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The prime factorization of 72 using exponential notation is 2³ x 3².

Prime factorization is a process of writing all numbers as a product of primes.

Given:

Prime factorization is representing a number in form of products of its primes.

Consider the given number 72

72 = 2 x 2 x 2 x 3 x 3

So, 72 can be written as 2 × 2 x 2 × 3 × 3.

Thus, exponential notation it can be written as 2³ x 3².

Also, Simplifying 12 /16 as

= 12/16

= 3/4

and, the equivalent fraction whose denominator is 32.

Then, 3/4 = x/32

4x = 96

x = 24

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So on solving the provided question, we can say that the value of k is 4, in this linear equation question.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

1/2k +6= 4k-8

Multiplying both sides by 2,

k+12= 8k-16

7k=28

Therefore,

       k=4

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Answer: 72 square units

Step-by-step explanation: It is 72 square units because if you count the sides p and q you get 9 and the same with sides q and r you get 8 and if you multiply them together you get 72.

Work Shown:

a = old price = 5000

b = new price = 2800

c = change in price

c = b-a

c = 2800-5000

c = -2200

The value of c is negative to indicate a price decrease.

d = percent change

d = (c/a)*100%

d = (-2200/5000)*100%

d = -44%

There is a 44% decrease or discount.

The coordinates of the vertices of the square with height x is given as follows:

A square is a figure for which all the four side lengths are congruent, that is, they have the same measure.

The side length of the square in this problem is given as follows:

x.

As the height is equals to the base.

The vertex J represents the origin, hence it has coordinates given as follows:

J(0,0).

Then the remaining coordinates of the square are given as follows:

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At the end of the eighth year, the amount Mr. Smith withdrew was $41,757.68.

The amount that Mr. Smith withdrew at the end of the eighth year is a product of a series of computations, involving future value determination.

In this situation, we have used an online finance calculator to determine the future value of the investment at each leg.

N (# of periods) = 20 years

I/Y (Interest per year) = 6%

PV (Present Value) = $0

PMT (Periodic Deposits) = $1,800

Results:

FV = $66,214.06

Sum of all periodic payments = $36,000 ($1,800 x 20)

Total Interest = $30,214.06

N (# of periods) = 5 years

I/Y (Interest per year) = 6%

PV (Present Value) = $,

PMT (Periodic Withdrawal) = $-7500

Results:

FV = $46,331.15

Sum of all periodic payments = $-37,500 ($7,500 x 5)

Total Interest $17,617.09

N (# of periods) = 2 years

I/Y (Interest per year) = 6%

PV (Present Value) = $46,331.15

PMT (Periodic Withdrawal) = $-5000

Results:

FV (Final Withdrawal) = $41,757.68

Sum of all periodic payments = $-10,000 ($5,000 x 2)

Total Interest = $5,426.53

Thus, the amount of $41,757.68 was withdrawn by Mr. Smith at the end.

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Answer:

X < - 50

Step-by-step explanation:

5 - 1/2 x > 30

Move 5 to the other side of the inequality

- 1/2 x > 25

Multiply both sides by 2, to get rid of the denominator on the left side

-x > 50

Now switch the inequality sign and multiply to get the minus on the other side

x < - 50

[tex]5-\dfrac{1}{2} x > 30[/tex]

Simplify:

[tex]-\dfrac{1}{2} x+5 > 30[/tex]

Subtract 5 from both sides:

[tex]-\dfrac{1}{2} x+5-5 > 30-5[/tex]

[tex]-\dfrac{1}{2} x > 25[/tex]

Multiply both sides by [tex]-\dfrac{2}{1}[/tex]:

[tex]-\dfrac{2}{1} \times(-\dfrac{1}{2} x) > -\dfrac{2}{1} \times(25)[/tex]

[tex]\fbox{x} < \fbox{-50}[/tex]

The correct solutions for this question are as:

(A) Bearing of B from A = 72°

(B) Bearing of B from C = 342°

(C) Bearing of A from B = 252°

(D) Bearing of A from C = 293°

Step by step solution:

