What is (GCD) of 24, 48 and 60?

Answer:

  (a)  140 sandwiches

Step-by-step explanation:

The total number sold can be found from the given relation:

  56 sandwiches = 40% × total sold

__

Dividing by the coefficient of the variable, we find ...

  total sold = (56 sandwiches)/0.40 = 140 sandwiches

The total number of sandwiches sold last week was 140.

1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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The given statement "If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B" is true.

The standard deviation is a measure of a data set's dispersion. It tells us how far the data values are from the mean.

A larger standard deviation means that the data points are more spread out, i.e., they are farther from the mean.

Therefore, if data set A has a standard deviation that is greater than data set B, it means that the values in data set A are more spread apart.

Hence, the given statement is true.

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Answer:

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

Answer:

\(f(x)=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}\)

Step-by-step explanation:

Given function:

\(f(x)=2x^2+13x+20\)

Factor out 2 from the terms in x:

\(f(x)=2\left(x^2+\dfrac{13}{2}x\right)+20\)

Add the square of half the coefficient of x inside the parentheses, and subtract the distributed equivalent outside the parentheses:

\(f(x)=2\left(x^2+\dfrac{13}{2}x+\left(\dfrac{\frac{13}{2}}{2}\right)^2\right)+20-2\left(\dfrac{\frac{13}{2}}{2}\right)^2\)

Simplify:

\(f(x)=2\left(x^2+\dfrac{13}{2}x+\left(\dfrac{13}{4}\right)^2\right)+20-2\left(\dfrac{13}{4}\right)^2\)

\(f(x)=2\left(x^2+\dfrac{13}{2}x+\dfrac{169}{16}\right)+20-\dfrac{169}{8}\)

\(f(x)=2\left(x^2+\dfrac{13}{2}x+\dfrac{169}{16}\right)-\dfrac{9}{8}\)

Factor the perfect trinomial inside the parentheses:

\(f(x)=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}\)

Answer:

The anwer is B 1200 in

Step-by-step explanation:

Answer:

it okay I can help you with that

Answer:

224

Step-by-step explanation:

360.-136.

Answer:

The Second Option as of 2022

Step-by-step explanation:

subtracting 3x4 + 9x3 + 3x2 from the

dividend and bringing down 13x .

Answer:

14x+12=x

or,14x-x=-12

or,13x=-12

or,x=-12/13

the relation between the angles like comparing position, measurement, and congruence between two or more angles.

The probability distribution of Y = X mod (4) is: 3/10, 3/10, 2/10, 2/10 and the probability distribution of Y = 6 mod (X + 1) is: 1/10, 1/10, 2/10, 1/10, 2/10, 2/10 , 1/10.

The probability distribution of Y = X mod (4) can be found as follows:

Y = 0, when X = 0, 4, 8

Y = 1, when X = 1, 5, 9

Y = 2, when X = 2, 6

Y = 3, when X = 3, 7

So, the probability distribution of Y = X mod (4) is:

Y = 0, P(Y = 0) = 3/10

Y = 1, P(Y = 1) = 3/10

Y = 2, P(Y = 2) = 2/10

Y = 3, P(Y = 3) = 2/10

The probability distribution of Y = 6 mod (X + 1) can be found as follows:

Y = 0, when X = 5

Y = 1, when X = 0

Y = 2, when X = 1, 6

Y = 3, when X = 2

Y = 4, when X = 3, 7

Y = 5, when X = 4, 8

Y = 6, when X = 9

So, the probability distribution of Y = 6 mod (X + 1) is:

Y = 0, P(Y = 0) = 1/10

Y = 1, P(Y = 1) = 1/10

Y = 2, P(Y = 2) = 2/10

Y = 3, P(Y = 3) = 1/10

Y = 4, P(Y = 4) = 2/10

Y = 5, P(Y = 5) = 2/10

Y = 6, P(Y = 6) = 1/10

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\(\left(2+\sqrt{10} \right)\left(2-\sqrt{10} \right)\\\\=2^2-\left(\sqrt{10} \right)^2\\\\=4-10\\\\=-6\)

Answer:

The correct option is (D).

Step-by-step explanation:

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

A small p-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you discard H₀.

A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The hypothesis is defined as follows:

H₀: The slope of the regression line is 0, i.e. β = 0.

