Marvin rides his bike at an average speed of 13 miles per hour. How far can he bike in 8 hours?
2 answers:
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Answer:
The value of x = 11 and y = 2
Step-by-step explanation:
Given : parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, and OP = (2x – 1) m.
We have to find values of x and y.
Let P be the point of intersection of diagonals OM and LN.
In a parallelogram diagonal bisects at right angles and point of intersection divide diagonal in equal parts.
Thus, OP = MP and LP = PN
OP = MP , substitute the values, we get,
(2x-1) = 21
⇒ 2x = 22
⇒ x = 11
LP = PN , substitute the values, we get,
y + 3 = 3y -1
⇒ 3y - y = 4
⇒ 2y = 4
⇒ y = 2
Thus, the value of x = 11 and y = 2
Answer:
a) Figure attached
b)
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:
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 95%
c)
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 34+34+13.5+2.35%=83.85%
d)
And using the z score we got:
And that correspond to approximately 0.15%
Step-by-step explanation:
Part a
For this case we can see the figure attached.
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".
Part b
Let X the random variable that represent the length of human pregnancy of a population, and for this case we know that:
Where and
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:
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 95%
Part c
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 34+34+13.5+2.35%=83.85%
Part d
We want this probability:
And using the z score we got:
And that correspond to approximately 0.15%
