Question

fill-in the blank with either:

(greater than), < (less than),

= (equal to) or n (not enough information to tell)

1. column a: a, column b: c

given: $a = \frac{1}{2}b \\ (a > 0)$, $b = \frac{1}{2}c$

1. column a: c, column b: 5a

given: $a = \frac{1}{2}b \\ (a > 0)$, $b = \frac{1}{2}c$

1. column a: 50 mils, column b: 5 cents

given: a mil is a tenth ($\frac{1}{10}$) of a cent.

1. column a: 25 cents, column b: 100 mils

given: a mil is a tenth ($\frac{1}{10}$) of a cent.

1. column a: 1,000 mils, column b: 100 cents

given: a mil is a tenth ($\frac{1}{10}$) of a cent.

1. column a: $10.00, column b: 10,000 mils

given: a mil is a tenth ($\frac{1}{10}$) of a cent.

1. column a: 6 bits, column b: 100 cents

given: 25 cents is equal to two bits.

1. column a: $2.00, column b: 25 bits

given: 25 cents is equal to two bits.

1. column a: 100 bits, column b: $5.00

given: 25 cents is equal to two bits.

1. column a: $10.00, column b: 1,000 bits

given: 25 cents is equal to two bits.

1. column a: a, column b: c

given: $a = 2b \\ (a > 0)$, $2b = 3c$

1. column a: a, column b: c

given: $a = 2b \\ (a > 0)$, $4b = 5c$

Explanation:

Step1: Substitute b for a

Given $a = \frac{1}{2}b$, so $b = 2a$. Then $b = \frac{1}{2}c$ becomes $2a = \frac{1}{2}c$, so $c = 4a$. Compare $a$ and $c$: $a < 4a$ (since $a>0$).

Step2: Compare c and 5a

From Step1, $c=4a$. $4a < 5a$ (since $a>0$).

Step3: Convert mils to cents

1 mil = $\frac{1}{10}$ cent, so 50 mils = $50 \times \frac{1}{10} = 5$ cents.

Step4: Convert mils to cents

100 mils = $100 \times \frac{1}{10} = 10$ cents. 25 cents > 10 cents.

Step5: Convert mils to cents

1000 mils = $1000 \times \frac{1}{10} = 100$ cents.

Step6: Convert mils to dollars

10,000 mils = $10000 \times \frac{1}{10} = 1000$ cents = $\$10.00$.

Step7: Convert bits to cents

2 bits = 25 cents, so 1 bit = 12.5 cents. 6 bits = $6 \times 12.5 = 75$ cents. 75 cents < 100 cents.

Step8: Convert bits to dollars

25 bits = $25 \times 12.5 = 312.5$ cents = $\$3.125$. $\$2.00 < \$3.125$.

Step9: Convert bits to dollars

100 bits = $100 \times 12.5 = 1250$ cents = $\$12.50$. $\$12.50 > \$5.00$.

Step10: Convert bits to dollars

1000 bits = $1000 \times 12.5 = 12500$ cents = $\$125.00$. $\$10.00 < \$125.00$.

Step11: Relate a and c

Given $a=2b$ and $2b=3c$, so $a=3c$. $a > c$ (since $a>0$, so $c>0$).

Step12: Relate a and c

$a=2b$ so $b=\frac{a}{2}$. Substitute into $4b=5c$: $4 \times \frac{a}{2}=5c$ → $2a=5c$ → $a=\frac{5}{2}c$. $a > c$ (since $a>0$, so $c>0$).

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