First department can choose the pair (delegate,alternate) by 7*6 = 42 ways.
Second department can choose the pair (delegate,alternate) by 10*9 = 90 ways.
Third department can choose the pair (delegate,alternate) by 6*5 = 30 ways.
Since these selections are INDEPENDENT, the resulting choice can be done in 42*90*30=113400
Answer:
Alvin traveled 150 miles downstream and 150 miles upstream, for a total distance on the river of 300 miles.
Step-by-step explanation:
Let d represent the distance Alvin traveled in one direction on the river. Then going downstream that distance took ...
... time = distance/speed
... time downstream = d/25
and the time going upstream that same distance to his point of origin took ...
... time upstream = d/15
The total of these times is 16 hours, so we have ...
... 16 = d/25 + d/15
Multiplying by 75 gives ...
... 1200 = 3d +5d = 8d
... 1200/8 = d = 150
Alving spent 6 hours going 150 miles downstream and 10 hours going 150 miles upstream. His total river distance was 300 miles. (We cannot tell which of these numbers will be considered to be the answer to the question.)
<span>1. 10 square units.
2. 16.9 units
1. The area of a triangle is 1/2bh where b is the base and h is the height of the triangle. Any of the 3 sides of the triangle may be the base. So looking at the 3 points, I'll consider the line segment DE to be the base since both D and E have an X value of 3, so the length of the base is 3 - (-1) = 4. Since the base of the triangle is a vertical line with X = 3, the height of the triangle will be the absolute value of the X value of vertex F minus 3. So abs(-2 - 3) = abs(-5) = 5. We now have a base of 4 and height of 5 and using the 0.5bh formula, that gives us 0.5 * 4 * 5 = 10.
2. I'll call the points A(-2,-2), B(3,-3), C(4,-6), D(1,-6), and E(-2,-4). Using the pythagorean theorem, we can calculate the length of each side. SO
length AB = sqrt((-2 - 3)^2 + (-2 - (-3))^2) = sqrt(-5^2 + 1^2) = sqrt(25 + 1) = sqrt(26) = 5.099
length BC = sqrt((3 - 4)^2 + (-3 - (-6))^2) = sqrt(-1^2 + 3^2) = sqrt(1 + 9) = sqrt(10) = 3.162
Do the same for the lengths of CD, DE, and EA getting 3.000, 3.606, and 2 respectively.
Now just add them together. So
5.099 + 3.162 + 3.000 + 3.606 + 2.000 = 16.867, which rounds to 16.9</span>
Answer:4
Step-by-step explanation:if you replace each "x" in the equation with the given x (-15) then it should go as such:
2(-15-5)-(3(-15)+1)
Then simplify
2(-20)-(-45+1)
2(-20)-(-44)
-40-(-44)
-40+44
4
Direct variation is y=kx, so you have to put those numbers and find the constant. Once you have done that, use the other number to find the answer