d) Three bus services A, B and C arrive at a station. Service A arrives at the station every 15 minutes, service B arrives every 20 minutes and service C arrives every 30 minutes. All three buses arrive at the station together at 9 a.m. At what time will the three buses next arrive at the station. (Decide which will you use to find the answer: GCF or LCM)​

A factor is a number that divides another number, leaving no remainder

The completion of the trend analysis for sales with 2010 as the base year is as follows:

                             2013           2012           2011           2010

Sales            $ 620,000   $ 580,000   $ 450,000   $ 600,000

Trend Analysis      103%             97%              75%             100%

Trend analysis is a technical analysis that uses historical data over some periods to predict and monitor future developments in a particular topic.

To undertake a trend analysis for sales, a base year is chosen and the sales account for the base year is set at 100% and used to check how sales have changed during the review periods.

The other years' results are compared to the base year's by dividing each year's result by the base year's.

Percentages are used to depict trend analysis so that the resulting increases and decreases can be easily compared to the base year.

2013 (D) = 103% ($620,000/$600,000 x 100)

2012 (C) 97% ($580,000/$600,000 x 100)

2011 (B) 75% ($450,000/$600,000 x 100)

2010 (A) = 100% ($600,000/$600,000 x 100)

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The length and breadth expressions where one dimension is the GCF are; 7y and (2y²-5).

Area of a Rectangle

Given that a rectangle is a two-dimensional shape with one of the dimensions being the GCF, as specified in the question;

Consequently, the length and breadth expressions are 7y and (2y²-5) respectively.

Additionally, the rectangle's area when y=2 is; 14(2³) - 35(2) = 52.

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Answer:

(A∩B)={1,15}

Step-by-step explanation:

The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].

The correct option is (C).

Given,

The fraction is given as:

[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]

To find the above fraction which choice is equivalent to the fraction?

Now, According to the question:

Simplify or expand

[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]

Rationalize the denominator:

[tex]\frac{2(\sqrt{x} -\sqrt{x+2} )}{(\sqrt{x} -\sqrt{x+2})(\sqrt{x} -\sqrt{x+2} ) }[/tex]

Expand the expression:

[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{(\sqrt{x})^2-(\sqrt{x+2} )^2 }[/tex]

[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{x-(x+2)}[/tex]

[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{-2}[/tex]

Determine the sign and cross out the common factor:

[tex]\sqrt{x+2}-\sqrt{x}[/tex]

Hence, The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].

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The slope intercept form equation of the straight line is y = -1/2x + 6

Slope intercept form

Slope intercept form of the equation used to calculate the equation of a straight line by using the slope and intercept value.

And the general form of slope intercept equation is

y = mx + c

where

m refers the slope

c refers the y - intercept

Given,

Here we have the graph of straight line.

Through the given graph we have to identify the equation of slope intercept form.

In order to find the slope intercept form equation we need two values they are slope and the y intercept.

So, to find these two values, we need two points,

So we have selected the points from the given graph. They are (2,5) and (4,4).

Now we have to use the slope formula to find the value of the slope,

m = (4 - 5) / (4 - 2)

m = -1/2

Now, we have to use the slope and one of the point (4,4), to find the value of y intercept,

4 = -1/2 (4) + c

4 = -2 + c

c = 6

Now, we have identified the values of slope and the intercept.

Then the slope intercept form equation of these straight line is written as,

y = -1/2x + 6

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The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47

acc to our question-

hence,The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47

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Considering the given figure we have that

< BAC = < CAD         definition of angle bisection

< BAC = < BCA         base angles of isosceles triangle

This refers to when angles are being shared or divided into two equal parts.

In the given problem, line AC is the bisector of < BAC. creating wo equal angles in the process. hence

< BAC = < CAD         definition of angle bisection

Triangle BAC is an isosceles triangle, since the sides BA and BC are equal. the angles are also equal therefore

< BAC = < BCA         base angles of isosceles triangle

Line AC is also a transversal line, connecting the two parallel lines BC and AD. This creates opportunity for alternate angle theorem

< BCA = < CAD        alternate internal angle theorem

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Answer:

36

Step-by-step explanation:

substitute m = - 3 into the expression

m² - 7m + 6

= (- 3)² - 7(- 3) + 6

= 9 + 21 + 6

= 36

The range of market return is 15.9% and the mean of market return is 2.94%

Productive Investments Limited provided the returns for Laska stocks for 2017 to 2021.

