Answer:
∠A= 45°....
Step-by-step explanation:
To find ∠A first we have to find the length of side B by cosine law:
b^2 = a^2 + c^2 – 2 a c cos B
b^2=(2)^2 +(√3 + 1)^2 - 2(2)(√3 + 1) cos 60
b^2 = 6
Taking square root at both sides:
√b^2 = √6
b= 2.45
Now we can calculate ∠A by sine law:
b / sin B = a / sin A
2.45 / sin 60 = 2 / sin A
sin A= 2* √3/2 /2.45
sin A = 2√3/2 * 1/2.45
sinA = 2√3/ 4.9
sin A = 0.7069
sin A = 0.707
A=45°
Thus ∠A= 45°....
Answer:
3/x + 2/(x+1) = 3/5x
[3 · 5(x + 1) + 2 · 5x] / 5x(x + 1) = 3(x + 1) / 5x(x + 1)
3 · 5(x + 1) + 2 · 5x = 3(x + 1)
15x + 15 + 10x = 3x + 3
15x + 10x - 3x = -15 + 3
22x = -12
x = -12/22 = -6/11
24- sqrt(720/4) divide 720 by 4
24 - sqrt (180) now break down 180 to 9*4*5
24- sqrt(9) *sqrt(4) *sqrt (5) so 9becomes 3, 4 becomes 2
24- 3*2*sqrt(5) multiply 3 and 2
24-6sqrt(5)
<span>Exactly 33/532, or about 6.2%
This is a conditional probability, So what we're looking for is the probability of 2 gumballs being selected both being red. So let's pick the first gumball.
There is a total of 50+150+100+100 = 400 gumballs in the machine. Of them, 100 of the gumballs are red. So there's a 100/400 = 1/4 probability of the 1st gumball selected being red.
Now there's only 399 gumballs in the machine and the probability of selecting another red one is 99/399 = 33/133.
So the combined probability of both of the 1st 2 gumballs being red is
1/4 * 33/133 = 33/532, or about 0.062030075 = 6.2%</span>
