1. it takes an elevator 4 seconds to travel from the first floor to the fourth floor. how long does it take the elevator to travel from the first floor to the sixteenth floor? 2. three positive numbers are in the ratio 7: 3: 2. the sum of the smallest number and the largest number exceeds twice the remaining number by 30. find the three numbers.

Step-by-step explanation:

1. From the first floor to the 4th floor is a distance of 3 floors. From the first floor to the 16th floor is a distance of 15 floors, a distance that is 5 times as far as the first trip. We expect the second trip to take 5 times as long, or ...

  (4 s) × 5 = 20 s

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2. The smallest and largest ratio number sum to 2+7=9. That sum exceeds twice the remaining ratio number by 9-2×3 = 3. Since this difference represents a difference of 30, each of the original numbers must be 30/3 = 10 times its corresponding ratio number.

The three numbers are 7×10 = 70, 3×10 = 30, and 2×10 = 20.

Check

(70 +20) -2×30 = 30 . . . true

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!