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4 years ago

For each of the following problems, identify whether it is a permutation or combination problem, and then give the answer.

Mathematics

1 answer:

Naddika [18.5K]4 years ago

8 0

Answer:

See below.

Step-by-step explanation:

a) Permutation because the order of the batting matters.

Answer is 15P9 = 15! / (15 - 9)!

= 1,816,214,400

b) Combination because the order of the 5 person squads does not matter.

Answer is 11C5 = 11! / 5!6!

= 462.

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the measure of the supplement angle is 24 more than three time the measure of the original angle. find the measures of the angle

Gala2k [10]

Step-by-step explanation:

Let x° be the original angle. Then the supplement angle is (180 - x)° and (180 - x) = 3x + 24.

180 - x = 3x + 24

4x = 156

x = 39

Hence the original angle is 39° and the supplementary angle is 141°.

4 0

4 years ago

Given s = 10 and h = 15. Find the total surface area of the square prism.

anastassius [24]

Answer:

150

Step-by-step explanation:

h = hight

s = sides

surface = 10 x 15

surface = 150

(V = 10 x 10 x 15

(V = 100 x 15)

(V = 1500)

(Base area = B)

(B = Lenght x Width)

(B = 10 x 10)

(B = 100)

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2 years ago

Pls help i dont get this and i want u to explain this pls

Oxana [17]

Answer:

$0.32/ $0.31

Step-by-step explanation:

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3.75÷12oz= $0.31

6 0

3 years ago

1. Find the sum of the following AP (i) 2, 4, 6, ... to n terms (ii) 7, 71, 72, 73, ... to 50 terms (iii) a, (a + b), (a + 2b),

Mrac [35]

Let $S_n$ be the sum of the first $n$ natural numbers.

$S_n = 1 + 2 + 3 + \cdots + n$

We can reverse the order of terms to write

$S_n = n + (n-1) + (n-2) + \cdots + 1$

so that doubling up, we get

$2S_n = (1 + n) + (2 + (n-1)) + (3 + (n-2)) + \cdots + (n + 1)$

$2S_n = (n + 1) + (n + 1) + (n + 1) + \cdots + (n + 1)$

and since there are $n$ terms in $S_n$ , it follows that

$2S_n = n(n+1) \implies S_n = \dfrac{n(n+1)}2$

Now, for an arithmetic sequence starting with $a_0$ and having common difference $d$ between consecutive terms, the sum of the first $n$ terms of this sequence is

$a_0 + (a_0 + d) + (a_0 + 2d) + \cdots + (a_0 + (n-1)d) \\\\ ~~~~~~~~ = (a_0 - d + d) + (a_0 - d + 2d) + (a_0 - d + 3d) + \cdots + (a_0 - d + nd) \\\\ ~~~~~~~~ = (a_0 - d) n + d S_n \\\\ ~~~~~~~~ = \dfrac d2 n^2 + \left(a_0 - \dfrac d2\right) n$

(i) This sum is simply

$2 + 4 + 6 + \cdots + 2n \\\\ ~~~~~~~~ = 2 (1 + 2 + 3 + \cdots + n) \\\\ ~~~~~~~~ = 2 S_n \\\\ ~~~~~~~~ = \boxed{n(n+1)}$

(ii) The first term in this sequence should be 70 if it's arithmetic. The common difference is then 1, the 50th term is 70 + (50 - 1)•1 = 119, so

$70 + 71 + 72 + \cdots + 119 \\\\ ~~~~~~~~ = \dfrac12\cdot50^2 + \left(70 - \dfrac12\right)\cdot50 \\\\ ~~~~~~~~ = \boxed{4725}$

(iii) The first term is $a$ and the common difference is $b$ , so

$a + (a + b) + (a + 2b) + \cdots + (a + b(n-1)) \\\\ ~~~~~~~~ = \boxed{\dfrac b2 n^2 + \left(a - \dfrac b2\right)n}$

(iv) The first term is $x+y$ and the common difference is $-2y$ . Then the 20th term in the sequence is $x+y - 19\cdot2y= x-37y$ , so

$(x + y) + (x - y) + (x - 3y) + \cdots + (x - 37y) \\\\ ~~~~~~~~ = -\dfrac{2y}2\cdot20^2 + \left(x + y + \dfrac{2y}2\right)\cdot20 \\\\ ~~~~~~~~ = \boxed{20x - 360y}$

(v) Note that the first term is

$(a - b)^2 = a^2 + b^2 - 2ab$

so that the common difference is $2ab$ . Then

$(a - b)^2 + (a^2 + b^2) + (a + b)^2 + \cdots + (a^2 + b^2 - 2ab + 2ab(n-1)) \\\\ ~~~~~~~~ = \dfrac{2ab}2 n^2 + \left(a^2 + b^2 - 2ab - \dfrac{2ab}2\right) n \\\\ ~~~~~~~~ = \boxed{abn^2 + (a^2 - 3ab + b^2)n}$

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2 years ago

Math need help please

Nutka1998 [239]

Answer:

same side interior

Step-by-step explanation:

6 0

3 years ago