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3 years ago

10

A telephone pole casts a 24 foot shadow. Belinda ,who is 5 feet 8inches tall,casts a 7 foot shadow.What is the height of the tel

ephone pole

1 answer:

nataly862011 [7]3 years ago

3 0

19.885 feet tall

The problem is similar triangles so you divide 24/7 to get the relation between them then multiply by 5.8 to get the height

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15 players for a softball team show up for a game: (a) How many ways are there to choose 10 players to take the field? 3003 (b)

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Answer:

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Step-by-step explanation:

Given

$n = 15$ --- 15 players

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This implies combination.

So, we have:

$r=10$

Using:

$^nC_r = \frac{n!}{(n-r)!r!}$

We have:

$^{15}C_{10} = \frac{15!}{(15-10)!10!}$

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Simplify

$^{15}C_{10} = \frac{15*14*13*12*11*10!}{5!10!}$

$^{15}C_{10} = \frac{15*14*13*12*11}{5!}$

$^{15}C_{10} = \frac{15*14*13*12*11}{5*4*3*2*1}$

$^{15}C_{10} = \frac{360360}{120}$

$^{15}C_{10} = 3003$

Solving (b) Ways of assigning positions to 10 players.

This implies permutation.

So, we have:

$r=10$

Using:

$^nP_r = \frac{n!}{(n-r)!}$

We have:

$^{15}P_{10} = \frac{15!}{(15-10)!}$

$^{15}P_{10} = \frac{15!}{5!}$

Solve each factorial

$^{15}P_{10} = \frac{1307674368000}{120}$

$^{15}P_{10} = 10897286400$

Solving (c) Ways of choosing at least 1 woman

We have:

$Men = 10$

$Women = 5$

Ways of selecting 10 players is: (a) 3003 ways

Since the number of men are 10, there is 1 way of selecting 10 men (i.e. selection without women)

Using complement rule:

At least 1 woman = Total - No woman

$At\ least\ 1\ woman = 3003 - 1$

$At\ least\ 1\ woman = 3002$

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