Answer:
Side x is adjacent to 30° angle.
<u>Correct method is:</u>
- cos 30° = x/15 ⇒ x = 15*cos 30° ⇒ x = 12.99
Diego is correct and Steven is wrong.
- when finding <u>sine</u> consider the <u>opposite side to the angle</u>, not hypotenuse
- when finding <u>cosine</u> consider <u>adjacent side to the angle,</u> not hypotenuse
Can u be specific pls , so can u send the picture of the task
Length of the box = 25 - 2x
Width of the box = 14 - 2x
Height of the box = x
a.) Volume of the box = x(25 - 2x)(14 - 2x) = x(350 - 50x - 28x + 4x^2) = 4x^3 - 78x^2 + 350x
Therefore, the function that models the volume of the box is V(x) = 4x^3 - 78x^2 + 350x
b.) 4x^3 - 78x^2 + 350x ≥ 240
4x^3 - 78x + 350x - 240 ≥ 0
x = 0.834, 5.438
The values of x for which the volume is greater than 240 in^3 is 0.834 ≤ x ≤ 5.438
c.) For maximum volume, dV/dx = 0
dV/dx = 12x^2 - 156x + 350 = 0
x = 2.882910931
Therefore, maximum volume = 4(2.882910931)^3 - 78(2.882910931)^2 +350(2.882910931) = 453.798 in^3
The square area is 6*6=36
For the two triangles, the area is base*height/2 = 6*3 = 18.
So the total area is 18+36+18=72
Answer:
The probability that between 79% and 81%of the 500 sampled wildlife watchers actively observed mammals in 2011 is P=0.412.
Step-by-step explanation:
We know the population proportion π=0.8, according to the 2011 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation.
If we take a sample from this population, and assuming the proportion is correct, it is expected that the sample's proportion to be equal to the population's proportion.
The standard deviation of the sample is equal to:
With the mean and the standard deviaion of the sample, we can calculate the z-value for 0.79 and 0.81:
Then, the probability that between 79% and 81%of the 500 sampled wildlife watchers actively observed mammals in 2011 is:
