Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $1000. wh
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At Venn diagram there are 4 parts (20 pieces):
1. Colored only in blue - quadrilaterals with four equal side lengths (3 pieces);
2. Colored only in orange - quadrilaterals with four right angles (6 pieces);
3. Colored in both blue and orange - quadrilaterals with four right angles and with four equal side lengths (2 pieces);
4. Colored in white - quadrilaterals withoutprevious two properties (9 pieces).
Consider events:
A - a randomly chosen quadrilateral has four right angles;
B - a randomly chosen quadrilateral has four equal side lengths;
Use formula to find the probability that a randomly selected quadrilateral with 4 right angles also has four equal side lengths:
Answer: Pr=0.25
The two gears are shown n the diagram below.
ω₁ and ω₂ are the angular velocities of the larger and smaller gears respectively.
Part 1.
When the smaller gear makes one revolution, it turns through an angle of 2π radians or 360°.
Because the gears do not slip, the larger gear turns through an angle of θ, so that
(θ radians)*(8 in) = (2π radians)*(2 in)
or
8θ = 4π
θ = π/2 radians = 90°
Answer: 90.0°
Part 2.
When the larger gear makes one revolution, it turns through an angle of 2π radians.
Because the gears do not slip, the smaller gear turns through an angle φ, such that
(2 in)*(φ radians) = (8 in)*(2π radians)
or
2φ = 16π
φ = 8π radians
= (8π radians)*(1/2π rotations/radian)
= 4 rotations
Answer: 4 rotations
ω₁ and ω₂ are the angular velocities of the larger and smaller gears respectively.
Part 1.
When the smaller gear makes one revolution, it turns through an angle of 2π radians or 360°.
Because the gears do not slip, the larger gear turns through an angle of θ, so that
(θ radians)*(8 in) = (2π radians)*(2 in)
or
8θ = 4π
θ = π/2 radians = 90°
Answer: 90.0°
Part 2.
When the larger gear makes one revolution, it turns through an angle of 2π radians.
Because the gears do not slip, the smaller gear turns through an angle φ, such that
(2 in)*(φ radians) = (8 in)*(2π radians)
or
2φ = 16π
φ = 8π radians
= (8π radians)*(1/2π rotations/radian)
= 4 rotations
Answer: 4 rotations