Sure, let's solve the problems step-by-step:
5. The following were the scores of Gandhi House in five rounds of an Inter House Quiz Competition: [tex]$-10,+5,-4,-3,$[/tex] and [tex]$+15$[/tex]. What was the final score?
To find the final score, we need to sum all the scores:
[tex]\[ -10 + 5 - 4 - 3 + 15 \][/tex]
Step-by-step addition:
1. Start with [tex]\(-10\)[/tex].
2. Add [tex]\(5\)[/tex]: [tex]\( -10 + 5 = -5 \)[/tex].
3. Add [tex]\(-4\)[/tex]: [tex]\(-5 - 4 = -9 \)[/tex].
4. Add [tex]\(-3\)[/tex]: [tex]\(-9 - 3 = -12 \)[/tex].
5. Finally, add [tex]\(15\)[/tex]: [tex]\(-12 + 15 = 3\)[/tex].
So, the final score for Gandhi House is [tex]\(\boxed{3}\)[/tex].
6. Find the sum.
(i) [tex]\( 100 + (-18) + (-25) + (-63) \)[/tex]
1. Start with [tex]\(100\)[/tex].
2. Add [tex]\(-18\)[/tex]: [tex]\( 100 - 18 = 82 \)[/tex].
3. Add [tex]\(-25\)[/tex]: [tex]\( 82 - 25 = 57 \)[/tex].
4. Add [tex]\(-63\)[/tex]: [tex]\( 57 - 63 = -6 \)[/tex].
So, the sum is [tex]\(\boxed{-6}\)[/tex].
(ii) [tex]\( 1295 + (-410) + (-878) + 312 \)[/tex]
1. Start with [tex]\(1295\)[/tex].
2. Add [tex]\(-410\)[/tex]: [tex]\( 1295 - 410 = 885 \)[/tex].
3. Add [tex]\(-878\)[/tex]: [tex]\( 885 - 878 = 7 \)[/tex].
4. Add [tex]\(312\)[/tex]: [tex]\( 7 + 312 = 319 \)[/tex].
So, the sum is [tex]\(\boxed{319}\)[/tex].
(iii) [tex]\( 1000 + 873 + (-874) + (-999) \)[/tex]
1. Start with [tex]\(1000\)[/tex].
2. Add [tex]\(873\)[/tex]: [tex]\( 1000 + 873 = 1873 \)[/tex].
3. Add [tex]\(-874\)[/tex]: [tex]\( 1873 - 874 = 999 \)[/tex].
4. Add [tex]\(-999\)[/tex]: [tex]\( 999 - 999 = 0 \)[/tex].
So, the sum is [tex]\(\boxed{0}\)[/tex].
(iv) [tex]\( 2004 + 516 + (-520) - 1999 \)[/tex]
1. Start with [tex]\(2004\)[/tex].
2. Add [tex]\(516\)[/tex]: [tex]\( 2004 + 516 = 2520 \)[/tex].
3. Add [tex]\(-520\)[/tex]: [tex]\( 2520 - 520 = 2000 \)[/tex].
4. Subtract [tex]\(1999\)[/tex]: [tex]\( 2000 - 1999 = 1 \)[/tex].
So, the sum is [tex]\(\boxed{1}\)[/tex].
(v) [tex]\( (-7) + (+10) + (-6) + (-11) + (+9) + (+2) \)[/tex]
1. Start with [tex]\(-7\)[/tex].
2. Add [tex]\(10\)[/tex]: [tex]\(-7 + 10 = 3 \)[/tex].
3. Add [tex]\(-6\)[/tex]: [tex]\( 3 - 6 = -3 \)[/tex].
4. Add [tex]\(-11\)[/tex]: [tex]\( -3 - 11 = -14 \)[/tex].
5. Add [tex]\(9\)[/tex]: [tex]\( -14 + 9 = -5 \)[/tex].
6. Add [tex]\(2\)[/tex]: [tex]\( -5 + 2 = -3 \)[/tex].
So, the sum is [tex]\(\boxed{-3}\)[/tex].
These are the step-by-step solutions to each of the given questions.
