9514 1404 393
Answer:
5 miles
Step-by-step explanation:
Time/speed/distance problems can be worked a number of ways. Here, we want to know the distance walked. We know the total time and the total distance and the two different speeds. So, we can use a variable to represent the value we want to know: w = distance walked (in miles).
The total time is 9:00 -6:50 = 2:10 = 2 1/6 hours = 13/6 hours.
The total time is the sum of times for the two parts of the trip: walking and riding.
walking time = walking distance/walking speed
= w/3
riding time = riding distance/riding speed
= (20-w)/30
The total time is that given above:
w/3 +(20-w)/30 = 13/6
10w +(20 -w) = 65 . . . . . . . . multiply by 30
9w = 45 . . . . . . . . . . . . subtract 20, collect terms
w = 5 . . . . . . . . . . . divide by 9
The girl walked 5 miles.
Answer:
x = 
Step-by-step explanation:
Using Pythagoras theorem,
Square of longer side = Sum of square of other sides .
Therefore,

Answer:
There is a 44.16% probability that exactly 1 of the tested bottles is contaminated.
Step-by-step explanation:
is the number of different combinatios of x objects from a set of n elements, given by the following formula.

In this problem, we have that:
Total number of combinations:

Desired combinations:
It is 1 one 5(contamined) and 2 of 17(non contamined). So:

What is the probability that exactly 1 of the tested bottles is contaminated?

There is a 44.16% probability that exactly 1 of the tested bottles is contaminated.
We know that the volume of a sphere of radius r is given by

Now, we have been given the initial volume was 4,188.79 cubic centimeters. Let us find the radius at this time.
Substituting the value of volume in the above equation, we get

Now, the final volume is given by 14,137.167 cubic centimeters. Thus, we have

Now, let us find the surface areas for these two radii.
For 
Surface area is given by

Similarly, for

Therefore, the increase in the surface area is given by

Hence, the average rate at which the surface area is changing is given by

Therefore, the average rate at which the surface area is changing is given by 130.8 square centimeters per second.