Year         Laska return

2017         -2.2%

2018          -3.4%

2019         12.5%

2020         -0.8%

2021          8.6%

The range of market return = Highest return - lowest return

= 12.5 - (-3.4)

= 15.9%

mean market return = (-2.2 +(-3.4) + 12.5 +(-0.8) + 8.6)/5

mean market return = 2.94%

Therefore, the range of market return is 15.9% and the mean of market return is 2.94%

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The ratio of the areas of these two photos is equal to 9:16.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities.

This ultimately implies that, a ratio is generally expressed as a quotient of two numerical quantities or variables.

Generally speaking, the corresponding ratio of the areas of two geometric figures (shapes) is equal to the square of the ratio of their corresponding side length:

Area of photos = (a:b)²

Substituting the given parameters into the formula, we have;

Area of photos = (3:4)²

Area of photos = 9:16

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Marissa will have $720 in 7 years when she has $48 in her saving account that earns 2% simple interest per year.

where

Calculation

From, A = P(1 + RT)

where, p = $48

R = 2%

T= 7 years

A = 48(1 + 2*7)

A = $720

Hence, Marissa will have $720 in her bank account after 7 years.

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Answer: -6

Step-by-step explanation:

Answer:

[tex] \huge{ \boxed{r =100( \sqrt[n]{ \frac{A}{P} } - 1)}}[/tex]

Step-by-step explanation:

[tex]A = P(1 + \frac{r}{100} )^{n} \\ [/tex]

First of all in order to make r the subject we have to first divide both sides of the equation by P

That's

[tex] \frac{A}{P} = \frac{P( {1 + \frac{r}{100} })^{n} }{P} \\[/tex]

We'll finally get

[tex] \frac{A}{P} = ( {1 + \frac{r}{100}) }^{n} \\ [/tex]

Next we have to remove the power n and to do that we find the square root of 'n' of both sides as

We have

[tex] \sqrt[n]{ \frac{A}{P} } = \sqrt[n]{( {1 + \frac{r}{100} })^{n} } \\ \\ \\ \sqrt[n]{ \frac{A}{P} } = 1 + \frac{r}{100} [/tex]

Next we subtract 1 from both sides to isolate r/100

We have

[tex]\sqrt[n]{ \frac{A}{P} } - 1 = 1 - 1 + \frac{r}{100} \\ \sqrt[n]{ \frac{A}{P} } - 1 = \frac{r}{100} [/tex]

Finally to isolate r , we multiply both sides by 100

[tex] \frac{r}{100} \times 100 =100 \times (\sqrt[n]{ \frac{A}{P} } - 1)[/tex]

We have the final answer as

[tex]r =100( \sqrt[n]{ \frac{A}{P} } - 1) \\ [/tex]

Hope this helps you

The capital is £430,600.

Define capital.

The money that a company has on hand to support both its current operations and potential expansion is known as capital. One source of funding for it is the earnings from its operations. When calculating a company's capital worth, all of the company's physical assets and financial assets would be included (minus its liabilities).

The capital account—also referred to as the capital and financial account—records the net flow of investment transactions into an economy and is used in macroeconomics and international finance.

Solution Explained:

Given, Assets = £451,100 and liabilities = £20,500

Capital = Assets - Liabilities

            = 451100 - 20500
            = £430,600

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Given graph represent the graph of  g(x) = [tex]-x^{2} (x -2)[/tex]

Given,

In the question;

The equation is:

g(x) = - [tex]x^{2} (x -2)[/tex] or h(x) = [tex]x^{2} (x -2)[/tex]

To find the is this the graph of g(x) or h(x).

Graph is given in the figure.

