A swim meet has 13 contestants signed up. To calculate the arrangement of first 6 swimmers in first heat we will use combinations because order doesn't matter.

So to select 6 swimmers out of 13 contestants number of different ways

= $^{13}C_{6}$

= $\frac{13!}{(6!)(13-6)!}$

= $\frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!}$

= $\frac{13\times 12\times 11\times 10\times 9\times 8}{6\times 5\times 4\times 3\times 2\times 1}$

= $\frac{1235520}{720}$

= 1716

Therefore, 6 swimmers in the first heat can be arranged in 1716 different ways.

5 0

3 years ago

Solve: 5 - 3x < 20 Help

Fed [463]

Answer:

hope this helps

Step-by-step explanation:

x > −5

7 0

3 years ago

Read 2 more answers

QUESTION 9 Write the expression by using exponents. 2.2.2.2.2.2 moginio QUESTION 10.

lozanna [386]

Answer:

2^6

Step-by-step explanation:

2*2*2*2*2*2

There are six 2's multiplied together so the base is 2 and the exponent is 6

2^6

3 0

3 years ago

In the opening scene of the movie Raiders of the Lost Ark, Indiana Jones replaces a golden statue with a bag of sand. The platfo

chubhunter [2.5K]

Answer:

1920π

Step-by-step explanation:

First, you need to find the volume of the statue in terms of pi.

Volume of cylinder formula:

V=πr²h

V=π4²15

V=π16×15

V=240π

Then, you need to find the mass of the statue.

Mass:

Mass= density × volume

Mass=20×240π

Mass=4800π

Now, you need to find the volume. Since the sand has to weigh the same as the statue, the mass is going to stay the same. To find the volume you need to do:

V=mass of sand/density

V=4800π/2.5

That gives you your answer:

1920π

Note: I had to do the exact same problem on Khan Academy. This is right.

3 0

3 years ago