Ask question

Ask question

All categories

2 years ago

5

Mr. Pratt has 26 students in his math class. He has three prizes to give away: a pencil, an eraser, and a homework pass. How man

y ways can he choose three students to win these awards?

1 answer:

Nikolay [14]2 years ago

3 0

Answer:

Mr.Pratt can select three students to win these awards in 2,600 ways.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!(n-k)!}$

Mr. Pratt has three prizes to give away.

The total number of students in his class is, <em>n</em> = 26.

He has <em>k</em> = 3 prizes, namely a pencil, an eraser, and a homework pass.

Compute the number of combinations of three students Mr. Pratt can select from 26 students to give away the prizes as follows:

${n\choose k}=\frac{n!}{k!(n-k)!}$

$=\frac{26!}{3!(26-3)!}$

$=\frac{26!}{3!\times 23!}$

$=\frac{26\times25\times24\times23!}{3!\times23!}$

$=2600$

Thus, Mr.Pratt can select three students to win these awards in 2,600 ways.

You might be interested in

Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three number

Dmitry [639]

Answer:

Part a) $2,50,18$

Part b) When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For $x=2$

$\sqrt{2}*\sqrt{2}=\sqrt{4}=2$ -----> the product is an integer

so

The number $x=2$ could be Jenny favorite positive integer

2) For $x=50$

$\sqrt{50}*\sqrt{2}=\sqrt{100}=10$ -----> the product is an integer

so

The number $x=50$ could be Jenny favorite positive integer

3) For $x=18$

$\sqrt{18}*\sqrt{2}=\sqrt{36}=6$ -----> the product is an integer

so

The number $x=18$ could be Jenny favorite positive integer

Part B)

1) For $x=2$

$\sqrt{2}/\sqrt{2}=\sqrt{1}=1$ -----> the result is an integer

2) For $x=50$

$\sqrt{50}/\sqrt{2}=\sqrt{25}=5$ -----> the result is an integer

3) For $x=18$

$\sqrt{18}/\sqrt{2}=\sqrt{9}=3$ -----> the result is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer

4 0

2 years ago

A pail contained 3.68L of water more than a bottle. After Bill poured away 1.2L of water from the pail, the pail contained 3 tim

julsineya [31]

For the sake of simplicity, let us say that the bottle contains x liters of water.

The pail originally contained x+3.68 L of water
After pouring out 1.2L, the pail contains x+(3.68-1.2)L or x+2.48 L
<span>
(a) How much more water did the pail contain than the bottle in the end?
Since the bottle contains x L of water, the pail (containing x+2.48 L of water) contains (x+2.48) - x more liters of water than the bottle or "the pail contained 2.48 L of water more than the bottle"

</span><span>(b) How much water did the bottle contain?
</span>We are told that after pouring the 1.2L of water out, the pail contained 3 times as much water as the pail. Therefore, 3x = x+2.48. Subtracting x from both sides gives us 2x = 2.48. Dividing both sides by 2 gives us x = 1.24L

7 0

2 years ago

Write an equation for “a number decreased by -4 is equal to 15”. Then solve the equation.

Alexxx [7]

Answer:

c

Step-by-step explanation:

6 0

2 years ago

Sarah wants to print copies of her artwork. At the local print shop, it costs her $1 to make 5 copies and $5 to make 25 copies.

Ierofanga [76]

Answer:

i wanna say B

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Determine whether the lines are parallel, intersect, or coincide. x-5y=0, y+1=1/5(x+5)

MAXImum [283]

<u>Answer-</u>

<em>The lines are two </em><em>coinciding lines</em><em> or the </em><em>same lines</em><em>.</em>

<u>Solution-</u>

The given line equations are

the first one,

$\Rightarrow x-5y=0$

the second one,

$\Rightarrow y+1=\dfrac{1}{5}(x+5)\\\\\Rightarrow 5y+5=x+5\\\\\Rightarrow 5y=x\\\\\Rightarrow x-5y=0$

As we know two line equations $A_1x+B_1y+C_1=0$ and $A_2x+B_2y+C_2=0$ will be,

Parallel if, $\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}$
Coincide if, $\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}=\dfrac{C_1}{C_2}$
Intersect if, $\dfrac{A_1}{A_2}\neq \dfrac{B_1}{B_2}$

As here,

$\Rightarrow \dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}=\dfrac{C_1}{C_2}$

$\Rightarrow \dfrac{1}{1}=\dfrac{-5}{-5}$

(C₁ and C₂ aren't considered as they are 0)

Therefore, the lines are two coinciding lines or the same lines.

4 0

2 years ago