Answer:
9.57 yd squared
Step-by-step explanation:
we can divide this figure into two shapes: a rectangle and a semi-circle
since we know the length and width of the rectangle, all we ahve to do is multiply them together to find the area: <u>8 yd squared</u>
for the semi-circle, we know the area is
raduis is half the diameter so 1 yd
<u />
<u>1.57 yd squared</u>
lastly, add the area of the two figures together 8+1.57
Answer:
Option (B) is true i.e segment B'D' will run through (2,2) and will be longer than the segment BD.
Step-by-step explanation:
As the assumption quadrilateral ABCD is shown in figure a.
First located the center of the dilation which is located at (2,2) as shown in figure b.
The next thing we want to do is to determine the distance of the center of dilation to each of the points of quadrilateral ABCD as shown in figure b.
Let’s just start with the distance from the center to the point A, but notice we don’t have to move up and down in y direction. So, what we have to do is to increase this by the factor 2. Because this horizontal distance is 1 i.e. the distance from dilation center (2,2) to point A, we just have to multiply by 2 which would be a distance of 2 and this point right here will be the new location of point A’ (0,2).
And the distance from the center to the point C is the horizontal distance of 2 i.e. the distance from dilation center (2,2) to point C, we just have to multiply by 2 which would be a distance of 4 and this point right here will be the new location of point C’ (6,2).
And the distance from the center to the point B is the upward vertical distance of 1 i.e. the distance from dilation center (2,2) to point B, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point B’ (2,4).
And similarly the distance from the center to the point D is the downward vertical distance of 1 i.e. the distance from dilation center (2,2) to point D, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point D’ (2,0).
So, Quadrilateral A'B'C'D' is dilated by a scale factor of 2 centered around (2, 2).
Just notice in figure b that the segment B'D' will run through (2,2) and will be longer than the segment BD.
<u>So,option (B) is true</u> <u>i.e segment</u><u> </u><u>B'D' will run through (2,2) and will be longer than the segment BD.</u>
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Answer:
61,239,550
Step-by-step explanation:
We let the random variable X denote the IQ scores. This would imply that X is normal with a mean of 100 and standard deviation of 17. We proceed to determine the probability that an individual chosen at random from the population would be a genius, that is;
Pr( X>140)
The next step is to evaluate the z-score associated with the IQ score of 140 by standardizing the random variable X;
The area to the right of 2.3529 will be the required probability. This area from the standard normal tables is 0.009314
From a population of 6,575,000,000 the number of geniuses would be;
6,575,000,000*0.009314 = 61,239,550