connor takes 7/8 of the cards from a deck, ethan took 1/6 of the cards from the same deck. how much more of the deck did connor take than ethan?

The solution set of the original system is

[tex]$\left[\begin{array}{l}x_1 \\ x_2 \\ x_3 \\ x_4\end{array}\right]=\left[\begin{array}{c}-3 \\ -5 \\ 6 \\ -3\end{array}\right]$[/tex]

Step 1

We are given with a row reduced matrix form.:

[tex]$$M=\left[\begin{array}{rrrrr}1 & -2 & 0 & 3 & -2 \\0 & 1 & 0 & -4 & 7 \\0 & 0 & 1 & 0 & 6 \\0 & 0 & 0 & 1 & -3\end{array}\right]$$[/tex]

We have to find the solution set using the appropriate steps.

Step 2: The Augmented matrix Form

[tex]$$\left[\begin{array}{cccc}1 & -2 & 0 & 3 \\0 & 1 & 0 & -4 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3 \\x_4\end{array}\right]=\left[\begin{array}{c}-2 \\7 \\6 \\-3\end{array}\right]$$[/tex]

Step 3: System of Equations

[tex]$$\begin{aligned}& x_1-2 x_2+3 x_4=-2 \\& x_2-4 x_4=7 \\& x_3=6 \\& x_4=-3\end{aligned}$$[/tex]

Step 4: The Back-Substitution

From last two rows, we have

[tex]$$\begin{aligned}& x_3=6 \\& x_4=-3\end{aligned}$$[/tex]

Now substitute in row-2, to get value of $x_2$

[tex]$$\begin{aligned}& x_2-4(-3)=7 \\& x_2+12=7 \\& x_2=7-12 \\& x_2=-5\end{aligned}$$[/tex]

Now substitute in row-1, to get value of $x_1$

[tex]$$\begin{aligned}& x_1-2(-5)+3(-3)=-2 \\& x_1+10-9=-2 \\& x_1+1=-2 \\& x_1=-3\end{aligned}$$[/tex]

So,

[tex]$\left[\begin{array}{l}x_1 \\ x_2 \\ x_3 \\ x_4\end{array}\right]=\left[\begin{array}{c}-3 \\ -5 \\ 6 \\ -3\end{array}\right]$[/tex]

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In reference to different sampling methods, systematic sampling includes the steps: divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group: [FALSE]

Systematic sampling is a method of sampling where the sample is selected using a fixed interval, rather than using random sampling. The sampling process begins by selecting a random starting point in the population and then selecting every kth element from the population.

For example, if the population has 100 elements and k=10, every 10th element would be selected for the sample.

Dividing the population into groups, and then using simple random sampling to identify a proportionate number of individuals from each group is a method called stratified sampling.

It is important to note that systematic sampling can be vulnerable to sampling bias if the sampling interval is not chosen carefully and the population is not randomly ordered, because in that case, it will not be a truly random sample.

Hence, the correct answer to this is False.

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The time it will take the camera to hit the floor of the ocean at the given rate would be = 446 secs ( to the closest whole seconds)

The descending rate of an object is defined as the rate at which an object dropped from a height falls to the base of a given height.

The rate of sinking of the camera in the ocean = -4.2 m/s

The height from the passenger to the ocean floor = -1,875 meters

If -4.2 m = 1 sec

-1,875 m = X sec

Make X sec the subject of formula;

X sec = -1,875/-4.2

X sec = 446 secs ( to the closest whole seconds)

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3 is the slope of the given function y=3x+5.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function rule is y=3x+5.

Let us find some x and y values to plot the graph.

x=0, then y=3(0)+5=5

x=1, then y=3(1)+5=8

x=2, then y=3(2)+5=11

x=3, then y=3(3)+5=14

x=4, then y=3(4)+5=17

Now by taking these value we plot the graph.

In the given graph slope is 3.

Hence, 3 is the slope of the given function y=3x+5.

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a) The blue graph is the graph of a function, f(x). This is because it is a continuous line with no breaks, and it is a smooth curve with no sharp corners.

The formula for this function is f(x) = x3 + 2x2 + 3x. To calculate the derivative of this function, we take the first derivative using the power rule. The derivative of f(x) is f'(x) = 3x2 + 4x + 3.

b) The red graph is the graph of the derivative of f(x), the first derivative. This can be seen because the red graph is a continuous line that is a smooth curve, with no sharp corners. The formula for this derivative is f'(x) = 3x2 + 4x + 3. To calculate the second derivative of f(x), we take the second derivative using the power rule. The second derivative of f(x) is f''(x) = 6x + 4.

c) The green graph is the graph of the second derivative of f(x), the second derivative. This can be seen because the green graph is a continuous line that is a smooth curve, with no sharp corners. The formula for this derivative is f''(x) = 6x + 4. To calculate the third derivative of f(x), we take the third derivative using the power rule. The third derivative of f(x) is f'''(x) = 6.

