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]
Erin has a rope that is 3 yards long.
Into how many pieces can she cut the rope if each piece is 1/4 yard long?
Answer:
12 pieces
Step-by-step explanation:
3/0.25 = 12 pieces
Answer:
12 pieces
Step-by-step explanation:
3/.25=12
Over the past ten years, the population in a small city decreased by 12%, resulting in a current population of 105,000 people. What was the approximate population of the city ten years ago?
Answer:
119400
Step-by-step explanation:
The approximate population of the city was 119400
Mary y Frank estan explorando diferentes eventos y registrando la probabilidad de cada
evento. Estan usando diferentes situaciones cada vez que involucran canicas de
diferentes colores.
1) Maty y Frank tenen dos bolsas frente a ellos. La bolsa de Mary tiene 4 canicas azul
amanilo rojo y verde la bolsa de Frank tiene 3 canicas morado naranja y rosa Recogerar
de su borso al mismo tiempo. Cuál es la probabilidad de que Mary seleccione rojo de su bolso
Frank seleccione violeta de su bolso? Utilice un espacio de muestra para
Probabilidad; la probabilidad os Mary y Frank combinan las canicas en una bolsa para
Bacer un expemento en el que toman wacanica de una bolsa y lanzan una moneda. En la
Suste tabla 1 registrado o resultados de cada evento cuales a probabilidad
experimental de la moneda agen cruz en una canica amarilla Muestrato
seberat
Answer:
250000
Step-by-step explanain
i jut d this hquaestions
what is the diameter of a circle with a radius of 4.375"? 2.187" or 2.375" or 8.375" or 8.750"
Could x = - 5 be a solution to the inequality
-6 < 3x + 9 < 21?
Step-by-step explanation:
[tex]3x + 9 = 3( - 5) + 9 \\ = - 15 + 9 \\ = - 6[/tex]
3x+9 is equals to -6 , not more than based on the inequality, but it is lesser than 21.
However, the solution must fulfil both criteria to be a solution to the inequality. Therefore x = -5 is not a solution to the inequality.
find two numbers that multiply to be -18 and add to be -7
Answer:
(-9 and 2)
Step-by-step explanation:
-9+2=-7
-9*2=-18
so -9 and 2 are the required numbers
Answer:
you can multiply 2 and -9 to get -18
you can add 2 and -9 to get -7
Step-by-step explanation:
Hope this helps :)
What is the approximate average rate of change for the function f(x)
from x = 3 to x = 6?
12(1.25)
Answer:
b
Step-by-step explanation:
WHATS THE LENGTH ROUND TO THE NEAREST 10th if NEEDED
Answer: 8.6
Step-by-step explanation:
Using pythagorean theorem, c²=a²+b² you can find the distance between AB.
c²=7²+5²
c²=74
√c²=√74
c=8.6
triangle A' B' C' is the result of dilating ABC about point C by a scale factor of two. Determine whether each claim about the properties of A' B' C' and ABC is true or false
True because all properties are preserved under dilation from triangle ABC to A'B'C'.
We have given a triangle ABC is dilated by a factor of 2/3 , result triangle A'B'C'
We have to determine after dilation, the properties of triangle ABC and A'B'C' is true or false.
What is the transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Dilation of a triangle are results in either decreases or increases in the corresponding length of the triangle, it depends on by which scale factor triangle is dilated ,and dilation does not affect the angle measures of the triangle.
here scale factor is 2/3 so the corresponding sides of the triangle A'B'C' decreases.
So, the dilation of the triangle is not congruent but similar to the original triangle ABC
Therefore, the basic properties of triangles are preserved under the dilation of triangle by a scale factor.
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Answer:
Step-by-step explanation:
The answer is FALSE for the first one AB and A'B' are on the same line.
and TRUE for the second one The measures of B and B' are equal.
the vertex of the parabola below is at the point (5,-3). which of the equations below could be the one for this parabola?
Answer: ty for the points
Step-by-step explanation:
x+-3(y+3)2+5
Find the area of each figure. Answer asap
Answer: There is no picture I will edit my answer when you add one
Step-by-step explanation:
Answer:
I need the picture or the shape please and thank you
Step-by-step explanation:
who is the best fnf mod character mine is sarvenette and ruv
Answer:
same my fav
Step-by-step explanation:
have a good day!!
Answer:Kapil or Matt
Step-by-step explanation: I would say Kapil better because of the DDR pad and his last Song Beathoven replicates beethoven virus. Matt Wiik 2 is great but can't beat
I need help please ????!!!
10 POINTS!!!!which polynomial represents the sum below ?
Answer:
b
Step-by-step explanation:
use calculator next time
B. 3x³ + 8x² + 9x + 12 is the answer.
hope it helps..
