Answer:
b. about 91.7 cm and 44.6 cm
Step-by-step explanation:
The lengths of the diagonals can be found using the Law of Cosines.
Consider the triangle(s) formed by a diagonal. The two given sides will form the other two sides of the triangle, and the corner angles of the parallelogram will be the measure of the angle between those sides (opposite the diagonal).
For diagonal "d" and sides "a" and "b" and corner angle D, we have ...
d² = a² +b² -2ab·cos(D)
The measure of angle D will either be the given 132°, or the supplement of that, 48°. We can use the fact that the cosines of an angle and its supplement are opposites. This means the diagonal measures will be ...
d² = 60² +40² -2·60·40·cos(D) ≈ 5200 ±4800(0.66913)
d² ≈ {1988.2, 8411.8}
d ≈ {44.6, 91.7} . . . . centimeters
The diagonals are about 91.7 cm and 44.6 cm.
Answer:
33
Step-by-step explanation:
angles on a straight line sum up to 180°
104+x+x+10=180
114+2x=180
2x=180-114
2x=66
x=33
Answer:
Step-by-step explanation:
You basicly want to use A=pe^rt to find the amount of money you now have. A is the total amount of money you have after a certian period of time (T) while your money grows at a steady rate (R). (E) is an irrational number 2.71828. (P) is the amount of money you started with. Your precentage is your rate and this means you earn 9% of what you have per year. The way the problem would be set up A=1500(2.71828)^(.09)(2). This problem allows for exponential growth to occur because your two variables are time and the amount you have in that time.
Answer:
A. 1.4*20 quarters
B.14
Step-by-step explanation:
- you start with 20 quarters= 20*1
- you find 40% of twenty quarters in your room= 4/100*20=0.4*20
- 20*1+20*0.4= 20*1.4
B
- 20*1.4=28
- 28*50/100=14
Given:
mean, μ = 11 lb
Std. deviation, σ = 2.1
Let x = the weight that separates the top 5% of the crop.
The z-score is
z = (x - μ)/σ
= (x - 11)/2.1
From standard z-table for normal distribution,
P(z=1.645) = 0.95
Therefore
(x - 11)/2.1 = 1.645
x - 11 = 1.645/2.1 = 0.7833
x = 11.783
Answer: 11.8 lb (nearest tenth)
