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frez [133]
3 years ago
12

Simulate the rolling of two dice 10,000 times. (b) Identify which rolls of the dice are in the event A, the dice add up to a per

fect square (4 or 9). Determine what proportion of the 10,000 rolls are in A. (c) Identify which rolls of the dice are in the event B, the dice add up to an even number. Determine what proportion of the 10,000 rolls are in B. (d) Find out which rolls are in A ∩ B. Find the proportion that are in A ∩ B. How does that compare to the proportion in A multiplied by the proportion that are in B?
Mathematics
1 answer:
dexar [7]3 years ago
4 0

Answer:

Answer explained below

Step-by-step explanation:

(a)

Simulate the rolling of two dice 10,000 times D1 and D2 are the 10,000 results of roll of dice 1 and dice 2.

D1 = sample(c(1:6), 10000, replace = TRUE)

D2 = sample(c(1:6), 10000, replace = TRUE)

Sum = D1 + D2

(b)

The event A, the dice add up to a perfect square (4 or 9).

A = Sum[Sum == 4 | Sum ==9]

Proportion of A, P(A) = 0.189

length(A) / length(Sum)

(c)

The event B, the dice add up to an even number.

B = Sum[Sum %% 2 == 0]

Proportion of B, P(B) = 0.5049

length(B) / length(Sum)

(d)

The  rolls are in A ∩ B (common to both A and B)

> intersect(A,B)

[1] 4

The proportion that are in A ∩ B is 0.0792

length(Sum[Sum == 4]) / length(Sum)

P(A) * P(B) = 0.189 * 0.5049 = 0.0954

The proportion in A multiplied by the proportion that are in B is not equal to P(A ∩ B)

(e)

Of the rolls in which B occurs, the proportion of those rolls are also in A is 0.4190476

length(Sum[Sum == 4]) / length(A)

This proportion is greater than the P(A) calculated in part (b).

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The circumference of a circle is 9π m. What is the area of the circle? ASAP!
liubo4ka [24]

Answer:

20.25 m²

Step-by-step explanation:

the area (A) and circumference (C) of a circle are calculated using the formulae

C = 2πr and A = πr² ( where r is the radius )

calculate the radius using the formula for circumference

2πr = 9π ( divide both sides by 2π )

r = \frac{9\pi }{2\pi } = \frac{9}{2} = 4.5, hence

A = π × 4.5² = 20.25π m²


4 0
3 years ago
Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April
Svetlanka [38]

Answer:

  d.  May

Step-by-step explanation:

Working through the chain, we have ...

  Feb = 1.10×Jan

  Mar = 0.85×Feb = 0.935×Jan

  Apr = 1.20×Mar = 1.122×Jan

  May = 0.90×Apr = 1.0098×Jan

  Jun = 1.05×May = 1.06029×Jan

The multiplier that is closest to 1 is 1.0098, so May has sales closest to January.

_____

The percentage increase or decrease can be converted to a multiplier by adding it to 1. If p% is the percentage change, then adding it to an original value looks like ...

  original + p% × original = original × (1 +p%) . . . . . . . distributive property

And p% translates to a decimal number by replacing % with /100 or ×0.01.

  10% increase:   original × (1 + 10/100) = original × 1.10

  15% decrease:   original × (1 - 15/100) = original × 0.85

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Find the value of x.
Paladinen [302]

Answer:

11

Step-by-step explanation:

4 0
2 years ago
12.) What is the value of x in the figure?
Maksim231197 [3]
What figure are we looking for?
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3 years ago
Given rs || qp, what is the value of x?
myrzilka [38]

In the given figure,

Angle 108° + 12x = 180°

because they for pair of co- interior angles which are supplementary.

so,

  • 12x + 108\degree = 180\degree

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  • x =  \dfrac{72\degree}{12}

  • x = 6\degree

hence , value of x = 6°

5 0
2 years ago
Read 2 more answers
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