Find the value of the combination. 13C5
Answers
Answer:
\(_{13}C_5=1287\)
Step-by-step explanation:
\(\displaystyle _nC_r=\frac{n!}{r!(n-r)!}\\\\_{13}C_5=\frac{13!}{5!(13-5)!}\\\\_{13}C_5=\frac{13!}{5!\cdot8!}\\\\_{13}C_5=\frac{13*12*11*10*9}{5*4*3*2*1}\\\\_{13}C_5=\frac{154440}{120}\\\\_{13}C_5=1287\)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5!(13 - 5)!} \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5!(8)!} \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5! \times 8!} \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8!}{5! \times 8!} \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 \times \cancel{8!}}{5! \times \cancel{8!}} \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 }{5 \times 4 \times 3 \times 2 \times 1} \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{156 \times 110 \times 9 }{20 \times 6 \times 1} \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{156 \times 990 }{20 \times 6 } \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{154440 }{120 } \\ \)
\( \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = 1287 \\ \)
Related Questions
NEED HELP!! I"LL GIVE YOU BRAINLIEST!! Find the value of b. a = 3 and c =12
Answers
Answer: b = 11.62
Step-by-step explanation:
We can use this formula to solve for b:
\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)
\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)
\(b^2= \sqrt{144-9}\)
= 11.61895004
We can round that to 11.62.
Hope this helped!
What is the best estimate of the perimeter of the figure on the grid if each square has side lengths of 1 mm?
Answers
Answer:
4mm
Step-by-step explanation:
you have to add both sides after substituting each of the 4 sides by 1mm
which gives you the total of 4
The largest possible circle is cut out of a square whose side length is feet. What will be the approximate area, in square feet, of the remaining board? ( where )
Answers
Assuming that the radius is half the length of the square:
• lenght (l) = 6ft
,• radius (r) = 3ft
Area of circle
\(\begin{gathered} A_c=\pi\cdot r^2=3.14\cdot(3)^2 \\ A_c=28.26 \end{gathered}\)Area needed:
\(\begin{gathered} A_s=6^2=36 \\ A_T=36-28.26=7.74\approx8 \end{gathered}\)Answer: 8ft^2
Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. Livia may eat only part of a cheese stick, so x may not always be a whole number.
A 2-column table with 4 rows. The first column is labeled x with entries 0, 2, 5, 7. The second column is labeled y with entries 11, 25, 46, 60.
What is the range of the function?
all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to 11
all integers greater than or equal to 11
Answers
The range of the function is (c) all real numbers greater than or equal to 11
How to determine the range?The table of values is given as:
x y
0 11
2 25
5 46
7 60
From the question, we understand that:
She eats 11 gram of protein from the chicken drumstick
This means that the minimum y value is 11
Also, we understand that:
x can take decimal numbers.
This means that y can take any decimal number above 11
Hence, the range of the function is (c) all real numbers greater than or equal to 11
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In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student who has an A is a female?
Female Male
Has an A 2 6
Does not have an A 11 5
Answers
Answer:
sd
Step-by-step explanation:
Divisor 99, = 99, Quotient Quotient = 125, Remainder = 20, Dividend =
Answers
Answer:
Dividend = Divisor x Quotient + Remainder
Dividend = 99 x 125 + 20
Dividend = 12395
Dividend = 99 x 125 + 20
Dividend = 12395
The total surface area and the curved surface area of cone are 704 sq. cm. and 550 sq. cm. respectively. Find the slant height of the cone. 20
Answers
l ≈ 17.72 cm
Step-by-step explanation:
Let's denote the slant height of the cone as "l" and the radius of the cone as "r".
We know that the total surface area of the cone is given by:
πrl + πr^2
And we also know that the curved surface area of the cone is given by:
πrl
So we can write two equations using these formulas:
πrl + πr^2 = 704 (1)
πrl = 550 (2)
Now, we can solve for "l" by substituting equation (2) into equation (1):
550 + πr^2 = 704
πr^2 = 154
r^2 = 154/π
r ≈ 6.223 cm
Substituting this value of "r" into equation (2), we get:
πl(6.223) = 550
l ≈ 17.72 cm
Therefore, the slant height of the cone is approximately 17.72 cm.
Fill in the blanks below.
