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gizmo_the_mogwai [7]
3 years ago
15

A bag contains 30 cookies: 9 vanilla, 9 chocolate, and 12 oatmeal. What is the probability that a chocolate is randomly selected

?
A) .30
B) .33
C) .40
D) .60
Mathematics
1 answer:
telo118 [61]3 years ago
3 0

There is 9 chocolate cookies, so the probability of choosing chocolate is \frac{9}{30}. We then simplify to get \frac{3}{10}, or 0.3.


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You always need some time to get up after the alarm has rung. You get up from 10 to 20 minutes later, with any time in that inte
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Answer:

a) P(x<5)=0.

b) E(X)=15.

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d) P=0.216.

e) P=1.

Step-by-step explanation:

We have the function:

f(x)=\left \{ {{\frac{1}{10},\, \, \, 10\leq x\leq 20 } \atop {0, \, \, \, \, \, \,  otherwise }} \right.

a)  We calculate  the probability that you need less than 5 minutes to get up:

P(x

Therefore, the probability is P(x<5)=0.

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P(8\leq x\leq 13)=P(10\leqx\leq 13)\\\\P(8\leq x\leq 13)=\int_{10}^{13} f(x)\, dx\\\\P(8\leq x\leq 13)=\int_{10}^{13} \frac{1}{10} \, dx\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot [x]_{10}^{13}\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot (13-10)\\\\P(8\leq x\leq 13)=\frac{3}{10}\\\\P(8\leq x\leq 13)=0.3

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d)  We calculate the probability that you will be late to each of the 9:30am classes next week:

P(x>14)=\int_{14}^{20} f(x)\, dx\\\\P(x>14)=\int_{14}^{20} \frac{1}{10} \, dx\\\\P(x>14)=\frac{1}{10} [x]_{14}^{20}\\\\P(x>14)=\frac{6}{10}\\\\P(x>14)=0.6

You have 9:30am classes three times a week.  So, we get:

P=0.6^3=0.216

Therefore, the probability is P=0.216.

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P(x>9.5)=\int_{10}^{20} f(x)\, dx\\\\P(x>9.5)=\int_{10}^{20} \frac{1}{10} \, dx\\\\P(x>9.5)=\frac{1}{10} [x]_{10}^{20}\\\\P(x>9.5)=1

Therefore, the probability is P=1.

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Step-by-step explanation:

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The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)

<h3>What are logarithms?</h3>

As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms

<h3>How to rewrite the number as a logarithm?</h3>

The number is given as:

x = -3

The base of the logarithm is given as:

Base = 2

To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2

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Number =2^-3

Apply the power rule of indices

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Evaluate the quotient

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Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)

Read more about logarithm at:

brainly.com/question/20785664

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