Answer:
[tex]1,\!848[/tex].
Step-by-step explanation:
There are two disjoint sets of ways to choose a lineup as required:
Include none of Alicia, Amanda, or Anna, orInclude exactly one of Alicia, Amanda, and Anna.Assume that none of Alicia, Amanda, or Anna is to be selected. This lineup of [tex]6[/tex] would then need to be selected from a set of [tex]14 - 3 = 11[/tex] players (which excludes Alicia, Amanda, and Anna.)
The number of ways of selecting (without order) [tex]6[/tex] items out of a set of [tex]11[/tex] (distinct) items is equal to the combination:
[tex]\begin{aligned}\begin{pmatrix}11 \\ 6\end{pmatrix} &= \frac{11!}{(6!)\, (11 - 6)!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].
Assume that Alicia is selected, but neither Amanda nor Anna is selected. The other [tex]6 - 1 = 5[/tex] players in this lineup would then need to be selected from a set of [tex]14 - 1 - 2 = 11[/tex] players. (This set of [tex]11[/tex] excludes Alicia, Amanda, and Anna.)
The number of ways to select [tex]5[/tex] items from a set of [tex]11[/tex] items is:
[tex]\begin{aligned}\begin{pmatrix}11 \\ 5\end{pmatrix} &= \frac{11!}{(5!)\, (11 - 5)!} \\ &= \frac{11!}{5! \times 6!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].
Similarly, there would be another set of [tex](11!) / (6! \times 5!)[/tex] distinct ways to select the lineup if Amanda is selected, but neither Alicia nor Anna is.
Likewise, the number of ways to select the lineup with Anna but neither Amanda nor Alicia would also be [tex](11!) / (6! \times 5!)[/tex].
These sets of configurations for the lineup are pairwise disjoint from one another. Thus, the total number of ways to select this lineup would be:
[tex]\begin{aligned}& \begin{pmatrix}11 \\ 6 \end{pmatrix} + 3 \times \begin{pmatrix}11 \\ 5 \end{pmatrix} \\ =\; & \frac{11!}{6! \times 5!} + 3 \times \frac{11!}{6! \times 5!} \\ =\; & \frac{4 \times 11!}{6! \times 5!} \\ =\; & \frac{4 \times 11 \times 10 \times 9 \times 8 \times 7}{5 \times 4 \times 3 \times 2} \\ =\; & \frac{11 \times 10 \times 9 \times 8 \times 7}{5 \times 3 \times 2} \\ =\; & 1,\!848\end{aligned}[/tex].
camilo uses 32 ounces of filling to make empanadas. he puts 8 empanadas on each of 3 trays. Write a fraction to show how many ounces of filling camilo uses in each empanada. Please reply quickly!
Answer:
32/4
Step-by-step explanation:
B. To make salad dressing for the fruit salad, Mrs. Santos uses 2/4 cup oil, 1 cup orange juice, and 3/4 cup honey. How many cups of salad dressing does this make? Explain how you found your answer.
Answer:
[tex]\sf 2 \frac14 \ cups[/tex]
Step-by-step explanation:
Add the amounts together:
[tex]\sf \implies \dfrac24+1+\dfrac34[/tex]
Convert the whole number 1 into a fraction with denominator 4:
[tex]\sf \implies \dfrac24+\dfrac44+\dfrac34[/tex]
As all the denominators are the same, we can simply add the numerators:
[tex]\sf \implies \dfrac{2+4+3}4[/tex]
[tex]\sf \implies \dfrac94[/tex]
Finally, convert the improper fraction into a mixed number:
[tex]\sf \implies 2 \frac14 \ cups[/tex]
Add all
[tex]\\ \rm\rightarrowtail \dfrac{2}{4}+\dfrac{3}{4}+\dfrac{4}{4}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{2+3+4}{4}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{9}{4}[/tex]
[tex]\\ \rm\rightarrowtail 2\dfrac{1}{4}cups[/tex]
How many terms are in the expression? 9a + 6b + 3c + 1 A) 1 B) 2 C) 3 D) 4
Answer:
D.) there is 9a and 6b ,3c and 1 thats four different terms
Step-by-step explanation:
Have a nice day! :D
the length of a rectagle is twice its width. if the perimeter of the rectangle is 36in, find its length and width
Answer:
Perimeter=36in
Length of one side=12
Length of the other side=12
Width of one side=6
Width of the other side=6
Step-by-step explanation:
6*2=12, so if the length is 12 half would be six. All of them added up is 36
Answer:
Length = 12inWidth = 6inStep-by-step explanation:
[tex]perimeter \: of \: a \: rectangle = 2(2x) + 2(x) \\ 36in = 4x + 2x = 6x \\ \frac{36in}{6} = \frac{6x}{6} \\ x = 6in \\ 2x = 2 \times 6in = 12in[/tex]
Mark me brainliest!
7. The area of the parallelogram is 450 m2. What is
the height?
A. 25 m
B. 36 m
C. 50 m
D. 72m
Help? Anything can help I’m in a rush
Answer: A vertical line from (-5 , 4 ) to (5 , 4)
Step-by-step explanation: The y axis is the vertical one. Go up 4 and draw a line connecting all the points with 4 in the coordinates.
Hope that helps :)
Answer:
Step-by-step explanation:
go up 4 lines on the y-axis then draw a straight line from left to right on y=4
I don't know if you can see the picture, but I drew a line on the picture you provided...
Please 5 stars if correct!!!
I hope this helps
Which of the following describes the solution to a system of linear inequalities?
A. The soultion is the region where both shaded parts overlap.
B. The solution is everything on the shaded graph.
Answer:
A. The solution is the region where both shaded parts overlap.
Step-by-step explanation:
The solution to a system of linear inequalities is the intersection region of the solution of both inequalities. Or you could also say that it's the region where the graphs of the inequalities in the system overlap.
The shaded area represents the solution and where the two inequalities overlap.
The measure of an angle is 107.4 what is the measure of its supplemental angle ?
Answer:
72.6
Step-by-step explanation:
180-107.4 = 72.6
If 12Kg of chicken feed cost 20 how much would 5kg cost?
and what is the unit rate? ( price per 1 kg)
Step-by-step explanation:
if you 12kg cost 20 what about 5kg that will be 5kg×20÷12kg= 8.33 when you round of to the nearest hundredth this is the price of 5kg
sorry but i dont think i know how to answer the other question i have done what i only know thankyou
The recent price of a car is Rs.10,00,000. If its price reduces by 10% yearly, after how many years it's price will be Rs. 7,29,000? Find it.
Answer:
hope it helps
also do write the givens
train covers 20 km in one hour then how much distance will it cover in 1 min?
[tex]\sf\large\underline{Given:-}[/tex]
Speed of the train = 20km / 1hr.
[tex]\rightarrow[/tex] 1 hour = 60 minutes.
So, speed of the train = 20km/60min.
[tex]\sf\large\underline{To\: Find:-}[/tex]
[tex]\rightarrow[/tex]Distance covered by train in 1min.
[tex]\sf\large\underline{Solution:-}[/tex]
Let the distance covered by train in 1 min be [tex]\sf{x}[/tex] m.
So, if train covers 20 km in 60min then it covers [tex]\sf{x}[/tex] m in 1 min.
It can be written as,
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}}[/tex] [tex]\sf{=\frac{x}{1}}[/tex](by cross multiplication)
[tex]\rightarrow[/tex][tex]\sf{20\: = \: 60x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{1}{3}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{0.33= x}[/tex](approx)
Therefore, distance covered by train in 1 min= 0.33km (approx).
_______________________________
Hope it helps you:)
Find the actual area of the triangle below.
Can someone pls help?
Answer:
200 meters2
Step-by-step explanation:
4 * 5 = 20
20 * 20 ÷ 2 = 200
what is the answer
how do i do it
Answer:
-8.9° C
Step-by-step explanation:
Question:
Doing a scientific experiment the temperature of a container decreased by 35.7° C at a constant rate over 8 1/2 hours.
What value represents the change in the temperature of the container each hour?
Answer:
-8.9° C
Brand 1 Brand 2 Brand 3 Store 1 Store 2 Store 3 Laptop Comparison Chart Criteria for laptop search: Laptop specifications: • At least 3GB of memory • At least 250 GB hard drive • At least 14” Screen • Weigh at most 7 pounds • At least a 1 year manufacturer warranty • Built-in wireless router • Must be new, not used of refurbished Spending Limit: $800 • Includes laptop, sales tax, and shipping • For the purpose of this project, use 7.5% sales tax
The total amount that will be paid for the products with a sales tax of 7.5% will be $1290.
How to compute the amount from the sales tax?Your information isn't complete as the table denoting the appropriate values aren't given.
Let's assume that the price of a product A is given as $800 ane product B is $400. If the sales tax is 7.5%, the total amount that will be paid will be:
= ($800 + $400) + (7.5% × $1200)
= $1200 + $90
= $1290
Learn more about sales tax on:
https://brainly.com/question/9437038
What is the area of the figure below?