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In year 2015 the sum of the age of maria, her mother, and her father, will be 100 years.

As the date and month of the birth is same for maria, her mother, and her father. Lets say in year X, the sum of the age will be 100 years.

The age of maria in year X = (X - 2000)

The age of her mother in year X, = (X - 1975)

The age of her father in year X, = (X - 1970)

Sum of their age,

100 = (X - 2000) + (X - 1975) + (X - 1970)

100 = 3X - (2000 + 1975 + 1970)

100 = 3X - 5945

3X = 5945 + 100

3X = 6045

X = 2015

Hence option (a) is correct.

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Answer: 20

Step-by-step explanation: Hello! The first thing you have to do is substitute m = 7 and n = 5 into the equation 4 + (m - n)^4.  After substituting m and n into the equation, you will get: 4 + (7 - 5)^4.  Use PEMDAS (parentheses, exponents, multiplication, division, addition, and subtraction).  Parentheses is first, so solve everything inside of the parentheses first.  7 - 5 = 2.  Now you have 4 + (2)^4.  Next is exponents in pemdas, so solve the exponents.  2^4 = 2 x 2 x 2 x 2, or 4 x 4, or 16.  Now you have 4 + 16.  The last thing you have to do is add 4 + 16, which is 20.  The answer is 20.

Answer:

55°

Step-by-step explanation:

2x + 5 + 2x + 3x = 180   Combine like terms  The sum of the interior angles of a triangle is 180

7x + 5 = 180  Subtract 5 from both sides

7x + 5 - 5 = 180 - 5

7x = 175  Divide both sides by 7

[tex]\frac{7x}{7}[/tex] = [tex]\frac{175}{7}[/tex]

x = 25

Substitute 25 for x

2x + 5

2(25) + 5

50 + 5

55 is the measurement of angle B

The simplified expression of 1 minus the quantity 1 over cosecant squared x is 1 - 1/cosec^2(x).

The expression 1 minus the quantity 1 over cosecant squared x can be simplified by dividing the 1 over cosecant squared x into its components. The cosecant squared x can be written as 1/cosec x, and then the 1/cosec x can be written as 1/sin x, with the cosecant being the reciprocal of the sine. Therefore, the expression 1 minus the quantity 1 over cosecant squared x can be written as 1 - 1/sin x. To simplify this expression further, the denominator of 1/sin x can be squared, resulting in 1 - 1/sin^2(x). Since the cosecant is the reciprocal of the sine, cosec^2(x) can be substituted for sin^2(x), giving us the simplified expression 1 - 1/cosec^2(x).

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The complete question: which of the following is the simplified expression of 1 minus the quantity 1 over cosecant squared x end quantity question mark 1 - csc^2(x)

Answer:

cos^2x

Step-by-step explanation:

Very simple, 1-1/csc^2 x

= 1-sin^2 x Using the reciprocal Identity 1/csc x = sin x

= cos^2 x Using the Pythagorean Identity 1 - sin^2 x = cos^2 x

therefore, the answer is cos^2 x.

Hope this helped

The simple interest is I = $ 303.33  and the amount after 2 months with rate of 13 % is A = $ 14,303.33

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as I

Let the amount with simple interest be A = P + I

Now , the principal P = $ 14,000

The rate of interest R = 13 %

The number of months = 2 months

The number of years = 2/12 years

Simple Interest I = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

Simple Interest I = ( 14,000 x 13 x ( 2/12 ) ) / 100

On simplifying the equation , we get

Simple Interest I = $ 303.33

Now , the amount after 2 months = P + I

Amount = $ 14,000 + $ 303.33 = $ 14,303.33

Hence , the interest is $ 303.33

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In circle the length of PQ = 24 inches.

What is Circle?

A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the centre. The line of reflection symmetry is formed by each line that traverses the circle. Additionally, it possesses rotational symmetry around the centre for each angle.

Since AB= 25 inches and AC = 16 inches then

=> BC = AB-AC = 25-16 = 9 inches.

∠APB is a right angle because it is inscribed in a semicircle.

The three right triangles ᐃAPB, ᐃACP and ᐃPCB are all similar

because their corresponding angles are equal.  Therefore

=> [tex]\frac{AC}{PC}=\frac{PC}{BC}[/tex]

=> [tex]\frac{16}{PC}=\frac{PC}{9}[/tex]

=> [tex]PC^2 = 25*9 = 144 = 12^2[/tex]

=> PC = 12 inches

By symmetry , PC = QC then,

=> PQ = 12*2 = 24 inches.

