Answer:
0.2601
Step-by-step explanation:
There are 19C16 = 969 ways for Lester to choose 16 of the 19 objects.
There are 12C11 = 12 ways to choose 11 vases, and 7C5 = 21 ways to choose a non-vase, for a total of (12)(21) = 252 ways to choose exactly 11 vases in 16 objects.
So, the probability of interest is ...
252/969 ≈ 0.2601
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nCk = n!/(k!(n-k)!) ... the number of ways to choose k objects from n
Answer:
- 892 lb (right)
- 653 lb (left)
Step-by-step explanation:
The weight is in equilibrium, so the net force on it is zero. If R and L represent the tensions in the Right and Left cables, respectively ...
Rcos(45°) +Lcos(75°) = 800
Rsin(45°) -Lsin(75°) = 0
Solving these equations by Cramer's Rule, we get ...
R = 800sin(75°)/(cos(75°)sin(45°) +cos(45°)sin(75°))
= 800sin(75°)/sin(120°) ≈ 892 . . . pounds
L = 800sin(45°)/sin(120°) ≈ 653 . . . pounds
The tension in the right cable is about 892 pounds; about 653 pounds in the left cable.
_____
This suggests a really simple generic solution. For angle α on the right and β on the left and weight w, the tensions (right, left) are ...
(right, left) = w/sin(α+β)×(sin(β), sin(α))
Answer:
6√2
Step-by-step explanation:
A 45 45 90 right triangle, so ratio of leg : leg: hypotenuse = a: a : a√2 (a = value of leg)
Given: leg = 6
So the ratio of leg : leg: hypotenuse = 6 : 6 : 6 √2
Answer:
x = 6√2
All the choices are in the slope-intercept form where,
y=mx+b
so, the number before the x is the slope. The given slope is -34. We just have to look for the -34 number before the x. So mong the choices, it is the letter a choice that has the slope -34. So the answer is A.
Answer:
7.5 square units
Step-by-step explanation:
Base of the triangle = 5 units
Height of the triangle = 3 units
Area of the triangle
