5. Daniel arrives at his campsite out of breath from his swim and jog. His sister tells him that he should have swam to the boat ramp that is only 200 feet from the campsite and then jogged. She claims that he would have arrived quicker this way. Is Daniel's sister correct? Support your answer mathematically.

hello your question is incomplete attached below is the complete question

answer :

Daniels sister is not correct because the time that will be taken by Daniel will be greater than the initial total time taken by Daniel.

Step-by-step explanation:

First determine the time it will take Daniel to reach the Boat and the jogging time

time = distance / rate

where distance can be calculated using this equation: sin 53° = 400 / x

hence x ( distance ) = 500 ft

rate = 150

therefore Time ( t )  to reach boat = 500 / 150 = 3.33 minutes

Time for jogging ( as calculated ) = 3.69 minutes

therefore total time taken by Daniel = 3.33 + 3.69 = 7.02 minutes

Finally determine if Daniel's sister is correct that he should have swam to the boat ramp and then jogged

lets assume Distance to swim  =  x  ( according his sister )

determine the value of x =   therefore X = 1456.02 feet

∴

Total time to be taken if Daniel follows his sister's instruction  = 1456.02 / 150 = 9.71 minutes

Daniels sister is not correct because the time that will be taken by Daniel will be greater than the initial total time taken by Daniel.

-50/3

step-by-step explanation:

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents