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The expression (72a³b⁴) / (6a²b) is equivalent to the expression 12ab³.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (72a³b⁴) / (6a²b)

Simplify the expression, then we have

⇒ (72a³b⁴) / (6a²b)

⇒ 12ab³

The expression (72a³b⁴) / (6a²b) is equivalent to the expression 12ab³.

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Answer:

An equation of the line that passes through the point (-4, -6) and is perpendicular to the line 2x - y = 6 is y = -2x + 10.

Take A, B, C, and D as the quadrilateral's vertices, and BA is created to E. The value of x = 40.

Draw the above diagram and add the angles that are missing.

To determine the value of x, use the information provided in the accompanying diagram.

Take A, B, C, and D as the quadrilateral's vertices, and BA is created to E. (say).

Observe the illustration.

[tex]$& \Rightarrow \angle \mathrm{EAD}=70 \\[/tex]

[tex]$& \Rightarrow \angle \mathrm{EAD}+\angle \mathrm{DAB}=180 \\[/tex]

[tex]$& \Rightarrow \angle \mathrm{DAB}=180-70=110[\because E A B \text { is a straight line and } \mathrm{AD} \text { stands on it. }] \\[/tex]

Apply the total of internal angles in step two.

We are aware that a quadrilateral's inner angle total is 360.

[tex]& \Rightarrow \angle \mathrm{DAB}+\angle \mathrm{ADC}+\angle \mathrm{DCB}+\angle \mathrm{CBA}=360 \\[/tex]

[tex]$& \Rightarrow 110+80+56+3 \mathrm{x}-6=360 \\[/tex]

[tex]& 0 \quad 0 \quad 0 \quad 0 \quad 0 \\[/tex]

[tex]$& \Rightarrow 3 \mathrm{x}-6=360-110-80-56[/tex]

[tex]\Rightarrow 3 x-6=114 \\0 \\[/tex]

[tex]\Rightarrow x=120 \\[/tex]

[tex]\Rightarrow x=40 \\[/tex]

0

Therefore the value of x = 40. Hence, option A is correct.

The complete question is:

Use the information given in the following figure to find the value of x.

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The interest that Marisol will earn in a period of 5 years is C. $ 1, 437. 50

The number of years that Marisol kept the account open, given the amount she receives when she closes her account is 12 years .

The simple interest on the account per year is :

= 5, 000 x 5. 75 %

= $ 287. 50

In 5 years, this is:

= 287. 50 x 5

= $ 1, 437. 50

The number of years that Marisol left the account open was :

= ( 8, 450 - 5, 000 ) / 287.50 per year

= 12 years

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The first part of the question is :

Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.

According to the figure of the rhombus ∠ UTV = 36 degrees

Angle UTV is solved learning some property of rhombus

The opposite angles are equal.

The diagonals divide the angles.

∠ UTV = ∠ UTW / 2

Assuming  ∠ UTW = ∠ UVW = x

Given: ∠ TWV = ∠ TUV = 108

2x + 2(108) = 360 sum of angles of a rhombus

x + 108 = 180

x = 180 - 108

x = 72

∠ UTV = 72/2

∠ UTV = 36 degrees

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The y-coordinate for the solution to the system of equations is 6.

Equation is a physical and mathematical statement the describing physical phenomenon the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.

The y-coordinate for the solution to the system of equations is 6. This is calculated by substituting the given y-value (2/3) into the equation -x+3y=9 and solving for x. Specifically, -x+3(2/3) = 9, which reduces to -x = 3. Therefore, x = -3 and substituting this value into the first equation yields 3y = 9, which simplifies to y = 3. Therefore, the y-coordinate for the solution to the system of equations is 6.

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550 ml was found to be equivalent to approximately 2.324 cups using conversion factor method.

To convert 550 ml (milliliters) to cups, you can use the following conversion factor:

1 cup = 236.588 ml

Dividing 550 ml by 236.588 ml/cup, we get:

550 ml / 236.588 ml/cup = 2.324 cups (rounded to three decimal places)

Therefore, 550 ml is equivalent to approximately 2.324 cups

A conversion factor is a mathematical ratio used to convert a quantity from one unit of measurement to another. The conversion factor is usually derived from the relationship between the two units of measurement.

For example, if you want to convert a length measurement from feet to meters, you can use the conversion factor 1 ft = 0.3048 m.

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Answer:

$50.00 is the amount of interest

Answer:

Each miner receive 2.5 ounces of gold dust.

Step-by-step explanation:

15/6= 2.5 ounces

Answer:2

Step-by-step explanation:

The ratio of the number of unshaded to shaded squares is 7 : 3.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

It is also defined as the fraction of one quantity with respect to other.