Hence the length of PQ is 24 inches.

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Answer:

the requisite equation for the given question is y=−5x

Step-by-step explanation:

firstly, select the coordinates (0, 0) through which the perpendicular line will cross (0,0)

then, locate the slope when y=15x+2y=15x+2.

The slope is 1/5 when expressed in the slope-intercept format.

therefore, m=1/5

since, a perpendicular line's equation must have a slope equal to the inverse reciprocal of its initial slope.

therefore, [tex]m_{perpendicular}[/tex]=−1/(1/5)

To determine the slope of the perpendicular line, simplify 1/(1/5).

[tex]m_{perpendicular}[/tex]=−5

By using point-slope method, determine the perpendicular line's equation.

y+0=−5.(x+0)

Solve for y.

y= -5x + 0

y=−5x

hence, the answer for the question is y=-5x

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The total number of boxes of muffins Jill and Mike brought to the bake sale is 9 1/12.

Mixed fractions are type of fractions which consist of a whole number part and a fractional part.

Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.

Given that,

Number of boxes of carrot muffins Jill brought = 3 1/3 = (3 × 3 + 1) / 3 = 10/3

Number of boxes of apple muffins Mike brought = 5 3/4 = (5 × 4 + 3) / 4 = 23/4

Total number of muffins = (10/3) + (23/4)

                                        = [(10 × 4) + (23 × 3)] / [3 × 4]

                                        = (40 + 69) / 12

                                        = 109/12

                                        = 9 1/12

Hence the total number of boxes is 9 1/12.

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The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions.

Explain the algebra?

A common thread that runs through nearly all of mathematics is algebra, which is the study of variables and the rules for using them in formulas. All applications of mathematics require knowledge of elementary algebra since it deals with manipulating variables as though they were numbers.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention.

y = -x + ____

y = x^2 + ____​

Given data :

The system of equations used to find the value of x is:

y = -x + 84

y = x² - 6

Let x represent the first number and y represent the second number.

The sum of the two numbers is 84, hence:

x + y = 84

y = -x + 84      (1)

The square of the first number is 6 more than the second number. Hence:

x² = 6 + y

y = x² - 6     (2)

The system of equations used to find the value of x is:

y = -x + 84

y = x² - 6

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Completed question:

Type the correct answer in each box. Use numerals instead of words. The sum of two numbers is 84. The square of the first number is 6 more than the second number. Write a system of equations to find the value of x, the first number, and y, the second number.

The octal representation of 7562.45 is 3654.36, the hexadecimal representation 1938.257 of is 774.4112, and the binary representation of 175.175 is 10101111.110111.

What are Number Systems?

A number system is a system representing numbers. It is also called the system of numeration and it defines a set of values to represent a quantity.

1- To convert 7562.45 to octal, we first convert the whole number part of the decimal, 7562, to octal.

7562 in decimal = (710^3) + (510^2) + (610^1) + (210^0) = (7512) + (564) + (68) + (21) = 3654.

So the whole number part in octal is 3654.

2- Next, we convert the fractional part of the decimal, 0.45, to octal.

0.45 in decimal = 0.45 * 8^1 = 0.36

So the fractional part in octal is 0.36

3- Combining the whole number and fractional parts, we get the final octal representation as 3654.36

4- To convert 1938.257 to hexadecimal, we first convert the whole number part of the decimal, 1938, to hexadecimal.

1938 in decimal = (110^3) + (910^2) + (310^1) + (810^0) = (11024) + (9256) + (316) + (81) = 774.

So the whole number part in hexadecimal is 774.

5- Next, we convert the fractional part of the decimal, 0.257, to hexadecimal.

0.257 in decimal = 0.257 * 16^1 = 0.4112

So the fractional part in hexadecimal is 0.4112

6- Combining the whole number and fractional parts, we get the final hexadecimal representation as 774.4112

7- To convert 175.175 to binary, we first convert the whole number part of the decimal, 175, to binary.

175 in decimal = (110^2) + (710^1) + (510^0) = (1100) + (710) + (51) = 10101111

So the whole number part in binary is 10101111

8- Next, we convert the fractional part of the decimal, 0.175, to binary.

0.175 in decimal = (12^-1) + (72^-3) + (5*2^-4) = 0.110111

So the fractional part in binary is 0.110111

9- Combining the whole number and fractional parts, we get the final binary representation as 10101111.110111

Hence, the octal representation of 7562.45 is 3654.36, the hexadecimal representation 1938.257 of is 774.4112, and the binary representation of 175.175 is 10101111.110111.