Hₐ: The slope of the regression line is greater than 0, i.e. β > 0.

A scatter-plot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables; lean body mass and maximal oxygen uptake.

The significance level of the test is, α = 0.05.

The p-value of the test is, p-value = 0.04

As the p-value = 0.04 < α = 0.05, we reject the null hypothesis.

So, it can be concluded that there is a statistical evidence of a relationship between lean body mass and maximal oxygen uptake for college athletes.

Since the scatter-plot shows a strong positive linear relationship, it implies that as the an increase in lean body mass causes an increase in maximal oxygen uptake for college athletes.

Thus, the correct option is (D).

If triangle ABC is reflected across the line x = -2, the new point is A'(-1, 2), B'(2, 1) and C'(-2, -3)

If triangle ABC is reflected across the x axis, the new point is A'(-3, -2), B'(0, -1) and C'(-2, 3)

If triangle ABC is reflected across the y axis, the new point is A'(3, 2), B'(0, 1) and C'(2, -3)

If triangle ABC is reflected across the line y = x, the new point is A'(2, -3), B'(1, 0) and C'(-3, -2)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Triangle ABC has vertices A(-3,2) B(0,1) and C(-2,-3).

1) If triangle ABC is reflected across the line x = -2, the new point is A'(-1, 2), B'(2, 1) and C'(-2, -3)

2) If triangle ABC is reflected across the x axis, the new point is A'(-3, -2), B'(0, -1) and C'(-2, 3)

3) If triangle ABC is reflected across the y axis, the new point is A'(3, 2), B'(0, 1) and C'(2, -3)

4) If triangle ABC is reflected across the line y = x, the new point is A'(2, -3), B'(1, 0) and C'(-3, -2)

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After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.

When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.

The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.

Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.

The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.

It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.

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Answer:

33.

Step-by-step explanation:

75%   x

100   44

x = (44 * 75 ) / 100 = 33.

Answer:

7 - 3 i

Step-by-step explanation:

Simplifying

(3 + -2i) + (4 + -5i) = 0

Remove parenthesis around (3 + -2i)

3 + -2i + (4 + -5i) = 0

Remove parenthesis around (4 + -5i)

3 + -2i + 4 + -5i = 0

Reorder the terms:

3 + 4 + -2i + -5i = 0

Combine like terms: 3 + 4 = 7

7 + -2i + -5i = 0

Combine like terms: -2i + -5i = -7i

7 + -7i = 0

Solving

7 + -7i = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-7' to each side of the equation.

7 + -7 + -7i = 0 + -7

Combine like terms: 7 + -7 = 0

0 + -7i = 0 + -7

-7i = 0 + -7

Combine like terms: 0 + -7 = -7

-7i = -7

Divide each side by '-7'.

i = 1

Simplifying

i = 1

Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

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Area of circle of diameter with 13cm is 132.74

What is area of circle?

Given :

Diameter of circle, d = 13cm

Radius of a circle, r = d/2

=13/2

=6.5

Area of circle = πr²

= 3.142 * 6.5 * 6.5

= 132.74

Hence, the Area of circle of diameter with 13cm is 132.74.

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Answer:

Maybe negative or undefined?

Step-by-step explanation:

Answer: The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 -12 0 -6 1 0 g(x) g(x) = 2x + 6 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).

PART B: y=mx +b is slope intercept form of linear equation where m=slope and b =y intercept

slope for line for function f(x) =-5-(-1) / -1-0 =-5+1/-1=-4/-1=4  

y = 4x+b

3=4(1)+b

3=4+b

-1 =b

y=4x-1

f(x)=4x-1     slope = 4

g(x)=2x -7    slope = 2

b) y intercept for f(x) is -1

and g(x) is -7

so f(x) is having greater y intercept

The dollar value of total revenue at each price is $\(0\), $\(10\), $\(12\), $\(12\), $\(10\), and $\(6\). Total revenue will be the greatest at a price of $\(4\), with \(3\) units sold.