The ratio of a and b is denoted as a : b.

Given is a grid of squares which is given below.

Total number of squares = 10

Of that,

Number of shaded squares = 3

Number of unshaded squares = 7

We have to find the ratio of unshaded to shaded squares in the grid which is 7 / 3 or 7 : 3.

Ratio of unshaded squares to shaded squares = 7 : 3

Hence 7 : 3 is the ratio of unshaded to shaded.

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The both are exponential functions from the fact that the both are raised to a give power. The constant  and rate of both functions are different.

A function is a block of code that performs a specific task. In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

We can see that the two functions that we here are all such that we can be able to see that they are exponential in nature as shown in the image that depicts the question that has been asked.

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Unit vector notation is a way of representing vectors in which magnitude of vector is equal to 1. A vector is mathematical object that has both magnitude (length) and direction, and can be represented as an arrow.

In unit vector notation, a vector is represented as a combination of a scalar (a numerical value) and a unit vector (a vector with a magnitude of 1 in the same direction).

The most common notation for unit vectors is to use a hat symbol (^) to indicate that a vector is a unit vector. For example, if we have a vector v, then its corresponding unit vector in the same direction would be represented as v. The unit vector in the x-direction is typically denoted as i, and the unit vector in the y-direction is denoted as j.

Unit vector notation is useful in many applications, including physics and engineering, where it is used to describe the direction of forces, velocities, and accelerations. It is also commonly used in computer graphics and game development, where it is used to represent the direction of movement or rotation of objects in a 3D space.

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Answer: C

Step-by-step explanation:

The two variables need to be eliminated. You can do this by multiplication or subtraction.

Multiply by -3 to the top equation will eliminate the x variable in the system

-3(2x - 4y = 5)

   6x - 3y = 10

==> -6x + 12y = -15

       6x - 3y = 10

adding a top with a bottom will eliminate the x

==> -6x + 6x = 0, 12y + (-3y) = 9y, -15 + 10 = -5

The number of students the van carry is 17

the number of students the bus carry is 30

Let's assume that a van can carry "v" students and a bus can carry "b" students.

From the information given, we can set up two equations:

5 vans + 4 buses = 205 students

5 vans + 13 buses = 475 students

We can write  these equations as

5v + 4b = 205

5v + 13b = 475

solving simultaneously we have

v = 17 and b = 30

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Answer:

3 2/5 feet

Step-by-step explanation:

It's smaller than 3 3/4 feet, but it's the largest option, besides 3 5/6 feet which is larger than 3 3/4.

Answer:

Step-by-step explanation:

To find an exponential regression equation for this set of data, we can use a calculator or spreadsheet software with built-in regression functions. Using a calculator, we can input the data points into lists and use the exponential regression function to find the equation:

x y

0 1353

1 1584

2 2037

3 2248

4 2630

5 3146

Using exponential regression, we get the equation y = 1323.119e^(0.216x).

To determine the number of bacteria present after 14 hours, we can plug in x = 14 into the equation:

y = 1323.119e^(0.216 * 14) ≈ 35433

Therefore, the number of bacteria present after 14 hours is approximately 35,433 (rounded to the nearest whole number).

The IQR is the best measure of variability, and it equals 4.

Answer:

Obtuse triangle

Step-by-step explanation:

Obtuse triangle has an interior angle measuring more than 90 degrees.

Answer:

Step-by-step explanation:

Let's call the number of cups sold in April "x".

The total sales in April were $31,250, so we can set up an equation to find x:

2.50 * x = 31,250

Dividing both sides by 2.50, we get:

x = 12,500

So in April, 12,500 cups of coffee were sold.

The total sales in May were 10,150 cups * $2.50 per cup = $25,375.

The average of the sales in April and May was $31,250 + $25,375 / 2 = $28,312.50.

So in June, they sold $28,312.50 / $2.50 per cup = 11,250 cups of coffee.

Answer: There were 12,500 cups sold in April. In May they made $25,375. They sold 11,325 cups and made $28,312.50 in June.

Step-by-step explanation:

       To find the cups of coffee sold in April, we will divide the total sales by price per cup.

    $31,250 / $2.50 = 12,500 cups

       To find the total sales for May, we will multiply the cups sold by the price per cup.

       10,150 * $2.50 = $25,375

       If they sold the average of April and May in June, we will find the average of April and May.

       12,500 cups in April + 10,150 cups in May = 22,650

       22,650 / 2 = 11,325 cups sold in June

       Then, to find the dollar sales, we will multiply by the price per cup again.

11,325 * $2.50 = $28,312.50

Yes, that is correct; If the sky is clear, we are able to see the stars at night.

