The ratio of boys to girls in Coach Sheppard's class is 3 to 5. There are 20 girls
in the class.
What is the total number of students in Coach Sheppard's class?

Using composition formula we get the value of x is 9/16 for G(H(X)) = 32x - 18

In mathematics, composing a function is the process by which two functions, f and g, produce a new function, h, such that h(x) = g(f(x)). This indicates that the function of g is being applied to the function of x. In essence, a function is then applied to the outcome of another function.

We F (2x-18) and G (4x)

By using the composition formula

H(x) = g(f(x))

That is

H(x) = g(2x-18)

      = 2(4x) - 18

      = 8x - 18

If H(x) = 8x - 18

Then, G(H(x))

⇒ G(8x - 18)

⇒ 8(4x) - 18

⇒ 32x - 18

Now, we find x in G(H(x))

⇒ 32x - 18 = 0

⇒ 32x = 18

⇒ x = 18/32

⇒ x = 9/16

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Median, mean, mode, first and third quartiles describe a statistical distribution because these are the measures of central tendency and dispersion of a distribution.

Median, mode and mean are known as the measures of central tendency of a statistical distribution. Because these three can even represent the whole data and its properties. Mean, median and mode gives the central value around which the whole distribution lies or its representative value.

Mean: It gives the average value of the distribution. That is the Total value/ Total number of values.

Median: It is a positional average and it is the middle value of the observations in a distribution.

Mode: Mode is also a positional average which gives the most repeated or frequent observation from the distribution

Now the first and third quartiles are measures of dispersion. It gives the variation of data values from the central value. It gives an idea of the scattering of the distribution around the central value.

First quartile: If the n observations are arranged in ascending order, then the n/4th value is the first quartile.

Third Quartile: It is the 3n/4th value in the ordered n observations.

These two are used to measure the quartile deviation from the central value. If the dispersion is large, then the measures of central tendency cannot be a representative value of the distribution.

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Answer: x = 23

Step-by-step explanation:

Angle in a X shape, the two 'opposite' eachother must be the same so angle HGC is 14

Angle in a Z shape where the lines of the Z are parralell, the two innercorner angles of the Z must be the same os angle GCE must be 14

In triangle GEC we now know two out of the three angles 78 and 14 and we know that angles in a trianlge add up to 180 so the missing angle GEC must be 180-78-14=88

Angles on a straight line must add up to 180 so 4x+88=180

Then this can be used to figure out x

4x+88=180

4x = 92

x = 23

Answer: 14 ==> 3rd option

Step-by-step explanation:

The median is the middle value of a set of ordered numbers. Since this set of numbers from 8 to 20 are already ordered, the median would be the average number between 8 and 20.

(8+20)/2=

28/2=14 ==> 3rd option

The slope of the line in the given graph = rise/run = 3.

To determine the value of the slope of a line on a coordinate plane, we can find the ratio of the rise of the line to that of its run. This means that, the formula for calculating the slope of a line would be:

Slope = rise/run.

Vertical distance across the line is the rise of the line

Horizontal distance across the line is the run of the line

In the graph given, we have:

The rise is labelled as the blue line = 9 units

The run is labelled as the red line = 3 units

Slope of the line (m) = 9 units/3 units

Slope (m) of the given line = 9/3 = 3

Therefore, the slope of the line in the given graph = rise/run = 3.

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Answer:

 [tex]\frac{x-7}{4} =f^{-1}( x)[/tex]

Step-by-step explanation:

→ Replace f(x) with y

y = 4x + 7

→ Minus 7 from both sides

y - 7 = 4x

→ Divide both sides by 4

[tex]\frac{y-7}{4} =x[/tex]

→ Replace y's with f⁻¹(x)

[tex]\frac{x-7}{4} =f^{-1}( x)[/tex]

Answer:

student is not correct

Step-by-step explanation:

3 1/5 ÷ 1/7 = 22/5

the mistake the student made was multiplying rather than dividing

The slope of the line shown is -2/5

The formula for calculating the slope of a line is expressed according to the formula

Slope = Rise/Run

Slope = y₂-y₁/x₂-x₁

Using the coordinate point (0,7) and (5, 5)

Slope = 5-7/5-0
Slope = -2/5

Hence the slope of the line shown is -2/5

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The multiplication of given fraction is 1 4/5 x 5/6 = 1 1/2

In this question, we have been given an expression 1 4/5 x 5/6

We need solve given mathematical expression.

First we write improper fraction 1 4/5 as proper fraction.

