5y + 10y²/2) dx

= ∫ (5y + 5y²) dx

Substituting the limits x and x² in the variable y

= ∫ (5x + 5x² - (5x² + 5x⁴)) dx

= ∫(5x + 5x² - 5x² - 5x⁴) dx

= ∫(5x - 5x⁴) dx

= (5x²/2 - 5x⁵/5)

= (5/2 - 1)

= 3/2

Hence, The integral is evaluated and the value of the integral is found to be 3/2.

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The competition took 2 minutes.

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

Given that, the Turtle and Achilles compete. They start at the same time from the same place. Achilles runs at a speed of 13 mph while the Turtle moves at a speed of 1 mph. When Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him.

Let t be the time taken in competition and the distance covered by Achilles be x miles.

We have been given that when Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him. This means that the distance covered by turtle will be: x - 2/5

Since we know that, speed = distance / time

So, we can set two equations for time taken by Achilles and turtle as:

t = x / 13

x = 13t......(i)

t = (x-2/5)/1....(ii)

Substituting this value in equation (2) we will get,

t = 13t - 2/5

5t = 65t - 2

60t = 2

t = 2/60

t = 1/30

So, the competition took 1/30 hour, let us convert our given time in minutes.

1/30 × 60 minutes

= 2 minutes

Hence, the competition took 2 minutes.

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a) The number of poker hands with exactly 2 aces and 3 kings is 24.

b) The probability that the first king is dealt out on the 13th card is approximately 0.0045, or approximately 0.45%.

a) To find the number of poker hands with exactly 2 aces and 3 kings, we have to choose which 2 aces out of the 4 available and which 3 kings out of the 4 available to include in our hand. We can do this in C(4,2) * C(4,3) ways, where C(n, k) is the number of combinations of n things taken k at a time.

Therefore, the number of poker hands with exactly 2 aces and 3 kings is C(4,2) * C(4,3) = 6 * 4 = 24.

b) The probability that the first king is dealt on the 13th card is the number of combinations of 12 cards that do not include any kings divided by the total number of combinations of the first 12 cards. This can be calculated as (48 choose 12) / (52 choose 12), where C(n, k) is the number of combinations of n things taken k at a time.

The probability is (48 choose 12) / (52 choose 12) = (48! / (12! * (48-12)!) ) / (52! / (12! * (52-12)!)) = (48 * 47 * 46 * 45 * 44 * 43 * 42 * 41 * 40 * 39 * 38 * 37) / (52 * 51 * 50 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41) = approximately 0.0045, or approximately 0.45%.

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Answer:

c = 72/0.45

c = 160

So the value of c =160

well, let's call "c" the 100%, and we know that 45% of that is 72, hmmm so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} c & 100\\ 72& 45 \end{array} \implies \cfrac{c}{72}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{ c }{ 72 } ~~=~~ \cfrac{ 20 }{ 9 }\implies 9c=1440\implies c=\cfrac{1440}{9}\implies c=160[/tex]

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

-5x-3(-3) = -7

Apply distributive property:

(-5x)*-3 + (-3)*-3

15x + 9 = -7

      -9    -9

15x = -15

Divide both sides by 15:

15x/15 = x

-15/15 = -1

[tex]x=-1[/tex]

Hope this helped!

The original number of CDs is between 1000 and 1500.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Number of copies of a popular CD left to be sold in the store = 20

According to question, this is between 15 and 1.5% of the original number of copies of the CD in the store.

Let the original number of copies of the CD be 'x'.

Now, 20 is equal to 1% of the original number of copies of the CD,

1% of x = 20

1/100 of x= 20

x= 2000

Or if 15 is equal to 1.5% of the original number

1.25% of x= 20

1.25/100 x = 20

x = 1600

Hence, the CDs is between 1000 and 1500.

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The same coordinate axes, with the x-axis denoting the first coordinate, the y-axis denoting the second coordinate, and the z-axis denoting the third coordinate, may be used to plot the points s1, 5, 3d, s0, 2, 23d, s23, 0, 2d, and s2, 22, 21d.

First, plot the coordinate axes using the point s1, 5, and 3D. This point's x, y, and z coordinates are 1, 5, and 3, respectively.

Step 2: Draw a coordinate axes plot of the position s0, 2, 23d. This point has the x, y, and z coordinates of 0, 2, and 23, respectively.

Step 3: Draw a coordinate axes plot of the point s23, 0, 2d. This point's x, y, and z coordinates are 23, 0, and 2, respectively.

Step 4: Draw a coordinate axes plot of the position s2, 22, 21d. This point's x, y, and z coordinates are 2, 22, and 21 respectively.

