All categories

3 years ago

11. How many different ways can the 16 numbered pool balls be placed in a line on the pool table?

Mathematics

1 answer:

nikklg [1K]3 years ago

7 0

Answer:

The number of ways are 16! or 20,922,789,888,000.

Step-by-step explanation:

Consider the provided information.

We need to determine the number of different ways 16 numbered pool balls be placed in a line on the pool table.

For the first place we have 16 balls.

For the second place we have 15 balls left.

Similarly for the third place we have 14 balls as two balls are already arranged and so on.

Or we can say that this is the permutation of 16 things taking 16 at a time.

Thus the number of ways are: $16!$ or $^{16}P_{16}$

$16!=16\times15\times14\times13......\times2\times1=20,922,789,888,000$

Hence, the number of ways are 16! or 20,922,789,888,000.

You might be interested in

A rectangular box is to have a square base and a volume of 70 ft3. The material for the base costs 38¢/ft2, the material for the

lakkis [162]

$x-length\ of\ one\ side\ of\ base\\y-high\ of\ box\\x^2-area\ of\ base\\x^2y-volume\\\\x^2y=70\\y=\frac{70}{x^2}\ \ \ \ \ \ \ \ and\ x\neq0\\\\38x^2+4\cdot10xy+27x^2\\65x^2+40xy\ in\ cents\\\\0.65x^2+0.4xy\ in\ dollars$

3 0

3 years ago

If there are 5 terms in a quadratic sequence

exis [7]

Answer:

7.2

Step-by-step explanation:

First differences:

0.8-0.2, 1.8-0.8, 3.2-1.8, 5.0-3.2

0.6, 1.0, 1.4, 1.8

Second differences:

1.0-0.6, 1.4-1.0, 1.8-1.4

0.4, 0.4, 0.4

For the next term, add 0.4 to the last term from the first differences, and add the sum to the last term of the quadratic sequence:

0.4+1.8=2.2

2.2+5.0=7.2

∴ The next term in the sequence is 7.2

7 0

3 years ago

When the sum of \, 528 \, and three times a positive number is subtracted from the square of the number, the result is \, 120. F

aleksandr82 [10.1K]

Let $x$ be the unknown number. So, three times that number means $3x$ , and the square of the number is $x^2$

We have to sum 528 and three times the number, so we have $528+3x$

Then, we have to subtract this number from $x^2$ , so we have

$x^2-(3x+528)$

The result is 120, so the equation is

$x^2 - 3x - 528 = 120 \iff x^2 - 3x - 648 = 0$

This is a quadratic equation, i.e. an equation like $ax^2+bx+c=0$ . These equation can be solved - assuming they have a solution - with the following formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

If you plug the values from your equation, you have

$x_{1,2} = \dfrac{3\pm\sqrt{9-4\cdot(-648)}}{2} = \dfrac{3\pm\sqrt{9+2592}}{2} = \dfrac{3\pm\sqrt{2601}}{2} = \dfrac{3\pm51}{2}$

So, the two solutions would be

$x = \dfrac{3+51}{2} = \dfrac{54}{2} = 27$

$x = \dfrac{3-51}{2} = \dfrac{-48}{2} = -24$

But we know that x is positive, so we only accept the solution $x = 27$

6 0

3 years ago

The first three terms of a sequence are given. Round to the nearest thousandth (if

Mumz [18]

Answer:

$\frac{3}{16}$

Step-by-step explanation:

The common ratio is $\frac{1}{2}$

24, 12, 6, 3, $\frac{3}{2}$ , $\frac{3}{4}$ , $\frac{3}{8}$ , $\frac{3}{16}$

so divide each term by 2

<em>plz mark m brainliest. :)</em>

6 0

3 years ago

When variables are being raised to a power what operation is performed with the exponents?

Ludmilka [50]

First you raise the expressions in the parentheses to their powers. Then multiply the two expressions together. You get to see multiplying exponents (raising a power to a power) and adding exponents (multiplying same bases).

4 0

3 years ago