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) How many ways are there to assign the 10 positions by selecting players from the 15 people who show up? 3003 (c) Of the 15 people who show up, 5 are women. How many ways are there to choose 10 players to take the field if at least one of these players must be a woman?

Answers

Answer 1

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]


Related Questions

What is the equation of the line that passes through the point (−0.5,8) and has a slope of −5?

Answers

Answer:

Slope=-1.8, X=-0.5, y=1.9

Equation is y^2-y^1=m(x^2-x^1).

Y-1.9=-1.8(X-(-0.5))

Y-1.9=-1.8x+0.90

Add 1.9 on both sides.

Y= -1.8x+1.

I hope this helps you.

Step-by-step explanation:

Which of the following shows 9x2 - 19x + 10 factored completely?
A. (9x - 10)(x - 1)
B. (9x - 2)(x - 5)
C. (9x - 5)(x - 2)
D. (3x - 2)(3x - 5)

Answers

the answer is A because you can multiply 9 and 10 and find that -10 times -9 is 90 and it also adds up to -19 and then you rewrite it and factor

10+(2x3)^2 divied by 4x1/2^3

Answers

Answer:

11.125

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

please mark this answer as brainlest

jose and two of his friends are collecting baseball cards. Their goal is for the three of them to collect at least 100 cards in total. At the moment they have 43 cards. If they all plan to now collect the same number of cards,Which inequality can jose use to determine the minimum number of cards each person needs to collect to reach their goal?

Answers

Answer:

A

Step-by-step explanation:

Help anyone? Math is not my strong suit

Answers

Answer:

the 3rd one

Step-by-step explanation:

Answer:

it's the 7 one

Step-by-step explanation:

math has patterns if you follow the patterns you can see the symbol and the 7 look alike. stuff like this works for me a lot but I don't know f it'll work this time. If it doesn't I'm sorry I tried.

You decide that you want new carpeting in your bedroom that measures 12 feet 6 inches wide by 15 feet 9 inches long. The price of the carpet and the underlying pad is $3.49 per square foot. You decide to upgrade to the deluxe underlying pad that costs an additional $0.62 per square foot. The fee for installation is a flat fee of $180. What is the total cost, including sales tax of 6.7%, of the carpet, pad, and installation? Round your answer to the nearest cent. Write the equation that represents the total cost.

Answers

Answer:

The total cost of the new carpeting is $ 1,055.43.

Step-by-step explanation:

Since I decide that I want new carpeting in my bedroom that measures 12 feet 6 inches wide by 15 feet 9 inches long, and the price of the carpet and the underlying pad is $ 3.49 per square foot, and I decide to upgrade to the deluxe underlying pad that costs an additional $ 0.62 per square foot, and the fee for installation is a flat fee of $ 180, to determine what is the total cost, including sales tax of 6.7%, of the carpet, pad, and installation, the following calculations must be performed:

1 inch = 0.08333 feet

6 inches = 0.08333 x 6 = 0.5

9 inches = 0.08333 x 9 = 0.75

12.5 x 15.75 = Bedroom area

196,875 square feet = Bedroom area

((196.875 x (3.49 + 0.62)) + 180) x 1.067 = Total cost

((196,875 x 4.11) + 180) x 1,067 = Total cost

(809.15625 + 180) x 1.067 = Total cost

989.15625 x 1.067 = Total cost

1,055,429 = Total cost

Therefore, the total cost of the new carpeting is $ 1,055.43.

791.26 x 42 please do step by step​

Answers

Answer:

33232.92

Step-by-step explanation:

Consider the following diagram below.
D
(4x-3)
(39)
(5y)
(6x+13)
F
Find the values of cand y.

Answers

Answer:

[tex]x = 19[/tex]

[tex]y = 22.5[/tex]

Step-by-step explanation:

[tex]5y + 3y = 180[/tex]

[tex]8y = 180[/tex]

[tex]y = 22.5[/tex]

[tex]6x + 13 + 4x - 3 = 180[/tex]

[tex]10x - 10 = 180[/tex]

[tex]10x = 190[/tex]

[tex]x = 19[/tex]

Answer: x=17

y=22.5

Step-by-step explanation: trial and error of math nation <333

I need help with question 3 part B please !

Answers

Answer:

Yes, one inch is a twlefth of a ft which is a porportion of a feet

Step-by-step explanation:

Please hurry!! 30 points!! Whats the answer??