Find the slope of the line passing through the points (7,-5) and (7, -1).
slope:
Find the slope of the line passing through the points (-7, 6) and (-7,-6).
slope:
Answers
Answer:
1. infinity
2. infinity
Julio tiene 12 años de edad y su padre tiene 42 años. ¿Cuántos años tendrá Julio cuando su padre tenga el doble de su edad?
Answers
Julio will be 30 years old when his father is twice his age.
To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.
Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.
For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.
Setting up an equation to solve for x:
x + 30 = 2x
Simplifying the equation, we subtract x from both sides:
30 = x
Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.
Therefore, Julio will be 30 years old when his father is twice his age.
Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?
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HELP PLEASE : For numbers 3 & 4, draw a triangle for each to find the missing side.
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 1) b = 2
2) c = 20
Explanation:
I hope this helped!
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*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer:
3) b = 2.24
4) c = 15.62
Step-by-step explanation:
Pythagorean formula:
a² + b² = c²
3)
a² + b² = c²
2² + b² = 3²
4 + b² = 9
b² = 5
b = 2.24
4)
a² + b² = c²
10² + 12² = c²
100 + 144 = c²
244 = c²
c = 15.62
I neeeeed heeeelp please
Answers
Answer:
10b/y^2
Step-by-step explanation:
Hope this helps! :)
What’s the correct answer for this question?
Answers
Answer:
A.
Step-by-step explanation:
JLK = 360-154 (Circle is 360°)
So
JLK = 206
If R is midpoint of QS, QR =5x-4 and RS= 2x+2, find QS
Answers
Answer:
QS=2.4
Step-by-step explanation:
First graph it out. Once you do that you can see that QR is the same as RS. So you can do the equation 5x-4=2x+2. Once you solve this out you would get 2.4. (I'm just an advanced 7th grader so you can redo the problem to make sure it's all good. :D)
Answer:
68
Step-by-step explanation:
;0
Select all that apply.
Which symbols could be used to make the following statement true?
-22 ___ 3
Answers
Please can anybody help me with this? A card is randomly selected from a standard 52-card deck. What is the probability of picking a club OR a face card? Answer needs to be in decimal form rounded to two decimal places.
Answers
Answer:
0.42
Step-by-step explanation:
To solve the problem, we need to add the probability of picking a club to the probability of picking a face card, and then subtract the probability of picking a club that is also a face card (because we would have counted it twice).
There are 13 clubs in a standard deck, so the probability of picking a club is 13/52 or 0.25.
There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck, so the probability of picking a face card is 12/52 or 0.23.
However, there are 3 cards that are both clubs and face cards (the jack of clubs, queen of clubs, and king of clubs), so we need to subtract the probability of picking one of those cards. There are 3 of them out of 52 total cards, so the probability of picking a club that is also a face card is 3/52 or 0.06.
Therefore, the probability of picking a club OR a face card is:
0.25 + 0.23 - 0.06 = 0.42 (rounded to two decimal places).
So the answer is 0.42.
Which expression is equivalent to 7/32 + 2/32
Answers
Answer:
36 square root 2 also known as C
Step-by-step explanation:
What is the volume of the prism 2.4in 1.5in 8in
Answers
Answer:
The answer is 28.8, When finding the Volume of a shape, you multiply all numbers.
A cannonball is fired vertically upward from a height of 8 feet above the ground and with an initial velocity of 48 feet per second. The height of the cannonball after x seconds is shown in the table below. Time (seconds) 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Height (feet) 8 19 28 35 40 43 44 43 40 Describe the symmetry of the height of the cannonball over time. The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds. The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 1.25 seconds is equal to the height of the cannonball at 1.75 seconds. The height of the cannonball over time is not symmetric. The height of the cannonball over time is symmetric about the line x = 1.0 seconds, which indicates the height of the cannonball at 0.75 seconds is equal to the height of the cannonball at 1.75 seconds.
Answers
The correct answer to the above question is option (a) The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds.
What is Symmetry?Symmetry refers to a property of an object or a function that remains unchanged when transformed by a specific operation.
For example, a geometric shape is symmetric if it can be divided into parts that are mirror images of each other.
According to the given information:The answer to the above question is The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds.