A star is a celestial body that maintains its shape thanks to its own gravity. Also, a star has the ability to generate its own light, an example of a star is the Sun.

The stars are always there, but during the day, the brightness of the sun makes it impossible for us to see them. However, at night when the sun is no longer visible, the stars become visible to us. This is why we can see the stars in the sky at night when there are no clouds obstructing our view.

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Answer:

this is true

Step-by-step explanation:

The correct statements regarding the data-set are given as follows:

The consistency of the data-set is obtained by the IQR of each data-set, subtracting Q3 by Q1, hence:

Due to the lower IQR, the clerks from store A were more consistent.

For mean/median, the lower the mean and median, the faster they were.

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The center of the face of a cube is the midpoint of the face and lies along the line that runs between the opposite vertices of the face.

This is the point of intersection of the two diagonals in a face. In other words, it is the point that is equidistant from all four corners of the face.

To visualize this, imagine dividing the face into four equal triangles by drawing lines from each corner to the center. The center of the face is at the intersection of these lines.

In three-dimensional space, the center of the face of a cube is also the center of the cube itself, as all faces of a cube are congruent (the same shape and size) and meet at the center of the cube.

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In psychology, a variable interval refers to a type of schedule of reinforcement, which is a pattern of delivering rewards or punishments following a specific behavior.

A variable interval schedule is one in which reinforcement is provided after a variable amount of time has elapsed following a behavior. This means that the amount of time between the behavior and the reinforcement varies from one instance to the next, and is determined by a predetermined average or range.

For example, in an experiment, a rat might receive a food reward for pressing a lever, but the amount of time between each reward might be unpredictable, with the average time between rewards being, say, 3 minutes. So, the rat might press the lever and receive a reward after 30 seconds, then have to wait 4 minutes before pressing the lever again and receiving another reward.

Variable interval schedules tend to be more effective than fixed interval schedules at maintaining behaviors over time, as they prevent the subject from anticipating exactly when the next reinforcement will occur and thus reduce the likelihood of extinction of the behavior. They are also associated with more consistent and stable responding, as the subject knows that the behavior will be reinforced eventually, but doesn't know exactly when.

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Answer:

Equations:

A: y = 2x + 30

B: y = 3x + 6

Time to fill to 71 inches:

A: 20.5 minutes

B: 25.5 minutes

Step-by-step explanation:

Pool A: starts at 30 inches, fills at 2 inches/minute

Equation: y = 2x + 30

Pool B: starts at 20 inches, fills at 3 inches/minute

Pool B slope = filling rate = (26 - 20)/(2 - 0) = 6/2 = 3

Equation: y = 3x + 20

Pool A: y = 71

71 = 2x + 30

2x = 41

x = 20.5

Pool B: y = 71

71 = 3x + 20

3x = 51

x = 25.5

The "line" function in MATLAB allows you to create horizontal lines. Drawing horizontal or vertical lines is possible by using the "line" function,

So the "line" function in MATLAB allows you to create horizontal lines. Drawing horizontal or vertical lines is possible by using the "line" function, which creates a line object. You must supply the x-coordinates of the starting and ending points of the line as well as the line's y-coordinate in order to draw a horizontal line. To draw a horizontal line in MATLAB, use the following syntax: CSS Copy Code: x = [x min x max]; percentage of the x-coordinates of the line's beginning and finish points, y = [y value y value]; line(x, y percentage )'s y-coordinate; % Create a horizontal line

The starting and stopping positions of the line are indicated by the x-coordinates "x min" and "x max," respectively, while the line's y-coordinate is shown by "y value." is the "line".

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Option (4):  The inverse of the function tells us the number of visits m that can be made for a cost of c.

What is meant by the inverse of a function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

A function that can reverse into another function is known as an inverse function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as " f ⁻¹ " or " F ⁻¹."

Given a function,

  c(m) = 60 + 10m

where c = cost of visiting the gym

            m = number of visits

Then the Inverse function is:

   c(m) - 60 = 10m

m = (c(m) - 60) / 10

Therefore the inverse of the function tells us the number of visits m that can be made for a cost of c.

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The missing lengths are 12 unit and 6 unit.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

we can use the property similar triangle which states the the ratio of corresponding sides of similar triangle are in proportion

Using proportion

x / 20 + x  = 9 / 24

24x = 180x + 9x

24x -9x = 180

15x = 180

x= 12

Again, Using proportion

y/ y+9 = 4/ 10

10y = 4y + 36

6y = 36

y= 6

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The solutions to the system of equations are given as follows:

(0, -4) and (2,0).

The number of solutions of the system of equations is given by the number of times which the two functions intersect.

The two intersection points are given as follows for this problem:

(0, -4) and (2,0).

Which are the solutions to the system of equations.

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