Mathematics, 17.03.2020 18:54 Rperez6491

A robot can complete 5 tasks in two thirds hour. Each task takes the same amount of time. A. How long does it take the robot to complete one task? B. How many tasks can the robot complete in one hour? A. It takes the robot nothing hour(s) to complete one task. (Simplify your answer.)

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Answers

A. 8 minutes; B. 7.5 tasks in one hour; C. It takes the robot about $\\ \frac{2}{15}\;hour$ or about 0.1333 hour to complete one task or 13.33% of one hour.

Step-by-step explanation:

Part A

Two thirds hours is

$\\ \frac{2}{3}*60 = 40\;min$

We know that each task takes the same amount of time. So, 40min can be divided by 5:

$\\ \frac{40}{5} = 8\;min$

Thus, each task takes 8 min to be completed. Then, it takes the robot 8 minutes to complete one task.

Part B

The robot can complete 5 tasks in 40 minutes, how many tasks can the robot complete in 60 minutes or one hour?

There are 20 minutes ahead to complete one hour. In the next 8 minutes, the robot can complete one task. There are still 12 minutes ahead. In the next 8 minutes, the robot completes another task. There is still 4 minutes ahead to complete the hour, but in 4 minutes the robot can complete half of the task because it takes 8 minutes for a complete task. Therefore, the robot can complete 5 tasks + 2 tasks + 0.5 task = 7.5 tasks in one hour or 60 minutes.

We can obtain the same answer using proportions. That is, if 5 tasks are completed in 40 minutes, how many of them will be completed in one hour or 60 minutes.

Then

$\\ \frac{5\;tasks}{40\;min} = \frac{x}{60\;min}$

$\\ \frac{5\;tasks}{40\;min}*60\;min = x$

$\\ x = \frac{5\;tasks*60\;min}{40\;min}$

$\\ x = \frac{300\;tasks}{40} = 7.5\;tasks$

Part C (A)

From part A, we already know that the robot can complete a task in 8 minutes, which is a fraction of one hour. What is this fraction? In one hour we have 60 minutes, then

$\\ 8\;min*\frac{1\;hour}{60\;min} = 1\;hour*\frac{8}{60} = 1\;hour*\frac{4}{30} = 1\;hour*\frac{2}{15} = 0.1333333....\;hours \approx 0.1333\;hours$ .

Therefore, it takes the robot about $\\ \frac{2}{15}\;hour$ or 0.1333 hour to complete one task (rounding to four decimal places) or 13.33% of one hour.

Answer from: Quest

29. because you will divide each number of months by 12 to find the number of years. which would mean, 5, 12.5, 16, 45, 50, 72.5. which is crazy. anyhow, i think you find the median in the middle. and yea hope your test goes good

Answer from: Quest

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at ( h , k ) .

center: ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center: ( 3 , 1 ).

radius: 4

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