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Sagot :
Sure, let's solve each of the conversion problems step by step. We will use the provided relationships between different units to convert them.
1. Convert 3 hours to seconds:
[tex]\(3 \text{ hrs} = 3 \times 3600 \text{ sec/hr} = 10800 \text{ sec}\)[/tex]
2. Convert 0.035 mg to cg:
[tex]\(0.035 \text{ mg} = 0.035 \times 0.1 \text{ cg/mg} = 0.0035 \text{ cg}\)[/tex]
3. Convert 5.5 kg to lbs:
[tex]\(5.5 \text{ kg} = 5.5 \times 2.20462 \text{ lbs/kg} = 12.1254 \text{ lbs}\)[/tex]
4. Convert 2.5 yds to inches:
[tex]\(2.5 \text{ yds} = 2.5 \times 36 \text{ in/yd} = 90 \text{ in}\)[/tex]
5. Convert 1.3 years to hours (1 year = 365 days):
[tex]\(1.3 \text{ yrs} = 1.3 \times 365 \text{ days/yr} \times 24 \text{ hrs/day} = 11388 \text{ hrs}\)[/tex]
6. Convert 3 moles to molecules (1 mole = [tex]\(0.02 \times 10^{25}\)[/tex] molecules):
[tex]\(3 \text{ moles} = 3 \times 0.02 \times 10^{25} \text{ molecules/mole} = 6 \times 10^{23} \text{ molecules}\)[/tex]
7. Convert [tex]\(2.5 \times 10^{21}\)[/tex] molecules to moles:
[tex]\(2.5 \times 10^{21} \text{ molecules} / (0.02 \times 10^{25} \text{ molecules/mole}) = 0.0125 \text{ moles}\)[/tex]
8. Convert 5 moles to liters (1 mole = 22.4 liters):
[tex]\(5 \text{ moles} = 5 \times 22.4 \text{ liters/mole} = 112 \text{ liters}\)[/tex]
9. Convert 100 liters to moles:
[tex]\(100 \text{ liters} / 22.4 \text{ liters/mole} = 4.464285714 \text{ moles}\)[/tex]
10. Convert 50 liters to molecules:
[tex]\[ 50 \text{ liters} / 22.4 \text{ liters/mole} = 2.232143 \text{ moles} \][/tex]
[tex]\[ 2.232143 \times 0.02 \times 10^{25} \text{ molecules/mole} = 4.464285714 \times 10^{23} \text{ molecules} \][/tex]
11. Convert [tex]\(5.0 \times 10^{25}\)[/tex] molecules to liters:
[tex]\[ 5.0 \times 10^{25} \text{ molecules} / (0.02 \times 10^{25} \text{ molecules/mole}) = 2500 \text{ moles} \][/tex]
[tex]\[ 2500 \times 22.4 \text{ liters/mole} = 56000 \text{ liters} \][/tex]
12. Convert [tex]\(7.5 \times 10^3\)[/tex] mL to liters:
[tex]\[ 7.5 \times 10^3 \text{ mL} / 1000 \text{ mL/liter} = 7.5 \text{ liters} \][/tex]
The answers are:
1. [tex]\(3 \text{ hrs} = 10800 \text{ sec}\)[/tex]
2. [tex]\(0.035 \text{ mg} = 0.0035 \text{ cg}\)[/tex]
3. [tex]\(5.5 \text{ kg} = 12.1254 \text{ lbs}\)[/tex]
4. [tex]\(2.5 \text{ yds} = 90 \text{ in}\)[/tex]
5. [tex]\(1.3 \text{ yrs} = 11388 \text{ hrs}\)[/tex]
6. [tex]\(3 \text{ moles} = 6 \times 10^{23} \text{ molecules}\)[/tex]
7. [tex]\(2.5 \times 10^{21} \text{ molecules} = 0.0125 \text{ moles}\)[/tex]
8. [tex]\(5 \text{ moles} = 112 \text{ liters}\)[/tex]
9. [tex]\(100 \text{ liters} = 4.4643 \text{ moles}\)[/tex]
10. [tex]\(50 \text{ liters} = 4.4643 \times 10^{23} \text{ molecules}\)[/tex]
11. [tex]\(5.0 \times 10^{25} \text{ molecules} = 56000 \text{ liters}\)[/tex]
