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
Seven people went to the movies. The
number of adults was one more than the
Children. Write a system of equations that
represents the number of adults and child-
ren. Solve the system algebraically.
Answer:
3 kids, 4 Adults
Step-by-step explanation:
x = kids
y = adults
Total = 7
x + y = 7
y = x + 1
do a bit of solvin, too much to type lol
2x = 6
x = 3
And since X = 3 and Y = X + 1
Y = 3 + 1 = 4
Someone can help me please?
Answer:
19 x 10^12 = 1.9 x 10 ^13
23 x 10^8 = 2.3 x 10^9
23 x 10^7 = 2.3 x 10^8
19 x 10^-12 = 1.9 x 10^-11
23 x 10^-8 = 2.3 x 10^-7
23 x 10^-7 = 2.3 x 10^-6
Step-by-step explanation:
What is the product?
(y3+3y+7) x (8y2+y+1)
Answer:
I believe that this is what you mean. (y^3+3y+7)*(8y^2+y+1)
Step-by-step explanation:
So your answer would be: 8y^5+y^4+25y^3+59y^2+10y+7
Have a nice day!
I really hope this helps!
You don’t have to do all 4 but if you can do some that would be great.
Find the measure of the indicated angle that makes lines u and v parallel.
Answer:
13) ?=90°
14) ?=180°-48° (int angles, u//v)
=132°
15) ?=93° (alt angles, u//v)
16) ?=96° (alt angles, u//v)
Answer:
13: 90°
14: 132°
15: 87°
16: 84°
Step-by-step explanation:
Just subtract the value given from 180
Hope this helps!
A car travels 78 miles on 3 gallons of gasoline. How many miles can the car travel on one gallon of gasoline?
Answer:
26 miles.
Step-by-step explanation:
you want to divide 78 by 3.
George practises his guitar for 1 1/5 hours per day on school days. On Saturday he increases to 2 1/2 times his normal time. How many hours does he practice on Saturdays.
Answer: 231/10
Step-by-step explanation: 11/5 x 21/2
= (11 x 21) = 231
= 231/5 x 2
= 231/10
Answer:
3 hours
Step-by-step explanation
It would be easier to convert your fractions into decimals.
1/5 is the same as 2/10. Since the denominator was multiplied by 2 then the numerator must be multiplied by 2 also.
2/10 in decimal form is 0.2
He would practice 1.2 hours per day on school days
On Saturday his practice is 2 1/2 times longer than 1.2 hours.
Convert 1/2 into decimal form. 1/2 is the same as 0.5.
So 2 1/2 is the same as 2.5
If you multiply the original time (1.2 hours) by 2.5, you'll know how long he practices on Saturday.
1.2 x 2.5 = 3 hours.
1.2
x 2.5
-------
60
24
------------
300
since you have 1 decimal place in the top number and 1 decimal in the bottom number, you must move your decimal 2 places to the left on your answer. Instead of 300, your answer becomes 3.00
An artist mixes 1.6 ounces of green paint with 1.85 ounces of white paint. She then divides the paint into 6 equal parts.How much paint is in each part?(Round to the nearest tenth.)
Answer:
0.6
Step-by-step explanation:
I took the quiz
Answer:0.6
Step-by-step explanation:
What is the weight, in kg, shown by the arrow on the scale below?
See pic attached
Step-by-step explanation:
according to arrow the weight is 1400 g.
we know,
1 kg = 1000 g
so,
1 g = 1/1000 kg
so,
1400/1000 = 1.4 kg ans
hope this answer helps you dear!
Answer:
1.4 kg
Step-by-step explanation:
1400 grams, to find kg you have to divide by 1000
help me find the answer im confused how to solve it
Answer:
A
Step-by-step explanation:
Since slope is rise over run:
The slope of KM would be [tex]\frac{KL}{LM}[/tex] and the slope of PS would be [tex]\frac{PR}{RS}[/tex]
So [tex]\frac{KL}{LM}[/tex] = [tex]\frac{PR}{RS}[/tex]
Larry's age if he is 5 years younger than twice his brother's age. Use b for his brothers age.
Answer:
(b2)-5
Step-by-step explanation:
Which of the following notations correctly describe the end behavior of the
polynomial graphed below?
A pipe can pump 1000 gallons of water in 4 hours.
How long would it take the pipe to fill a 2500 gallon pool?
10 hours
Step-by-step explanation:
4 hours 1000 gallon
4 hours 1000 gallon
2000 gallon
500 gallon 2 hours
Enter the polynomial function with the least degree and a leading coefficient of 1 that has the given zeros. Enter your answer in standard form. 1,-1(multiplicity 3), and 3i
Answer:
0
Step-by-step explanation:
Translate the phrase into an algebraic expression.
The product of x and 4.
Answer: x4
Step-by-step explanation:
please help me with number four
The force (F) needed to cause the acceleration (a) of an object mass, m, is given by the equation, F=ma where m is the object's mass. If a 12-Newton force causes the object to accelerate to 3 m/s2, what is that object's mass? The unit for this mass is kg.
Answer: the answer is 4 kg
because your force was 12
and your accelerate was 3 m/s2
next .... you divide 12/3 and that =4kg
Step-by-step explanation:
The points (2, 10) and (0, 4) fall on a particular line. What is its equation in slope-intercept form?
Answer:
slope=x^2-x^1/y^2-y^1
this is the formula.
Translate this sentence into an equation. 39 is the product of Hector's height and 3. Use the variable h to represent Hector's height.
Answer:
3h=39
Step-by-step explanation:
452.16 rounded to the nearest tenth
Answer: 452.2
Step by Step Explanation: Find the number in the tenth place 1 and look one place to the right for the rounding digit 6 round up if this number is greater than or equal to 5 and round down if it is less than 5
.
Rounding 452.16 to the nearest tenth gives us: 452.1.
Given that we need to round 452.16 to the nearest tenth,
We look at the digit in the hundredth place, which is the second decimal place, and round 452.16 to the nearest tenth.
One is the digit at the hundredth position.
We round down because 1 is less than 5, therefore.
Simply drop all the digits following the tenths place and leave the tenths place digit alone if you want to round down.
Rounding 452.16 to the nearest tenth, we obtain: 452.1.
Hence rounding 452.16 to the nearest tenth gives us: 452.1.
Learn more about rounding figures click;
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HELP 100 POINTS & BRAINLIEST!!!!
What is the domain of the following points?
{-1, 2, 1}
{-2, 1, 2}
{1, 2}
{-2, -1, 1, 2}
Answer:
-2,1,2
Step-by-step explanation:
Answer:
I hope this helps.
Step-by-step explanation:
anybody help me please?
Answer:
I can help but im going to need a question
Step-by-step explanation:
We need the question so we are able to help :P
what is the
The value of y varies directly with x. If x = 3, then y
value of x when y= 168?
Mrs. Chiu checks 30 problems in 2 minutes. How many problems can Mrs. Chiu check in 68 minutes?
If a rotation takes triangle CAT to C'A'T', what is C'T'?
Answers:
3
square root of 17
5
Cannot be determined
Answer:
its B
Step-by-step explanation:
the A point is in line with 10 squared and its in line with the 17 squared
The measure of C'T' after rotation of transformation is option (B) square root of 17 is the correct answer.
What is a rotation transformation?A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction on the coordinate plane. In both transformations the size and shape of the figure stays exactly the same.
For the given situation,
The graph shows the triangle CAT.
If a rotation takes triangle CAT to C'A'T',
then from the definition of rotation transformation the size and shape of the figure stays exactly the same.
Thus the measure of C'T' is same as CT.
⇒ [tex]C'T' =\sqrt{17}[/tex]
Hence we can conclude that the measure of C'T' after rotation of transformation is option (B) square root of 17 is the correct answer.
Learn more about rotation transformation here
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According to the image below What does n=
Answer:
N=3
Step-by-step explanation:
When we divide we substract the powers when we multiply we add up the powers of the same number.
Answer:
n = 3
Step-by-step explanation:
19) If manish saves 40% percent of his monthly income and he spends Rs. 15,000 every month, find his monthly income.
Answer:
Rs 25000
Step-by-step explanation:
Saves 40%
Spends 60%
Spending 60% = 15000
If 60% = 15000
Then divide it by 6 to get 10%
10% = 15000 ÷ 6
10% = 2500
100% = 25000
Aimee went to a stationary shop. She purchased 2 packs of red pens, 4 packs of black pens, and 3 packs of blue pens.
The cost of each pack of pens was $2.50. Which expression shows the total amount Aimee spent on the pens?
A ($2.50 x 2 x 4x3)
B $2.50 x (2+4+3)
C($2.50 x 2) + 3+4
D (52.50 +2 +4+3)
Answer:
A.
Step-by-step explanation:
The answer is B.
Each pack costs 2.50, so this means we can add all of our packs brought together, before multiplying. (2+4+3)=7. So our final equation should be 7 x 2.50 ,therefore B is our correct answer.
Hope this helps. & don't forget to drink water !!
Find x to the nearest tenth.
18.7
1.3
19.3
To solve this problem, we will need to use trigonometry.
Remember: SOH-CAH-TOA
Looking from the angle, we know the opposite side and want to find the adjacent side. Therefore, we should use the tangent function.
tan(15) = 5 / x
x * tan(15) = 5
x = 5 / tan(15)
x = 18.7 units
Hope this helps!! :)
If i get good grades in 9th grade will it affect the classes I will receive in 9th grade?
Had a stroke reading this.
Find the value of x that makes p||q
Answer:
x = 30
Step-by-step explanation:
The angle on the opposite side as the identified angle (80°) is whatever is left over from 180° (which would be 100°). Therefore, the angle on the diagonally opposite side is identical.