9514 1404 393
Answer:
0.344
Step-by-step explanation:
There are 20C10 = 184,756 ways to choose 10 problems at random from a list of 20.
There are 10C5 = 252 ways to choose 5 of the 10 algebra problems, and the same number of ways to choose 5 of the 10 geometry problems. Then there are 252² = 63,504 ways to choose 5 problems each of algebra and geometry.
The probability of choosing 5 problems in each category is ...
63504/184756 ≈ 0.344
Answer:
-0.5
Step-by-step explanation:
Area is 6000 yd2
LW = 6000
field must be 40 yards longer than its width
L = W + 40
Replace L with W+40 in 1st equation to solve for Width
(W+40)(W) = 6000
W2 + 40W - 6000 = 0
This is a quadratic but is factorable
Factors of -6000 that add to 40 are (100)(-60)
(W+100)(W-60) = 0
W = -100 or W = 60
Since the width will not be negative discard -100
The width is 60 yards
Length is W+40 = 100 yards
X = 69o
2x + 42 = 180
=> x = 69
Apply the Law of Sines.
sin A sin B sin C
------- = -------- = --------
a b c
Inserting the given data,
sin 36 sin B sin C
--------- = -------- = --------
250 300 420
300 sin 36
Then 300 sin 36 = 250 sin B, and sin B = ---------------- = 0.705
250
Thus, arcsin B = 0.783 rad = 44.857 degrees, or about 45 degrees.
Taking B to be 45 degrees and the given angle 36 deg, then the 3rd angle must be 180 - (45+36) = 99 degrees (which is opposite the 420-ft side).
At this point we apply Heron's formula. You should look this up on the 'Net.
a + b + c 250 + 300 + 420
First, we calculate S = --------------- = ------------------------ = 970/2 = 485
2 2
and then calculate sqrt (S(S-A)(S-B)(S-C):
Area of triangle / lot is then:
A = sqrt(485(485-250)(485-300)(485-420))
= sqrt(485(235)(185)(65) )
= 37021 square feet
