John is a quarterback. This year, he completed 350 passes, which is 70 percent of all the passes he's attempted this year.

Mathematics

1 answer:

Ahat [919]3 years ago

7 0

So we're given the information that 350 is 70% of "x".

So let's make "x" the total amount of attempted passes.

We can re-write 70% like this: 70/100.

This means that 70/100 * x = 350.

Solve:

70/100x = 350.

Multiply 10 on both sides to get normal number:

70/100x * 10 = 350 * 10.

700/100x = 3500

7x = 3500

Divide by 7:

7x/7 = 3500/7

x = 500

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A boy has 3 red , 2 yellow and 3 green marbles. In how many ways can the boy arrange the marbles in a line if: a) Marbles of the

Ilya [14]

Answer:

The total number of different arrangements is 560.

Step-by-step explanation:

A multiset is a collection of objects, just like a set, but can contain an object more than once.

The multiplicity of a particular type of object is the number of times objects of that type appear in a multiset.

Permutations of Multisets Theorem.

The number of ordered n-tuples (or permutations with repetition) on a collection or multiset of $n$ objects, where there are $k$ kinds of objects and object kind 1 occurs with multiplicity $n_1$ , object kind 2 occurs with multiplicity $n_2$ , ... , and object kind $k$ occurs with multiplicity $n_k$ is:

$\begin{equation*}\frac{n!}{n_1!*n_2!*\dots * n_k!}\end{equation*}$

We know that a boy has 3 red, 2 yellow and 3 green marbles. In this case we have n = 8.

If marbles of the same color are indistinguishable, then the total number of different arrangements is

${8 \choose 3, 2, 3} = \frac{8 !}{3 ! 2 ! 3 !} = \frac{8\cdot \:7\cdot \:6\cdot \:5\cdot \:4}{2!\cdot \:3!}=\frac{6720}{2!\cdot \:3!}=\frac{6720}{12}=560$