Question

Which of these scales are equivalent to 3 cm to 4 km? select all that apply. recall that 1 inch is 2.54 cm

1. 0.75 cm to 1 km

2. 1 cm to 12 km

3. 6 mm to 2 km

4. 0.3 mm to 40 m

5. 1 inch to 7.62 km

Answer 1

1. 0.75 cm to 1 km

4. 0.3 mm to 40 m

Explanation:

we have the scale

`(3)/(4)(cm)/(km)=0.75(cm)/(km)`

Verify each case

case 1) 0.75 cm to 1 km

`(0.75)/(1)(cm)/(km)=0.75(cm)/(km)`

therefore

The scale is equivalent to the given value

case 2) 1 cm to 12 km

`(1)/(12)(cm)/(km)=0.08(cm)/(km)`

`0.08(cm)/(km) \\eq 0.75(cm)/(km)`

therefore

The scale is not equivalent to the given value

case 3) 6 mm to 2 km

Remember that

1 cm= 10 mm

1 mm=0.1 cm

we have

`(6)/(2)(mm)/(km)=(0.6)/(2)(cm)/(km)=0.30(cm)/(km)`

`0.30(cm)/(km) \\eq 0.75(cm)/(km)`

therefore

The scale is not equivalent to the given value

case 4) 0.3 mm to 40 m

Remember that

1 cm= 10 mm -----> 1 mm=0.1 cm

1 km=1,000 m ----> 1 m=0.001 km

we have

`(0.3)/(40)(mm)/(m)=(0.03)/(0.04)(cm)/(km)=0.75(cm)/(km)`

`0.75(cm)/(km)=0.75(cm)/(km)`

therefore

The scale is equivalent to the given value

case 4) 1 inch to 7.62 km

Remember that

1 in= 2.54 cm

we have

`(1)/(7.62)(in)/(km)=(2.54)/(7.62)(cm)/(km)=0.33(cm)/(km)`

`0.33(cm)/(km) \\eq 0.75(cm)/(km)`

therefore

The scale is not equivalent to the given value