(A) Bearing of B from A:

= 72° (Given in question)

(B) Bearing of B from C: = 342°

Solution:

As sum of co-interior angles is 180° , i.e.  ∠NBC +∠NCB =180°

so, 162° + ∠NCB = 180°

     ∠NCB = 180°-162°

     ∠NCB = 18°

reflexive angle NCB =360° - ∠NCB

reflexive angle NCB = 360° - 18°

reflexive angle NCB = 342°

So, bearing of B from C: = 342°

(C) Bearing of A from B: = 252°

Solution:

First extend the line AB to any point (let's say "X")

So, ∠NBX = 72°   [BY USING CORRESPONDING ANGLES]

Bearing of A from B = ∠NBX + 180°

Bearing of A from B =72° + 180°

Bearing of A from B =252°

(D) Bearing of A from C: = 293°

Solution:

Bearing of A from C= 360° - (∠BCA + ∠BCN)

Bearing of A from C= 360° - (49° + 18°)

Bearing of A from C= 360° - (67°)

Bearing of A from C= 293°

Important Points for "Bearing of Angles":

A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.

The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.

Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.

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The value of x is -4 and the value of y is 1.

In order to use the elimination method, rearrange the given linear equations.

y - 3x = 13 equation 1

y - 2x = 9 equation 2

Subtract equation 2 from equation 1:

-x = 4

x = -4

Substitute for x in equation 2

y - 2(-4) = 9

y  + 8 = 9

y = 9 - 8

y = 1

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The value of (2/3 - 5/6) / 3/4 is -2/9.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

(2/3 - 5/6) / 3/4

2/3 - 5/6

= (4 - 5)/6

= -1/6

Now,

(-1/6 )/(3/4)

= -1/6 x 4/3

= -4/18

= -2/9

Thus,

The value is -2/9.

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The equation in the slope-intercept form is y = x + 3.8

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A line that contains the points (–6.4, –2.6) and (5.2, 9).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

So, the equation,

y + 2.6 = {(9 + 2.6)/(5.2 + 6.4)} (x + 6.4)

y + 2.6 = x + 6.4

y = x + 6.4 - 2.6

y = x + 3.8

Therefore, the equation y = x + 3.8 is in the slope-intercept form.

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Answer:

The average minutes per song would be 3.

Since "slope" tells us the angle of the line being graphed, the word "slope" is commonly used in mathematics.

Planar geometry states that all lines have slopes. Any slope can be calculated by comparing it to another line, usually the x-axis. A line's slope, or angle, in relation to that x-axis value is how steep it is.

In mathematics, slope is the proportion of the change in the y value to the change in the x value.

Two perpendicular lines have a slope such that the reciprocal of the negative slope of one line equals the slope of the other. The slope of perpendicular lines is -1 as a result.

The relationship between the slopes of parallel lines can be demonstrated using the formula m1.m2 = -1, if the slopes of the two perpendicular lines are m1, m2.

Like a fraction, a slope works by favoring the rise, up-and-down movement, over-the-run, or side-to-side movement. If a line rose up one unit for every rightward unit traveled, the slope would be a positive one.

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Answer: 12

Step-by-step explanation: There are about 12 grams of carbohydrates in a 8 fluid ounce (240 mL) glass of whole milk. The amount of carbohydrates in milk can vary slightly depending on the type of milk you are drinking. For example, skim milk has slightly fewer carbohydrates (about 11 grams per 8 fluid ounces) than whole milk because the fat has been removed. On the other hand, milk that is high in fat, such as heavy cream, has even more carbohydrates (about 4 grams per fluid ounce).

The rate of inflation of potatoes is 0.019.

The rate of inflation of Oranges is 0.019.

The rate of inflation of Ground beef is 0.019.

Inflation is an increase in the level of prices of the goods and services that households buy. It is measured as the rate of change of those prices.

