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Nutka1998 [239]
3 years ago
7

The denominator of a fraction is three more than its numerator. When both the numerator and denominator are increased by one the

fraction becomes 1/2. What is the original fraction?
Mathematics
1 answer:
horrorfan [7]3 years ago
7 0

Answer:

The original fraction is \frac{2}{5}

Step-by-step explanation:

Let the numerator by X

Denominator is three more than its numerator i.e X +3

When both the numerator and denominator are increased by one the fraction becomes 1/2

\frac{X + 1}{X+3+1} = \frac{1}{2} \\\frac{X+1}{X+4} = \frac{1}{2} \\2X + 2 = X+4\\X = 2

Thus, numerator = 2

Denominator = X +3 = 2+3 = 5

The original fraction is \frac{2}{5}

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F(3) occurs when x =3. So lets plug 3 into our equation.

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F(3) = -28

I hope this helps! :)

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There is a bag filled with 5 blue and 6 red marbles.
Afina-wow [57]

Answer:

The probability of getting two of the same color is 61/121 or about 50.41%.

Step-by-step explanation:

The bag is filled with five blue marbles and six red marbles.

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If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.

In other words, we can find the independent probability of each case and add the probabilities together*.

The probability of getting a red marble first is:

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Since the marble is replaced, the probability of getting another red is: \displaystyle P\left(\text{Red, Red}\right)=\frac{6}{11}\cdot \frac{6}{11}=\frac{36}{121}

The probability of getting a blue marble first is:

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And the probability of getting another blue is:

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So, the probability of getting two of the same color is:

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*Note:

We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.

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