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Answer:

[tex] \displaystyle 27150200[/tex]

Step-by-step explanation:

we are two conditions

In choosing a committee, order doesn't matter; in case of teachers we need the number of combinations of 3 people chosen from 12

remember that,

[tex] \displaystyle\binom{n}{r} = \frac{n!}{r!(n - r)!} [/tex]

with the condition we obtain that,

therefore substitute:

[tex] \displaystyle\binom{12}{3} = \frac{12!}{3!(12 - 3)!} [/tex]

simplify Parentheses:

[tex] \displaystyle\binom{12}{3} = \frac{12!}{3! \cdot9!} [/tex]

rewrite:

[tex] \rm \displaystyle\binom{12}{3} = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(1 \times 2 \times 3 )\cdot1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9} [/tex]

reduce fraction:

[tex] \rm \displaystyle\binom{12}{3} = \frac{12 \times 11 \times 10}{1 \times 2 \times 3 } [/tex]

rewrite 12 and 10:

[tex] \rm \displaystyle\binom{12}{3} = \frac{3 \times 2 \times 2 \times 11 \times 10}{1 \times 2 \times 3 } [/tex]

reduce fraction:

[tex] \rm \displaystyle\binom{12}{3} = 2 \times 11 \times 10[/tex]

simplify multiplication:

[tex] \rm \displaystyle\binom{12}{3} = 220[/tex]

In case of students we need the number of combinations of 4 students choosen from 43 therefore,

[tex] \displaystyle\binom{43}{4} = \frac{43!}{4!(43 - 4)!} [/tex]

simplify which yields:

[tex] \displaystyle\binom{43}{4} = 123410[/tex]

hence,

The committee of 7 members can be selected in BLANK different ways is

[tex] \displaystyle 123410 \times 220[/tex]

[tex] \displaystyle \boxed{27150200}[/tex]

and we're done!

Answer:

the area is 1235

Step-by-step explanation:

Answer:

2714.33 sq in

explanation-

Answer:

C

Step-by-step explanation:

Answer:

A=90, B=86.896551724,C=90/29

Step-by-step explanation:

B+C=90

(x28)+x=90

x=90/ 29

((90/29)28)=B

A=90° because there is the symbol indicating a right angle

Answer:cvg

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

let (2,1)be x1 and y1 respectively

(3,-10) be x2 and y2 respectively

From,slope= (y2-y1)/(x2-x1)

=(-10-1)/(3-2)

= -11/1

= -11

Answer:

c. 4

Step-by-step explanation:

I'm correct if I'm rwong

Answer:

h = -50

Step-by-step explanation:

- 3/10h = 15

Multiply each side by -10/3 to isolate h

-10/3 * - 3/10h = 15 * -10/3

h = -150/3

h = -50

Answer:

h = -50

Step-by-step explanation:

Answer:

16.7 miles

Step-by-step explanation:

6.7+10=16.7

The two of them ran 16.7 miles.

Answer:

there is no figure sorry

Answer:

a and d i think bc they are negative-positive

This answer is Nonlinear

Answer:

I'm pretty sure it's D becuase you can't have a power be a fraction

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the first angle = x

Let the second angle = y

They are complementary so

x + y = 90

x = y + 30

Substitute for x

y + 30 + y = 90

2y + 30 = 90             Subtract 30 from each side

2y = 90 - 30

2y = 60                     Divide by 2

2y/2 = 60/2          

y = 30

x = y + 30

x = 30 + 30

x = 60

Answer:

y = -x - 2

Step-by-step explanation:

The slope is -1 and the y-intercept is (0, -2).

Statistics & Data

For this data set, there is an outlier. The outlier is four.

This is representing a small number of assignments required in math class that month.

This means that the correct answer is B.

Answer:

B

Step-by-step explanation:

The answer should be B or the second choice because the number 4 is unusually low compared to the rest of homework assignments given in the other math classes for that month. I made a graph to show how the number 4 is not near the number of homework assignments given in the other math classes.

If you think I missed something or made a mistake, please let me know.

Answer:

3x^3 + 6x^2

Step-by-step explanation:

2x^2 + 3x^3 + 4x^2

Combine like terms

3x^3  + (2x^2+4x^2)

3x^3 + 6x^2

Answer:

b. 6 x² + 4 x³

Step-by-step explanation:

2x ² + 3x³ + 4x²

Combine like terms, we get

2 x² + 4 x² + 3 x³

6 x² + 3 x³

option a and b both are similar.

Answer:

x( x^2+4)

Step-by-step explanation:

factor out x from the expression

xx (x^2+4)

than your answer is x( x^2+4)

Answer:

[tex] x(x + 2)(x + 2)[/tex]

Step-by-step explanation:

as the x is the common factor...get x out

[tex] {x}^{3} + 4x[/tex]

[tex]x( {x}^{2} + 4)[/tex]

Then

[tex]x( {x}^{2} + 4) \\ x( {x}^{2} + {2}^{2} ) \\ x(x + 2)(x + 2)[/tex]

Hope this helps you

Answer:

The correct option is (2,1);maximum. The explanation is given below. The vertex of the parabola is the point where the parabola crosses its axis of symmetry. the vertex will be the lowest point on the graph, the point at the bottom of the " U "-shape.

Step-by-step explanation:

thank me later

Step-by-step explanation:

D. 321 square feet

26-15= 11

6*11= 66ft²

15*17= 255ft²

255+66= 321ft²

Area= 321ft²

Might be wrong but hope it helped!

Answer:

9 cm

Step-by-step explanation:

Applying,

P = a+b+c................. Equation 1

Where P = Perimeter of the triangle, a, b,c are the three sides of the triangle respectively.

From the question,

Given: P = 31 cm, a = x cm, b = (x-1) cm, c = (x+2) cm

Substitute these values into equation 1, and solve for x

31 = x+(x-1)+(x+2)

31 = 3x+1

3x+1 = 31

3x = 31-1

3x = 30

divide both side by 3 to get x

3x/3 = 30/3

x = 10.

Therefore,  the sides of the triangle are

a = x = 10 cm,

b = (x-1) = (10-1) = 9 cm

c = (x+2) = (10+2) cm = 12 cm

Hence the shortest side is 9 cm

Answer:

(h/g)(x) = x² - 2x

Step-by-step explanation:

h(x) = x³ - 4x

g(x) = x + 2

(h/g)(x) = h(x)/g(x) = (x³ - 4x) / (x + 2) = x² - 2x

Answer:

x = -8

x = 8

Step-by-step explanation:

x(18 – x) = 2(9x – 32)

distribute

18x - x² = 18x - 64

Subtract 18x from both sides

-x² = -64

multiply both sides by -1

x² = 64

Take the square root of both sides

x = ± 8

x = -8

x = 8

Answer:

a. x^(5/6) + 2x^(7/3)

Step-by-step explanation:

____

Answer:

x = 25

Step-by-step explanation:

Angle 1 = 2x + 10

Angle 2 = 4x + 20

These two angles are going to add up to 180 because 180 is a straight line so we get the equation:

2x + 10 + 4x + 20 = 180

6x + 10 + 20 = 180

6x + 30 = 180

6x = 150

x = 25

Answer:

n = 3/5

Step-by-step explanation:

Represent this quotient as:

   n

---------

-2/3

and set it equal to -9/10:

   n           -9

--------- = -------

-2/3          10

Cross multiplication yields:

10n = 6, so that n = 6/10 or n = 3/5

Answer:

Answer Of this question is 1000