Given:

Here, the annual rate of inflation r (in decimal form) is given by

r = [tex](p_2/ p_1)^{1/n[/tex] - 1

Now, The average price of a  potatoes increased from $0.620 in 2009 to $0.749 in 2019.

Thus, The required rate of inflation,

r = [tex](0.749/ 0.620)^{1/10[/tex] - 1

r = 1.019 - 1

r = 0.019

Now, The average price of a Oranges increased from $0.910 in 2009 to $1.280 in 2019.

Thus, The required rate of inflation,

r = [tex](1.280/ 0.910)^{1/10[/tex] - 1

r = 1.034 - 1

r = 0.034

Now, The average price of a Ground beef increased from $2.251 in 2009 to $3.375 in 2019.

Thus, The required rate of inflation,

r = [tex](3.775/ 2.251)^{1/10[/tex] - 1

r = 1.0321 - 1

r = 0.0321

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Note that in the attached Geometric Figure (Diagram) which features QR as parallel to NO, if NQ = 12, QR 20, and NO = 35, then the length of QP is equal to 16.

[tex]\overline {QR}[/tex] is Parallel to [tex]\overline {NO}[/tex]; therefore

QR/NO = PQ/PN

⇒ 20/35 = PQ/PQ +12

This is because:

PN = PQ + NQ; which is also
PN = PQ +12

(PQ + 12) x 20 = 35PQ
20PQ + 240= 35PQ ; Collect like terms

240= 35 PQ - 20 PQ

240 = 15PQ; Divide both sides by 15

⇒ 240/15 = 15PQ/15
⇒ 16 = PQ

Therefore, QP = PQ which is equal to 16.

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Considering the definition of a line, the equation of the line in standard form is y - 7/10x= -4

A linear equation o line can be expressed in the form y = mx + b

where

The standard form of a linear equation is Ax + By = C. In this type of equation, x and y are variables and A, B, and C are integers.

In this case, you know:

So, the line can be expressed as:

y=7/10x -4

Expresed in standard form:

y - 7/10x= -4

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On solving the provided question, we can say that -  here in graph we have on solving equation  [tex]2x^2+ 9y^2 \\[/tex] = [tex]8 + 9 = 17[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

[tex]2x^2+ 9y^2 \\[/tex]

[tex]8 + 9 = 17[/tex]

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The transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

An isometric transformation is one that keeps the angles and distances between the original and changed shapes the same. There are numerous techniques that can be used to alter any image in a plane.

The two figures are isometric only if they are congruent. In the given figure the angles remain the same however the lengths of the side are transformed as the figure is dilated.

Hence, the transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

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Answer:

2√2- 4√5

Step-by-step explanation:

√2 (2-2√10)

2√2- 2√20

2√2- 2√(4*5)

2√2- 2*2√5

2√2- 4√5

The expression which could be used to determine the product of -4 and 3 and one-fourth as required is; negative 4) (3) + (negative 4) (one-fourth).

As evident in the task content; the expression which could be used to determine the product of; -4 and 3 and one-fourth is required to be determined.

Since the given expression is; -4 and 3 and one-fourth; we have that;

-4 × 3 ¼

However, since 3 ¼ can be written as; ( 3 + ¼ ), it follows that we have;

-4 × ( 3 + ¼ )

Ultimately, the resulting expression using the distributive property is;

( -4 ) ( 3 ) + ( -4 ) ( ¼ )

Therefore, the correct answer is; (negative 4) (3) + (negative 4) (one-fourth).

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Answer:

Step-by-step explanation:

if 2021 is 35% decrease of the original number then 2020 is 100% ,and 2021 = 65%.

so, we do the rule of three:

x = (94900 * 100)/ 65

x = 146000

and that is the population in 2020.

Answer:

Hey there! Based on the information provided, it seems that the population of the town decreased by 35% between 2020 and 2021. We can use this information to calculate that in 2021, the population of the town was 65% of its population in 2020. If the population of the town in 2021 was 94,900, then we can use this information to calculate that the population of the town in 2020 was 146,155. Does that make sense?

