A company has 11 male and 8 female employees, and needs to nominate 2 men and 2 women for
the company bowling team. How many different teams can be formed?

Answer:

[tex]18x-9=18x-9\\\\3(6x-3)=18x-9\\\\x=4.5[/tex]

Step-by-step explanation:

Each equation is =72. So for the first 4 options, just find equivalent expressions for the left side:

[tex]\frac{3}{5}(30x-15)=18x-9\\\\18x-15\neq 18x-9\\\\50x-25\neq 18x-9\\\\18x-9=18x-9\\\\3(6x-3)=18x-9[/tex]

For x=4.5, must solve original equation:

18x-9 = 72

18x = 81

x = 4.5

Answer:

53 5/7

Step-by-step explanation:

2 + 5/21 = (42 +5)/21 = 47/21

47/21 : 1/12 = x : 2

x = 2 * 47/21 / 1/12

x = 2 * 47/21 * 12

x = 2 * 47/7 * 4

x = 8 * 47/7

x = 376/7

x = 371/7 + 5/7

x = 53 5/7

Answer:

Step-by-step explanation:

168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

The scatter plot shows the daily oil production in the United States in the years since 1994.

The equation y=-168x+6,750 is the trend line for the data.

According to the equation of the trend line, we need to find how many thousands of barrels of oil will be produced daily in the United States 6 years from 1994

In the equation y=-168x+6,750

The 168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994

Hence, 168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994

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Answer:

[tex](6,2)[/tex]

Step-by-step explanation:

When rotating 180° about the origin, [tex](x,y) \longrightarrow (-x, -y)[/tex].

Answer:

Step-by-step explanation:

The polygons that are congruent are those whose vertices and sides line up perfectly. The 4 triangle congruence theorems that help in finding if the triangles are congruent or not are SSS, SAS, ASA, AAS, and RHS.

The polygons that are congruent are those whose vertices and sides line up perfectly. Congruent polygons are polygons having the same size and shape, even if they can be rotations, translations, or mirror reflections of one another. This is another way to conceive of the idea.

A triangle's congruence can be established using the triangle congruence theorem or triangle congruence criterion. The definition of congruent is "absolutely equivalent in shape and size regardless of rotation, flipping, or turning." Congruent figures are described in geometry as shapes that are superimposed on one another, such as triangles and quadrilaterals.

The following are the triangle congruence criteria that aid in demonstrating triangle congruence.

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[tex]\fbox{4x+2}[/tex]

Simplify:

[tex]8x-3x+2[/tex]

[tex]8x+-3x+2+-x[/tex]

Combine Like Terms:

[tex](8x+-3x+-x)+(2)[/tex]

[tex]4x+2[/tex]

Transforming the function f(x) = 2x by compression of a factor of 1/4 gives g(x) = 1/2x

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f(x) = x2 + 3 is obtained by just moving the graph of g(x) = x2 by 3 units up. Function transformations are very helpful in graphing the functions just by moving/expanding/compressing/reflecting the curve without actually needing to graph it from scratch.

In the given function;

f(x)= 2x;

After a compression by a factor of 1/4, the function becomes

g(x) = 2x * 1/4 = 1/2x

The compressed function g(x) is 1/2x

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Answer:

28:50

Step-by-step explanation:

22+28=50, and that is the total amount of students. The number of boys go first in the ratio, then total students.

The number of students who like the book is 64 students.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

Given: Total students in English class = 100

Nine twenty-fifths of the class did not like the book.

Thus, the number of students did not like the book = 9/25 × 100

= 36

Therefore, the number of students like the book =Total students- students did not like the book will be:

= 100-36

= 64 students.

The number of students is 64.

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Complete question

After reading a book for English class, 100 students were asked whether or not they enjoyed it. Nine twenty-fifths of the class did not like the book. How many students liked the book?

Answer:

Step-by-step explanation:

The rate of change from the hour 4 to hour 7 is equal to the slope of 0 miles per hour.