A. 16
B. 45
C. 51
D. None of these
Answer:
C. 51
Step-by-step explanation:
For Square:
Length x Height
7 x 6 = 42
For Triangle:
Base x Height x 1/2
(6x3)1/2 = 9
42 + 9 = 51
A flag is created by sewing together
Answer:
yes, a flag is created by sewing it together
100.2and 19.400 which is greater
Answer:
19.400
Step-by-step explanation:
19.400 equals out to 42769.67886386625
Can someone please help me with this thank you
Answer:
The skeletal system has many functions. Besides giving us our human shape and features, it:
Allows movement: Your skeleton supports your body weight to help you stand and move. Joints, connective tissue and muscles work together to make your body parts mobile.
Produces blood cells: Bones contain bone marrow. Red and white blood cells are produced in the bone marrow.
Protects and supports organs: Your skull shields your brain, your ribs protect your heart and lungs, and your backbone protects your spine.
Stores minerals: Bones hold your body’s supply of minerals like calcium and vitamin D.
1. quadrilateral with 4 right angles
Answer:
Square
Step-by-step explanation:
Tan^2xsin^2x=tan^2x-sin^2x
Prove identity
Answer:
See below for proof
Step-by-step explanation:
[tex]\tan^2x\sin^2x\\\\(\sec^2x-1)(\sin^2x)\\\\(\frac{1}{\cos^2x}-\frac{\sin^2x}{\sin^2x})(\sin^2x)\\\\(\frac{\sin^2x-\sin^2x\cos^2x}{\sin^2x\cos^2x})(\sin^2x)\\\\\frac{\sin^2x-\sin^2x\cos^2x}{\cos^2x}\\\\\frac{\sin^2x}{\cos^2x}-\sin^2x\\\\\tan^2x-\sin^2x[/tex]
Hence, the identity is proven
Cassie has 10 1/2 feet of string to make 15 beaded bracelets. She needs 9 inches of string for each bracelet. Does she have enough string to make all the bracelets? Explain. (1 foot = 12 inches)
Answer:
unfortunately one person will be without a bracelet
Convert to vertex form: f(x) = x2 + 16x + 64
Answer:
Step-by-step explanation:
hello :
note : the vertex form is :
ax²+bx+c = a(x+(b)/(2a))²- delta/4a² and delta = b²- 4ac
in this exercice you have : a =1 b = 16 and c=64
continu ..........
Is a 779 a good MI score
Answer:
yes
explanation:
Your score falls within the range of scores, from 740 to 799, that is considered Very Good. A 779 FICO Score is above the average credit score. Consumers in this range may qualify for better interest rates from lenders.
What is the average rate of change of the function y = 3 cos x on the interval [π/2, π]?
Answer:
¹
Step-by-step explanation:
Average Rate of Change is
ts
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
Here b is pi, a is pi/2,
[tex] \cos(\pi) = - 1[/tex]
[tex] \cos( \frac{\pi}{2} ) = 0[/tex]
So we have
[tex] \frac{ - 1 - 0}{ \frac{\pi}{2} } = \frac{ - 1}{ \frac{\pi}{2} } [/tex]
Answer:
-2/pi
Step-by-step explanation:
If two chords are the same distance from the center of a circle, then they are ______.
Answer:
1 is the answer to have the distance same
Solve for X -3x + -6 = 21
Answer:
x= -13.5
Step-by-step explanation:
X-3x+(-6)=21
-2x-6=21
-2x=27
2x=-27
x=-13.5
Find the area of the figure
Answer:
88 cm²
Step-by-step explanation:
88 cm² is your answer
Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 'of an inch, it is 4 3/4 'inches.
a) What is the largest the actual height the plant could be?
b) What is the smallest the actual height the plant could be?
c) How large could the percent error in Jada’s measurement be?
Answer:
See below.
Step-by-step explanation:
a) 4 7/8 inches
b) 4 5/8 inches
c) 12.5%
The mean weight of three people in a lift was 62kg. If two of them weighed 55kg each, how much did the third person weigh?
Answer:
72 kg
Step-by-step explanation:
let weight of third person=x
62-55=x-62
7=x-65
x=7+65=72 kg
A point located at (1, 8) is reflected over the x-axis. What are the coordinates of the image?
(-1, 8)
(8, 1)
(-1, -8)
(1, -8)
Answer:
(1, -8)
Step-by-step explanation:
In this case, we are reflecting. Since we are reflecting over the x axis, the only thing that will change will be the y.
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The x is staying the same because it is not moving. The y, however, is changing sides.
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Since the y is positive in its original spot, when you reflect over the x axis, you will have a negative y value, which is why it is a -8.
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I hope this helps!
-No one