Answer:

8.3

Step-by-step explanation:

The number after three is below 5 so it stays as 8.3

Answer:

300 milligrams are in aa cup of milk.

Step-by-step explanation:

.25 x 1200 = 300

There are total 12 lines of symmetry may be found in the image.

We have to given that;

A image is shown in figure for find the lines of symmetry .

Since, We know that;

Exactly dividing a form in half, a line of symmetry exists. This indicates that the form would fold perfectly in half if you did so along the line.

Hence, By definition of line of symmetry we get;

There are total 12 lines of symmetry may be found in the image.

Thus, The correct answer is,

⇒ 12 line of symmetry

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The cost of the computer if the sales tax is 6% is  924.96 dollars.

You bought a new laptop and paid an initial payment of $150. You will make 12 payments of $69.50.

The amount the computer cost if the your state charge 6% sales tax can be calculated as follows;

Install mental payment = 12 × 69.50

Install mental payment = 834 dollars

You already made payment of 150 dollars.

Therefore,

total payment including sale tax = 150 + 834

total payment including sale tax = 984 dollars

Sales tax = 6% of 984

Sales tax =  6 / 100 × 984

Sales tax = 5904 / 100

Sales tax = 59.04 dollars

Therefore,

cost of the computer = 984 - 59.04

cost of the computer = 924.96 dollars

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There are 9 full cases and 2 additional items are needed to fulfill the order 56 items ordered 6 items per case.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

56 items ordered for 6 items per case.

Now, After divide the quotient shows the number of full case and remainder shows the additional items.

Hence, We get;

 6 ) 56 ( 9

      54

   ---------

        2

Thus, There are 9 full cases and 2 additional items are needed to fulfill the order 56 items ordered 6 items per case.

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The present value of the tax benefits from depreciation which is a non cash expenditure under capital budgeting decisions is $10432.80

According to the prudence concept of accounting convention, Depreciation is a non cash expenditure that has been charged against the profit. Depreciation is value that amortized over useful life of tangible fixed asset. The absolute decline in the value of asset due to obsolesce, usage of asset, wear & tear of fixed asset is referred as depreciation.

As per accounting standard on property, plant & equipment depreciation can be computed by straight line method and written down value method.

While analyzing the capital budgeting decision from the equipment to be acquired the cash inflows and outflows during the currency of the project shall be accounted for.

The tax benefit from depreciation expenses will be consider as cash inflow. The same shall be calculated by the present value annuity factor for the as follows:

cost of capital = 12 %

Depreciation = $10000

Life of the project = 8 years

Tax rate = 21%

Present value annuity factor (PVAF) at 12% for 8 years will be:

0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404

Grand total of the (PVAF) at 12% = 4.968

Now multiply the PVAF with depreciation amount

Present Value of Depreciation = 4.968 × 10000 = $49,680

Tax benefit from depreciation = $49,680 × 21% = $10432.8

Thus the tax Tax benefit from depreciation is $10432.80

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Answer:

The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:

Area of small square = s^2

Area of big square = b^2

Since the area of the big square is 30 units more than the area of the small square, we can write the equation:

b^2 = s^2 + 30

To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:

s^2 = b^2 - 30

s = sqrt(b^2 - 30)

Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:

s = sqrt(d^2 - 30)

To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:

r = d/2 = sqrt(d^2 - 30)/2

So to find the radius of the circle, we just need to know the diameter of the circle. Can you provide the diameter of the circle in the question?:

The radius of the circle is: r = d/2 = sqrt(d^2 - 30)/2

The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately  3.142

Here, we have,

The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:

Area of small square = s^2

Area of big square = b^2

Since the area of the big square is 30 units more than the area of the small square, we can write the equation:

b^2 = s^2 + 30

To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:

s^2 = b^2 - 30

s = sqrt(b^2 - 30)

Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:

s = sqrt(d^2 - 30)

To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:

r = d/2 = sqrt(d^2 - 30)/2

So to find the radius of the circle, we just need to know the diameter of the circle.

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