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g100num [7]
3 years ago
9

If an ant runs randomly through an enclosed

Mathematics
1 answer:
liraira [26]3 years ago
4 0
The area of a circle is π (radius²)

The area of the outer (2-ft) circle is π (2²) = 4 π square feet.

The area of the inner (1-ft) circle is π (1²) = 1 π square feet.

The inner circle covers 1/4 of the area of the outer circle.

So if the ant wanders around totally aimlessly and randomly, and there's no way to
know where he came from, where he is now, or where he's going next, and there's
an equal chance of him being <em><u>anywhere in the big circle</u></em> at any time, then there's a
<u>25% chance</u> of him being inside the small circle at any time, because 1/4 of the
total area is in there.

That's choice c).

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A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a s
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Answer:

88.51 is the minimum score needed to receive a grade of A.          

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 73

Standard Deviation, σ = 11

We are given that the distribution of exam grades is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

We have to find the value of x such that the probability is 0.0793.

P( X \geq x) = P( z \geq \displaystyle\frac{x - 73}{11})=0.0793  

= 1 -P( z \leq \displaystyle\frac{x - 73}{11})=0.0793  

=P( z \leq \displaystyle\frac{x - 73}{11})=0.9207  

Calculation the value from standard normal z table, we have,  

P(z \leq 1.410) = 0.9207

\displaystyle\frac{x - 73}{11} = 1.410\\x =88.51  

Hence, 88.51 is the minimum score needed to receive a grade of A.

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Write an counter example for the statement: all square roots are rational numbers
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Step-by-step explanation:

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Answer:

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