Hurry When solving a system of equations, Jared found y = x 10 for one equation and substituted x 10 for y in the other equation
2 answers:
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The percentage of change in the area of the rectangle is -25% ⇒ B
Step-by-step explanation:
The given is:
- Sides AB and DC of the rectangle are increased in length by 50%
- Sides AD and BC are decreased in length by 50%
We need to find the percentage change in the <em>AREA</em> of the rectangle
Assume that the length of AB ans DC is x units, and the length of AD and BC is y units
∵ The length of the sides AB and DC increased by 50%
∵ The length of AB and CD = x
- That means x will increase by 50% of x
∵ 50% of x = (50 ÷ 100) × x = 0.5 x
∴ The length is increased by 0.5 x
∴ The new length of AB and CD = x + 0.5 x = 1.5 x units
∵ The length of the sides BC and AD decreased by 50%
∵ The length of BC and AD = y
- That means y will decrease by 50% of y
∵ 50% of y = (50 ÷ 100) × y = 0.5 y
∴ The length is decreased by 0.5 y
∴ The new length of BC and AD = y - 0.5 y = 0.5 y units
∵ The area before the change = x × y = xy units²
∵ The area after the change = 1.5 x × 0.5 y = 0.75 xy units²
∵ The new area is less than the old area
∴ The area is decreased
- To find the the percentage of change in the area subtract the
new area from the old area and divide the difference by the
old area and then multiply the quotient by 100%
∴ The percentage of the change = × 100%
∴ The percentage of the change = × 100%
∴ The percentage of the change = 0.25 × 100%
∴ The percentage of the change = 25%
∴ The area of the rectangle is decreased by 25% ⇒ (-25%)
The percentage of change in the area of the rectangle is -25%
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So we have a set of integers,
And we need to compute some stats.
First the range,
The range of data set is difference between the maximum and the minimum of the data set.
So the minimum is 15 and maximum is 34 therefore the range is 34 - 15 = 19.
Second the interquartile range,
The interquartile range of data set is the difference of the first and third quartiles.
First quartile is the value separating the lower quarter and higher three - quarters of the set. The first quartile is computed by taking median of the lower half of the sorted set. This is 15, 20, 25, 25 and it's median is 22.5
Third quartile is therefore the median of 27, 28, 30, 34 which is 29.
Next up, variance.
The variance of set measures how much data is spread out. For data set with an average
,
So first compute the average value which is actually a mean,
The sum of numbers in set is 204.
Divide this by number of elements in the set (8).
Then compute the variance,
And finally standard deviation,
Since have computed variance the standard deviation is nothing too hard. It's defined as a square root of variance,
Hope this helps.
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