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3 years ago

Prove that (n-1, r)+(n, r-1)=(n,r)

Mathematics

1 answer:

vlabodo [156]3 years ago

6 0

Answer:

$\binom{n - 1}{r} + \binom{n}{r - 1} = \binom{n}{r} \\( n - 1) + n = n \\ n - 1 = 0 \\ n = 1 \\ r + (r - 1) = r \\ r = 1 \\ \binom{0}{1} + \binom{1}{0} = \binom{1}{1}$

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Sue Brown is a salesperson at a car dealership. She earned a gross pay of $8000 for the month of June. Her state tax rate is 3.5

Neporo4naja [7]

Sue Brown owes $280.00 in state taxes for the month.

Step-by-step explanation:

Given,

Gross pay of Sue in June = $8000

Tax rate = 3.5%

As full amount is taxable; therefore

Amount of tax to be paid = 3.5% of pay of June

Amount of tax to be paid = $\frac{3.5}{100}*8000$

Amount of tax to be paid = 0.035*8000

Amount of tax to be paid = $280.00

Sue Brown owes $280.00 in state taxes for the month.

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3 years ago

15 round to the nearest ten

babymother [125]

15 round by the nearest 10 is 20.

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3 years ago

9/11=?/22<br> A.12<br> B.4<br> C.9<br> D.18

Yanka [14]

9/11 is equal to 18/22, so then D.

8 0

4 years ago

Simplify the expression(a4−6a2b2+ b4)−(−2a4+5a2b2+ 3b4) and hence, find its value for a = 2and b = −1.

ELEN [110]

Answer:

(a) $3a^4 - 11a^2b^2 -2b^4$

(b) $3a^4 - 11a^2b^2 -2b^4= 2$

Step-by-step explanation:

Given

$(a^4 - 6a^2b^2+ b^4) - (-2a^4+5a^2b^2+ 3b^4)$

Solving (a): Simplify

$(a^4 - 6a^2b^2+ b^4) - (-2a^4+5a^2b^2+ 3b^4)$

Open brackets

$a^4 - 6a^2b^2+ b^4 +2a^4-5a^2b^2- 3b^4$

Collect Like Terms

$a^4 +2a^4- 6a^2b^2-5a^2b^2+ b^4 - 3b^4$

Simplify Like Terms

$3a^4 - 11a^2b^2 -2b^4$

Solving (b): Simplify when a = 2 and b = -1

$3a^4 - 11a^2b^2 -2b^4$

$3*(2)^4 - 11*(2^2)*(-1)^2 -2*(-1)^4$

$3 * 16 - 11 * 4 * 1 - 2 * 1$

$48 - 44 - 2$

$= 2$

Hence:

$3a^4 - 11a^2b^2 -2b^4= 2$

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3 years ago

Find the perimeter of the figure below, in centimeters.

SIZIF [17.4K]

Answer:

The answer to this is 127.8

Step-by-step explanation:

Perimeter is the outside of a shape so adding them all up would equal to 127.8

5 0

3 years ago

Prove that (n-1, r)+(n, r-1)=(n,r)​

Prove that (n-1, r)+(n, r-1)=(n,r)