<u>Answer:</u>
The correct answer option is 43%.
<u>Step-by-step explanation:</u>
We are given that 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair.
We are to find the probability of a student getting selected will have dark hair with blue eyes.
P(D|B) = P(D∩B) / P(B)
Substituting the given values in it to get:
P(D|B) = 0.3 / 0.7 = 0.428
Rounding it to the nearest whole percent we get:
0.428 × 100 = 42.8% ≈ 43%
Answer: 267.947 (or 267.95) inches^3
Step-by-step explanation:
The formula for the volume of a sphere is 
.
To find your radius (r), divide the diameter of 8 inches by 2. <em>The radius is 4 inches.</em>
Plug in your numbers to the volume equation to get 
. The first step is to cube 4 (4*4*4) to get <em>64</em>. Now your equation is 
.
Multiply 3.14 and 64 to get <em>200.96</em>. The equation is now 
or 
.
Multiply the numerators (4 * 200.96) and denominators (1 * 3) to get a final equation of 
.
Finally, divide 803.84 by 3 to get the final answer of 267.947 in^3.
A cosine is just a sine shifted to the left by π/2. A cosine of 4x is shifted to the left by only π/8 because of the factor 4. Sketch them.
The region we're looking for is this sausage-shaped part between the cos and the sin.
The x intercepts are at π/8 for the cosine and π/4 for the sine. The midpoint between them is at (π/8 + π/4)/2 = 3/16π.
The region is point symmetric around the x axis, so the y coordinate of the centroid is 0.
So the centroid is at (3/16π, 0)
<span>OK, here's a *very* approximate "creative" method:
</span><span>
sin(a+b)=sin(a)cos(b) + cos(a)sin(b) </span>
<span>
choose a=30deg and b=5deg </span>
- sin(a)=0.5 (exact)
- b is a small number so we say sin(b)~b (in radians). We can do a long division for this: 3.14/36 = 0.087 radians
- similarly, for b sufficiently small, cos(b)~1
<span>- now we only need cos(a) = sqrt(3)/2. We can approximately calculate sqrt(3) as 1.73, (by trial-and-error or better, by using the Babylonian method; so sqrt(3)/2 = 0.865 </span>
<span>
Finally, sin(30 + 5) = (0.5 x 1) + (0.087 x 0.865) = 0.575 (calculating more digits is of no use because the sin(b)=b and cos(b)=1 are quite inaccurate approximations). </span>
<span>So that wasn't all too much effort, and we're close to the correct answer (0.574)
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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