Answer:
angle 1=94 degree
Step-by-step explanation:
-x + 106=5x + 34 (they are alternate interior angles)
106-34=5x+x
72=6x
72/6=x
12=x
substitute the value of x in 5x + 34
5*12 + 34
60+34
94
Now,
angle 1 =5x +134 ( they are vertically opposite angles)
angle 1=94 degree
1 yard=36 inches.
2 feet= 24 inches.
36+24= 60 inches
hope this helps!
Answer:
3/8 π radians
Step-by-step explanation:
The Area of a sector when then central angle is in radians = 1/2r² θ
Where
θ = central angle = ?
r = 16 cm
Area of the sector = 48πcm²
Hence
Central angle = Area of a sector ÷ (1/2r²)
= 48πcm² ÷ (1/2 × 16²)
= 48πcm² ÷ 128
Central angle = 3/8π radians
Therefore, Central angle = 3/8π radians
Answer:
a) 3/64 = 0.046 (4.6%)
b) 63/64 = 0.9843 (98.43%)
c) 1/64 = 0.015 (1.5%)
d) 1/4 = 0.25 (25%)
Step-by-step explanation:
in order to verify that the f(x) is a probability mass function , then it should comply the requirement that the sum of probabilities over the entire space of x is equal to 1. Then
∑f(x)*Δx = 1
if f(x)=(3/4)(1/4)^x , x = 0, 1, 2, ...
then Δx=1 and
∑f(x) = (3/4)∑(1/4)^x = (3/4)* [ 1/(1-1/4)] = (3/4)*(4/3) = 1
then f represents a probability mass function
a) P(X = 2)= f(x=2) = (3/4)(1/4)^2 = 3/64 = 0.046 (4.6%)
b) P(X ≤ 2) = ∑f(x) = f(x=0)+ f(x=1) + f(x=2) = (3/4) + (3/4)(1/4) + 3/64 = 63/64 = 0.9843 (98.43%)
c) P(X > 2)= 1- P(X ≤ 2) = 1 - 63/64 = 1/64 = 0.015 (1.5%)
d) P(X ≥ 1) = 1 - P(X < 1) = 1 - f(x=0) = 1- 3/4 = 1/4 = 0.25 (25%)
Answer:
If you work over 5 hours in a day, you are entitled to a meal break of at least 30 minutes that must start before the end of the fifth hour of your shift.
Step-by-step explanation:
