Simplify the expression 6C5.
a.6.
b. 24
C. 30
d. 720

Answers

Answer 1
Answer:  A) 6

=====================================================

Explanation:

Plug n = 6 and r = 5 into the nCr combination formula

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_6 C _5 = \frac{6!}{5!*(6-5)!}\\\\_6 C _5 = \frac{6!}{5!*1!}\\\\_6 C _5 = \frac{6*5*4*3*2*1}{5*4*3*2*1*1}\\\\_6 C _5 = \frac{720}{120}\\\\_6 C _5 = 6\\\\[/tex]

Or you could use the shortcut

[tex]_n C _{n-1} = n\\\\[/tex]

Yet another path you could take is to use Pascal's Triangle. Locate the row that starts with 1,6,... and then locate the second to last item. That value in the triangle is 6.

A real world interpretation is to consider having 6 people and you are selecting 5 of them to form a group where order doesn't matter. How many ways are there to do this? Well there are 6 such ways because there are 6 ways to leave someone out of the group.


Related Questions

A triangle has side lengths of 2 feet, 5.4 feet, and 5 feet. The angle measures are 90 degrees, 73 degrees, 17 degrees. Another triangle has side lengths of 3 feet, 8.1 feet, 7.5 feet. The angle measures are 90 degrees, 73 degrees, 17 degrees. Are the triangles similar? If so, what is the scale factor going from the top triangle to the bottom triangle?

Answers

Answer:

Yes. The factor is 3/2 (=1,5)

Step-by-step explanation:

They have all the 3 angles congruent, so they are similar. You calculate the scale factor by dividing the hypotenuse (for example) of the second triangle by the hypotenuse of the first one.

Answer:

1) yes 2) 1.5

Step-by-step explanation:

have a nice day! <:

Are quantity and amount are same thing, if no so tell the difference ?

no spam ​

Answers

Answer:

No

Amount should be used when you're talking about a singular noun that CAN'T be measured. ... –Quantity should be used for an inanimate, single or plural noun that CAN be counted or measured.

Step-by-step explanation:

Hope this helps you !!!

Help please
Simplify the difference quotient (f(x + h) − f(x) )/h if h ≠ 0.
f(x) = x2 + 38

Answers

Answer:

2x + h

Step-by-step explanation:

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

= [tex]\frac{(x+h)^2+38-(x^2+38)}{h}[/tex]

= [tex]\frac{x^2+2hx+h^2+38-x^2-38}{h}[/tex]

= [tex]\frac{2hx+h^2}{h}[/tex]

= [tex]\frac{h(2x+h)}{h}[/tex] ← cancel h on numerator/ denominator

= 2x + h

Which graph best represents the solution to this system of inequalities?

A.
B.
C.
D.

Answers

Answer:

letter A po

Step-by-step explanation:

thanks for brain less

2(1+a) * 5(1+a)
help u u want to help or else continue helping

Answers

Step-by-step explanation:

We simply multiply what there is to multiply:

10(1+a)^2 = 10a^2 + 20a + 10

= (2+2a)*(5+5a)
=10+10a+10a+10a^2
=10+20a+10a^2

Find sum of arithmetic series where a1 = 7, n=31, nth a =127

Answers

Answer:

Sum of arithmetic series is [tex]2077[/tex]

Step-by-step explanation:

We have [tex]n[/tex]th term of arithmetic sequence

[tex]a+(n-1)d[/tex]

Here

[tex]a+(n-1)d=127\\\\7+(31-1)d=127\\\\d=\frac{120}{30} \\\\=4[/tex]

Sum of arithmetic sequence [tex]=\frac{n}{2} (2a+(n-1)d)[/tex]

[tex]=\frac{31}{2} (2\times7+(31-1)4)\\\\=\frac{31}{2} (14+120)\\\\=31\times67\\\\=2077[/tex]

Answer:

The sum of arithmetic series is 2077.

Step-by-step explanation:

Solution :

Here we have provided that :

»» [tex]\rm{a_1}[/tex] = 1»» [tex]\rm{n}[/tex] = 31»» [tex]\rm{a_n}[/tex] = 127

We need to find :

»» The sum of arithmetic series.

Here's the required formula to find the sum of arithmetic series :

[tex]\longrightarrow{\pmb{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]

Substituting all the given values in the formula to find the sum of arithmetic series :

[tex]{\longrightarrow{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(7 + 127 \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(134 \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \times 134 }}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{\cancel{2}} \times \cancel{134 }}}[/tex]

[tex]{\longrightarrow{\sf S = 31 \times 67}}[/tex]

[tex]{\longrightarrow{\sf S = 2077}}[/tex]

[tex]\star \: {\underline{\boxed{\sf{\red{S = 2077}}}}}[/tex]

Hence, the sum of arithmetic series is 2077.

[tex]\rule{300}{1.5}[/tex]

Will mark brainly!! :)

If f(2) for f(x) = [tex]\frac{2}{x-1}[/tex]+6 is 8. then what is [tex]f^{-1} (8)[/tex]

Answers

Answer:

2

Explanation:

we get inverse functions by interchanging places of domain and range of the original fuction so rhe domain becomes a range and the range becomes a domain.

so if 2 belongs to the domain of the original fuction and its corresponding element in the range is 8, we simply interchange between 2 and 8 in order to solve the fuction without any subistitution in the original function.

6x+3y=-3 how to graph it need answers quick

Answers

Answer:

Equation in slope intercept form: y = -2x -1

Step-by-step explanation:

First you must convert this equation from standard form to slope intercept form (y=mx+b).

Subtract 6x on both sides to get 3y = -6x - 3. Then divide by 3 on both sides to get y = -2x - 1.

Now to graph:

First we will plot the y-intercept, which will be (0,-1). The point will be on the y-axis, since that's the point in which the line will cross.

Next we will go down 2 units and over to the right 1 unit, until we get to the next point.

(Picture is attached above for your convenience⤴⤴⤴)

Hope this helps you :)

Blake gives piano lessons in the evenings. He earns $20 for each piano lesson and has between 0 and 6 lessons each evening. The amount he earns in an evening depends on the number of lessons he gives. What is the range of this relation?.

Answers

The range of the relation will be expressed as 0 ≤ g(x) ≤ 120

Let the number of lessons he gives be x

If he earns $20 for each piano lesson, the amount he will earn on x lessons will be $20x

Writing this as a function will give:

g(x) = 20x

where g(x) is the range of the relation.

If he has between 0 and 6 lessons each evening, the corresponding range at x = 0 and x = 6 is given as;

g(0) = 20(0) = 0g(6) = 20(6) = 120

Therefore the range of the relation will be expressed as 0 ≤ g(x) ≤ 120

Learn more on range of a function here: https://brainly.com/question/10878781

Answer: {0, 20, 40, 60, 80, 100, 120}

Step-by-step explanation: Remember we only use inequality signs for continuous relations with an infinite amount of values or data points or values or points. When we're given a set finite amount of data points we use brackets for this data because it is a discrete relation.

And for this problem we're looking for the range of the relation and recall the range is the dependent values or variables that depend on the domain or independent variables. The amount of money he earns depends on the amount of hours he works. Hence, the range is {0, 20, 40, 60, 80, 100, 120} the amount of possible money he can earn.

Find the unknown side (w) of the rectangular solid. Please help..

Answers

Answer:

the answer should be 2

Step-by-step explanation:

8×13=104

208÷104=2

Answer:

w = 2

Step-by-step explanation:

V_rectangular prism = l * w * h

208 = 13 * w * 8

208 = 104 * w

w = 208/104

w = 2

-Chetan K

Pls help plss

Right answer = Brainliest
Wrong answer = Reported​

Answers

Answer:

Step-by-step explanation:

1. 15/50 = 3/10

2. 8/24 = 1/3

3. 14/49 = 2/7

4. 6/63 = 2/21

5. 18/81 = 2/9

Ok done. Thank to me :>

The sum of a number and six is 22. What is the number?

Answers

Answer:

16

Step-by-step explanation:

22-6=16 16+6=22

hope this helps! :)

16 because if you add 16 you should get your answer

A ball is thrown upward from a height of 15 feet with an initial upward velocity of 5 feet per second. Use the formula b(t)= -16t^2 + 5t + 15 to find the time it takes for the ball to reach the maximum height of the ball. Round to the nearest tenth

A. 0.2 seconds

B. 0.1 seconds

C. 0.3 seconds

D. 0.9 seconds​​

Answers

Answer:

0.2 seconds

Step-by-step explanation:

The graph of b(t) = -16t^2 + 5t + 15 is a parabola opening downward.  The maximum value of b(t) occurs at the vertex.  The t-coordinate of the vertex is t = -5 / (2(-16)) = 5/32 = 0.15625 sec ≈ 0.2 sec.  

Answer:

A) 0.2 seconds

Step-by-step explanation:

[tex]b(t)=-16t^2+5t+15[/tex]

[tex]v(t)=-32t+5[/tex] <-- Take the derivative

[tex]0=-32t+5[/tex] <-- Set equal to 0

[tex]-5=-32t[/tex]

[tex]\frac{5}{32}=t[/tex]

[tex]t=\frac{5}{32}[/tex]

[tex]t\approx0.2[/tex]

Therefore, it will take the ball about 0.2 seconds to reach its maximum height (which happens to be about 15.4 feet BTW).

Alternatively, another non-calculus approach is the fact that the parabola opens downward, and as such, the maximum of [tex]b(t)[/tex] occurs at the vertex where [tex]t=-\frac{b}{2a}[/tex], therefore [tex]t=-\frac{5}{2(-16)}=\frac{-5}{-32}=\frac{5}{32}\approx0.2[/tex]

A store owner bought 15001500 pencils at \$0.10$0.10 each. If he sells them for \$0.25$0.25 each, how many of them must he sell to make a profit of exactly \$100.00$100.00

Answers

Based on the information given, the number of pencils that should be sold will be 1000 pencils.

Let the number that should be sold be x.

A store owner bought 1500 pencils at $0.10 each. Therefore, the cost price will be:

= 1500 × $0.10 = $150

Profit = Selling price - Cost price

100 = 0.25x - 150

0.25x = 100 + 150

0.25x = 250

x = 250/0.25

x = 1000

Therefore, 1000 pencils should be sold.

Learn more about equations on:

https://brainly.com/question/13802812

. Macy's mom gives her $100 for her birthday. She buys shirts that're $15 each and pairs of pants that're $25 each. Which expression can be used to calculate how much money she has left? (Use s for shirts and p for pants.) *

Answers

Answer:

100-(15s+25p)

Step-by-step explanation:

(3x-16) = (6x+7) = (11y-32)

Answers

Answer:

11y = -32  

Step-by-step explanation:

mr farmer rectangular land measures 2000 meters by 3000 meters. if he walks around the perimeter of his land, how far does he walk

Answers

Answer:

10000 meters

Step-by-step explanation

To find perimeter you add the length of each side of the shape. Since the land is a rectangle there are two pairs that are parrallel, being 2000 and 3000. Making the distance 2000 + 2000 + 3000+ 3000 = 10000

Hope this helps!

Ryan equation for the perimeter

Answers

2x+16+20=60

2x+ 36=60

2x=60-36

2x=24

X= 24/2

X= 12

Sketch the graph of each linear inequality

Answers

Answer:

hope you can see these, the red graph is problem 3 and the blue graph is problem 5 :)

y=1.5x+8 which represents the equation when solved for x?

Answers

[tex]y=1.5x+8\\\\\implies 1.5x = y-8\\\\\implies x = \dfrac{y-8}{1.5}\\\\\implies x = \dfrac{y-8}{\tfrac 32}}\\\\\implies x = \dfrac{2(y-8)}{3}\\\\\implies x = \dfrac 23 y- \dfrac{16}3[/tex]

How to rationalize the denominator that is a radical.

Answers

Answer:

Option B is the correct answer, 3√2

Need help please if anyone one can help me now I will like that. Thanks

Answers

The answer is the last on

Sally saved 65% of her pay check. If she made $500, how much did she save?

Answers

Answer: 325 dollars

Step-by-step explanation:

In order to find out a percentage of somethin, you can simply multiply and divide

[tex]500*65=32500[/tex]

32500÷100= 325

Please help me with percentages.

Answers

If there were no tip, each person would have to pay $5. They pay this much because if the bill is $50 and there are 10 people, would would calculate by 50 divided by 10 which would equal 5 so 10 people pay $5 dollars. The total would be $50.

Answer:

I think the answer would be 10%.

A ream of paper contains 480 sheets. Each sheet is 0.014 cm thick. Find the thickness of the ream of paper.

Answers

Answer:

19.2 cm

Step-by-step explanation:

480×0.014

=19.2

Please answer circle theorem question.
Many thx.

Answers

Answer:

x = 125

Step-by-step explanation:

Tangents from an external point to a circle are congruent , that is

CA = CB

Then Δ ABC is isosceles with base angles being congruent

∠ BAC = ∠ ABC = [tex]\frac{180-70}{2}[/tex] = [tex]\frac{110}{2}[/tex] = 55°

∠ ABC and x are adjacent angles on a straight line and sum to 180° , so

x = 180° - 55° = 125°

Then x = 125

pls pls pls help im very behind

the options for A) 0 24.5 39.2 44.1

the options for B are the same for A

Answers

Answer: A is 24.5

B is 0

Step-by-step explanation:

The first 3 sec are increasing. On sec 4 it starts to decrease. .

what is the solution to the equation 4(x - 3) - 8 = 16?

Answers

Step-by-step explanation:

4(x-3)-8=16

4x-12-8=16

4x-20=16

4x-20+20=16+20

add

4x=36

divide both

4x/4  36/4

Simplify

x = 9

hi pls help me solve this​

Answers

Answer:

-23.33

Step-by-step explanation:

C = 5/9 (F - 32)

C = 5/9 (-10 - 32)

C = 5/9 (-42)

C = -23.33

Please answer!!!!!!!!!!!!!! 25 PTS!

Answers

Answer:

b

Step-by-step explanation:

b

It’s b I hope it helps
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