Answer:
47 is your answer
Step-by-step explanation:
For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.
So, all we have to do is substitute θ=45° to the function given.
A = 16 sin 45° ⋅ (cos 45° + 1)
The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.
A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8+8√2
A = 19.31 square inches
For this case we must find the product of the following expression:

We apply distributive property term to term:

We add similar terms:

Finally, the expression is as:

Answeer:

Answer:
0.0359
Step-by-step explanation:
Data provided:
mean values of three independent times are 15, 30, and 20 minutes
the standard deviations are 2, 1, and 1.6 minutes
Now,
New Mean = 15 + 30 + 25 = 65
Variance = ( standard deviation )²
or
Variance = 2² + 1² + 1.6² = 7.56
therefore,
Standard deviation = √variance
or
Standard deviation = 2.75
Thus,
Z-value = 
or
Z-value = - 1.81
from the Z-table
the Probability of Z ≤ -1.81 = 0.0359
Answer:
A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.