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4 years ago

Which situation can be represented by the inequality 4x − 25 < 125?

1 answer:

8 0

First add 25 to both sides of the inequality.
You get 4x < 150
Now divide both sides by 4.
You get x < 37.5
So x can be anything less than 37.5, such as 36, 35 or 34.

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All athletes at the Olympic Games (OG) are tested for performance-enhancing steroid drug use. The basic Anabolic Steroid Test (A

Semenov [28]

Answer:

a ) the probability of using steroids and having a negative test is 0.5%

b) The probability of testing positive is 6.4%

c) The probability of not using steroids, given that the test is negative is 99.47%

d) No, they are not statistically indepent.

e) The probability that the athlete will either use steroids or test positive is 6.9%

Step-by-step explanation:

Let A be the event that the test result is positive and B the event that the athlete uses Steroids. We are given the following

$P(A|B) = 90%, P(A|B^c) = 2%, P(B) = 5%$

From which we deduce that

$P(A^c|B) = 10%, P(B^c) = 95%$

a) We are asked for the probability $P(A^c\cap B)$ . REcall the conditional probability formula that, given two events C,D the conditional probability $P(C|D) = \frac{P(C\cap D)}{P(D)}$ . Then we have that

$P(A^c\cap B) = P(A^c|B)P(B) = 10\% \cdot 5\%=0.5\%$ .

b) We are asked for the probability P(A). We can use the fact that given two mutually exclusive events(that is, whose intersection is empty) A,B the probability P(C) of an event is given by $P(C) = P(C|A)P(A)+P(C|B)P(B)$ . Then

$P(A) = P(A|B)P(B)+P(A|B^c)P(B^c) = 90\%\cdot5\% + 2\% \cdot 95% = 6.4\%$

c) We are asked for the probability P(B^c|A^c). Recall that $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$ . Then

$P(B^c|A^c) = \frac{P(A^c|B^c)P(B^c)}{P(A^c)}= \frac{P(A^c|B^c)P(B^c)}{1-P(A)}= \frac{(1-P(A|B^c))P(B^c)}{1-P(A)}=\frac{98\%\cdot 95\%}{1-6.4\%}= 99.47\%$

d) We say that two events A,B are statistically indepent if P(A|B) = P(A). Note that from point B the probability of testing negative is 1- 6.4% = 93.6%. Since 93.6% is different from 99.47% this means that testing positive and using steroids are not statistically independent.

e) We are asked for the probability $P(A\cup B)$ . We use the following

$P(A\cupB) = P(A)+P(B)-P(A\cap B) = P(A) +P(B)-P(A|B)P(B) = 6.4\%+5\%-90\%\cdot 5\%=6.9\%$

4 0

4 years ago

Lee Jenkins worked the following hours as a manager for a local Pizza Hut: 67, 9,6 and 8 How many total hours did Lee

PSYCHO15rus [73]

Answer:

90 hours

Step-by-step explanation:

67 + 6 + 9 + 8 = 90 hours

8 0

3 years ago

Which polynomial is prime

Vikentia [17]

We need more information. You don't give us enough information....? Provide an image please. Or at least name the polynomials...

7 0

4 years ago

Help please like please

lara31 [8.8K]

Answer:

A and D’s area is 50

B and F’s area is 120

C and E’s area is 60

Adding all of the areas together will give you a surface area of 460

7 0

3 years ago

-Write 0.875 as a reduced fraction

ValentinkaMS [17]

<span>We can reduce this fraction, 875 / 1000 to lowest
terms by dividing both the numerator and denominator by 125 ;
</span><span>Why divide by 125? 125 Greatest Common Factor (GCF) of the numbers 875 and 1000.
So, this fraction reduced to lowest terms is 7 / 8 ;
In the same way, 35 / 100 is reduced to lowest terms as 7 / 20 ;</span>

7 0

3 years ago

Read 2 more answers