A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed
of the boat in still water? What is the speed of the current?
1 answer:
Try this solution:
Answer: 6 & 4.5 (m-per-h)
Step-by-step explanation:
- The basic formula used in this task is S=V*t, where S - distance, V - speed, t - time.
- the downstream speed is: V+Vc, where V - the speed of the boat in still water, Vc - the speed of the current.
- the upstream speed is: V-Vc.
- according to the described above the distance for downstream is S1=(V+Vc)*t1, where t1=10; the distance for upstream is S2=(V-Vc)*t2, where t2=70.
- for whole travel down- and upstream: S=S1+S2.
- Using these it is possible to make up the system of the equations:
V - the speed of the boat in still water - 6 miles per hour, Vc - the speed of the current - 4.5 miles per hour. All the details for the system of the equations are in the attachment.
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Answer:
a)
b)
c) The value of height that separates the bottom 75% of data from the top 25% is 9.9745.
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
3) Part b
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
4) Part c
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.6745. On this case P(Z<0.6745)=0.75 and P(z>0.6745)=0.25
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 75% of data from the top 25% is 9.9745.
Answer:
x² + y² = 34
Formula:
- (x - h)² + (y - k)² = r² where (h, k) is the center
<u>Here find the radius using distance formula</u>: → origin : (0, 0)
- √(x2-x1)²+(y2-y1)²
- √(3-0)²+(5-0)²
- √9+25
- √34
<u>Thus the equation of circle</u>:
- (x - 0)² + (y - 0)² = (√34)²
- (x - 0)² + (y - 0)² = 34
- x² + y² = 34
