Which best explains if quadrilateral WXYZ can be a parallelogram?
1 answer:
A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is A.
<h3>What is a parallelogram?</h3>A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram, the pair of opposite sides are equal and parallel. Therefore,
1.) For the first pair.
(x+8) = 15
x = 7
2.) For the second pair
(x+2)=(2x-5)
x + 2 = 2x - 5
2 + 5 = 2x - x
x = 7
(x+2) = (7+2) = 9
Since the measure of the pair of opposite sides is 15 units, the pair of the other two sides measure 9 units.
Hence, the correct option is A.
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Answer:
a) Standard Deviation = 2.74
b) Significantly Low = values below 24.52 (or equal)
Significantly High = values above 35.48 (or equal)
Step-by-step explanation:
This is binomial probability distribution problem.
Where n = 40 [groups of 40, total trials]
p = 0.75 [probability of success]
a)
The formula for standard deviation is:
We know n = 40 and p = 0.75, so the standard deviation is:
b)
the range rule of thumb tells us that usual range of values is within 2 standard deviation of the mean. First let's calculate mean.
We know,
Mean = n * p = 40 * 0.75 = 30
So
Mean - 2* Standard Deviation = 30 - 2(2.74) = 24.52
and
Mean + 2* Standard Deviation = 30 + 2(2.74) = 35.48
Significantly Low = values below 24.52 (or equal)
Significantly High = values above 35.48 (or equal)
The rationalized expression in general term is given by: (-8 -4√2) / 3
<h3>What is rationalization?</h3>Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.
(8√2 / 6-3√8 ) Multiply by ( 6+3√8)/( 6+3√8)
(8√2 / 6-3√8 )( 6+3√8)/( 6+3√8)
8√2(6+3√8) / (6-3√8)² Expand the denominator using the FOIL method.
8√2(6+3√8) / (36 - 18√8 + 18√8 - 72)
8√2(6+3√8) / -36
48√2 + 24√2√8 / -36 ::::. √8 = 2√2
48√2 + 96 / -36
-12(4√2 + 8) / 12x3
(-8 -4√2) / 3 is the result.
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