Answer:
And we can find this probability using the normal standard table or excel and we got:
The figure shows the calculation for this case.
Step-by-step explanation:
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".
Solution to the problem
Let X the random variable that represent the hardness of a population, and for this case we know the distribution for X is given by:
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 using the normal standard table or excel and we got:
The figure shows the calculation for this case.
The given quadrilateral ABCD is a parallelogram since the opposite sides are of same length AB and DC is 4 and AD and BC is 2.
<u>Step-by-step explanation</u>:
ABCD is a quadrilateral with their opposite sides are congruent (equal).
The both pairs of opposite sides are given as AB = 3 + x
, DC = 4x
, AD = y + 1
, BC = 2y.
- AB and DC are opposite sides and have same measure of length.
- AD and BC are opposite sides and have same measure of length.
<u>To find the length of AB and DC :</u>
AB = DC
3 + x = 4x
Keep x terms on one side and constant on other side.
3 = 4x - x
3 = 3x
x = 1
Substiute x=1 in AB and DC,
AB = 3+1 = 4
DC = 4(1) = 4
<u>To find the length of AD and BC :</u>
AD = BC
y + 1 = 2y
Keep y terms on one side and constant on other side.
2y-y = 1
y = 1
Substiute y=1 in AD and BC,
AD = 1+1 = 2
BC = 2(1) = 2
Therefore, the opposite sides are of same length AB and DC is 4 and AD and BC is 2. The given quadrilateral ABCD is a parallelogram.
Answer:
9.67
Step-by-step explanation:
32-22.33=9.67
Hope it helps ;)
Answer:
H = 20.5 hours
I = 19.5 Hours
Step-by-step explanation:
Start by creating a system.
I = time which the inlet pipe takes alone to fill the pond
H = time which the hose takes alone to fill the pond
10/I + 10/H = 10
H - I = 1
H = 20.5 hours
I = 19.5 Hours
My teacher taught me a simple equation for these types of problems:
(percent of solution × amount of solution) + (percent of solution × amount of solution) = (percent of solution × total amount of solution)
in simple terms: %amount + %amount = %total amount
We know don't know how much gallons of 60% solution we need so it will be represented as x. We dont know the total amount either so it would have to be both solutions added together so 50 + x. Now lets solve:
(0.60)(x) + (0.24)(50) = (0.50)(50 + x) simplify/ distribute
0.6x + 12 = 25 +0.5x get all xs on one side and numbers on other
0.1x + 12 = 25
0.1x = 13 divide both sides by 0.1 to find x
x = 130
You need 130 gallons of 60% solution.