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fiasKO [112]
3 years ago
12

The figure below shows a shaded circular region inside a larger circle: A shaded circle is shown inside another larger circle. T

he radius of the smaller circle is labeled as r and the radius of the larger circle is labeled as R. On the right side of the image is written r equal to 2 inches and below r equal to 2 inches is written R equal to 5 inches. What is the probability that a point chosen inside the larger circle is not in the shaded region? A)84% B)50% C)42% D)16%
Mathematics
2 answers:
Aleks [24]3 years ago
7 0
Short answer: 84% A
Remark
This sounds like there are only 2 circles that matter. The small one is inside the larger and the small one is shaded.

Step One
Find the area of the small circle.

<em>Givens</em>
r = 2
pi = 3.14

<em>Formula</em>
A = pi*r*r = pi r^2

<em>Sub and Solve</em>
A = 3.14 * 2^2
A = 12.56

Step Two
Find the area of the larger circle
A = pi*r^2
pi = 3.14
r = 5

Area = 3.14 * 5^2
Area = 3.14 * 25
Area = 78.5

Step Three
Find the area of the unshaded region between the larger and smaller circles.

<em>Formula</em>
Area unshaded region = Area of the Large Circle - The area small circle

<em>Givens</em>
Area Large Circle = 78.5
Area Small Circle = 12.56

<em>Solve</em>
Area of unshaded region = 78.5 - 12.56 = 65.94

Find the probability of a point being in the unshaded region.

P(unshaded region) = (Area of Unshaded region / Entire Area)*100%
P(unshaded region) = (65.94 / 78.5) *100%
P(unshaded region) = 84%

Answer: A <<<< 84%


Taya2010 [7]3 years ago
3 0
Area of larger circle:  3.14 x 5^2 = 78.5

Area of small circle: 3.14 x 2^2 = 12.56

Difference of the 2 areas: 78.5 - 12.56 = 65.94

Probability of being in large circle but not small circle: 65.94 / 78.5 = 0.84 = 84%


 The answer is A) 84%

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This diagram is a straightedge and compass construction. A is the center of one circle, and B
Serhud [2]

Answer:

Correct choices are a, b, e

Step-by-step explanation:

As per diagram, the circles are equal.

<u>Since the distance AB is the radius of both circles:</u>

  • AB = AC = BC = BD = AD = r

<u>So the answer choices:</u>

a. AC = BC

  • Correct, both equal to r

b. AC = BD

  • Correct, both equal to r

C. CD = AB

  • Incorrect. Half of CD is the leg of 30-60-90 triangle and is equal to  r√3/2, so CD = AB√3

d. ABCD is a square

  • Incorrect. ACBD is rhombus

e. ABD is an equilateral triangle

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3 years ago
The letters in the word STATISTICS are printed on identical index cards with one letter per card. The ten cards are
Alex17521 [72]

Answer:

a.

Outcome ---------- Probability

S -------------------------- 0.3

T -------------------------- 0.3

A -------------------------- 0.1

I --------------------------- 0.2

S -------------------------- 0.1

b.

P(V) = 2/10

P(F) = 2/10

c.

Events V and F are not mutually exclusive

Step-by-step explanation:

Given

Text: STATISTICS

Solving (a): Outcomes and Probabilities

The text is made of the following makeup.

S = 3

T = 3

A = 1

I = 2

C = 1

Total = 10

The probability of each outcome is calculated by dividing the occurrence of each alphabet by the total number of alphabets

So:

S = 3/10 = 0.3

T = 3/10 = 0.3

A = 1/10 = 0.1

I = 2/10 = 0.2

C = 1/10 = 0.1

In tabular form, we have:

Outcome ---------- Probability

S -------------------------- 0.3

T -------------------------- 0.3

A -------------------------- 0.1

I --------------------------- 0.2

S -------------------------- 0.1

Solving (b)

V = Vowels

F = A - M

Calculating P(V)

P(V) = Number of vowels divided by total

The vowels are A and I.

So, number of vowels is 2

P(V) = 2/10

Calculating P(F)

P(F) = Number of alphabets from A to M divided by total

Alphabets from A and M are A and I

So, number of alphabets in this category is 2

So:

P(F) = 2/10

Solving (c):

Events V and F are not mutually exclusive because both can occur at the same time.

i.e.

An event can be a vowel and still be between A and M

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Answer:

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