Answer:
1. The second number line, the third number line, the first number line.
2.
The life span of a battery is the amount of time the battery will last. The distribution of life span for a certain type of batt
1 answer:
Answer:
0.0548
Step-by-step explanation:
The distribution of life span for a certain type of battery is approximately normal with mean 2.5 hours and standard deviation 0.25 hour.
To find the the probability that a selected battery will have a life span of at most 2.1 hours, we need to first determine the z-score for x=2.1 hours using
We substitute the values to get:
We read read -1.6 from the standard normal distribution table to get:
P(X≤2.1)=0.0548
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Answer:
0.20 and 0.36
Step-by-step explanation:
y(t) = 2 sin (4π t) + 5 cos (4π t)
We wish to convert this to:
y = A sin(ωt + φ)
We know that ω = 4π. We also know the following:
5 = A sin φ
2 = A cos φ
Divide the first equation by the second equation:
5/2 = tan φ
φ = tan⁻¹(5/2)
Now, square the two equations and add them together.
5² + 2² = (A sin φ)² + (A cos φ)²
29 = A²
A = √29
The equation of the wave is therefore:
y = √29 sin(4π t + tan⁻¹(5/2))
The maximum negative position is -√29. And half of that is -½√29.
-½√29 = √29 sin(4π t + tan⁻¹(5/2))
-½ = sin(4π t + tan⁻¹(5/2))
7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)
7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π
t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24
Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.
t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24
t ≈ 0.20 or 0.36
