Step-by-step explanation:
We have,
[tex]\displaystyle\sf{\,^{n}C_{n-1}+\,^{n}C_{n-2}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n!}{(n-1)!(n-(n-1))!}+\dfrac{n!}{(n-2)!(n-(n-2))!}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n!}{(n-1)!(n-n+1)!}+\dfrac{n!}{(n-2)!(n-n+2)!}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n!}{(n-1)!(1)!}+\dfrac{n!}{(n-2)!(2)!}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n(n-1)!}{(n-1)!(1)!}+\dfrac{n(n-1)(n-2)!}{(n-2)!(2)!}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n}{1}+\dfrac{n(n-1)}{2}}[/tex]
[tex]\displaystyle\sf{=n+\dfrac{n^2-n}{2}}[/tex]
[tex]\displaystyle\sf{=\dfrac{2n+n^2-n}{2}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n^2+n}{2}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n(n+1)}{2}}[/tex]
Using the combination formula, it is found that the value of the expression is given by:
(b) n(n + 1)/2
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
[tex]C_{n, n-1} = \frac{n!}{(n-1)!(n - n + 1)!} = \frac{n(n-1)!}{(n-1)!} = n[/tex]
[tex]C_{n, n-2} = \frac{n!}{(n-2)!(n - n + 2)!} = \frac{n(n-1)(n-2)!}{(n-2)!2!} = \frac{n(n-1)}{2}[/tex]
Then, adding these values:
[tex]n + \frac{n(n-1)}{2} = \frac{2n + n^2 - n}{2} = \frac{n(n + 1)}{2}[/tex]
Hence option b is correct.
More can be learned about the combination formula at https://brainly.com/question/25821700
What percent of 91 is 79
86.81
-----------------
baii ^^
Answer:
79/91 = x%
0.8681318681 %
79 is about 86.81% of 91
Step-by-step explanation:
Find the volume of the cylinder. Round your answer to the nearest tenth.
6 m
4 m
And I will report and get your account deleted if you answer with a link
Answer:
It should be 75.4
Step-by-step explanation:
The formula for a cylinders volume is V=[tex]\pi[/tex]r^2h
so plugging those in would be
V=[tex]\pi[/tex](2)^2(6)= 75.4
Hope this helps!
Se ha construido un cuadrado sobre cada lado del triángulo rectángulo, Pitágoras dice que el cuadrado de área 25 cm2, es igual a sumar las áreas de los otros dos cuadrados, es decir, 16 cm2 y 9 cm2. Escribir la expresión algebraica que mejor represente la relación entre las áreas en la figura.
Answer:
Tenemos la siguiente expresión algebraica:
[tex]c^{2} = a^{2}+b^{2}[/tex] (1)
Donde:
[tex]c[/tex] - Hipotenusa, en centímetros.
[tex]a, b[/tex] - Catetos, en centímetros.
Step-by-step explanation:
Este ejercicio ofrece un recurso mnemotécnico para la comprensión y aplicación del Teorema de Pitágoras, el cual establece que el cuadrado de la hipotenusa es igual a la suma de los catetos elevados al cuadrado, siendo cada componente equivalente al área de un cuadrado hipotético, entonces, la expresión algebraica que representa esa relación entre las áreas es:
[tex]25\,cm^{2} = 16\,cm^{2} + 9\,cm^{2}[/tex]
[tex](5\,cm)^{2} = (4\,cm)^{2}+(3\,cm)^{2}[/tex]
Por analogía, tenemos la siguiente expresión algebraica:
[tex]c^{2} = a^{2}+b^{2}[/tex] (1)
Donde:
[tex]c[/tex] - Hipotenusa, en centímetros.
[tex]a, b[/tex] - Catetos, en centímetros.
Help me pleaseeeeeeee
Answer:
10
Step-by-step explanation:
Find the area of the shape. 2
Answer:
4
Step-by-step explanation:
factor completely x^2+6x-27?
