If we had the info on with this "data" is, we then can solve it.
Answer: Any of the following angles are <u>not</u> congruent to angle 5.
- angle 2
- angle 4
- angle 6
- angle 8
The only exception being that if angle 5 is 90 degrees, then so are the remaining four angles shown above (in fact, all 8 angles are right angles).
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Explanation:
Angles 2 and 5 are supplementary since line p is parallel to line r. This means angle 2 and angle 5 add to 180 degrees. The two angles are only congruent if both are right angles (aka 90 degree angles); otherwise, they are not congruent angles.
Angle 2 = angle 4 because they are vertical angles. So because these two angles are congruent, and angle 2 does not have the same measure as angle 5, this consequently leads to angle 4 also not being the same measure as angle 5 (unless both are right angles).
Angle 2 = angle 8 because they are alternate interior angles. Following the same logic path as the last paragraph, we see that angles 8 and angle 5 aren't the same measure. Or we could note that angle 5 and angle 8 form a straight angle, so they must add to 180 degrees. The two angles are only congruent if they were 90 degrees each, or otherwise not congruent at all.
Similar logic can also show that angle 6 is not congruent to angle 5.
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An alternative path is to find all the angles that are always congruent to angle 5 and they are...
- angle 1 (corresponding angles)
- angle 3 (alternate interior angles)
- angle 7 (vertical angles)
And everything else is not congruent to angle 5.
Answer:
Step-by-step explanation:
Use the normal approximation to the binomial distribution
mean µ = np
standard deviation σ = √npq
Where,
n is sample size
p is probability of success.
q is probability of failure
Given that
q = 6% =0.06
Then, p = 1-q = 1-0.06 = 0.94
Therefore:
µ = pn
µ = 0.94n
Also
σ = √npq
σ = √(n)(0.94)(0.06)
σ = √(.0564n)
Using z-scores:
z = (x — µ )/σ
Using the data above
1.645 = (160 — 0.94n)/√(0.0564n)
Cross multiply
1.645√0.0564n = 160—0.94n
Square both sides
1.645²× 0.0564n = (160-0.94n)
0.153n=25600— 300.8n + 0.8836n²
0.8836n²-300.8n-0.153n +25600=0
0.8836n² — 300.953n + 25600 = 0
Using quadratic formula method.
a = 0.8836 b = -300.953 c = 25600
n = [-b±√(b²-4ac)]/2a
n = [--300.953±√((-300.953)²-4×0.8836×25600)] / (2 × 0.8836)
n = [300.953±√(92.07)]/1.7672
n = (300.953±9.6)/1.762
n = (300.953-9.6)/1.762
n = 168.22
Or
n = (300953+9.6)/1.762
n = 176.25
The maximum number of reservation is approximately 168.
Answer:
Interpreting as: + 40 = 0
Input:
+40 = 0
Result:
False