The same coordinate axes, with the x-axis denoting the first coordinate, the y-axis denoting the second coordinate, and the z-axis denoting the third coordinate, may be used to plot the points s1, 5, 3d, s0, 2, 23d, s23, 0, 2d, and s2, 22, 21d. Plotting these points begins with the point s1, 5, 3d, which has the x, y, and z coordinates of 1, 5, and 3. Plot this point on the coordinate axes with the x, y, and z coordinates as 1, 5, and 3 respectively. The junction of the x, y, and z axes should be at this location. Plot the point s0, 2, 23d, which has coordinates of 0 on the x-axis, 2 on the y-axis, and 23 on the z-axis. The z-coordinate of this point should be 23 units above the x-y plane, and it should be located where the x- and y-axis meet. Plot the points s23, 0, 2d, and s2, 22, 21d to finish. These points should be located at 0 and 22 units above the x-z plane, respectively, and on the x and z axis. Plotting all the points should result in a three-dimensional figure.

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Answer:

Basket A contains 8 balls, basket B contains 8 + 6 = 14 balls, and basket C contains 17 - (8 + 6) = 3 balls.

Let's call the number of balls in basket A "x".

Since there are 6 more balls in basket B than in basket A, we can write the equation for the number of balls in basket B as x + 6.

And since the total number of balls in baskets B and C is 17, we can write the equation for the number of balls in basket C as 17 - (x + 6) = 17 - x - 6.

So the total number of balls in baskets A, B and C is x + (x + 6) + (17 - x - 6) = x + x + 6 + 17 - x - 6 = 22.

Therefore, we can solve for x:

2x + 6 = 22

2x = 16

x = 8

So basket A contains 8 balls, basket B contains 8 + 6 = 14 balls, and basket C contains 17 - (8 + 6) = 3 balls.

Regarding the carpet, a room measuring 5 m x 7 m is 35 m². If each box of carpet covers 10 m², then 35 m² will need 35/10 = 3.5 boxes of carpet. This means that there will be 3.5 boxes * 10 m²/box = 35 m² of carpet. So there will be no carpet left over.

Answer:

-----------------------------

We have:

Use the difference of the first two equations to find A:

Then find B, using third equation:

Finally find C, using second equation:

Area of the room is:

If each box covers 10 m² we need to buy 4 boxes:

Carpet left over:

The investor is doing a two-stage sampling or a two-phase sampling. This type of sampling involves two steps: first, a simple random sampling is used to create a set of groups, and then individuals are selected from within the selected groups for analysis.

In this case, the investor created 10 groups through simple random sampling and then selected and analyzed all the individuals in two groups. Random sampling is a statistical sampling technique where a sample is selected from a larger population so that each member of the population has an equal chance of being selected. This means that the sample should be selected randomly and not based on systematic or predetermined criteria.

The goal of random sampling is to produce a sample representative of the population, allowing for more accurate inferences about the population as a whole. Random sampling helps to eliminate bias in the sample selection process, improving the accuracy and validity of the results obtained from the sample.

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Angelita needs to sell at least 32 rugs to make money on her rugs.

The demand function for Angelita's rugs is p=150x-7000, which represents the linear relationship between the price per rug and the number of rugs sold. The cost function for the rugs is p=80x+2400, which is calculated by taking the same percentage of her average monthly costs to run the store as the percentage of display space needed by the product in question, which is 120 square feet of the total 1200. The revenue function for the rugs is p=150x-7000+220x, and the domain of this function is all real numbers. The maximum revenue is achieved when 40 rugs are sold, at $8800. The profit function for the rugs is p=150x-7000+220x-80x-2400, and the domain of this function is all real numbers. The maximum profit is achieved when 37 rugs are sold, at $4940. The break-even point is 32 rugs, which is the point where the cost and revenue functions intersect. This means that Angelita needs to sell at least 32 rugs to make money on her rugs.

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Answer:

see below

Step-by-step explanation:

second one

fourth one

Answer:

  9. Cylinder

  10. 14 in

  11. 20π in³

  12. circle, ellipse, rectangle, truncated ellipse

Step-by-step explanation:

You want the solid obtained by revolving a rectangle around one edge, the perimeter of the rectangle, the volume of the solid, and the names of at least 2 cross sections of the solid.

Every point on the outside edge of the solid will be 2 inches from the center axis. That is, the cross section perpendicular to the axis of revolution will be a circle. The solid is a cylinder.

The perimeter of a rectangle is given by the formula ...

  P = 2(L +W)

  P = 2(2 in + 5 in) = 2(7 in) = 14 in

The perimeter is 14 inches.

The radius of the cylinder is 2 inches, and its height is 5 inches. The volume is given by ...

  V = πr²h

  V = π(2 in)²(5 in) = 20π in³

The volume is 20π cubic inches, about 62.8 cubic inches.

The four attachments show possible cross sections of the cylinder. They include a circle, ellipse, rectangle, and truncated ellipse. The truncated ellipse may be cut off on one or both ends.