The rate of change of a segment of a graph is represented by its slope, the slope that can be determined by the secant line formula:

m = Δd / Δt

Where:

First, determine the coordinates of the initial and final points of the graph:

(t₁, d₁) = (4, 120), (t₂, d₂) = (7, 120)

Second, find the rate of change of the segment:

m = (120 - 120) / (7 - 4)

m = 0 mi / h

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Answer:

is there a photo because this dosent help

Step-by-step explanation:

The value of x is 4/3

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangles be ΔRST and ΔQRT

Now , from the figure

∠S = 90° in the triangle ΔRST

And RS = 2/√3

∠T = 60° in the triangle ΔRST

Now ,

sin 60° = opposite / hypotenuse

           = RS / RT

           = ( 2/√3 ) / RT

We know , sin 60° = √3 / 2

Substituting the value of  sin 60° in the equation , we get

√3 / 2 = ( 2 / √3 ) / RT

Multiply by RT on both sides , we get

RT x ( √3 / 2  ) =  ( 2 / √3 )

Divide by ( √3 / 2  ) on both sides , we get

RT = ( 2 / √3 ) x ( 2 / √3 )

RT = 4 / 3

Therefore , the value of RT = 4/3

Now , from the figure

∠R = 90° in the triangle ΔQRT

and ∠T = 45° in the triangle ΔQRT

So ,

tan 45° = opposite / adjacent

We know tan 45° = 1

Substituting the value for tan 45° = 1 in the equation , we get

1 = opposite / adjacent

1 = x / RT

Multiply by RT on both sides , we get

x = RT

So , x = 4/3

Hence , The value of x is 4/3

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Answer:

x = 3

Step-by-step explanation:

we are here given a figure in which we have to calculate the value of x . The given figure is made up of two right angled triangles , ∆RST and ∆QRT . So , firstly in ∆RST, we have ,

sinθ = p/h = RT/RS

sinθ = RT/2√3

and here θ = 60° , so that,

sin60° = RT/2√3

√3/2 = RT/2√3

RT = 2√3 * √3/2

RT = 3 . . . . . . . (1)

again in ∆RTQ , we have;

tanθ = p/b = RQ/RT

tanθ = x/3 ( from equation 1 )

and here , θ = 45° , so that ;

tan45° = x/3

1 = x/3

x = 3

and we are done!

The statements that are true for any value of x are

The equations are given as

A. 7x + (2x + 7) = 9x + 7

B. 7x + (2x - 1) = 9x + 1

C. 1/2x + (3 - 1/2x) = 3

D. 5x – (8 - 6x) = -x - 8

E. 0.4x - (0.2x + 8) = 0.2x - 8

F. 6x - (2x - 4) = 4x + 4

Next, we solve one side of the equations and then compare them with the other side

So, we have the following representations

A. 7x + (2x + 7) = 9x + 7

Evaluate

9x + 7 = 9x + 7 --- true

B. 7x + (2x - 1) = 9x + 1

Evaluate

9x - 1 = 9x + 1 --- false

C. 1/2x + (3 - 1/2x) = 3

Evaluate

3 = 3 --- true

D. 5x – (8 - 6x) = -x - 8

Evaluate

11x - 8 = -x - 8 --- false

E. 0.4x - (0.2x + 8) = 0.2x - 8

Evaluate

0.2x - 8 = 0.2x - 8 --- true

F. 6x - (2x - 4) = 4x + 4

Evaluate

4x + 4 = 4x + 4 -- true

Hence, the true statements are (a), (c), (e) and (f)

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The inequality is 8 + 3 n < 5 n. Plane A is less expensive when n > 4

What is inequality ?

Inequality of wealth in major cities Economic inequality comes in many forms, but two stand out above the rest: wealth inequality as measured by the distribution of wealth and income inequality as measured by the distribution of income.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are universal.

Plan A: flat rate $8 per month and $3 per video viewed

Plan B: $5 per video viewed

The number of viewing videos is n

∵ The number of viewing videos is n

→ Plan A

∵ The cost per viewing is $3

∵ Cost per month is $8

∴ The cost = 8 + 3 n

→ Plan B

∵ The cost per viewing is $5

∴ The cost = 5 n

We need the cost of viewing n videos using  Plan A is less than the

cost of viewing n videos using Plan B

→ Cost Plan A < Cost Plan B

∵ Cost Plan A is 8 + 3 n

∵ Cost Plan B is 5 n

∴ 8 + 3 n < 5 n

* The inequality is 8 + 3 n < 5 n

∵ 8 + 3 n < 5 n

Subtract 3 n from both sides

∴ 8 < 2 n

Divide both sides by 2

∴ 4 < n

∴ n > 4

* Plane A is less expensive when n > 4

The inequality is 8 + 3 n < 5 n. Plane A is less expensive when n > 4

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The point (12,489) will be the solution of our given equations.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

number of men given by y=3.9x+441 ​,

and for​ women equation is ​y=14.3x+312,

Now, Let us find the coordinates of the point of intersection of both lines by equating our both equations as:

3.9x+ 441 = 14.3x + 312

14.3x - 3.9x = 441 - 312

10.4x= 129

x= 129/10.4

x = 12.40

and, y= 3.9(12.4)+ 441

y= 489.36

Hence, the point (12,489) will be the solution of our given equations.

