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Annette [7]
3 years ago
11

John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere o

n the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%

Mathematics
1 answer:
yulyashka [42]3 years ago
3 0

Answer:

Probability = 51\%

Step-by-step explanation:

Given

Radius of inner circle = 5ft

Radius of outer circle = 7ft

Required

Determine the probability that the thumbtack will be placed on the inner circle

We start by calculating the area of both circles;

Inner Circle

Area = \pi r^2

Area = 3.14 * 5^2

Area = 3.14 * 25

Area = 78.5

Outer Circle

Area = \pi R^2

Area = 3.14 * 7^2

Area = 3.14 * 49

Area = 153.86

At this point, the probability can be calculated;

The probability = Area of Inner Circle / Area of Outer Circle

Probability = \frac{78.5}{153.86}

Probability = 0.51020408163

Convert to percentage

Probability = 0.51020408163 * 100\%

Probability = 51.020408163\%

Approximate

Probability = 51\%

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jasenka [17]

Answer: the length and width are

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Step-by-step explanation:

The rug has an area represented by the expression

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The factors in the factored expressions represent the length and width of the rug.

Dividing the the equation by 4, it becomes

x² + 16x + 64 = 0

We would find two numbers such that their sum or difference is 16x and their product is 64x^2.

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The factors are

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7 0
3 years ago
On the basis of data collected during an experiment, a biologist found that the growth of a fruit fly population (Drosophila) wi
Ket [755]

Answer:

(a). 15

(b). 78

Step-by-step explanation:

Growth of the population of a fruit fly is modeled by

N(t) = \frac{600}{1+39e^{-0.16t} }

where t = number of days from the beginning of the experiment.

(a). For t = 0 [Initial population]

N(0) = \frac{600}{1+39e^{-0.16\times 0} }

       = \frac{600}{1+39}

       = \frac{600}{40}

       = 15

Initial population of the fruit flies were 15.

(b).Population of the fruit fly colony on 11th day.

N(11) = \frac{600}{1+39e^{-0.16\times 11} }

       = \frac{600}{1+39e^{-1.76} }

       = \frac{600}{1+39\times 0.172 }

       = \frac{600}{1+6.71}

       = \frac{600}{7.71}

       = 77.82

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3 years ago
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Answer:

x=36

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Step-by-step explanation:

Plug in 0 for x to find the y-intercept

0 + 4y = 36

4y = 36

y = 9

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Plug in 0 for y to find the x-intercept

x + 4(0) = 36

x = 36

x-intercept (36, 0)

4 0
3 years ago
There are often fees associated with investments that reduce the return you actually have. True False
cestrela7 [59]
True, there are fees associated with investments. These fees are collected by institutions where the investments are placed. Fees include transaction fees, investment management fees, front end and back end fees among others. These fees are placed in order for the services of the financial institutions to continue and these are also mandated and regulated by the government. 
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tamaranim1 [39]

Answer:

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7 0
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