Answer:
- boat: 6 mph
- current: 2 mph
Step-by-step explanation:
The relationship between time, speed, and distance is ...
speed = distance/time
For boat speed b and current speed c, the speed downstream is ...
b +c = (16 mi)/(2 h) = 8 mi/h
The speed upstream is ...
b -c = (16 mi)/(4 h) = 4 mi/h
Adding the two equations eliminates the c term:
2b = 12 mi/h
b = 6 mi/h . . . . . divide by 2
Solving the second equation for c, we get ...
c = b -4 mi/h = 6 mi/h -4 mi/h = 2 mi/h
The speed of the boat in still water is 6 mi/h; the current is 2 mi/h.
The answers that would fill in the blanks are
- 2r
- a circle
- an annulus
- 1/3πr³
- 4/3πr³
<h3>What is the Cavalier's principle?</h3>
This principle states that if two solids are of equal altitude then the sections that the planes would make would have to be parallel and also be at the same distances from their bases which are equal such that the volumes of the solids would be equal.
Now we have to fill in the blanks with the solution.
For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius r and height<u> 2r</u> minus the volume of two cones, each with a radius and height of r. A cross section of the sphere is a <u>circle</u> base of cylinder, is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is an <u>annulus_ </u>.The volume of the cylinder with radius r and height 2r is 2πr³, and the volume of each cone with radius r and height r is 1/3πr³. So the volume of the cylinder minus the two cones is 4/3πr³. Therefore, the volume of the sphere is by Cavalieri's principle
Read more on Cavalieri's principle here
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The answer is 9 Dollars per hour because 36 divided by 9 is 4 and 9 times 9 is 81.
Answer:
The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the population, we have that:
Mean = 0.5
Standard deviaiton = 0.289
Sample of 12
By the Central Limit Theorem
Mean = 0.5
Standard deviation 
The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.