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2 years ago

15

In a group of 38 pupils, 5 play flute only.

1 answer:

Ne4ueva [31]2 years ago

3 0

5+14+12 = 31
38-31= 7
7 students play neither the flute or piano

7/38= 18.42%

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A teacher places n seats to form the back row of a classroom layout. Each successive row contains two fewer seats than the prece

Alex_Xolod [135]

Answer:

The number of seat when n is odd $S_n=\frac{n^2+2n+1}{4}$

The number of seat when n is even $S_n=\frac{n^2+2n}{4}$

Step-by-step explanation:

Given that, each successive row contains two fewer seats than the preceding row.

Formula:

The sum n terms of an A.P series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{n}{2}[a+l]$

a = first term of the series.

d= common difference.

n= number of term

l= last term

$n^{th}$ term of a A.P series is

$T_n=a+(n-1)d$

n is odd:

n,n-2,n-4,........,5,3,1

Or we can write 1,3,5,.....,n-4,n-2,n

Here a= 1 and d = second term- first term = 3-1=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=1 and d=2

$n=1+(t-1)2$

⇒(t-1)2=n-1

$\Rightarrow t-1=\frac{n-1}{2}$

$\Rightarrow t = \frac{n-1}{2}+1$

$\Rightarrow t = \frac{n-1+2}{2}$

$\Rightarrow t = \frac{n+1}{2}$

Last term l= n,, the number of term $=\frac{ n+1}2$ , First term = 1

Total number of seat

$S_n=\frac{\frac{n+1}{2}}{2}[1+n}]$

$=\frac{{n+1}}{4}[1+n}]$

$=\frac{(1+n)^2}{4}$

$=\frac{n^2+2n+1}{4}$

n is even:

n,n-2,n-4,.......,4,2

Or we can write

2,4,.......,n-4,n-2,n

Here a= 2 and d = second term- first term = 4-2=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=2 and d=2

$n=2+(t-1)2$

⇒(t-1)2=n-2

$\Rightarrow t-1=\frac{n-2}{2}$

$\Rightarrow t = \frac{n-2}{2}+1$

$\Rightarrow t = \frac{n-2+2}{2}$

$\Rightarrow t = \frac{n}{2}$

Last term l= n, the number of term $=\frac n2$ , First term = 2

Total number of seat

$S_n=\frac{\frac{n}{2}}{2}[2+n}]$

$=\frac{{n}}{4}[2+n}]$

$=\frac{n(2+n)}{4}$

$=\frac{n^2+2n}{4}$

4 0

2 years ago

The difference between a number divided by 3 and 4 is 20.

Alexxandr [17]

Let, the number be "a"

Now, according to the question,
$\frac{a}{3} - 4=20$

$\frac{a-12}{3} =20$

$a-12 =20*3$

$a-12=60$

$a = 60 + 12$

$a = 72$

So, the number is 72

7 0

2 years ago

Read 2 more answers

X +(-5) = 4<br> Step by step equations and I want to give you guys points so yeah love you

lubasha [3.4K]

Answer:

X - 5 = 4

Step-by-step explanation:

lol love u too no homo

4 0

2 years ago

Read 2 more answers

The volume of construction work was increased by 60% but the productivity of labor increased by only 25%. By what percent must t

ss7ja [257]

<span>The number of workers must be increased by 28%.</span>

5 0

2 years ago

On a map, 3 centimeters represents 150 kilometers. If a line between two cities measures 4.5 centimeters, how many kilometers ap

SCORPION-xisa [38]

Answer: 225km

Step-by-step explanation:

3cm --- 150

1cm ---- 50

Therefore 4.5cm * 50 = 225km

7 0

2 years ago