Answer:
x = 105
Step-by-step explanation:
the sum of all interior angles of any four-sided figure has 360 degrees
∡F and ∡H are equal
add all four expressions and set them equal to 360
x + (x + 5) +( x + 5) + (140 - x) = 360
combine like terms
2x + 150 = 360
2x = 210
x = 105
The cheetah runs 2 meters/sec faster than the gazelle. Eventually the cheetah will overcome the gazelle. Since distance = rate times time, time = distance/rate.
Thus,
300 meters / (2 meters/sec) = 150 sec = 2 min 30 sec
Answer:
The dimensions are 6 by 6
Step-by-step explanation:
Calculus answer:
2x +2y= 24
xy= A
2x=24-2y
x=12-y
(12-y)(y)= 12y- y^2
the Derivative is = 12-2y
Then set that equal to zero 0=12-2y
-12=-2y
y=6
Confirm that 6 is a maximum by using a wiggle graph
wiggle graph -∞<---inc--6---dec-->∞
6 is a maximum
plug into original equation
2x + 2(6)=24
2x+12=24
2x=12
x=6
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y=6
x=6
Answer:
It’s 3/2 mph
Step-by-step explanation:
<span>If there has to be 2 men and 2 women, we know
that we must take a group of 2 men out of the group of 15 men and a group of 2
women out of the group of 20 women. Therefore, we have:
(15 choose 2) x (20 choose 2)
(15 choose 2) = 105
(20 choose 2) = 190
190*105 = 19950
Therefore, there are 19950 ways to have a group of 4 with 2 men and 2women.</span>
<span>If there has to be 1 man and 3 women, we know
that we must take a group of 1 man out of the group of 15 men and a group of 3
women out of the group of 20 women. Therefore, we have:
(15 choose 1) x (20 choose 3)
(15 choose 1) = 15
(20 choose 3) = 1140
15*1140 = 17100
Therefore, there are 17100 ways to have a group of 4 with 3 women and 1 man.</span>
<span>We now find the total outcomes of having a group
with 4 women.
We know this is the same as saying (20 choose 4) = 4845</span>
Therefore, there are 4845 ways to have a group of
4 with 4 women.
We now add the outcomes of 2 women, 3 women, and
4 women and get the total ways that a committee can have at least 2 women.
19950 + 17100 + 4845 = 41895 ways that there will
be at least 2 women in the committee
