Answer:
B -o.60
Step-by-step explanation:
34 - 40 = -6. -6 divide by 10 = -3/5 or - 0.6. So answer is B
The width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.
<h3>How to find the dimensions of the rectangle of maximum area by optimization</h3>
In this problem we must use <em>critical</em> values and <em>algebraic</em> methods to determine to determine the dimensions of the rectangle such that the area is a <em>maximum</em>. The equation of the quadrilateral is formed by definition of the area of a rectangle:
A = w · h (1)
Where:
- w - Width of the rectangle.
- h - Height of the rectangle.
And the area of the entire triangle is:
0.5 · (5) · (12) = w · h + 0.5 · w · (12 - h) + 0.5 · (5 - w) · h
30 = w · h + 6 · w - 0.5 · w · h + 2.5 · h - 0.5 · w · h
30 = 6 · w + 2.5 · h
2.5 · h = 30 - 6 · w
h = 12 - 2.4 · w (2)
The quadrilateral of <em>maximum</em> area is always a square, then we must solve for w = h:
w = 12 - 2.4 · w
3.4 · w = 12
w = 3.529
Then, the width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.
To learn more on optimizations: brainly.com/question/15319802
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Answer:
(a) 0.8655
(b)0.8655
Step-by-step explanation:
X is the number of respodents who agree
P(x ≥4), n=12, p=0.45
P(x ≥4)=1-P(x<4)
P(x<4)=P(0 ≤x<4)= P(0 ≤x≤3)=P(x=0,1,2,3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)
P(x ≥4)=1-P(x<4)=1-0.134468=0.8655319
(b)
Y represent those who agree
P(Y≤8), n=12, p=0.45
P(Y≤8)=1-P(Y>8)
P(Y>8)=P(8<Y≤12)=P(9≤Y≤12)=P(Y=9,10,11,12)
Total =0.134468
P=1-0.134468=0.8655319
Find the side length:
Side = 68/4 = 17
Now use Pythagorean theorem:
Diagonal = sqrt(17^2 + 17^2)
Diagonal = sqrt(289 + 289)
Diagonal = sqrt(578)
Diagonal = 24 feet
The answer is B. 24 feet