First you would add the 12 to 30 to find the length of the crate and 12 to 12 to find the width of the crate. Then add 6 to the height of the dog. You need that information to find the volume of the crate. Then you would multiply those numbers of the crate.
(30 + 12) (12 + 12) (24 + 6) = 30,240 in^3
<span>Orthocenter is at (-3,3)
The orthocenter of a triangle is the intersection of the three heights of the triangle (a line passing through a vertex of the triangle that's perpendicular to the opposite side from the vertex. Those 3 lines should intersect at the same point and that point may be either inside or outside of the triangle. So, let's calculate the 3 lines (we could get by with just 2 of them, but the 3rd line acts as a nice cross check to make certain we didn't do any mistakes.)
Slope XY = (3 - 3)/(-3 - 1) = 0/-4 = 0
Ick. XY is a completely horizontal line and it's perpendicular will be a complete vertical line with a slope of infinity. But that's enough to tell us that the orthocenter will have the same x-coordinate value as vertex Z which is -3.
Slope XZ = (3 - 0)/(-3 - (-3)) = 3/0
Another ick. This slope is completely vertical. So the perpendicular will be complete horizontal with a slope of 0 and will have the same y-coordinate value as vertex Y which is 3.
So the orthocenter is at (-3,3).</span>
Answer:
D
Step-by-step explanation:
∠ABC= ∠DBE (vert. opp. ∠s)
(6x -7)°= (4x +23)°
6x -7= 4x +23
<em>Being</em><em> </em><em>x</em><em> </em><em>terms</em><em> </em><em>to</em><em> </em><em>1</em><em> </em><em>side</em><em>,</em><em> </em><em>constant</em><em> </em><em>to</em><em> </em><em>the</em><em> </em><em>other</em><em>:</em>
6x -4x= 23 +7
<em>Simplify</em><em>:</em>
2x= 30
<em>Divide</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>2</em><em>:</em>
x= 15
<em>Substituting</em><em> </em><em>the</em><em> </em><em>value</em><em> </em><em>of</em><em> </em><em>x</em><em>:</em>
m∠ABC
= 6(15) -7
= 83
Answer:
Mean = 910.2
Standard deviation = 12.8
Step-by-step explanation:
82% over the age of 25 are high school graduates.
A survey randomly selected students of certain country included 1110 who were over the age of 25 and 871 of them were high school.
n = 1110
p = 82% = 0.82
q = 1 - 0. 82
q = 0.18
Mean = np
= 1110*0.82
= 910.2
Standard deviation = √npq
= √ 1110*0.82*0.18
=√163.836
= 12.8
