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

Answer 1

Answer:

1. 0.75 cm to 1 km

4. 0.3 mm to 40 m

Step-by-step explanation:

we have the scale

$\frac{3}{4}\frac{cm}{km}=0.75\frac{cm}{km}$

Verify each case

case 1) 0.75 cm to 1 km

$\frac{0.75}{1}\frac{cm}{km}=0.75\frac{cm}{km}$

therefore

The scale is equivalent to the given value

case 2) 1 cm to 12 km

$\frac{1}{12}\frac{cm}{km}=0.08\frac{cm}{km}$

$0.08\frac{cm}{km} \neq 0.75\frac{cm}{km}$

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

$\frac{6}{2}\frac{mm}{km}=\frac{0.6}{2}\frac{cm}{km}=0.30\frac{cm}{km}$

$0.30\frac{cm}{km} \neq 0.75\frac{cm}{km}$

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

$\frac{0.3}{40}\frac{mm}{m}=\frac{0.03}{0.04}\frac{cm}{km}=0.75\frac{cm}{km}$

$0.75\frac{cm}{km}=0.75\frac{cm}{km}$

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

$\frac{1}{7.62}\frac{in}{km}=\frac{2.54}{7.62}\frac{cm}{km}=0.33\frac{cm}{km}$

$0.33\frac{cm}{km} \neq 0.75\frac{cm}{km}$

therefore

The scale is not equivalent to the given value