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The advantages and disadvantages of bases other than ten are shown below.

The base-10 system is a way to give numbers a place value. As the position of the decimal point determines a number's mathematical value, it is often referred to as the place value number system or the decimal system.

In software systems, number systems with a base of 16 are frequently used. They have the fundamental benefit of being quickly convertible to binary systems.

The advantage of using number bases on 60 is that 60 may be divided by 2, 3, 4, and 6.  Its downside is that it is cumbersome.

Number systems based on 12 provide advantages comparable to those of number systems based on 60, but they give up the advantage of being divisible by 5 for the benefit of a less cumbersome system.

Therefore, base-10 number systems are not the best.

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The solution for n in the chemistry formula is n = PV/RT

From the question, we have the following parameters that can be used in our computation:

Important formula from chemistry is PV = nRT

Write out the formula

So, we have the following representation

PV = nRT

Divide both sides of the equation by R

So, we have the following representation

PV/R = nT

Divide both sides of the equation by T

So, we have the following representation

PV/RT = n

Rewrite the equation as

n = PV/RT

Hence, the solution is n = PV/RT

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The distance that Zoe rode while the car was behind her was of:

160 kilometers.

The relation between velocity, distance and time is that the velocity is the distance divided by time, hence the equation is presented as follows:

v = d/t.

The values of the parameters in this problem are given as follows:

(both of these measures are taken from the first sentence of the problem).

Then the total distance is obtained replacing the values into the equation as follows:

80 = d/4

d = 80 x 4

d = 320 kilometers.

The car was behind her for half the trip, hence the distance that the car spent behind her was of:

d = 0.5 x 320 = 160 kilometers.

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Answer:

y-2=7(x+6)

Step-by-step explanation:

You got it there bro

The second term in the binomial expansion of (2r - 3s)¹² is -73728 r¹¹ s option (A) is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

(2r - 3s)¹²

Using nth term of the binomial expansion is:

= C (12, 2-1) (2r)¹²⁻²⁺¹ (-3s)²⁻¹

After solving

= -73728 r¹¹ s

Thus, the second term in the binomial expansion of (2r - 3s)¹² is -73728 r¹¹ s option (A) is correct.

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Answer:

180-81=

Step-by-step explanation:

Answer:

It should be 42.4

Answer:4

Step-by-step explanation:

replace x with -3

f(x) = 2x-2

find f(-3)

f(-3) = 2(-3) - 2

f(-3) = -6 -2

f(-3) = -8

Answer:

Mex$7,056

Step-by-step explanation:

$1 = Mex$20.16

$350 = x

cross multiply

$350 * Mex$20.60 = Mex$7,056

Answer: Mex$7056

Step-by-step explanation:

Make the proportion:

$1         -      Mex$20.16

$350    -          x

[tex]\displaystyle\\x=\frac{ 350(20.16)}{1} \\\\x=350(20.16)\\\\[/tex]

x=Mex$7056

The two positive numbers are 71 and 48

We shall apply algebra in finding the unknown numbers as follows;

Let us represent the two numbers with the letters x and y

so that;

x - y = 23...(1)

xy = 3408...(2)

from equation (1),

x = 23 + y {adding y to both sides}

putting the value 23 + y for x in equation (2) we get;

(23 + y)y = 3408 {by expansion}

23y + y² = 3408

y² + 23y - 3408 = 0 {we rearrange to get a quadratic equation}

we factorize as follows;

y² + 48y - 71y - 3408 = 0

y(y + 48) - 71(y + 48) = 0

(y + 48)(y - 71) = 0

so by factorization; y = -48 or y = 71

the numbers are positive hence we take y = 71

putting the value 71 for y in equation (2) we get;

x71 = 3408 {divide through by 71}

x = 3408/71

x = 48

Thus; 71 - 48 = 23 and 71 × 48 = 3408, and we can say that the two positive numbers are 71 and 23.

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