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2 years ago

9

Five different awards are to be given to three students. Each student will receive at least one award. In how many different way

s can the awards be distributed?

1 answer:

AleksandrR [38]2 years ago

5 0

Answer:

It is 150.

Step-by-step explanation:

This clarifies it https://artofproblemsolving.com/wiki/index.php/2020_AMC_8_Problems/Problem_23

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Suppose we have an unfair coin that its head is twice as likely to occur as its tail. a)If the coin is flipped 3 times, what is

Alenkinab [10]

Answer: a) 0.2222, b) 0.3292, c) 0.1111

Step-by-step explanation:

Since we have given that

Let the probability of getting head be p.

Since, its head is twice as likely to occur as its tail.

$p+\dfrac{p}{2}=1\\\\\dfrac{3p}{2}=1\\\\p=\dfrac{2}{3}$

a)If the coin is flipped 3 times, what is the probability of getting exactly 1 head?

So, here, n = 3

$p=\dfrac{2}{3}$

$q=\dfrac{1}{3}$

Now,

$P(X=1)=^3C_1(\dfrac{2}{3})^1(\dfrac{1}{3})^2=0.2222$

b)If the coin is flipped 5 times, what is the probability of getting exactly 2 tails?

2 tails means 3 heads.

So, it becomes,

$P(X=3)=^5C_3(\dfrac{2}{3})^3(\dfrac{1}{3})^2=0.3292$

c)If the coin is flipped 4 times, what is the probability of getting at least 3 tails?

$P(X\leq 1)=\sum _{x=0}^1^4C_x(\dfrac{2}{3}^x(\dfrac{1}{3})^{4-x}=0.1111$

Hence, a) 0.2222, b) 0.3292, c) 0.1111

8 0

2 years ago

anastassius [24]

Answer:

Whats the question?

Step-by-step explanation:

5 0

3 years ago

Substitute the values of x and y into the expression -3x 2 + 2y 2 + 5xy - 2y + 5x 2 - 3y 2. Match that value to one of the numbe

seropon [69]

X = 2, y = -1 Answer = -1
x = 0, y = 2.5 Answer = -11.25
x = -1, y = -3 Answer = 14
x = 0.5, y = -0.1 (one tenths) Answer = 0.44
x = 0.75 (three quarters), y = 0.4 (two fifths) Answer = 1.665
x = 1.41 (sqareroot of 2), y = 1.41 (sqareroot of 2) Answer = 9.17

I hope this helps!

5 0

2 years ago

7-4i divided by <br> 2+i <br> how to solve it?

cupoosta [38]

$\cfrac{7-4i}{2+i}\\\\ = \cfrac{(7-4i)(2-i)}{(2+i)(2-i)} \\\\ =\cfrac{14-7i-8i-4}{4+1} \\\\= \cfrac{10-15i}{5} \\\\= \cfrac{5(2-3i)}{5} \\\\=2-3i$

8 0

3 years ago

Select the correct answer from each drop-down menu. y = x2 + 2x − 1 y − 3x = 5 The pair of points representing the solution set

katen-ka-za [31]

ANSWER

(-2,-1)

(3,14)

EXPLANATION

The given system is

$y = {x}^{2} + 2x - 1$

$y - 3x = 5$

or

$y = 3x + 5$

Equate both of them:

${x}^{2} + 2x - 1 = 3x + 5$

This implies that,

${x}^{2} - x - 6 = 0$

$(x - 3)(x + 2) = 0$

x=-2 or x=3

When x=-2, y=y=3(-2)+5=-1

(-2,-1) is a solution.

When x=3 , y=3(3)+5=14

(3,14) is also a solution.

7 0

3 years ago