Answer:

The answer is C

Step-by-step explanation:

This is because the graph shifts to the right as the value correlated with x is 6, meaning the new zeros of the graph would be at (0,0) and (6,0)

The width of the enlargement would be 34.2857 cm.

The distance separating an object's ends is its length. The longest dimension is this one. The width of an object is the separation between its two sides. The shortest dimension is this one.

Initial dimension of shorter side = 10 cm

Initial dimension of longer side = 7 cm

Final dimension of shorter side = 24

Final dimension of longer side = x cm

The enlargement always ensure the aspect ratio = longer side / shorter side

10/7 = x/24

Solving for x, we get

[tex]$\frac{x}{24}=\frac{10}{7}$$[/tex]

simplifying the above equation, we get

[tex]$\frac{24 x}{24}=\frac{10 \cdot 24}{7}$$[/tex]

[tex]$x=\frac{240}{7} cm$$[/tex]

Therefore, the  value of x be 34.2857 cm.

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The minimal degree of the Taylor Polynomial required to calculate to 4 decimal places depends on the smoothness of the function and the error term in the Taylor Series is 0.0001

Taylor Polynomial is a mathematical tool used to approximate a function near a point using a polynomial. The degree of the polynomial determines how accurate the approximation is.

To calculate a Taylor Polynomial to 4 decimal places, we need to use a minimal degree that provides us with the desired accuracy.

The minimal degree depends on the smoothness of the function we are trying to approximate. The smoother the function, the lower the degree we need.

However, if the function has many twists and turns, we may need a higher degree to get the desired accuracy.

To calculate a Taylor Polynomial to 4 decimal places, we need to consider the error term in the Taylor Series.

The error term represents the difference between the actual value of the function and its approximation.

If the error term is less than 0.0001, we can be confident that our approximation is accurate to 4 decimal places.

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Withdrawing money from a checking account and depositing it into a savings account will only affect M1 and reduce the amount of money in this measure of the money supply. M2 will remain unchanged.

The actions of withdrawing $ from your checking account and depositing it into a savings account will affect the measures of money supply, M1 and M2, as follows:

M1: M1 is a measure of the narrowest definition of the money supply, which includes all currency (including coins), checking accounts, and travelers' checks. Withdrawing money from your checking account will reduce the amount of money in M1. However, depositing the funds into a savings account will not have any impact on M1 since savings accounts are not included in this measure of the money supply.

M2: M2 is a measure of the broader definition of the money supply, which includes M1 and all-time deposits, savings accounts, and money market securities with a value of less than $100,000. Depositing money into a savings account will increase the amount of money in M2, as savings accounts are included in this measure of the money supply. However, withdrawing money from a checking account will not have any impact on M2 as the decrease in M1 will be offset by the increase in savings accounts.

Therefore, In conclusion, withdrawing money from a checking account and depositing it into a savings account will only affect M1 and reduce the amount of money in this measure of the money supply. M2 will remain unchanged.

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Question Correction: Suppose you withdraw $6,000 from your checking account and use the funds to invest in a savings account at the bank. How will these actions affect M1 and M2?

A. M1 wil decrease and M2 wil not change

B. M1 and M2 will increase

C. M1 and M2 will not change.

D. M1 wil decrease and M2 will increase

Answer:

rotation on x axis;

(x, y) 》(x, -y)

So,(-6,5) is the correct answer.

Answer:

(-6,5)

Step-by-step explanation:

(x,y) ------》 (x,-y) {reflection over x-axis}

Volume of the cement required to pave the driveway is = 125/9 cubic yards.

A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid may become a cube by varying the lengths of the edges or the angles between the faces.

Features of a Cuboid :

A cube is a specific instance of a cuboid in which the length, width, and height are all equal. Accordingly, a cuboid is a cube.

Length of the Driveway = 150 ft = 50 yards

Width of the driveway = 10 ft = 10/3 yards

Thickness of the cement pavement = 3 inches = 3/36 = 1/12 yards

Volume of the cement required is = length*breadth*width = 50*(10/3)*1/12 = 125/9 cubic yards

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Changing a figure's location without spinning, reflecting, or changing its size is known as a translation in geometry.So g(x) = ln[1/8(x - 3)] + 1.

When you group "3" with the "right-left" variable, which is "x," you will have 3 units to the right.

However, "x" is the opposite of what it seems to be, therefore in order to shift right, you must subtract 3 from "x," making ln(x) into ln (x - 3).

Simply add 1 to the function to advance it up one unit, making ln(x-3) become ln(x-3) + 1.

In order to multiply the "horizontal variable" (also known as "x") by a factor of 8, you must divide by 8 (or multiply by 1/8), because "x" is the opposite of what it seems to be.

Ln(x - 3) + 1 so becomes Ln[1/8(x - 3)] + 1.

so that g(x) = ln[1/8(x - 3)]

+ 1.

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