Answer:
x = 82°
y = 59°
z = 39°
Step-by-step explanation:
∠x = 1/2(134° + 30°) = 82°
∠z = 180° - 59° - 82° = 39°
arc DF = 2(39°) = 78°
arc DB + arc DF = 134° + 78° = 212°
draw a diameter down from point B to the opposite side of the circle, call that point P:
arc BDP = 180°
(arc BDF) 212° - 180° = 32° (arc PF)
∠PBG = 1/2(32°) = 16°
∠DEB = 1/2(134°) = 67°
∠DBE = 180° - 59° - 67° = 54°
(∠DBE) 54° - (∠z) 39° + (∠PBG) 16° = (∠PBE) 31°
y = 90°- 31° = 59°
Answers:
- angle1 = 156 degrees
- angle2 = 24 degrees
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Explanation:
The two angles form a straight line, which is 180 degrees
Add up the angle expressions and set the sum equal to 180.
(angle1) + (angle2) = 180
(4x) + (x-15) = 180
(4x+x)-15 = 180
5x-15 = 180
5x = 180+15
5x = 195
x = 195/5
x = 39
We use that x value to find each missing angle
- angle1 = 4x = 4*39 = 156 degrees
- angle2 = x-15 = 39-15 = 24 degrees
Then notice how angle1+angle2 = 156+24 = 180 to verify the answer.
Side note: Angles that add to 180 are considered supplementary.
<span>1. Find the magnitude and direction angle of the vector.
2. Find the component form of the vector given its magnitude and the angle it makes with the positive x-axis.
<span>3. Find the component form of the sum of two vectors with the given direction angles.</span></span>
C, see explanation in the picture attached below.
Answer:
77.64% probability that there will be 0 or 1 defects in a sample of 6.
Step-by-step explanation:
For each item, there are only two possible outcomes. Either it is defective, or it is not. The probability of an item being defective is independent of other items. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The true proportion of defects is 0.15
This means that 
Sample of 6:
This means that 
What is the probability that there will be 0 or 1 defects in a sample of 6?
In which
77.64% probability that there will be 0 or 1 defects in a sample of 6.