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The radius of the right circular cylinder is 4 inches and the height is 3.33 inches.

Radius of cone=6inches

height of cone = 10 inches

Let the radius and height of the right circular cylinder be x and y respectively.

According to triangle similarities,

10-y/x=10/6

⇒10-y/x=5/3

⇒30-3y=5x

⇒y=10-5x/3 ----1

The volume of the right circular cylinder is π[tex]r^{2}[/tex]h

v=  πx∧2y

substituting the value of y from 1

v=  π[tex]x^{2}[/tex](10-5x/3)

v=10πx^{2}- 5x∧3/3

We differentiate volume w.r.t radius

DV/dx= 20πx-5[tex]x^{2}[/tex]

setting derivative = 0

DV/dx= 20πx-5[tex]x^{2}[/tex]=0

5πx(4-x)=0

x=0 , x=4

[tex]D^{2}[/tex]V/Dx =20π-10πx

putting the maximum value of x in the second derivative we get,

X=Radius = 4inches

Y=height= 10-5x/3=3.33 inches

Therefore, The radius of the right circular cylinder is 4 inches and the height is 3.33 inches.

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The property used to solve 7r + 2r is distributive property.

The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.

In other words,  the distributive property states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers .

Therefore,

7r + 2r

Using distributive law,

7r + 2r = r(7 + 2) = 9r

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Answer:

(4+9)+(4·9)=13+36=49

Step-by-step explanation:

True

If the equation for every x and x in the domain of f holds, then a function f is odd.  −f(x)=f(−x) − f ( x ) = f ( − x )

If the equation for every x and x in the domain of f holds, then a function f is odd. −f(x)=f(−x) − f ( x ) = f ( − x ) An odd function has a graph that, geometrically speaking, is rotationally symmetric with respect to the origin, meaning that the graph is unaffected by a 180° rotation of the origin.

An even function exists if an expression is obtained that is equivalent to f(x); an odd function exists if an expression is obtained that is equivalent to -f(x); and neither occurs, in which case it is neither.

An odd function is a function having a symmetrical graph about the origin. If a function doesn't display either symmetry, it cannot be either even or odd.

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The solution to the expression when x = 2 is 8

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

8x - 8

Also, we have

x = 2

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

8 * 2 - 8

Evaluate the product

16 - 8

Evaluate the difference

8

Hence, the solution is 8

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Complete question

Given that 8x - 8, calculate the expression when x = 2

We can start solving the problem by using a system of equations. Let's call the number of ounces of solution a x and the number of ounces of solution b y. From the problem statement, we know that:

x + y = 150 (because the total amount of the mixture is 150 ounces)

0.6x + 0.9y = 0.65(x + y) (because the mixture is 65% salt, and we can find the amount of salt in the mixture by multiplying the percentage by the total amount)

We can use the first equation to solve for one of the variables in terms of the other:

y = 150 - x

Now we can substitute this expression for y into the second equation:

0.6x + 0.9(150 - x) = 0.65(150)

0.6x + 135 - 0.9x = 97.5

-0.3x = -37.5

x = 125

Now we can use the first equation to find the value of y:

y = 150 - x

y = 150 - 125

y = 25

So the scientist should use 125 ounces of solution a and 25 ounces of solution b to obtain 150 ounces of a mixture that is 65% salt.

The solution is 6 units by 12 units.

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.

here, we have,

Since the measurements in meters are multiples of 4, it makes this problem a little easier.

First you divide 8 by 4 to get 2

Then divide 16 by 4 to get 4

After that you're going to multiply 3 units by both quotients separately.

So you multiply 3 by 2 to get 6

Then you multiply 3 by 4 to get 12

So, then you end up with a 6 unit by 12 unit drawing.

therefore, the answer is 6 units by 12 units.

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The probability that the total weight of the three randomly selected grapefruits is more than 3.4 pound will be equal to 0.842.  

From the data given in the question,

x > 3.4 lb

The mean is 1 lb.

The difference from the mean is 0.12 lb.

The z-score will be,

z = (3.4 - 1) / 0.12

z = 20

This is equivalent to an 84.20% or 0.842 probability.

The complete question is,

The weights of grapefruits of a certain variety are approximately normally distributed with a mean of 1 pound and a standard deviation of 0.12 pounds. Use scenario 6-9. what is the probability that the total weight of three randomly selected grapefruits is more than 3.4 pounds?

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using simple  product and quotient, The annual pay of the fourth worker is 49650.

