Evaluate the expression.

Answer:

(a) 3003 ways

(b) 10897286400 ways

(c) 3002 ways

Step-by-step explanation:

Given

[tex]n = 15[/tex] --- 15 players

Solving (a) Ways of selecting 10 players.

This implies combination.

So, we have:

[tex]r=10[/tex]

Using:

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

We have:

[tex]^{15}C_{10} = \frac{15!}{(15-10)!10!}[/tex]

[tex]^{15}C_{10} = \frac{15!}{5!10!}[/tex]

Simplify

[tex]^{15}C_{10} = \frac{15*14*13*12*11*10!}{5!10!}[/tex]

[tex]^{15}C_{10} = \frac{15*14*13*12*11}{5!}[/tex]

[tex]^{15}C_{10} = \frac{15*14*13*12*11}{5*4*3*2*1}[/tex]

[tex]^{15}C_{10} = \frac{360360}{120}[/tex]

[tex]^{15}C_{10} = 3003[/tex]

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

This implies permutation.

So, we have:

[tex]r=10[/tex]

Using:

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

We have:

[tex]^{15}P_{10} = \frac{15!}{(15-10)!}[/tex]

[tex]^{15}P_{10} = \frac{15!}{5!}[/tex]

Solve each factorial

[tex]^{15}P_{10} = \frac{1307674368000}{120}[/tex]

[tex]^{15}P_{10} = 10897286400[/tex]

Solving (c) Ways of choosing at least 1 woman

We have:

[tex]Men = 10[/tex]

[tex]Women = 5[/tex]

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

[tex]At\ least\ 1\ woman = 3003 - 1[/tex]

[tex]At\ least\ 1\ woman = 3002[/tex]

Answer:

trapazoid

Step-by-step explanation:

A trapezoid is a shape that belongs in the overlapped section of the

Venn diagram.

Regular polygons have all sides the same and that apothem bisects the side in two parts, (provable by symmetry).

Apothem for a regular polygon is a line segment that originates from the center of the regular polygon and touches the mid of one of the sides of the regular polygon.

It is perpendicular to the regular polygon's side it touches.

The fifth-grade art class is making quilts. There are some of the shapes they are putting in their quilts.

A trapezoid is a shape that belongs in the overlapped section of the

Venn diagram.

Learn more about apothem here:

https://brainly.com/question/12090932

#SPJ2

Answer:

12 days

Step-by-step explanation:

3/8=.375

16.5 divided by 1.375 equals to 12. I hope that helps.

Answer:

The answer would be true.

Step-by-step explanation:

Since 10 equals y that means that 60=6y is true because 6x10 is 60.

Answer:

hexagonal prism

Step-by-step explanation:

has 6 sides

Answer:

y=5x+25

Step-by-step explanation:

The slope is (30-25)/(1-0)=5.

Also, the y-intercept is 25.

So, the equation is y=5x+25.

Answer:

c

Step-by-step explanation:

2(2x+3y)

as 4x+6y

hope this helps and makes sense

Answer:

3.49

Step-by-step explanation:

subtract 2.01 from 5.5

Answer:

im pretty sure its 67, sorry if I'm wrong

Answer:6000 cm3

Step-by-step explanation:You do 20x10x15=3000. Then you do 3000x2= 6000. So your answer will be 6000cm3

Answer:

they would eat 3500 pounds of food in 1 week

Step-by-step explanation:

its simple math just multiply 500 by 7 and you would get 3500

Answer:

Your average speed was 3.29 Miles per hour (mph)

Please Consider Marking Brainliest.

Answer:

D

Step-by-step explanation:

Root square of 3 is 1.732, the root square of Pi is 1.77, the root square of 8 is 2.82 and the estimated value of Pi itself is 3.14.