This is because the heights at 0.5 seconds and 2 seconds are equidistant from the line x=1.5 seconds, and they have the same magnitude but opposite signs. Therefore, the graph of the height of the cannonball over time is symmetric with respect to the vertical line x=1.5 seconds.
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.
Which point on the number line shows the graph of ?
point C
point D
point E
point B
Answers
Answer:
i believe point b
Step-by-step explanation:
$6.56 for 8.2 grams what is the unit rate
Answers
$6.56 for 8.2 grams unit rate is 4/5 or 80%.
A ratio that compares two amounts of Distinct types of UNITS is called a rate. When a rate is expressed as a fraction, the denominator is 1 unit. Divide the numerator and denominator of the rate by the denominator to represent a rate as a unit rate. When the numbers that make up a rate have no common elements, the rate is in its simplest form. Keep in mind that the units are listed with the rate. A rate with a denominator of 1 is referred to as a unit rate. Divide the numerator and denominator of the rate by the number in the numerator to obtain unit rates.
Based on the given conditions, formulate:
6.56/8.2
Calculate.
6.56/8.2
Rewrite the fraction.
656/820
Simplify.
4/5 or 0.8.
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f(x)=x^3+5x+k and x+2 is a factor of f(x), then what is the value of k?
Answers
The value of k is 18.
If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.
Substituting x = -2 into f(x), we have:
f(-2) = (-2)³ + 5(-2) + k
= -8 - 10 + k
= -18 + k
Since f(-2) should equal zero, we have:
-18 + k = 0
k = 18
Therefore, the value of k is 18.
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Vita wants to center a towel bar on her door that is 27 inches wide.
end of the door is 9 inches. Write and solve an equation to find the length
She determines that the distance from each end of the towel bar to the
of the towel bar.
Answers
The length of the towel bar is 9.5 inches.
How to solve the equation?Length is used to measure distance, In the International System of Quantities, a quantity with the distance dimension is referred to as length. The majority of measurement systems select a base unit for length from which all other units are derived. The metre serves as the International System of Units' fundamental unit of length.
Suppose, the length of the towel bar is x inches
The distance from each end of the towel bar to the end of the door is 9
inches. So, the total width of the door will be:[(x+(9*2)]=(x+18) inches
Given that, the width of the door is 27 inches 27.5 So, the equation will be.
x+18=27.5
x=27.5-18=9.5
Thus, the length of the towel bar will be 9.5 inches.
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I need help for this
Answers
Answer:
1
Step-by-step explanation:
To find the slope take two points on the line
(-1,0) and (0,1)
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 1-0)/(0- -1)
= (1-0)/(0+1)
= 1/1
= 1
~!!!! HELP ME PLEASE IM IN 7TH GRADE AND LEARNING 9TH AND 8TH iM SUFFERING !!!!~
QUESTION~
Find the vertex of the graph of
f(x) = −|0.75x + 1.5|. Tell whether the
graph opens upward or downward.
Answers
this is what it looks like when I graphed it.
half of the quantity of 6 less than a number f is 4
Answers
Answer:
I believe 10
Step-by-step explanation:
the reason I believe it is 10 is because that is the main mathematical explanation for this equation
Why might it be useful to covert radians to degrees?
Answers
Answer:
Protractor measures degrees
Step-by-step explanation:
help me out with this question
Answers
Need helppppppppppppppppp
Answers
Answer:
45.95% is the correct answer
Answer:
free freeee3eeeeeuuuuuu
Danny bought 8 rolls of paper towels. He has 204.8 meters of paper towels in all. How many meters of paper towels are on each roll? A) 21.52 B) 25.12 C) 25.60 D) 26.52
Answers
Answer:C) 25.60
Step-by-step explanation:204.8÷8=25.60
Answer:
:C) 25.60
Step-by-step explanation:
please help me solve this
Answers
The area of triangle EFG is given as follows:
A = 18.63 square units.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:
A = 0.5bh
The base is given by segment EF as follows:
\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)
EF = 5.4.
The midpoint of EF is given as follows:
M(6.5, -8).
The height is given by the segment MG as follows:
\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)
MG = 6.9.
Hence the area is given as follows:
A = 0.5bh
A = 0.5 x 5.4 x 6.9
A = 18.63 square units.
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