1 4/5 = 9/5

So, given expression becomes,

1 4/5 x 5/6

= 9/5 x 5/6

= 9/6

= 3/2

Now we write 3/2 as improper fraction.

If we divide the 3 by 2,then we will get 1 as quotient and 1 as remainder.

3/2 = 1 1/2

Therefore, the multiplication of given fraction is 1 4/5 x 5/6 = 1 1/2

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A scale factor of 2 would be the perfect scale for the scale drawing.

We are given original dimensions of  tech fingerboard as;

Length = 100 mm

Width = 25 mm

Now, from conversions we know that;

1 inch = 25.4 mm

Since Giovanni wants to make a larger scale drawing on an 8 1/2 inch by 11-inch piece of paper, then we can say that;

11-inch = 25.4 * 11 = 279.4 mm

8 1/2 inch = 8 1/2 * 25.4 = 215.9 mm

Thus;

New Length/old length = 279.4/100 = 2.794

Since that is the maximum scale for the drawing paper, then we can say that something lesser like a scale factor of 2 would be the perfect scale for the scale drawing.

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Answer: k(8z - 2)=448z^2-224z+35

z(q^2)​=-10q^4 - 5

Step-by-step explanation:

k(z) = 7z^2 + 7

k(8z - 2)=7(8z - 2)^2 + 7

k(8z - 2)=7(8z - 2)(8z - 2) + 7

k(8z - 2)=7(64z^2-16z-16z+4) + 7

k(8z - 2)=7(64z^2-32z+4) + 7

k(8z - 2)=7(64z^2-32z+4+1)     ==> 7*1=7, so +1 is added in parentheses while +7 is removed outside of parentheses.

k(8z - 2)=7(64z^2-32z+5)

k(8z - 2)=448z^2-224z+35

z(q) = -10q^2 - 5

z(q^2)​=-10(q^2)^2 - 5

z(q^2)​=-10(q^(2*2)) - 5

z(q^2)​=-10q^4 - 5

The desired odd function is sketched at the end of the question.

An odd function is a function in which the following statement is true for all values of x.

f(-x) = -f(x).

The domain of a function is the set that contains all possible input values for a function. In a graph, it is the set that contains the values of x for which the function is defined.

The domain of a function is the set that contains all possible output values for a function. In a graph, it is the set that contains the values of y for which the function is defined.

Looking at the graph, we get that a function f(x) is decreasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y decreases.

Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.

Considering these definitions, the function with the desired characteristics is plotted at the end of the answer.

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The side lengths of RS and PR are 12 units

Similar triangles are triangles whose corresponding sides are in proportion to one another.

In most cases, one triangle is dilated to form the other triangle

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The corresponding triangles are given as:

PQR and PSQ

This means that

PQ corresponds to PS

PR corresponds to PQ

QR corresponds to QS

Where

PQ = 18

QR = 14

QS = 21

So, we have:

PR : QR = PQ : QS

This gives

PR : 14 = 18 : 21

Express as fraction

PR / 14 = 18 / 21

Multiply through by 14

PR = 14 * 18 / 21

Evaluate

PR = 12

The corresponding triangles are given as:

PQR and PSQ

This means that

PQ corresponds to PS

PR corresponds to PQ

QR corresponds to QS

Where

PQ = 18

QR = 14

QS = 21

So, we have:

RS = PR

This gives

RS = 12

Hence, the side lengths of RS and PR are 12 units

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The perimeter of the playground is 16x + 20

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

P = 2(l+w)

Given the following

l = 3x-2

w = 5x+12

Substitute to have:

P = 2(3x-2+5x+12)

P = 2(8x + 10)

p = 16x + 20

Hence the perimeter of the playground is 16x + 20

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Answer: 157.5

"Of" means to multiply. When multiplying percentages by whole numbers, the percentage becomes smaller. The commonly asked question in scenarios just like this is, "what is x% of y?" where x is the percentage and y is your number you want a percentage out of. This question requires you to use multiplication, because it uses the word, "of".

[tex]\bold{Step-by-step}[/tex]

[tex]\mathrm{"What}[/tex] [tex]\mathrm{is}[/tex] [tex]\mathrm{x\%}[/tex] [tex]\mathrm{of}[/tex] [tex]\mathrm{y?"}[/tex]

[tex]P = (x\% \times y)\\P = (75\% \times 210)\\p = 75\% = 0.75\\P = (0.75 \times 210)\\P = 157.5[/tex]

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The time it takes the driver to travel from Point A to Point B is 8 minutes, the same as the helicopter but through a more longer path, such that, we have;

Based on a similar question, the first part required to determine if a driver that drives from Point A to Point B in 8 minutes obeyed the speed limit of 55 miles per hour.

