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3 years ago

What is the solution to the system of equations?

Mathematics

2 answers:

mixer [17]3 years ago

8 0

The answer is (1,11). You can solve for x first and plugged it in to find y.

Sveta_85 [38]3 years ago

7 0

Answer:

(1, 11)

Step-by-step explanation:

If you plug both of these values in for the x and y in both equations you will get a true statement.

10(1) + 3(11) = 43

10 + 33 = 43

-9(1) - (11) = -20

-9 - 11 = -20

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3 years ago

Given P(A and B) 0.20, P(A) 0.49, and P(B) = 0.41 are events A and B independent or dependent? 1) Dependent 2) Independent

blsea [12.9K]

Answer: The correct option is (1) Dependent.

Step-by-step explanation: For two events, we are given the following values of the probabilities :

P(A ∩ B) = 0.20, P(A) = 0.49 and P(B) = 0.41.

We are to check whether the events A and B are independent or dependent.

We know that

the two events C and D are said to be independent if the probabilities of their intersection is equal to the product of their probabilities.

That is, P(C ∩ D) = P(C) × P(D).

For the given two events A and B, we have

$P(A)\times P(B)=0.49\times0.41=0.2009\neq P(A\cap B)=0.20\\\\\Rightarrow P(A\cap B)\neq P(A)\times P(B).$

Therefore, the probabilities of the intersection of two events A and B is NOT equal to the product of the probabilities of the two events.

Thus, the events A and B are NOT independent. They are dependent events.

Option (1) is CORRECT.

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4 years ago

It is known that 2.2< sq root 5 <2.3. Find all possible values of the expression: a sq root 5 +2 3- sq root 5 It is known

NISA [10]

Answer:

4.2 < sq. 5< 4.3

Step-by-step explanation:

since square root of 5 was +2 you just add +2 to both sides and you will get your answer, however it is different with different operations.

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3 years ago

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