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Eva8 [605]
3 years ago
10

A bag contains n blue and m red marbles. You randomly pick a marble from the bag, write down its color, and then put the marble

back in the bag. This process is repeated until you pick either two consecutive blue or two consecutive red marbles. Given that the process stopped because you picked two consecutive blue marbles, what is the probability that the first marbled you picked was blue
Mathematics
1 answer:
Oksana_A [137]3 years ago
3 0

Answer:

(mn+n²)/(m+n)

Step-by-step explanation:

probability of blue marble= n/(n+m)

probability of red marble= m/(n+m)

probability that process stops = Probability of both blue + probability of both red=  n/(n+m) × n/(n+m) + m/(n+m)×m/(n+m)

                        = (n²+m²)/(n+m)²

P(1st marbel is blue)= P(blue and red) + P(blue and blue)

                                  = mn/(n+m) + n²/(n+m)

                                   = (mn+n²)/(m+n)

P(1st marble is blue | process stops)= ( (mn+n²)/(m+n)× (n²+m²)/(n+m)²)/ ((n²+m²)/(n+m)²)

= (mn+n²)/(m+n)

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One gallon is equal to about 3.785 liters. What is this amount rounded to the nearest tenth? To the nearest hundredth? Show your
Leokris [45]

Answer:

3.8 ; 3.79 ; 3

Step-by-step explanation:

Given that:

1 gallon is equal to about 3.785 litres

3.785 to the nearest tenth :

Tenth digit = 7 ; round up 8 to 1 and add to 7

Hence,

3.785 = 3.8 (nearest tenth)

3.785 to the nearest hundredth :

Hundredth digit = 8 ; round up next digit 5 to 1 and add to 8

3.785 = 3.79 ( nearest hundredth)

What is the greatest number of whole liters of water you could pour into a one-gallon container without it overflowing?

The greatest Number of whole liters of water that could be poured into a 1 gallon container without it overflowing is 3 liters because, rounding up 3.785 to the nearest integer of 4 means we will exceed the maximum litres by about 0.215 gallons and hence, cause the container to overflow.

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2 years ago
How many different triangles can you make from 6 cm,6 cm, and 4 cm?
lubasha [3.4K]

Answer:

Step-by-step explanation:

The sides of a triangle are 6cm, 6cm, and 4cm.

According to triangle inequality, the sum of the length of any two sides of a triangle must be greater than the length of the third side.

So,

6+6=12>4

6+4=10>6

4+6=10>6

Therefore, the theorem of triangle inequality is satisfied for all three possible cases. This implies that only one triangle can be constructed with sides measuring 6cm, 6cm, and 4cm.

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3 years ago
Find the domain of the function f(x)=Log(|x-7|-3) and give the solution in interval notation
Alecsey [184]

Answer:

(-∞, 4) ∪ (10, ∞)

Step-by-step explanation:

A logarithm y = log x can only take x-values greater than 0. It's domain is (0, ∞). If you put log(0) or log of any negative number into a calculator, it'll return an error. So when you have a logarithm like yours, f(x) = log(|x - 7| - 3), you need to make sure you take out any x value that could give you a negative result or 0.

Take the argument of the logarithm, |x - 7| - 3, and pull it aside. You can solve it one of two ways: by looking at it and plugging in values and figuring out which values give you zero or a negative number (trial and error), or by setting it equal to zero and solving for x. I'll show you the second approach:

|x - 7| - 3 = 0 ... get the absolute value bars alone

|x - 7| = 3 ... absolute value means "this distance from 0 on a number line", so what your equation means is |x - 7| is 3 units away from zero. But we don't know if it's three units to the left (negative 3) or three units to the right (positive three). So we set up both.

x - 7 = 3

x - 7 = -3

Solve both equations, and get x = 10 for the top equation, and x = 4 for the bottom equation. This gives you the values you need to use in your interval notation. 4 and 10 both will give you 0 if you plug them into |x - 7| - 3, and 0 is outside of the domain of a logarithm. You can't have negative numbers either, and you'll see that if you try to plug in 5, 6, 7...all the way up to 10, you'll either get a negative result or 0. Basically, anything between 4 and 10, including 4 and 10 won't do it for you. x has to be less than 4 or greater than 10 for your original f(x) function to be defined.

Now that you've identified what ISN'T in your domain, all you have to do is set it up in interval notation. You're clear for everything from negative infinity up to 4, but at exactly 4 (if you set x = 4 and plug it in), your result is undefined. Exactly at 10, it's undefined, but anything greater than 10 works fine. So (-∞, 4) ∪ (10, ∞) is your answer.

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Answer:

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Step-by-step explanation:

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