Now, According to the question;

g(x) = [tex]-x^{2} (x -2)[/tex]        and      h(x) = [tex]x^{2} (x -2)[/tex]

g(x) = 0                                    h(x) = 0

[tex]-x^{2} (x -2) = 0[/tex]                         [tex]x^{2} (x -2)[/tex] = 0

x = 0, 2                                    x = 0, 2

If we put x = 1 then,

g(1) = [tex]-(-1)^2(1-2)[/tex]     and   h(1) = [tex](1)^2(1-2)[/tex]

g(1)  =  -1 (-1)                          h(1) = 1(-1)

g(1)   = 1                                 h(1) = -1

But as shown in graph, graph take positive value at x = 1

∴Given graph is the graph of g(x) = [tex]-x^{2} (x -2)[/tex]

Hence, Given graph represent the graph of  g(x) = [tex]-x^{2} (x -2)[/tex]

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The numbers that are correctly written in scientific notation are:

Scientific notation is a shorthand (approximate) manner of writing long or short numbers using decimal forms raised to 10 power a baseline.

The rules for correctly writing a scientific notation include the following:

Thus, the scientific notation rules are correctly satisfied by Options B and D, unlike Options A, C, and E.

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A) 42 x 10⁵

B) 1.1 x 10⁴

C) 7.0 x 20⁴

D) 6.01 x 10⁻⁴

E) 18.0 x 10³

The possible values for n and m are:

m = √5 and n = 7/5

In this question, we have been given the locations of numbers n and m.

From their locations in the diagram, we need to find the possible values for n and m.

From the location of n we can say that the value of n is a rational number but not an integer.

We know that rational numbers are of the form p/q where p, q are integers with q ≠ 0

And the value of m is an irrational number.

So, the possible value of n am m:

m = √5 and n = 7/5

Therefore, the possible values for n and m are:

m = √5 and n = 7/5

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The number of touchdowns is 4.

The number of extra-point kicks is 4.

and the number of field goals is 2.

What are linear equations in three variables?

If a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables.

How to solve the system of linear equations in three variables?

Select two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. then, solve the system of the two newly obtained equations using the Addition/Subtraction method.

Let the number of touchdowns be "x", the number of extra-point kicks be "y", and the number of field goals is "z".

Total points scored in game = 20+14 =34

Now,

According to the given question,

                                6x + y + 3z = 34 -----------(I)

                                x = y ----------(II)

                                x = 2z

                                z = [tex]\frac{x}{2}[/tex] -----------(III)

Putting the values of "y" and "z" in equation (I), we get

                              6x + x + 3×[tex]\frac{x}{2}[/tex] = 34

                               [tex]\frac{17x}{2}[/tex] = 34

                               x = 4

Now, putting the value of "x" in equations (II) and (III), we get

                               y = 4.

                               z = 2.

Hence, The number of touchdowns is 4. The number of extra-point kicks is 4, and the number of field goals is 2.

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The  Weight  of Mary is 80. Students who are having trouble solving a problem can use the "draw a picture" method to create a visual representation of the issue.

Students who are having trouble solving a problem can use the "draw a picture" method to create a visual representation of the issue.

the justifications.

Inquiry 1.

Formula: w = 10 8 pound

Answer: x = 80 lb

Inquiry 2:

Formula: d = 108 lb - 8 pound

d = 72 lb

Explanation:

First of all

When Mary was born, she weighed 8 pounds.

Statement 2: Mary weight 10 times as much when she was 10 years old.

w = 10 8 pounds, or 80 pounds.

Description of the illustration:

She was born weighing 8 pounds, which is represented by each cell. The 10 cells indicate that the number 8 lbs. has been repeated 10 times.

Next, the sum of the multiplication is shortened:

8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 10 × 8 = 80.

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The dimensions of the playground are;

Width = 60 feet

Length = 160 feet

The formula for calculating perimeter of a rectangle is expressed as;

Perimeter = 2( l + w)

Where;

We have the values as;

Perimeter = 440 feet

Length = 3w - 20

Width = w

Now, substitute the values into the formula, we have;

440 = 2( 3w - 20 + w)

expand the bracket

440 = 2( 4w - 20)

440 = 8w - 40

collect like terms

8w = 480

Make 'w' the subject of formula

w = 60 feet

Length = 3(60) - 20

Length = 180 - 20

Length = 160 feet

Hence, the values are 60feet and 160 feet

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The graph of the linear equation for question 12 can be seen in the image at the end of the answer.

If we have a linear equation with a slope m and a point (h, k=, the point-slope form of that linear equation is:

y = m*(x - h) + k

Here the slope is m = -7/4 and the point is (2, -6)

Then the linear equation is:

y = (-7/4)*(x - 2) - 6

To graph the linear equation we need two points on it, and we already know one, so we need to find the other.