The path of the driver consists of a short path, a bend changing the direction, then a long straight path.

The path of the helicopter is directly from Point A to Point B.

Therefore;

The length of the path of the driver, d1, is longer than that the helicopter, d2, which gives;

d1 > d2

From kinematics, we have;

[tex]Speed = \frac{Distance}{Time} [/tex]

The time taken by the helicopter and the and the driver are equal to 8 minutes, therefore;

[tex] Speed \: of \: the\: driver = \frac{d_1}{8} [/tex]

[tex] Speed \: of \: the \: helicopter = \frac{d_2}{8} [/tex]

[tex] d_1 > d_2 [/tex]

According to the division property of equality, we have;

[tex] \frac{d_1}{8} > \frac{d_2}{8} [/tex]

[tex] \frac{d_2}{8} < \frac{d_1}{8} [/tex]

Therefore;

The speed of the helicopter is lesser than the speed of the driver, which gives;

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Answer:

y = - 2x + 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x - 1 ← is in slope- intercept form

with slope m = - 2

• Parallel lines have equal slopes , then

y = - 2x + c ← is the partial equation of the parallel line

to find c substitute (4, 3 ) into the partial equation

3 = - 8 + c ⇒ c = 3 + 8 = 11

y = - 2x + 11 ← equation of parallel line

Answer:

[tex]\mathsf e^{t-1}[/tex]

Step-by-step explanation:

Definition of an inverse function

[tex]\textsf {A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\:[/tex]

In order to find the inverse of p(t) = 1 + ln(t)...

The expression is simplified -x^4 -3x³ -x² + 4x + 6

Algebraic expressions are expressions consisting of variables, constants, factors and coefficients.

They are also made up of arithmetic operations such as addition, subtraction, multiplication, division, etc

Given the expression:

(-x² - 2x - 2) (x² + x - 3)

expand the bracket

-x^4 - x³ + 3x² -2x³ - 2x² +6x - 2x² - 2x + 6

collect like terms

-x^4 - x³ - 2x³ + 3x² - 2x² - 2x² + 6x - 2x + 6

Add or subtract like terms

-x^4 -3x³ -x² + 4x + 6

The expansion of the expression is -x^4 -3x³ -x² + 4x + 6

Hence, the expression is simplified -x^4 -3x³ -x² + 4x + 6

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Answer:

5 trips

Step-by-step explanation:

330 people / 68 spots = 4.853

Because passengers cannot take 0.853 of a bus, it rounds up to 5.

Answer:

6/5

Step-by-step explanation:

m = (y_2 - y_1)/(x_2 - x_1) = (20 - 8)/(12 - 2) = 12/10 = 6/5

Applying the tangent ratio, the length of side x, in simplest radical form is: 8√3.

The tangent ratio is: tan ∅ = opposite side length / adjacent side length of the right triangle.

Given the following:

Reference angle (∅) = 30 degrees.

Opposite side length = 8

Adjacent side length = x = ?

Using the tangent ratio, we have: tan 30 = 8/x

x(tan 30) = 8

Divide both sides by tan 30

x(tan 30)/tan 30 = 8/tan 30

x = 8/tan 30

x = 8/1/√3

x = 8 × √3

x = 8√3

Therefore, applying the tangent ratio, the length of side x, in simplest radical form is: 8√3.

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Answer:

x = 5

Step-by-step explanation:

7/17 = x/12

17x = (7)(12)

17x/17 = 84/17

     x = 5

All the questions have been solved in the above pictures 7,8,9,10,11,12 & 13

The final step of the given inequality is x < 3. Therefore, option C is the correct answer.

The given inequality is -2(5 - 4x) < 6x - 4.

We need to solve and write the final step of the given inequality.

Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The inequality -2(5 - 4x) < 6x - 4 can be solved as follows:

⇒ -10 + 8x < 6x - 4

⇒ -10 + 8x-8x < 6x - 4-8x (Subtract 8x on both the side of the inequality)

⇒ -10 < -4 -2x

⇒ -10+4 < -4 -2x+4 (Add 4 on both the side of the inequality)

⇒ -6 < -2x

⇒ -6 < -2x (Divide -2 on both the side of the inequality)

⇒ x < 3

The final step of the given inequality is x < 3. Therefore, option C is the correct answer.

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The odds against selecting an ace when a card is drawn from a standard deck of cards is 12:1.

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