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Problem Solving and Data Analysis

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A typical image taken of the surface of Mars by a camera is 11.2 gigabits in size. A tracking station on Earth can receive data from the spacecraft at a data rate of 3 megabits per second for a maximum of 11 hours each day. If 1 gigabit equals 1,024 megabits, what is the maximum number of typical images that the tracking station could receive from the camera each day?

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3

Correct Answer: 
No

10

Correct Answer: 
Yes

56

Correct Answer: 
No

144

Correct Answer: 
No

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Choice B is correct. The tracking station can receive 118,800 megabits each day 

left parenthesis fraction numerator 3 space text megabits end text over denominator 1 space text second end text end fraction cross times fraction numerator 60 space text seconds end text over denominator 1 space text minute end text end fraction cross times fraction numerator 60 space text minutes end text over denominator 1 space text hour end text end fraction cross times 11 space text hours end text right parenthesis comma 

which is about 116 gigabits each day left parenthesis fraction numerator 118.800 over denominator 1 comma 024 end fraction right parenthesis.

If each image is 11.2 gigabits, then the number of images that can be received each day is fraction numerator 116 over denominator 11.2 end fraction space almost equal to space 10.4.

Since the question asks for the maximum number of typical images, rounding the answer down to 10 is appropriate because the tracking station will not receive a completed 11th image in one day.

Choice A is not the correct answer. The student may not have synthesized all of the information. This answer may result from multiplying 3 (rate in megabits per second) by 11 (hours receiving) and dividing by 11.2 (size of image in gigabits), neglecting to convert 3 megabits per second into megabits per hour and to utilize the information about 1 gigabit equaling 1,024 megabits.

Choice C is not the correct answer. The student may not have synthesized all of the information. This answer may result from converting the number of gigabits in an image to megabits (11,470), multiplying by the rate of 3 megabits per second (34,410), and then converting 11 hours into minutes (660) instead of seconds.

Choice D is not the correct answer. The student may not have synthesized all of the information. This answer may result from converting 11 hours into seconds (39,600), then dividing the result by 3 gigabits converted into megabits (3,072), and multiplying by the size of one typical image.

Question Difficulty: 
medium
Objective: 

Students must use the unit rate (data-transmission rate) and the conversion between gigabits and megabits as well as conversions in units of time.