Question

A speedometer has a percent error of 10%. The actual speed of the car is 40 mph. Select from the drop-down menus to correctly complete the statement. The speedometer is likely to show the speed is either ____ mph or ____ mph.
Worth 20 pts and brainliest if correct :)

options for the two drop down menus

a. 30.0
b. 36.0
c. 38.4
d. 40.4

and for the other the options are

a. 40.6
b. 41.6
c. 44.0
d. 50.0

Answer 1

Answer

Answer

The speedometer is likely to show the speed is either 36.0 mph or 44.0 mph.        

To prove

Formula

$Percentage\ error = \frac{error\times 100}{Exact\ value}$

Where error = |Approx value - Exact value |

First case

As given

A speedometer has a percent error of 10%. The actual speed of the car is 40 mph.    

Here

Percentage error = 10%

Exact value = 40 mph

error = - (Approx value - Exact value )

          = - (Approx value - 40 )

          = - Approx value + 40

Put in the formula

$10 = \frac{(-Approx\ value + 40)\times 100}{40}$

$400 = {(-Approx\ value + 40)\times 100}$

$\frac{400}{100} =-Approx\ value + 40$      

$\4 =-Approx\ value + 40$      

Thus

Approx value = 40 - 4

Approx value = 36 mph

Therefore Option (b) is correct .

Second Case

error =  (Approx value - Exact value )

          =  (Approx value - 40 )

          =  Approx value - 40

Put in the formula

$10 = \frac{(Approx\ value - 40)\times 100}{40}$

$400 = {(Approx\ value - 40)\times 100}$

$\frac{400}{100} = Approx\ value - 40$      

$\4 = Approx\ value - 40$      

Thus

Approx value = 40 + 4

Approx value = 44 mph

Therefore Option (c) is correct .