Answers

Answer:

2

Step-by-step explanation:

Answer:

11.25 or 11 1/4

Step-by-step explanation:

seeing as how tiled in this sense essentially means 'cut' we have to look at the following rectangle as 2 separate rectangles instead of one whole

so we'll let the biggest rectangle be rectangle one and the smallest rectangle two-

now we need the dimensions of each one-

rectangle one

l=5 w=2

rectangle two

l=5 w=1/4

now let us set up the equation and solve-

a=lw

rectangle one

a=5*2=10

rectangle two

a=5*1/4=1.25

and the last step is to add together the areas of both rectangles

10+1.25=11.25

and since you need your answer as a mixed number the answer is 11 1/4

(to do this you just put 11.25 over 100 and then simplify)

good luck :)

i hope this helps

brainliest would be highly appreciated

have a nice day!

If f(x) = 2x + 5 then f(?) = 5
0
5
3
8

Answers

Answer:

0.

Step-by-step explanation:

When you multiply 2*0, it will be equal to 0. 0+5= 5.

How would you write the Pythagorean theorem for a right triangle with sides of 9 inches, 41 inches, and 40 inches?
A.
9² + 41² = 40²
B.
9² + 40² = 41²
C.
40² + 41² = 9²

Answers

A
9^2+21^3=80

B
9^2+50^3=100

C
60^2+20^2=80

Tom sells the hot dogs for £3.15 each

Answers

Answer:

Then what???

Step-by-step explanation:

Ok what I don’t get it

The label of a snack says it has 530calories per 20ounces.

Answers

Answer:

can you just mark me brainlest pls

Step-by-step explanation:

Do you want to know how much calories per oz?

Answer: 26.5 calories per oz

A 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. How many containers of sugar will the 9 pound bag create? (sorry i forgot the 2/3 last time!)

Answers

Answer:

You would create 13 and a half containers of sugar from the 9 pound bag.

Step-by-step explanation:

You divide 9 by 2/3 and it would give you 13.5 which is 13 and a half containers of sugar.

In which step does a mistake first occur?
8 + 2 + (3 X 3 -2)
Step 1: 8 +2 + (3 x 1)
Step 2: 8 +2 + 3
Step 3: 4 + 3
Step 4: 7

Answers

Answer:

Step 3 because they didn't add correctly

Last one, Estimate the perimeter and the area of the shaded figure


Show how u got it please.

Answers

Answer:

13 and a half

Step-by-step explanation:

I just counted the squares bro

What is the lateral area of the cone?

Answers

your answer would be ~ 305.83 !!

help please, i need it asap. tyty

Answers

Answer:

Step-by-step explanation:

[tex]\frac{3}{x}[/tex] = [tex]\frac{2}{5}[/tex]

2x = 15

x = 7.5

help me and I’ll give you brainliest

Answers

Answer:

r = 16

Step-by-step explanation:

6/6 = r/16

6r = 96

/6     /6

r = 16

6r I would say I believe

The distance from Detroit, MI to Paris, France is approximately 3930 mi. Flying from Detroit to Paris takes 8 hr with the jet stream. The return flight takes 8.3 hr since the plane is flying against the jet stream.
a. The speed of the plane in still air, rounded to the nearest whole number, is
b. The speed of the jet stream, rounded to the nearest whole number, is

Answers

Answer:

a. 482

b. 9.0

Step-by-step explanation:

The speed of the plane in still air is approx 482 miles per hour(mph). The speed of the jet stream, rounded to the nearest whole number, is 9 mph

How does air stream affects speed of flight?

Flight speed in air stream = Flight speed in still air + effect of air stream

If the flight is going opposit, then:

Flight speed in air stream = Flight speed in still air - speed of air stream

If the flight is going along with flight, then:

Flight speed in air stream = Flight speed in still air + speed of air stream

For this case, we're specified that:

Distance from Detroid to Paris is approx 3930 milesTime it takes by flight along the air stream = 8 hoursTime it takes by flight against the air stream = 8.3 hours

Speed of flight along the stream is:

[tex]S = \dfrac{\delta D}{\delta T} = \dfrac{3930}{8} = 491.25 \: \rm mph[/tex]

Speed of flight against the stream is:

[tex]S = \dfrac{\delta D}{\delta T} = \dfrac{3930}{8.3} \approx 473.49 \: \rm mph[/tex]

Let the speed of air stream be y, and that of the flight in still air be x miles per hour, then we get:

Along air stream:

[tex]x + y =491.25\\[/tex] (in miles per hour)

and Against the stream:

[tex]x - y =473.49\\[/tex] (in miles per hour)

Adding both the equations side by side, we get:

[tex]2x + y - y = 491.25 + 473.49\\\\x = \dfrac{964.74}{2} =482.37 \: \rm mph[/tex]

Using this value, we get the value of y as:

[tex]x + y =491.25\\y = 491.25 - x = 491.25 - 482.37 = 8.88 \: \rm mph[/tex]

Rounding to the nearest whole numbers, we get:

x = 482 mph, and y = 9 mph

Thus, the speed of the plane in still air is approx 482 miles per hour(mph). The speed of the jet stream, rounded to the nearest whole number, is 9 mph

Learn more about motion in stream here:

https://brainly.com/question/14297576

At baseball camp, Freddie got a hit 15%
of the times that he was at bat. Based
on this information, which is the best
prediction of the number of hits Freddie
will have in 40 times at bat?
A 25
B 15
C 15
D 14​

Answers

The correct answer is letter A

Show work please it has to be done at 2:35

Answers

Step-by-step explanation:

1. -10b+b=-9

It is like you are doing this:

-10+1=-9

5. 5k+7k=12k

5+7=12

3. 1+5v+v= 1+6v

Like: 5+1

2.-x-3x=-4x

Like:-3-1=4 (both are negative numbers and you just add the second one)

4.-7n-7-8+10n=3n-15

You are doing this with n:

10-7=3 and this with numbers:

-7-8=-15 (both negative again)

6.a-2+1+4a= 5a-1

Like this: 4+1=5 and -2+1=-1

7. 8(x+10)= 8*x+8*10= 8x +80

8. 8(1+6p)= 8*1+8*6p= 8+48p

9.-5(-7+7n)= 35-35n ( when you * negative and positive numbers you get negative result and when you * negative and negative numbers you get positive result)

10.-(9m+7)= -9m-7 ( when you have - before () every number changes its sign).

Sorry for messy writing... Hope this helps.


Brandon is rolling two six-sided dice. What is the probability that one die lands on an even number and the other die lands on an odd number?

Answers

Answer:

50-50 on both because there 3 even and 3 odd numbers

Answer:

50% chance of either or 1/2

Step-by-step explanation:

50% of either

Look a die has 12 sides

6 numbers are odd and the other 6 even

If you randomly roll a die you will have 6/12 chances of landing on a even number and a 6/12 chance of landing on a odd number

now 6/12 can be simplified to 1/2 which is 50%

Hope that helps!

which event is unlikely, but not impossible?
A. spinning a spinner split into a 16 equal sections labeled 1-16 and landing on a 3

Answers

Is there supposed to be more answer choices ?
I only see A

SOLVE FOR X PLS!! 50 POINTS! URGENT

Answers

Answer:

5

Step-by-step explanation:

The given two triangles are similar , therefore ,

⇒ 5x /20 = 45/36

⇒ x/4 = 5/4

⇒ x = 5/4 × 4

x = 5

Hence the value of x is 5.

What’s the measure of an arc with radius 45 inches and central angle of 135°?

Answers

Answer:

106.028752

Step-by-step explanation:

First, find the circumference which is 2 pi r.

2pi(45), 90pi, 282.743339

135 out of 360 degrees is 135/360 or 3/8

and 3/8 out of 282.743339 is 106.028752

what is the mean of 8,445,276,1198

Answers

Answer:

1028.5 is the mean

Answer:

481.75

Step-by-step explanation:

To find the mean add up all the numbers in the data set :

8 + 445 + 276 + 1198 = 1927

divide the numbers by how many numbers are in the data set :

1927 ÷ 4 = 481.75

Therefore, the mean in the data set 481.75

A triangle has two sides of length 17 and 4. What is the smallest possible whole-number
length for the third side?

Answers

Answer:

14

Step-by-step explanation:

because the sum of the 2 smaller side have to add up to greater than the larger side

x+4 > 17

x > 13

14 is the next biggest whole number

HELP NOW WHOEVER ANSWERS FIRST WILL GIVE BRAINLYIST

Answers

Answer:

if these are the same pictures but just tilted then the answer should be 5 units

Step-by-step explanation:

Answer:

it is 5

Step-by-step explanation:

i dont feel like a step by step

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