Answer:
The area is rational because the numbers in the formula are rational.
Step-by-step explanation:
All repeating decimals are still rational because they can be expressed as fractions. For example,
So every recurring decimal must be a fraction.
Also every terminating decimal can be represented as a fraction.
0.25 = 
So the area is rational because the numbers are rational.
Area = 
X Base X Height
Base is Rational and Height is Rational. Hence Area=Rational.
When these rational numbers are substituted into the formula,the area must be rational.
,
,
We find the probability of intersection using the inclusion/exclusion principle:
By definition of conditional probability,
For
and
to be independent, we must have
in which case we have
, which is true, so
and
are indeed independent.
Or, to establish independence another way, in terms of conditional probability, we must have
which is also true.
Answer:
53/100
Step-by-step explanation:
40/75=53/100
Answer:
Step-by-step explanation:
<u>16.8% of 152 pounds is:</u>
- 168*152/100 = 25.5 pounds (rounded)
Answer:
- shortest: 3 ft
- other: 4 ft
Step-by-step explanation:
The right triangle with hypotenuse 5 that has legs that differ by 1 is the 3-4-5 right triangle. The legs are 3 ft and 4 ft.
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<em>Alternate solution</em>
If you have never heard of a 3-4-5 right triangle, you can figure the leg lengths algebraically using the Pythagorean theorem. Let x represent the length of the "other" leg. Then the shortest is (x-1). The Pythagorean theorem tells you ...
5^2 = (x)^2 +(x -1)^2
25 = 2x^2 -2x +1
12 = x^2 -x = x(x -1)
Factors of 12 that differ by 1 are 3 and 4 or -3 and -4. We want x to be positive, so the value of interest is x=4
The "other" leg is 4 ft; the shortest leg is 3 ft.
