Answer:
length l = 32.25 m
width w = 8223.75 m
height h = 12.5 m
diagonal d = 8223.82273 m
total surface area Stot = 736831.875 m2
lateral surface area Slat = 206400 m2
top surface area Stop = 265215.938 m2
bottom surface area Sbot = 265215.938 m2
volume V = 3315199.22 m3
Step-by-step explanation:
Answers: ∠a = 30° ; ∠b = 60° ; ∠c = 105<span>°.
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1) The measure of Angle a is 30°. (m∠a = 30°).
Proof: All vertical angles are congruent, and we are shown in the diagram that angle A — AND the angle labeled with the measurement of 30°— are vertical angles.
2) The measure of Angle b is 60°. (m∠b = 60<span>°).
Proof: All three angles of a triangle add up to 90 degrees. In the diagram, we can examine the triangle formed by Angle A, Angle B, and a 90</span>° angle. This is a right triangle, and the angle with 90∠ degrees is indicated as such (with the "square" symbol). So we know that one angle is 90°. We also know that m∠a = 30°. If there are three angles in a triangle, and all three angles must add up to 180°, and we know the measurements of two of the three angles, we can solve for the unknown measurement of the remaining angle, which in this case is: m∠b.
90° + 30° + m∠b = 180<span>° ;
</span>180° - (<span>90° + 30°) = m∠b ;
</span>180° - (120°) = m∠b = 60<span>°
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Now we need to solve for the measure of Angle c (<span>m∠c).
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All angles on a straight line (or straight "line segment") are called "supplementary angles" and must add up to 180</span>°. As shown, Angle c is on a "straight line". The measurement of the remaining angle represented ("supplementary angle" to Angle c is 75° (shown on diagram). As such, the measure of "Angle C" (m∠c) = m∠c = 180° - 75° = 105°.
Given:
μ = 89 ng/ml, population mean
σ = 23 ng/ml, population standard deviation
Random variable, x = 100
To test P(x < 100), calculate the z-score.
z = (x-μ)/σ = (100 - 89)/23 = 0.4783
From standard tables, obtain
P(x < 100) = 0.6838 = 68.4%
Answer: 68.4%
Volume of a cone = [(pi)r^2(h)]:3 = [3.14 (25m^2)(12m)]:3 = 314in^3.
Answer:
28x +196 in^2
Step-by-step explanation:
The outside dimension of the square green rug is (x+14), so its area is (x+14)^2. The area of the green band will be the difference between this and the area of the yellow square, (x^2).
green band area = (x +14)^2 -(x^2) = x^2 +28x +196 -x^2
green band area = 28x +196 . . . . square inches