PRODUCT - The outcome of multiplying two or more numbers is the product of those numbers. QUOTIENT - The outcome of dividing two numbers is the quotient of the two numbers.

Formulate the following supplied conditions: 46800 × 4 - 45900 - 44200 - 47450

Make a calculation for the following: 187200 - 45900 - 44200 - 47450.

Add up or subtract 141300, 44200, and 47450.

Calculate the difference or total of 97100 minus 47450.

Calculate the difference or sum: 49650

get the outcome: 49650

The annual pay of the fourth worker is 49650

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Utilize the fact that the sum of all triangles is 180 to determine that angle C is 42.

Therefore,

There is no other way to resolve this, thus you must employ the Law of Cosines. You cannot apply the Pythagorean Theorem since it is not a right triangle. We can apply the Law of Cosines to determine the missing side length, and then the Law of Sines to determine an additional angle.

The Triangle Angle-Sum theorem will then be used to complete it. Ready?

The Cosine Law to find side b is

[tex]$b^2=a^2+c^2-2 a c \cos B$[/tex]

and fill in the info we know, which is everything but the b.

[tex]$b^2=(21)^2+(29)^2-2(21)(29) \cos 109$[/tex]

Doing all that math gives us that side

b = 40.9 or 41 .

Now the Law of Sines to find missing angle

A or C. Let's find

[tex]$A \cdot \frac{\sin A}{21}=\frac{\sin 109}{41}$[/tex].

That gives us that angle A is 29 .

Now use the fact that all triangles add up to 180 to get that angle C is 42

The complete question is:

Solve each triangle. Round your answers to the nearest tenth

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Only the integer 12 is a divisor of every other integer which is a part of the set S.

This is a classic problem where we are asked to find such an integer that is going to be a divisor of the above set S of integers. The set S of integers consists of those integers that when squared are both divisible by 24 and 108. Now we know 24 can be written as 2*2*2*3 and similarly 108 can be written as 2*2*3*3*3. The smallest perfect square (n^2) which is a multiple of both 24 and 108 is 2^4*3^4, thus the smallest n is 2^2*3^2 = 36. So, only 12 is a divisor of all integers in S.

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The correct order of functions, in increasing order of growth rate, is g1, g4, g3, g5, g2, g7, and g6.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Here,

The list of function is attached in image.

g1, g4, g3, g5, g2, g7, g6 is the correct sequence of functions in increasing order of growth rate.

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La cantidad de comida de 7 / 2 de un bote sirve para un número de días de 5 días.

En este problemas tenemos que Antonio da una ración fija de comida a su perro, se indica que consume siete décimos (7 / 10) de un bote de comida cada día para alimentar a su perro. Tenemos aquí un situación de relación directa entre la cantidad de comida (y) y el número de días para provisiones (x).

A partir del enunciado, se deriva la siguiente ecuación:

y = (7 / 10) · x

Si tenemos que y = 7 / 2, entonces el número de días para provisiones es:

7 / 2 = (7 / 10) · x

x = 10 / 2

x = 5

La cantidad de comida de 7 / 2 de un bote sirve para un número de días de 5 días.

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Answer:

y = 1/4x

Step-by-step explanation:

A proportional relationship is similar to a linear relationship, with one distinction, it's y-intercept is equal to zero, so it can be expressed in the form: [tex]y=kx[/tex], where "k" is some constant. More specifically, when we divide y by x, we always get a constant amount, denoted as "k": [tex]\frac{y}{x}=k[/tex].

Using this knowledge, we can kind of immediately tell it's [tex]y=\frac{1}{4}x[/tex] as it's the only one in the form: [tex]y=kx[/tex], but let's look at why [tex]x=\frac{3}{8}[/tex] is not a proportional relationship.

It's important to note that [tex]x=\frac{3}{8}[/tex] is a vertical line, since the x value is constant while the y value varies. This means "y/x" cannot be constant, since "y" changes, except what it's being divided by will remain the same, equal to 3/8.

Manufacturing overhead costs typically include the depreciation of equipment, wages provided to factory personnel, and power used to operate the equipment. $10.8 million, $8.4 million, and $17.4 million will make up the three divisions.

Manufacturing overhead (MOH) cost is the sum of all indirect costs incurred during the production of a good.

It is included in the cost of the final good along with the costs of direct materials and direct labor.

In the manufacturing sector, the three major cost components are materials, labor, and overhead. There are no hidden expenses.

In other words, while the foreman's pay and supplies are covered, neither the office's nor the corporation's accountant's pay is. To calculate applicable production overhead, multiply the overhead allocation rate by the amount of labor or equipment used. Therefore, if your allocation rate is $25, your applied manufacturing overhead for this product is $25.

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