Simplify the expression. 3m - 3m 3m

In a math class, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. What is the probability that in a randomly

SashulF [63]

Answer:

$P(2FG|3FB) = \frac{605}{7917}$

Step-by-step explanation:

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.To calculate combinations the below formula is used:

$nCr = \frac{n!}{r!(n-r)!}$

where $n$ represents the total number of items and $r$ represent the number of items being chosen at a time. The '!' represents factorial function which is the product of all integers equal to and less than the given integer. This can be calculated manually using the formula or by using the nCr function on a scientific calculator.

Thus, the number of ways to select 2 freshmen girls (2FG) and 3 freshmen boys (3FB) can be determined. The number of ways to select 5 students (5S) can be determined in the same way.

$2FG = 12C2 = \frac{12!}{2!(12-2)!} = \frac{12!}{2!(10)!} = 66$

$3FB = 11C3 = \frac{11!}{3!(11-3)!} = \frac{11!}{3!(8)!} = 165$

$5S = 30C5 = \frac{30!}{5!(30-5)!} = \frac{30!}{5!(25)!} = 142506$

The probability of selecting 2 freshmen girls (2FG) and 3 freshmen boys (3FB) when selecting 5 students out of 30 is given as below:

$P(2FG|3FB) = \frac{2FG*3FB}{5S} = \frac{66*165}{142506} = \frac{605}{7917}$

4 0

3 years ago

1.) Distance formula Find the distance between the pair of points.

PilotLPTM [1.2K]

Answer:

5

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (-1, 0) and (x₂, y₂ ) = (3, - 3) ← coordinates of endpoints

d = $\sqrt{(3+1)^2+(-3-0)^2}$

= $\sqrt{4^2+(-3)^2}$

= $\sqrt{16 +9}$ = $\sqrt{25}$ = 5

8 0

2 years ago

5 ft is ____ % of 37 1 2 ft; 37 1 2 ft is ____ % of 5 ft

hichkok12 [17]

Answer:

The answer is:

5 ft is 13.33% of 37 1/2 ft; 37 1/2 ft is 750% of 5 ft.

Step-by-step explanation:

Given:

5 ft is ____ % of 37 1 2 ft.

Now, to find the __ :

Let __ be $x.$

So, 5 ft is $x\%$ of 37 1/2

$5=x\% of 37\frac{1}{2}$

⇒ $5=\frac{x}{100} \times \frac{75}{2}$

⇒ $5=\frac{75x}{200}$

Multiplying both sides by 200 we get:

⇒ $1000=75x$

Dividing both sides by 75 we get:

⇒ $13.33=x$

⇒ $x=13.33\%.$

Now, 37 1/2 ft is $x$ % of 5 ft.

$\frac{75}{2} =x\%\ of\ 5$

$\frac{75}{2}=\frac{x}{100}\times 5$

$\frac{75}{2} =\frac{5x}{100}$

Multiplying both sides by 100 we get:

$\frac{7500}{2} =5x$

Dividing both sides by 5 we get:

$750=x$

$x=750\%$

Therefore, the answer is 5 ft is 13.33% of 37 1/2 ft; 37 1/2 ft is 750% of 5 ft.

8 0

2 years ago

What’s the answer to -6( 7/6) + 2( 1/3)

Alexxandr [17]

Answer:

-6( 7/6) + 2( 1/3) = - (19)/(3) or 2/3 depending on your answers.

Step-by-step explanation:

5 0

3 years ago

How many 1/4 ft cubed make up the volume of this prism ?

DIA [1.3K]

Answer:

Each cube with side lengths of 1/4 has a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes.

Step-by-step explanation:

6 0

3 years ago

Simplify the expression. 3m - 3m 3m - 3m =