To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:

Price: $\(6\)

Quantity: \(0\)

Total Revenue: $\(6 \times 0\) = $\(0\)

Price: $\(5\)

Quantity: \(2\)

Total Revenue: $\(5 \times 2\) = $\(10\)

Price: $\(4\)

Quantity: \(3\)

Total Revenue: $\(4 \times 3\) = $\(12\)

Price: $\(3\)

Quantity: \(4\)

Total Revenue: $\(3 \times 4\) = $\(12\)

Price: $\(2\)

Quantity: \(5\)

Total Revenue: $\(2 \times 5\) = $\(10\)

Price: $\(1\)

Quantity: \(6\)

Total Revenue: $\(1 \times 6\) = $\(6\)

To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $\(3\), and the corresponding quantity sold is \(4\) units.

Therefore, at a price of $\(3\), the total revenue will be the greatest, with \(4\) units sold.

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Answer:

2^(1/6) (cos(-pi/12)+i sin(-pi/12))

2^(1/6) (cos(3pi/12)+i sin(3pi/12))

2^(1/6) (cos(7pi/12)+i sin(7pi/12))

2^(1/6) (cos(11pi/12)+i sin(11pi/12))

2^(1/6) (cos(5pi/4)+i sin(5pi/4))

2^(1/6) (cos(19pi/12)+i sin(19pi/12))

Step-by-step explanation:

Let's convert to polar form.

-2i=2(cos(A)+i sin(A) )

There is no real part so cos(A) has to be zero and since we want -2 and we already have 2 then we need sin(A)=-1 so let's choose A=-pi/2.

So z=2(cos(-pi/2)+i sin(-pi/2)).

There are actually infinitely many ways we can write this polar form which we will need.

z=2(cos(-pi/2+2pi k)+i sin(-pi/2+2pi k))

where k is an integer

Now let's find the 6 6th roots or z.

2^(1/6) (cos(-pi/12+2pi k/6)+i sin(-pi/12+2pi k/6))

Reducing

2^(1/6) (cos(-pi/12+pi k/3)+i sin(-pi/12+pi k/3))

Plug in k=0,1,2,3,4,5 to find the 6 6th roots.

k=0:

2^(1/6) (cos(-pi/12+pi (0)/3)+i sin(-pi/12+pi (0)/3))

=2^(1/6) (cos(-pi/12)+i sin(-pi/12))

k=1:

2^(1/6) (cos(-pi/12+pi/3)+i sin(-pi/12+pi/3))

2^(1/6) (cos(3pi/12)+i sin(3pi/12))

k=2:

2^(1/6) (cos(-pi/12+2pi/3)+i sin(-pi/12+2pi/3))

2^(1/6) (cos(7pi/12)+i sin(7pi/12))

k=3:

2^(1/6) (cos(-pi/12+3pi/3)+i sin(-pi/12+3pi/3))

2^(1/6) (cos(11pi/12)+i sin(11pi/12))

k=4:

2^(1/6) (cos(-pi/12+4pi/3)+i sin(-pi/12+4pi/3))

2^(1/6) (cos(15pi/12)+i sin(15pi/12))

2^(1/6) (cos(5pi/4)+i sin(5pi/4))

k=5:

2^(1/6) (cos(-pi/12+5pi/3)+i sin(-pi/12+5pi/3))

2^(1/6) (cos(19pi/12)+i sin(19pi/12))

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Answer:

g= -2x+1

Step-by-step explanation:

-2x because it goes down two boxes for every one box to the right.

+1 because that is the y intercept

There are 8 to take Lara and Hayden to volunteer the same number.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Lara already volunteered 50 hours and will volunteer 5 hours more each week.

And, Hayden already volunteered to 10 hours and will volunteer 10 hours each week .

Now, For Lara;

⇒ 50 + 5x

And, For Hayden;

⇒ 10 + 10x

So, For same number of volunteer is,

⇒ 50 + 5x = 10 + 10x

⇒ 50 - 10 = 10x - 5x

⇒ 40 = 5x

⇒ x = 40/5

⇒ x = 8

Thus, There are 8 to take Lara and Hayden to volunteer the same number.

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The equation that have the same value of x as Three-fifths (30 x minus 15) = 72 will be 18x - 9x = 72

It should be noted that an equation simply means the relationship that exists between the variables.

It should be noted that the equation given is:

3/5(30x - 15) = 72

3/5(30x) - 3/5(15) = 72

18x - 9x = 72

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