To do so we can evaluate in some value of x.

If we use x = -2 we will get:

y = (-7/4)*(-2 - 2) - 6

y = (-7/4)*(-4) - 6

y = 7 - 6 = 1

So we also have the point (-2, 1)

Now we just need to graph the two given points and connect them with a line.

Below you can see the graph.

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The distance and direction of the ship from the starting point is found using vectors as follows;

The ship is 48.03 nautical miles from the starting point at a directional bearing of N 18.53° E

A vector is a quantity that has a property of magnitude or size and direction.

The ship's speed = 36 nautical miles per hour

Direction of the ship = Due east

The duration the ship continues in the direction = 1 hour

The new direction of the ship = N32°E

The duration in which the ship continues in the new direction = Half an hour

The vector of the distances traveled by the ship are;

[tex]\overrightarrow{d_1}[/tex] = 36·i

[tex]\overrightarrow{d_2}[/tex] = 0.5 × 36×sin(32°)·i + 0.5 × 36×cos(32°)·j = 18×sin(32°)·i + 18×cos(32°)·j

The sum of the distances traveled by the ship is therefore;

36·i + 18×sin(32°)·i + 18×cos(32°)·j = (36 + 18×sin(32°))·i + 18×cos(32°)·j

(36 + 18×sin(32°))·i + 18×cos(32°)·j = 45.54·i + 15.26·j

The distance of the ship from the starting point, d, is therefore;

d ≈ √(45.54² + 15.26²) ≈ 48.03

The distance of the ship from the starting point is approximately 48.03 miles.

The direction from the North of the ship from its starting point, θ, is therefore;

[tex]\theta = arctan\left(\dfrac{15.26}{45.54} \right) \approx 18.53^{\circ}[/tex]

Then direction of the ship is N 18.53° E

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If Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip .The currency needed is 200 euro and 500 pounds.

Formulate an equation

1.30x + 1.60y = 3400

Hence,

x =4y Equation 1

1.30x + 1.60y = 3400 Equation 2

Substitute eq1 into eq2

1.30(4y) + 1.60y = 3400

5.2y +1.60y =3400

6.8y =3400

Divide both side by 6.8y

y =3400/6.8

y = 500

Number of euro

4y where y = 500

4(500)

=2000

Therefore  the answer in practical terms is : 2000 euro of European currency and 500 pounds of Britain currency are needed.

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Answer:

2

Step-by-step explanation:

y    4-2=2

x     2-1=1    

2/1=1

hope it helps.

Answer:

Step 1: Simplify both sides of the equation.

1/3(6y+3)−24 = 3(1/3y−6)

1/3(6y) + 1/3(3) -24 = 3(1/3y) + 3(-6)

2y +1 −24 = y−18

2y −23 = y −18

Subtract y from both sides.

2y−23−y=y−18−y

y−23=−18

Step 3: Add 23 to both sides.

y−23+23 = −18+23

y = 5

Step-by-step explanation:

If Midland is 20 miles from Odessa, and Lubbock is 113 miles from Midland. Then 111.22 miles is Odessa from Lubbock.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

The cities of Midland, Lubbock, and Odessa form a triangle.

The distance between Midland and Odessa is 20 miles.

The distance between Lubock and Odessa is unknown, we need to find this.

This can be find by using Pythagorean theorem

Odessa  from Lubbock=20²+x²

113²=20²+x²

12769=400+x²

12369=x²

x=111.22

Hence, 111.22 miles, Odessa could possibly be from Lubbock.

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Answer:

13/3

Step-by-step explanation:

3 [tex]\frac{12}{9}[/tex]

[tex]\frac{12}{9}[/tex]= 1 [tex]\frac{1}{3}[/tex]

3+1 1/3

4 [tex]\frac{1}{3}[/tex]

13/3

Answer:

Step-by-step explanation:

step one just add 5/9 +7/9 since they have the same denominator then that will equal 4/3

2nd step add the 1 and 2 together since they are both whole numbers. which equals 3

3rd step 4/3 + 3/1 which equals 13/3 maybe or if the answers wants a mixed number than the answer might be 4 1/3!

I'm not quite sure but try and see if its correct! :)