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3 years ago

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads?

Mathematics

2 answers:

CaHeK987 [17]3 years ago

7 0

A is the correct answer.

Inessa05 [86]3 years ago

5 0

Answer: First Option is correct i.e. $^9C_3(0.5)^3(0.5)^6$

Step-by-step explanation:

Since we have given that

Number of times Aron flips a penny = 9 times

Number of heads getting by him exactly = 3

Probability of getting a head (success) is given by

$\frac{1}{2}$

Probability of getting a tail ( failure ) is given by

$\frac{1}{2}$

So, We need to find the probability of getting exactly 3 heads:

$P(x=3)=^9C_3(\frac{1}{2})^3\times \frac{1}{2}^6\\\\P(x=3)=^9C_3(0.5)^3\times (0.5)^6\\\\P(x=3)=\frac{9!}{3!\tiems 6!}\times (0.5)^9\\\\P(x=3)=0.16$

Hence, First Option is correct i.e. $^9C_3(0.5)^3(0.5)^6$

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Find the radian measure of the central angle of a circle of radius r = 60 inches that intercepts an arc of length s = 70 inche

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Step-by-step explanation:

s = rθ

70 in = (60 in) θ

θ = 7/6 radians

θ ≈ 1.167 radians

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3 years ago

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Answer:

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3 years ago

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Maksim231197 [3]

Answer:

Step-by-step explanation:

Hello There!

The mean is pretty much the average

So to find the mean we first add up all of the values

2+3+6+6+7+8+8=40

Then we count the amount of points

There are 8 points

our final step is to divide the total value by the total number of points

40/8=5

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3 years ago

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given examples of relations that have the following properties 1) relexive in some set A and symmetric but not transitive 2) equ

rodikova [14]

Answer: 1) R = {(a, a), (а,b), (b, a), (b, b), (с, с), (b, с), (с, b)}.

It is clearly not transitive since (a, b) ∈ R and (b, c) ∈ R whilst (a, c) ¢ R. On the other hand, it is reflexive since (x, x) ∈ R for all cases of x: x = a, x = b, and x = c. Likewise, it is symmetric since (а, b) ∈ R and (b, а) ∈ R and (b, с) ∈ R and (c, b) ∈ R.

2) Let S=Z and define R = {(x,y) |x and y have the same parity}

i.e., x and y are either both even or both odd.

The parity relation is an equivalence relation.

a. For any x ∈ Z, x has the same parity as itself, so (x,x) ∈ R.

b. If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R.

c. If (x.y) ∈ R, and (y,z) ∈ R, then x and z have the same parity as y, so they have the same parity as each other (if y is odd, both x and z are odd; if y is even, both x and z are even), thus (x,z)∈ R.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial but not transitive, so the relation provided in (1) satisfies this condition.

Step-by-step explanation:

1) By definition,

a) R, a relation in a set X, is reflexive if and only if ∀x∈X, xRx ---> xRx.

That is, x works at the same place of x.

b) R is symmetric if and only if ∀x,y ∈ X, xRy ---> yRx

That is if x works at the same place y, then y works at the same place for x.

c) R is transitive if and only if ∀x,y,z ∈ X, xRy∧yRz ---> xRz

That is, if x works at the same place for y and y works at the same place for z, then x works at the same place for z.

2) An equivalence relation on a set S, is a relation on S which is reflexive, symmetric and transitive.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial and not transitive.

QED!

6 0

3 years ago

Ruben bought 6 new books for his collection. This increased his collection by 12%. How many books did he have before his purchas

Norma-Jean [14]

Answer: The required number of books that Ruben had before purchases is 50.

Step-by-step explanation: Given that Ruben bought 6 new books for his collection that increased his collection by 12%.

We are to find the number of books that Ruben had before purchases.

Let x denotes the number of books that Ruben had before purchases.

Then, according to the given information, we have

$x+6=x+12\%\times x\\\\\\\Rightarrow 6=\dfrac{12}{100}x\\\\\\\Rightarrow 6=\dfrac{3x}{25}\\\\\\\Rightarrow 3x=150\\\\\Rightarrow x=\dfrac{150}{3}\\\\\Rightarrow x=50.$

Thus, the required number of books that Ruben had before purchases is 50.

4 0

3 years ago