Answer:

i dont know but can you pick me brainiest

Step-by-step explanation:

Answer:

G = 3

Step-by-step explanation:

Answer:

g=3

Step-by-step explanation:

reverse the whole question:

so all the minus would convert into an addition sign

hope that helps

please mark as brainliest if correct

have a great day/night.

thank you

19NBoli

Answer:

Volume = 646.0 cm³

Step-by-step explanation:

The solid is made up of a hemisphere and a cube

Therefore,

Volume of the composite solid = ⅔πr³ + a³

Where,

r = ½(8) = 4 cm

a = 8 cm

Plug in the values

Volume of the composite solid = ⅔*π*4³ + 8³

= 134.04 + 512

= 646.0 cm³ (nearest tenth)

Answer:

1356cm3

Step-by-step explanation:

when the stone is dropped in to the water the new height is 17.4cm(14+3.4)

find the volume when the height is 14cm and when the height is 17.4cm

24*14*17.4=4716

24*14*14=3360

then subtract the two volumes

4716-3360=1356cm3

Answer:

816 cm^3

Step-by-step explanation:

First you want to find the volume of the container with the stone, and then without the stone.

The formula for finding the volume of a rectangular container is V= l x w x h

We substitue in:

With stone:

V= 24cm x 10 cm x (14+3.4 cm)

V= 4,176 cm^3

Without stone:

V= 24 cm x 10 cm x 14 cm

V= 3,360 cm^3

Then, you want to subtract the two volumes to get the stone by itself.

4,176 - 3,360= 816 cm^3

Hope this helps!

PS- I think the answer above me got their numbers mixed up, but they had the right idea.

Answer:

The 96th term of the arithmetic sequence is -1234.

Step-by-step explanation:

first term (a)=1

second term (t2)=-12

common difference (d)= t2-a

d=-12-1

d=-13

96th term (t96)=?

We know that,

t96=a+(n-1)d

t96=1+(96-1)(-13)

t96=1+95(-13)

t96=1-1235

t96=-1234

Answer:

Area is 364

Step-by-step explanation:

A parallelogram's area is equal to base times height. So it doesn't depend on the angle at all, as long as the base and height are constant.

That means that the area of the parallelogram on the left is the same as if it was a rectangle (an extension of the rectangle part on the right).

This brings us to the answer - the area is the same as the area of a 14x26 rectangle.

14*26=364

Alternatively, let's compute the area of the rectangle on the right:

18*14 = 252

And the area of the parallelogram

14 * (26-18) = 14*8 = 112

And the area of the composite figure is 252+112 = 364

Answer:

The 95​% confidence interval for the mean birth weight of all ​non-premature babies is between 3350.4 grams and 3662.4 grams. This means that we are 95% sure that true mean birth weight of all non-premature babies is in this interval.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 41 - 1 = 40

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0211

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0211\frac{494.2}{\sqrt{41}} = 156[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 3506.4 - 156 = 3350.4 grams

The upper end of the interval is the sample mean added to M. So it is 3506.4 + 156 = 3662.4 grams

The 95​% confidence interval for the mean birth weight of all ​non-premature babies is between 3350.4 grams and 3662.4 grams. This means that we are 95% sure that true mean birth weight of all non-premature babies is in this interval.

Answer:

the answer's 5.6

5.56 but rounded its I think 5.6

don't trust my answer.

Answer:

its F

Step-by-step explanation:

because 1+1 is AxB is 21

Answer:

five and three ninths

six and seven tenths

nine and one fifth

Answer:

should be 27

Step-by-step explanation:

60% of 180 is 108

25% of 108 is 27

Answer:

So 153 girls were dressed up

Step-by-step explanation:

Total percent of girls =60 percent + 25 percent =85 percent

now,

= 85÷100×180

= 153

Plz mark me as brainest answer

Answer: 1 3/13

Step-by-step explanation:

Answer:

69 hours

Step-by-step explanation:

just subtract 72-3 and 69 is the answer

Answer:

Molly watches television for 69 hours

Step-by-step explanation:

72-3= 69

Answer:

lol the is no equation there to solve

Answer:

1,3, and 4

Step-by-step explanation: