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ArbitrLikvidat [17]
3 years ago
6

Evaluate 7C3 OA) 25 O B) 45 OC) 35 OD) 20

Mathematics
2 answers:
SpyIntel [72]3 years ago
8 0

Answer:

C) 35

Step-by-step explanation:

^7C_3 \\  =   \frac{7!}{3!(7 - 3)!}  \\=   \frac{7!}{3! \: 4!}   \\ =   \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times   4!}  \\ =   \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times   4!}    \\ = 35 \\ \huge \red{ \boxed{  \therefore \: ^7C_3  = 35}}

Morgarella [4.7K]3 years ago
8 0

Answer:

C=35

Step-by-step explanation:

⁷C₃

These is combination

using the rule it states that

ⁿCₐ= n!/(n-a)!a!

so therefore ⁷C₃= 7!/(7-3)!3! = 7!/4!3!=7x6x5x4x3x2x1/{(4x3x2x1)x(3x2x1)}

4x3x2x1 cancels itself as it appears up and down

7x6x5/6

6 cancels each itself as it appears up and down

7x5 = 35

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If TU =UV and T has a coordinate of -17 and U has coordinate 2, what is the coordinate of V?
Alex787 [66]

Step-by-step explanation:

this is one-dimensional ? everything just on one number line ?

TU = 2 - -17 = 2 + 17 = 19

TU is 19 units long (17 units on the negative side, and 2 units on the positive side of the number line).

therefore, to make TU = UV a true statement, UV has also to be 19 units long.

as U = 2,

V = U + UV = 2 + 19 = 21

5 0
1 year ago
Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)
viktelen [127]
\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}

The first line segment can be parameterized by \mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle with 0\le t\le1. Denote this first segment by C_1. Then

\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt
=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt
=108

The second line segment (C_2) can be described by \mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle, again with 0\le t\le1. Then

\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt
=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt
=-\dfrac{229}3

Finally,

\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3
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3 years ago
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Step-by-step explanation:

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He spent $30.99 and has $10.01 left
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Read 2 more answers
A wise man once said, “400 reduced by 3 times my age is 163.” What is his age? ( I need the step by step equation to solve this)
Ainat [17]

Answer: the wise man is 79

Step-by-step explanation:

400 - 3x = 163

400–163 =3x

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2 years ago
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