All categories

3 years ago

In how many ways can a teacher arrange 6 students in the front row of a classroom with a total of 20 students?

1 answer:

8 0

This is a combination of 20 studants, 6 to 6:

$C_{2,6}=\frac{20!}{(20-6)!6!}=\frac{20!}{14!6!}=\frac{20.19.18.17.16.15.14!}{14!.6.5.4.3.2.1}=38,760 \ ways$

You might be interested in

The area of a triangle is 14 square units it has a side length of a and b what is the value of b if a is 1/5

Ilia_Sergeevich [38]

Answer:

140 ft

Step-by-step explanation:

Given data

Area= 14 square feet

Height a = 1/5 ft

Base b=????

We know that the area of a triangle is given as

Area= (1/2)B*H

substitute

14= 1/2* B* 1/5

14= B/10

cross multiply

B= 140

Hence the base is 140 ft

7 0

3 years ago

Find the intercepts of the line.y=−5x−17

GaryK [48]

Answer:

Step-by-step explanation:

y = -5x - 17

in y = mx + b form, the y int is in the m position

y = mx + b

y = -5x - 17......so the y int (b) = -17 or (0,-17) <=== y intercept

u can also find the y intercept by subbing in 0 for x and solving for y

u can find the x intercept by subbing in 0 for y and solving for x

y = -5x - 17

0 = -5x - 17

5x = -17

x = -17/5......so the x intercept is -17/5 or (0,-17/5) <==== x intercept

5 0

3 years ago

Simplify the following expressing. Show your work and explain each step. <br><br> 7-(5-3(2+6(2^2)))

Anon25 [30]

Answer:

Step-by-step explanation:

7-(5-3(2+6(2^2)))

When a question has multiple signs, the rule of BODMAS is used. That is, Bracket Of Division Multiplication Addition and Subtraction. The question above will therefore be solved in that order.

The first bracket, we have 2^2

That gives 4

Rewriting the question will give

7-(5-3(2+6(4)))

The question in the next bracket will follow

(2+6(4))

In this bracket too, we have the plus sign and the multiplication sign, so the multiplication will first be solved, them addition will follow.

(2+24)

(26)

Rewriting the question again, we have

7-(5-3(26))

And then, we have the last bracket

(5-3(26))

But we have both the Subtraction sign and the Multiplication sign in this bracket also, so the multiplication will first be solved, before the Subtraction.

(5-3(26))

(5-78)

(-73)

And lastly we have

7-(-73)

7+73

5 0

3 years ago

Which two tables represent the same function?

topjm [15]

Answer:

The 1st and the 5th tables represent the same function

Step-by-step explanation:

* Lets explain how to solve the problem

- There are five tables of functions, two of them are equal

- To find the two equal function lets find their equations

- The form of the equation of a line whose endpoints are (x1 , y1) and

(x2 , y2) is $\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

* Lets make the equation of each table

# (x1 , y1) = (4 , 8) and (x2 , y2) = (6 , 7)

∵ x1 = 4 , x2 = 6 and y1 = 8 , y2 = 7

∴ $\frac{y-8}{x-4}=\frac{7-8}{6-4}$

∴ $\frac{y-8}{x-4}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 8) = -1(x - 4) ⇒ simplify

∴ 2y - 16 = -x + 4 ⇒ add x and 16 for two sides

∴ x + 2y = 20 ⇒ (1)

# (x1 , y1) = (4 , 5) and (x2 , y2) = (6 , 4)

∵ x1 = 4 , x2 = 6 and y1 = 5 , y2 = 4

∴ $\frac{y-5}{x-4}=\frac{4-5}{6-4}$

∴ $\frac{y-5}{x-4}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 5) = -1(x - 4) ⇒ simplify

∴ 2y - 10 = -x + 4 ⇒ add x and 10 for two sides

∴ x + 2y = 14 ⇒ (2)

# (x1 , y1) = (2 , 8) and (x2 , y2) = (8 , 5)

∵ x1 = 2 , x2 = 8 and y1 = 8 , y2 = 5

∴ $\frac{y-8}{x-2}=\frac{5-8}{8-2}$

∴ $\frac{y-8}{x-2}=\frac{-3}{6}=====\frac{y-8}{x-2}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 8) = -1(x - 2) ⇒ simplify

∴ 2y - 16 = -x + 2 ⇒ add x and 16 for two sides

∴ x + 2y = 18 ⇒ (3)

# (x1 , y1) = (2 , 10) and (x2 , y2) = (6 , 14)

∵ x1 = 2 , x2 = 6 and y1 = 10 , y2 = 14

∴ $\frac{y-10}{x-2}=\frac{14-10}{6-2}$

∴ $\frac{y-10}{x-2}=\frac{4}{4}======\frac{y-10}{x-2}=1$

- By using cross multiplication

∴ (y - 10) = (x - 2)

∴ y - 10 = x - 2 ⇒ add 2 and subtract y in the two sides

∴ -8 = x - y ⇒ switch the two sides

∴ x - y = -8 ⇒ (4)

# (x1 , y1) = (2 , 9) and (x2 , y2) = (8 , 6)

∵ x1 = 2 , x2 = 8 and y1 = 9 , y2 = 6

∴ $\frac{y-9}{x-2}=\frac{6-9}{8-2}$

∴ $\frac{y-9}{x-2}=\frac{-3}{6}======\frac{y-9}{x-2}=\frac{-1}{2}$

- By using cross multiplication

∴ 2(y - 9) = -1(x - 2) ⇒ simplify

∴ 2y - 18 = -x + 2 ⇒ add x and 18 for two sides

∴ x + 2y = 20 ⇒ (5)

- Equations (1) and (5) are the same

∴ The 1st and the 5th tables represent the same function

3 0

3 years ago

Show how you can use the distributive property to multiply 22x85

Zepler [3.9K]

22 x 85 = (20+2)*85= 20*85+ 2*85 = 1700 + 170 = 1870

4 0

2 years ago