12. [tex]\(7.5 \times 10^3 \text{ mL} = 7.5 \text{ liters}\)[/tex]
1. Convert 3 hours to seconds:
[tex]\(3 \text{ hrs} = 3 \times 3600 \text{ sec/hr} = 10800 \text{ sec}\)[/tex]
2. Convert 0.035 mg to cg:
[tex]\(0.035 \text{ mg} = 0.035 \times 0.1 \text{ cg/mg} = 0.0035 \text{ cg}\)[/tex]
3. Convert 5.5 kg to lbs:
[tex]\(5.5 \text{ kg} = 5.5 \times 2.20462 \text{ lbs/kg} = 12.1254 \text{ lbs}\)[/tex]
4. Convert 2.5 yds to inches:
[tex]\(2.5 \text{ yds} = 2.5 \times 36 \text{ in/yd} = 90 \text{ in}\)[/tex]
5. Convert 1.3 years to hours (1 year = 365 days):
[tex]\(1.3 \text{ yrs} = 1.3 \times 365 \text{ days/yr} \times 24 \text{ hrs/day} = 11388 \text{ hrs}\)[/tex]
6. Convert 3 moles to molecules (1 mole = [tex]\(0.02 \times 10^{25}\)[/tex] molecules):
[tex]\(3 \text{ moles} = 3 \times 0.02 \times 10^{25} \text{ molecules/mole} = 6 \times 10^{23} \text{ molecules}\)[/tex]
7. Convert [tex]\(2.5 \times 10^{21}\)[/tex] molecules to moles:
[tex]\(2.5 \times 10^{21} \text{ molecules} / (0.02 \times 10^{25} \text{ molecules/mole}) = 0.0125 \text{ moles}\)[/tex]
8. Convert 5 moles to liters (1 mole = 22.4 liters):
[tex]\(5 \text{ moles} = 5 \times 22.4 \text{ liters/mole} = 112 \text{ liters}\)[/tex]
9. Convert 100 liters to moles:
[tex]\(100 \text{ liters} / 22.4 \text{ liters/mole} = 4.464285714 \text{ moles}\)[/tex]
10. Convert 50 liters to molecules:
[tex]\[ 50 \text{ liters} / 22.4 \text{ liters/mole} = 2.232143 \text{ moles} \][/tex]
[tex]\[ 2.232143 \times 0.02 \times 10^{25} \text{ molecules/mole} = 4.464285714 \times 10^{23} \text{ molecules} \][/tex]
11. Convert [tex]\(5.0 \times 10^{25}\)[/tex] molecules to liters:
[tex]\[ 5.0 \times 10^{25} \text{ molecules} / (0.02 \times 10^{25} \text{ molecules/mole}) = 2500 \text{ moles} \][/tex]
[tex]\[ 2500 \times 22.4 \text{ liters/mole} = 56000 \text{ liters} \][/tex]
12. Convert [tex]\(7.5 \times 10^3\)[/tex] mL to liters:
[tex]\[ 7.5 \times 10^3 \text{ mL} / 1000 \text{ mL/liter} = 7.5 \text{ liters} \][/tex]
The answers are:
1. [tex]\(3 \text{ hrs} = 10800 \text{ sec}\)[/tex]
2. [tex]\(0.035 \text{ mg} = 0.0035 \text{ cg}\)[/tex]
3. [tex]\(5.5 \text{ kg} = 12.1254 \text{ lbs}\)[/tex]
4. [tex]\(2.5 \text{ yds} = 90 \text{ in}\)[/tex]
5. [tex]\(1.3 \text{ yrs} = 11388 \text{ hrs}\)[/tex]
6. [tex]\(3 \text{ moles} = 6 \times 10^{23} \text{ molecules}\)[/tex]
7. [tex]\(2.5 \times 10^{21} \text{ molecules} = 0.0125 \text{ moles}\)[/tex]
8. [tex]\(5 \text{ moles} = 112 \text{ liters}\)[/tex]
9. [tex]\(100 \text{ liters} = 4.4643 \text{ moles}\)[/tex]
10. [tex]\(50 \text{ liters} = 4.4643 \times 10^{23} \text{ molecules}\)[/tex]
11. [tex]\(5.0 \times 10^{25} \text{ molecules} = 56000 \text{ liters}\)[/tex]
12. [tex]\(7.5 \times 10^3 \text{ mL} = 7.5 \text{ liters}\)[/tex]
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