Solve each one to find that D is the answer
Answer:

Step-by-step explanation:
First we'll work out the surface area of the pink figure.
That's the area of the two 5 by 6 rectangles on the top and bottom, plus the area of the two 5 by 20 and two 6 by 20 rectangles on the sides.
However, we note that the purple figure is blocking out a 6 by 12 section on the pink figure, so we'll need to subtract this.
The above works out to
.
Then we'll work out the surface area of the purple figure.
This will be the area of the two 4 by 6 rectangles at the top and bottom, plus the area of the two 4 by 12 and one 6 by 12 rectangles on the sides. Note that there's only one 6 by 12 rectangle because the other face is joined to the pink figure, so it's blocked out.
That's
.
So the total surface area is
.
Answer:
Proportion of all bearings falls in the acceptable range = 0.9973 or 99.73% .
Step-by-step explanation:
We are given that the diameters have a normal distribution with a mean of 1.3 centimeters (cm) and a standard deviation of 0.01 cm i.e.;
Mean,
= 1.3 cm and Standard deviation,
= 0.01 cm
Also, since distribution is normal;
Z =
~ N(0,1)
Let X = range of diameters
So, P(1.27 < X < 1.33) = P(X < 1.33) - P(X <=1.27)
P(X < 1.33) = P(
<
) = P(Z < 3) = 0.99865
P(X <= 1.27) = P(
<
) = P(Z < -3) = 1 - P(Z < 3) = 1 - 0.99865
= 0.00135
P(1.27 < X < 1.33) = 0.99865 - 0.00135 = 0.9973 .
Therefore, proportion of all bearings that falls in this acceptable range is 99.73% .
100 is the correct answer
<u>Prove that:</u>

<u>Proof: </u>
We know that, by Law of Cosines,
<u>Taking</u><u> </u><u>LHS</u>
<em>Substituting</em> the value of <em>cos A, cos B and cos C,</em>



<em>On combining the fractions,</em>

<em>Regrouping the terms,</em>



LHS = RHS proved.