How are these two events related: Ben Franklin became a vegetarian and the writing of Declaration of Independence

At a college campus, random drug tests are carried out to prevent use of prohibited drugs by athletes. Of all the athletes on ca

saw5 [17]

Answer:

a) 0.3064 = 30.64% probability that athlete will test positive for prohibited drug use.

b) 0.2693 = 26.93% probability that this drug user never used the prohibited drug.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

A. If an athlete is selected at random, what is the probability that athlete will test positive for prohibited drug use?

100 - 5 = 95% of 8%

100 - 13 = 87% of 17%

11% of 75%

So

$p = 0.95*0.08 + 0.87*0.17 + 0.11*0.75 = 0.3064$

0.3064 = 30.64% probability that athlete will test positive for prohibited drug use.

B. If an athlete tests positive after a drug test, what is the probability that this drug user never used the prohibited drug?

Conditional Probability

Event A: Tests Positive

Event B: Never used the drug.

0.3064 = 30.64% probability that athlete will test positive for prohibited drug use

This means that $P(A) = 0.3064$

Probability of testing positive while never using the drug.

11% of 75%. So

$P(A \cap B) = 0.11*0.75 = 0.0825$

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0825}{0.3064} = 0.2693$

0.2693 = 26.93% probability that this drug user never used the prohibited drug.

8 0

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What is equivalent to 2/4

padilas [110]

1/2, 4/8, etc. Because they all equal to one half. <span />

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A swimmer swam the 50-meter freestyle in a time of 21 seconds. What was the speed to the nearest tenth of a meter per second?

Mila [183]

The answer would be 2.4 meters per second. To find this, you would divide the 50 meters by 21 seconds. It equals 2.380952, and rounds to 2.4m/s.

5 0

3 years ago

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Rewrite the rational exponent as a radical by extending the properties of integer exponents. 2 to the 7 over 8 power, all over 2

MrRa [10]

Recall the quotient rule of exponents: x^a/x^b = x^(a-b)

So
2^(7/8) / 2^(1/4)
=2^(7/8-1/4)
=2^((7-2)/8)
=2^(5/8)
=8 radical 2^5
=8 radical (32)

5 0

3 years ago

A triangle has an area of 30 cm2. The base and height are scaled by a factor of 3. What is the are of the resulting triangle.

Lera25 [3.4K]

The base and height scaled to some factor, simply means,
they're blown up by that much, or multiplied by that much,

in this case is 3, so.. the area would be 1/2 bh, now,
with 3b and 3h, what would it be?

$\bf \begin{cases}
A=\cfrac{1}{2}bh
\\\\
\textit{now, scaling "b" and "h" by 3}
\\\\
A=\cfrac{1}{2}\cdot 3b\cdot 3h\to \cfrac{1}{2}\cdot 9bh
\\\\
A=\cfrac{9}{2}bh\to 9\left(\cfrac{1}{2}bh \right)\\
--------------\\
9\left(\cfrac{1}{2}bh \right)\textit{ is really 9 times }\cfrac{1}{2}bh
\\\\
\textit{whatever the value of }\cfrac{1}{2}bh \textit{may be}
\end{cases}$

-------------------------------------------------------------------------

$\bf A=\cfrac{1}{2}bh\qquad 
\begin{cases}
b=2\\
h=3
\end{cases}\implies A=\cfrac{1}{2}\cdot 2\cdot 3\to 3
\\\\\\
\textit{now, let us scale "b" and "h" by 3}
\\\\
A=\cfrac{1}{2}\cdot 3b\cdot 3h\qquad 
\begin{cases}
b=2\\
h=3
\end{cases}\implies A=\cfrac{1}{2}\cdot (3\cdot 2)\cdot (3\cdot 3)
\\\\\\
A=\cfrac{1}{2}\cdot 6\cdot 9\to 3\cdot 9\to 27$

3 0

4 years ago