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2 years ago

Is substitutions the best method to use when one variable is already known

2 answers:

8 0

There’s two ways to substitute, but i think you mean if you know x but don’t know y. if that is true, then yes use substitution

Mama L [17]2 years ago

7 0

Substitution Method is used for solving equations in 2 Variables, where you find the value of one variable in terms of the other and then substitute that value into any one of the equations. It can also be used when one Variable is known to you and you have to find the other.

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Alex and bob are playing 5 chess games. Alex is 3 times more likely to win than bob. What is the probability that both of them w

givi [52]

Answer:

12.2%

Step-by-step explanation:

Lets firstly find out the probabilities for Alex and Bob. We know that the prb that Alex wins is 3 times the prob for Bob, so:

P(A) = 3P(B)

And, as these values are probabilities they must sum 1:

P(A) + P(B) = 1

Replacing the first equation in the second:

3P(B) + P(B) = 1

4P(B) = 1

Dividing both sided by 4:

4P(B)/4 = 1/4

P(B) =1/4

So, the probability for Bob is 1/4. Then the probability for Alex is 3*1/4 = 3/4

Now we have to find the probability that both win at least two games. Lets think about the possible combination of cases. As they play 5 games and both have to win at least to there is a remaining game that cane variate, this is, can be won by Alex or Bob. So, we can have:

AABBB

AABBA

Where A is "Alex win" and B is "Bob win" (here we do not pay attention to the order).

Thus, we have to find the probability that Alex wins 3 games and Bob 2 games, and the probability that Alex wins 2 games and Bob 3 games. As the games are independent, i.e., the result of one games does not affect the followings we can just multiply the probabilities:

P(3A and 2B) = (3/4)*(3/4)*(3/4)*(1/4)*(1/4) = 0.42*0.06 = 0.026

P(2A and 3B) = (3/4)*(3/4)*(1/4)*(1/4)*(1/4) = 0.56*0.016 = 0.096

So,

P (at least 2) = P(3A and 2B) + P(2A and 3B) = 0.026 + 0.096 = 0.122 = 12.2%

7 0

3 years ago

1-4

Oksi-84 [34.3K]

Answer:

282 Hours after 6 weeks

Step-by-step explanation:

Multiply the 6 weeks and the 48 hour a week adverage and theres your answer!

3 0

2 years ago

What is 6.16×10*6 in standard form?

Paladinen [302]

Answer:

6.16×10*6

Step

6=2+_AT ERATLION

Question

What is in standard form?-by-step explanation:

8 0

2 years ago

Suppose you cool a pot of soup in a 20°C room. Right when you take the soup off the stove, you measure its temperature to be 180

dezoksy [38]

Answer:

28.3 minutes
53.6°C

Step-by-step explanation:

The temperature of the soup is described by Newton's Law of Cooling, which says the rate of change of temperature is proportional to the difference between the temperatures of the soup and the room. The solution to this differential equation is the exponential function ...

f(t) = a +b·c^(t/τ)

where a is the room temperature, b is the initial difference in temperature, and c is the fractional change in the difference in temperature over time period τ.

<h3>application</h3>

For the given scenario, we find ...

a = room temperature = 20 . . . . degrees C

b = (180 -20) = 160 . . . . degrees C

c = (100 -20)/(180 -20) = 80/160 = 1/2 . . . . in τ = 20 minutes

So, the formula for the temperature of the soup is ...

f(t) = 20 +160(1/2)^(t/20) . . . . . . . degrees C after t minutes

Solving for t when f(t) = 80, we find ...

80 = 20 +160(1/2)^(t/20)

3/8 = (1/2)^(t/20) . . . . . subtract 20, divide by 160

20×log(3/8)/log(1/2) = t ≈ 28.3 . . . take logarithms, divide by coefficient of t

It will take about 28.3 minutes to cool to 80°C.

<h3>temp at 45 minutes</h3>

The temperature after 45 minutes is ...

f(45) = 20 +160(1/2)^(45/20)

f(45) ≈ 53.6 . . . . degrees C

After 45 minutes the temperature of the soup will be about 53.6°C.

3 0

1 year ago

Read 2 more answers

1 3 fourth +1half+1 fourth+ 1 half

Leona [35]

The answer is 2
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6 0

3 years ago