Answer:
24.0 square feet
Step-by-step explanation:
The area of the sector is given by ...
A = (1/2)r²θ . . . . . where θ is the angle in radians
The area of the circle is the same, with θ=2π, so is ...
A = πr²
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In this problem, the area of the sector is ...
A = (1/2)(9 ft)²(24π/180) = 27π/5 ft² ≈ 16.9646 ft²
The area of the circle is ...
A = π(1.5 ft)² = 9π/4 ft² ≈ 7.0686 ft²
Then the total area of the exclamation point is ...
16.9646 +7.0686 ≈ 24.0 . . . ft²
The area is about 24.0 square feet.
Answer:
Step-by-step explanation:
<u>Options:</u>
A. m∠C + m∠E = m∠A
- Correct. Exterior angle equals to sum of non-adjacent interior angles.
B. m∠D + m∠F = m∠B
- Incorrect. Exterior angles have greater value.
C. m∠B + m∠C + m∠E = 180°
- Correct. Interior angles of a triangle sum to 180°
D. m∠B + m∠C + m∠D = 180°
- Incorrect. Angles C and D sum to 180°
E. m∠A + m∠ B = m∠E + m∠F
- Correct. Both sides of equation refer to straight angle.
F
. m∠B + m∠C + m∠ E = m∠A + m∠D + m∠F
- Incorrect. Some of interior angles is not equal to sum of exterior angles.
Answer:
The answer is below
Step-by-step explanation:
a) For a normal model the sample size has to be equal or greater than 30 so that it can be a normal distribution.
b) Given that:
μ = 11.2 minutes, σ = 4.8 minutes, n = 45
The z score determines how many standard deviations the raw score is above or below the mean. It is given by:
For x < 10 minutes
Therefore from the normal distribution table, P(x < 10) = P(z < -1.68) = 0.0465
Answer:
C) 
Step-by-step explanation:
Therefore, C is correct. Recall that 
If x represents the width of the poster (including borders), the area of the finished poster can be written as
.. a = x*(390/(x -10) +8)
.. = 8x +390 +3900/(x -10)
Then the derivative with respect to x is
.. da/dx = 8 -3900/(x -10)^2
This is zero at the minimum area, where
.. x = √(3900/8) +10 ≈ 32.08 . . . . cm
The height is then
.. 390/(x -10) +8 = 8 +2√78 ≈ 25.66 . . . . cm
The poster with the smallest area is 32.08 cm wide by 25.66 cm tall.
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In these "border" problems, the smallest area will have the same overall dimension ratio that the borders have. Here, the poster is 10/8 = 1.25 times as wide as it is high.