Answer:
(x+9)(x-3)
Step-by-step explanation:
Find the number that multiplies to make -27 and adds to make 6. In this case it is 9 and -3. Use these numbers to factorise.
Answer:
(x-3) (+9)
Step-by-step explanation:
To know what numbers to use, factor out the constant (-27).
You would get the numbers : 1,3,9,27.
Then figure out which numbers would make the 6x true. In this case, we would need the 3 and 9. They also need to add up to 6x, so the 3 needs to be negative.
-3 & 9
Then form the factors:
(x-3) (x+9)
--------------------------
You can also check this to make sure.
Have a nice day!
A. Zara is learning about surface area and volume in math class. She begins to notice that she can apply this geometry in everyday life. When her
mom makes a jelly sandwich for her lunch, Zara notices it is similar to a rectangular prism and decides to measure its dimensions. She measures
the length as 13 cm, the width as 10.8 cm, and the height as 3 cm, as shown below.
Answer:
Volume fomlua is LxWxH, just multiply the numbers with a calculator:)
ASAP someone please simplify these two exponents
Answer:
3) [tex]qm^{-17}[/tex]
4) [tex]np^{-3}[/tex]
These should be your answer! Make sure to double check!
Step-by-step explanation:
Just simplify.
What is the solution to
this system of linear
equations?
Dog food bad contains 18 cups to fill it up his friend dog eats 1 1/2 each day he says he'll be able to feed his dog for 27 days that true?
Answer:
It's not true because 18 cups will only last 12 days, not 27 days.
Step-by-step explanation:
1 1/2 = 3/2
3/2(27) = 40.5 cups
18 = 3/2c
c = 12
how do you translate a figure in a coordinate plane?
Answer:
Answer down below
Step-by-step explanation:
When you perform translations, you slide a figure left or right, up or down. This means that on the coordinate plane, the coordinates for the vertices of the figure will change. To graph a translation, perform the same change for each point. You can identify a reflection by the changes in its coordinates.
2.5:3.5 simplified ratio
Answer:
5:7
Step-by-step explanation:
Help me with this problem please
Answer:
I'm not 100% sure, but I think the answer is 10 units squared.
Step-by-step explanation:
Find the area of each triangle, by multiplying each side, and dividing the answer in half. Add both of the triangles together, ending up as 6. Now we just find the area of the square. 2x2=4, add that to both of the triangles, and we're done. (2x2) ÷ 2 = 2 | (2x4) ÷ 2 = 4 | 2x2 = 4 | 4+4+2=10
Answer:
area=10 units^2
Step-by-step explanation:
[tex]a=\frac{(2+2+4)+(2)}{2} *2\\ =\frac{8+2}{2} *2\\ =\frac{10}{2} *2\\ =5*2\\ =10[/tex]
a=10 units^2
If your roots are -3 and -1, your factors will be (x+3)(x+1), yes? But if your roots are positive, like 3 and 1, would it still be (x+3)(x+1), or would you then make it negative?
Determine the number of possible positive and negative real roots of the equation:
x - 4x + 5x² + 9x² + 2x 8
a 2 or 0 negative roots; 3 or 1 positive roots
b. 5, 3, or 1 negative roots;
4, 2 or 0 positive roots
c.
d.
2 or 1 neative roots; 3 or 2 positive roots
3 or 1 negative roots; 2 or 0 positive roots
Find the area I will mark the BRAINIEST
Answer:
Step-by-step explanation:
Marissa had a $25 gift card for Roosters on Oxford. Each morning she purchases her $3 vanilla latte. Write an equation in slope- intercept form where y represents the amount of money on the card, after x visits.
Answer:
Y=3/1x+25
Step-by-step explanation: I believe this is correct. I was doing this a while ago so I might have it wrong. Y Is the money on the card, m, or 3/1 is the slope. B is the Y-intercept, which is 25.
