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If the areas of rectangles A, B, and C are 11, 33, and 75, respectively. Then the area of the rectangle D will be 25 square units.
<h3>What is a rectangle?</h3>It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
In the figure below, the areas of rectangles A, B, and C are 11, 33, and 75, respectively.
Then the area of the rectangle D will be
Let a be the length and b be the width of the rectangle D. Then we have
The ratio of the area of the rectangles will be
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Answer:
Γ = 15
Step-by-step explanation:
Given
f(x) = x² - 8x + Γ
with a = 1, b = - 8 and c = Γ , then
sum of zeros α + β = - = -
= 8
product of zeros = αβ = = Γ
Given α - β = 2 , then
(α - β)² = 2²
α² - 2αβ + β² = 4 → (1)
and
(α + β)² = 8²
α² + 2αβ + β² = 64 → (2)
Add (1) and (2) term by term
2α² + 2β² = 68 ( divide through by 2 )
α² +β² = 34
Substitute α² + β² = 34 into (1)
34 - 2αβ = 4 ( subtract 34 from both sides )
- 2αβ = - 30 ( divide both sides by - 2 )
αβ = 15
Now
αβ = Γ = 15
Thus
f(x) = x² - 8x + 15
The mean and (sample) standard deviation σ = 0.2098.
<h3>What exactly would the standard deviation indicate?</h3>The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
<h3>According to given information:</h3>The mean is the product of the dataset's total and the sample size. Mathematically.
The individual periods are Xi.
The sample size is N.
= 1.06 + 1.31 + 1.28 + 0.99,+ 1.48 + 1.37+ 0.98 + 1.31 + 1.59 + 1.55
= 12.92
N = 10
While substituting the value we get:
x = 12.96/10
x = 1.292
The samples' average is 1.292.
The standard deviation:
= (1.48-1.292)^2+(1.37-1.292)^2+(0.98-1.292)^2+(1.31-1.292)^2+(1.59-1.292)^2+(1.55-1.292)^2.
= 0.43996
Putting into the formula we get:
σ = √(0.043996)
σ = 0.2098
The mean and (sample) standard deviation σ = 0.2098.
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I understand that the question you are looking for is:
You measure the period of a mass oscillating on a vertical spring ten times as follows:
Period (s): 1.06, 1.31, 1.28, 0.99, 1.48, 1.37, 0.98, 1.31, 1.59, 1.55
Required:
What are the mean and (sample) standard deviation?
a. Mean: 1.228, Standard Deviation: 0.2135
b. Mean: 1.325, Standard Deviation: 0.1674
c. Mean: 1.292. Standard Deviation: 0.2211
d. Mean: 1.228, Standard Deviation: 0.2098
e. Mean: 1.292, Standard Deviation: 0.2135