Connect with a global community of experts on IDNLearn.com. Get step-by-step guidance for all your technical questions from our knowledgeable community members.
Sagot :
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.
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.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.