Answer:
The angle subtended by the arc is 171.8873385 degrees (3 radians)
Step-by-step explanation:
The formula of the length of an arc of a sector is L =
× 2 π r, where
- x is the central angle subtended by the arc
- r is the radius of the circle
∵ An arc of a sector is three times its radius
∴ L = 3r
→ Equate the formula of the length of the arc by 3r
∵
× 2 π r = 3r
→ Divide both sides by r
∴
× 2 π = 3
→ Simplify the left side
∵
x = 3
→ Divide both sides by ![\frac{\pi }{180}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20%7D%7B180%7D)
∴ x = 171.8873385°
∴ The angle subtended by the arc is 171.8873385 degrees (3 radians)
Answer:
![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
Step-by-step explanation:
Flipping a coin and rolling a number cube are both independent events. Independent events do not rely on the outcome of any previous events. This means that whatever you flip on the coin will have no effect on whatever you roll on the number cube and each flip of the coin or roll of the cube has the same probability as the flip or roll before.
The probability of getting tails on a coin toss is: ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
The probability of getting a number less than 3 (so 1 or 2) on a number cube is: ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Since we are combining these events, we need to multiply the fractions together to get our overall probability:
*
=![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
Answer:
Top right: quadrant 1
Top left: quadrant 2
Bottom left: quadrant 3
Bottom right: quadrant 4
The first number of an ordered pair is the x axis, and the second is the y axis
A: 10,3 quadrant 4
B:8, 9 quadrant 2
c: 3,2 Q 3
D: 4,0 Q4
E:4,7 Q3
F: 8,7 Q1
G: 0,7 Q4
H: 1,5 Q1
Answer:
y=4x+5
Step-by-step explanation:
y=mx+c
gradient =m
y intercept=c
m=4
c=5
so
y=4x+5