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Answer :
We begin by converting each mixed number to an improper fraction.
First, for
[tex]$$13 \frac{5}{12},$$[/tex]
we have
[tex]$$13 \frac{5}{12} = \frac{13 \times 12 + 5}{12} = \frac{156 + 5}{12} = \frac{161}{12}.$$[/tex]
Next, for
[tex]$$3 \frac{3}{5},$$[/tex]
we obtain
[tex]$$3 \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5}.$$[/tex]
Now, we add these two fractions to find the total descent below sea level:
[tex]$$\frac{161}{12} + \frac{18}{5}.$$[/tex]
To add these fractions, we need a common denominator. The least common multiple of 12 and 5 is 60. Converting each fraction:
[tex]$$\frac{161}{12} = \frac{161 \times 5}{12 \times 5} = \frac{805}{60},$$[/tex]
[tex]$$\frac{18}{5} = \frac{18 \times 12}{5 \times 12} = \frac{216}{60}.$$[/tex]
Thus, the sum is
[tex]$$\frac{805}{60} + \frac{216}{60} = \frac{1021}{60}.$$[/tex]
Since the descents are below sea level, we denote the final location as negative:
[tex]$$\text{Final location} = -\frac{1021}{60}.$$[/tex]
This improper fraction can also be expressed as a mixed number. Dividing 1021 by 60:
- The quotient is 17 (since [tex]$17 \times 60 = 1020$[/tex]),
- The remainder is 1.
Thus,
[tex]$$-\frac{1021}{60} = -17 \frac{1}{60}.$$[/tex]
Therefore, the correct statement about the scuba diver's location relative to sea level is that the diver is at
[tex]$$-17 \frac{1}{60} \text{ feet}.$$[/tex]
The correct answer is D.
First, for
[tex]$$13 \frac{5}{12},$$[/tex]
we have
[tex]$$13 \frac{5}{12} = \frac{13 \times 12 + 5}{12} = \frac{156 + 5}{12} = \frac{161}{12}.$$[/tex]
Next, for
[tex]$$3 \frac{3}{5},$$[/tex]
we obtain
[tex]$$3 \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5}.$$[/tex]
Now, we add these two fractions to find the total descent below sea level:
[tex]$$\frac{161}{12} + \frac{18}{5}.$$[/tex]
To add these fractions, we need a common denominator. The least common multiple of 12 and 5 is 60. Converting each fraction:
[tex]$$\frac{161}{12} = \frac{161 \times 5}{12 \times 5} = \frac{805}{60},$$[/tex]
[tex]$$\frac{18}{5} = \frac{18 \times 12}{5 \times 12} = \frac{216}{60}.$$[/tex]
Thus, the sum is
[tex]$$\frac{805}{60} + \frac{216}{60} = \frac{1021}{60}.$$[/tex]
Since the descents are below sea level, we denote the final location as negative:
[tex]$$\text{Final location} = -\frac{1021}{60}.$$[/tex]
This improper fraction can also be expressed as a mixed number. Dividing 1021 by 60:
- The quotient is 17 (since [tex]$17 \times 60 = 1020$[/tex]),
- The remainder is 1.
Thus,
[tex]$$-\frac{1021}{60} = -17 \frac{1}{60}.$$[/tex]
Therefore, the correct statement about the scuba diver's location relative to sea level is that the diver is at
[tex]$$-17 \frac{1}{60} \text{ feet}.$$[/tex]
The correct answer is D.
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