Could someone check this answer for me?
Answer:
Yes you are correct! :)
For which equation does n= 7?
2n = 3
n+ 4 = 7
4n = 4
n-4=7
Answer:
does 1+1 still =2
Step-by-step explanation:
i hope so
please help me with this question thank you
Answer:
Shindeu NANI?!?
Step-by-step explanation:
Answer: X=0
Step-by-step explanation:
help me please.. im doing 8th grade math with pythagorean theorem i really need help please 10 points!!
Answer:78.1 is the answer and B or D will be your answer hope this helped
Step-by-step explanation:
THIS IS VERY IMPORTANT I WILL GIVE BRAINLIEST TO THE PERSON WHO DOES ALL 5 QUESTIONS FOR ME.
Answer:
Step-by-step explanation:
406525%Answer:
Q1; 40
Q2; 65
Q3; B (25)
Q4; A (?)
Q5; 63
Step-by-step explanation:
I believe
Is my work correct here I'm supposed to find the first four terms using the recursion formula?
Answer:
yes your formula is correct
Step-by-step explanation:
[tex]5^{-2}[/tex] × [tex]\sqrt[3]{8}[/tex]
Give your answer in decimal
Answer:
0.08
Step-by-step explanation:
∛8 = 2 as 2*2*2 = 8
[tex]5^{-2}[/tex] = [tex]\frac{1}{5^{2} }[/tex] = [tex]\frac{1}{25}[/tex]
[tex]\frac{1}{25}[/tex] * 2 = [tex]\frac{2}{25}[/tex] = 0.08
It costs $520 to plant 4 acres of corn. How much would it cost to plant \large \frac{3}{5} acre of corn?
Answer:
$78 to plant 3/5 an acre of corn
Step-by-step explanation:
you can set up a fraction.
520/4 = x/6
Cross multiply
312 = 4x
Divide both sides by 4 equal to
x=78
$78 to plant 3/5 an acre of corn
Given: the function f defined by f(x) = 3x2 . Which statement is true? 1) f(0) = 0 2) f(−2) = f(2) 3) f(5) + f(2) = f(7) 4) f(5) − f(2) = f(10)
Answer:
f(0) = 0 and f(−2) = f(2)
Step-by-step explanation:
Given: the function f defined by f(x) = 3x²
f(0) = 3(0)²
f(0) = 0
f(-2) = 3(-2)²
f(-2) = 3(4)
f(-2) = 12
f(2) = 3(2)²
f(2) = 3(4)
f(2) = 12
Hence f(-2) = f(2)
Therefore the correct options are f(0) = 0 and f(−2) = f(2)
Find the value or X. Round your answer to the nearest tenth.
Answer:
x = 9.3
Step-by-step explanation:
tan 25° = x/20
0.4663 = x/20
x = 9.3
HELP DUE IN 10 MINS!
x=??
Answer:
x = 3°Step-by-step explanation:
S and T are supplementary angles
m∠S + m∠T = 180°105° + 24x + 3° = 180°24x = 180° - 108°24x = 72°x = 72°/24x = 3°A pyramid at a museum has a height of 21 meters and a square base with side lengths of 30 meters. 21 m 30 m What is the approximate volume of the pyramid?
Answer: 6,300 m^3
Step-by-step explanation:
Put numbers into calculator
commen denominaor for 1/4 2/3
Answer:
The least common denominator is 12.
Step-by-step explanation:
Here's how I got my answer.
First, I listed out the multiples of 4, which is the denominator of 1/4.
4: 4, 8, 12, 16
Next, I listed out the multiples of 3, which is the denominator of 2/3.
3: 3, 6, 9, 12
The smallest number they have in common is 12.
Therefore, the least common demoninator (LCM) is 12.
Write two equivalent area to represent the perimeter of this rectangle. 5 X-2
Answer:
area = x-2 * 5
perimeter = 2(x-2) + 10