HELP ASAP NO LINKS
What is the solution to the equation X=
56 8
co
O x = 448
Ox=64
O x = 48
Ox=7
Answer:
the answer is x=7 cause you have to divide 56 by 8 and that will give you 7 cause 8×7=56
A town has a population of 20,000 and grows at 4.5% every year how long will it be in to the population is 42,800
Answer:
It will take 17 years to get a population of 42,800. (Specifically 17.3)
Step-by-step explanation:
We will use the equation
y = population
x = amount of years
y = 20000(1 + 0.045)^x
20000 is the original population.
(1 + 0.045) is the increase of 4.5% every year
Please help me pls ASAP thank YOUU
Answer:
I think D
Step-by-step explanation:
Sorry if it's wrong, but it's the only one I think makes sense. Brainlist me if u get it right! :)
which expression is equivalent to n+n+n+n? pick outta these A n4 B 4n C4n to the power of 4 D n+4
Answer:
B
Step-by-step explanation:
Answer:
the answers b sorry if it's wrong
Step-by-step explanation:
have a great day
please help this is Due!!
Answer:
c=6d
Step-by-step explanation:
calculate the value of 36²-27²
Answer:
36×36=1296
27×27=729
1296-729=576
The answer is 567
) Which value is the solution of the equation 54 = 6n?
54 = 6n divide 6 on both sides, 6's will cancel on the right.
__ __ solve for 54 ÷ 6 = 9
6 6
n = 9, choice 4 -- final answer
hope this helps :)
The solution of the given equation 54 = 6n will be 9 thus option (D) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given equation,
54 = 6n
Divide by 6 into both sides,
n = 9
Hence "The solution of the given equation 54 = 6n will be 9".
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A rectangle has a length of 17 less than 6 times it's width. If the area of the rectangle is 7585 square feet find the length of the rectangle
9514 1404 393
Answer:
205 ft
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is (6w-17) and the area is ...
A = LW
7585 = (6w-17)(w)
6w² -17w -7585 = 0
Perhaps most straightforward is using the quadratic formula to solve this.
For ax² +bx +c = 0, the solution is x = (-b±√(b²-4ac))/(2a). For the above quadratic, the solution is ...
[tex]x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot6\cdot(-7585)}}{2\cdot6}=\dfrac{17\pm\sqrt{182329}}{12}\\\\x=\dfrac{17\pm427}{12}=\{-34\frac{1}{6},37\}[/tex]
The width is 37 feet, so the length is ...
6(37) -17 = 205 . . . feet
The length of the rectangle is 205 feet.
The area of the rectangle below is
sq. units.
3
22
A. 25
B. 66
O c. 50
D. 33
Answer:
66
Step-by-step explanation:
The area of a rectangle can be found with the formula 'length time width' (lw). The length is 22, and the width is 3. Multiply 3 and 22 and you get 66 as your area.
66 square units is the area of the given rectangle.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
To find the area of a rectangle, we multiply its length by its width.
In this case, the length is 22 and the width is 3.
Therefore, the area of the rectangle is:
Area = length × width = 22 × 3 = 66 square units.
So, the area of the rectangle is 66 square units.
Learn more about Area here:
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I need help if correct I will mark you
Step-by-step explanation:
option 1: 15+15+15=45
option 2: 50 usd
you tell me which is better
Find the area of the sector.
Answer:
359.1887600604 so D should be right
An Oil Rig is 30 meters tall. Mr. Clanton is standing 12 meters from the base of the Rig. At what angle of elevation does he need to look to see the eagle on top of the Rig ? What is the distance from Mr. Clanton to the Eagle ?
Answer:
Angle of elevation: 68.2°, distance from Mr. clanton to the eagle: 32.3m.
Step-by-step explanation:
I can't draw the diagram , but will try to explain:
the diagram is a right angled triangle, with the opposite as the rig, the adjacent as the distance between mr. clinton and the base of the rig, and the hypotenuse as x.
∅ is the angle of elevation from clinton to the eagle.
Using SOH CAH TOA,
Tan∅ =30÷12
tan∅ =2.5.
∅ =tan^-1( tan raised to power -1 )
∅ =tan^-1(2.5)
∅ = 68.19859051≅68.2 to 3s.f.
To get the distance between mr. clinton and the eagle:
Using SOH CAH TOA;
Cos68.2 =12/x cross multiplying....
x*cos68.2 =12
∴ x = 12 ÷ cos 68.2
= 12 ÷ 0.3713678356
= 32.31297611≅32.3 to 3s.f.
Hope this helps.....
what linear equation is represented by the table
0 -2
1 2
2 6
3 10
y=3x+5
you have to graph it
9. A resident drank three ounces of apple
juice, three ounces of coffee, and one
ounce of cream today. What is the intake
in cubic centimeters?
Answer:
Step-by-step explanation:
Total ounces = 3+ 3+ 1= 7 ounces
1 Ounce = 29.574 cubic centimetres
7 ounces = 207.015 cubic centimetres
What is the area in square feet of the ceilling