Solve each equation. Round to the nearest ten-thousandth. Check your answers. 25²x⁺¹=144
1 answer:
=> x = 0.272, by properties of logarithm.
- The opposite of exponentiation is the logarithm.
- This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
- A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Given:
Taking logarithm on both sides:
log () = log (144)
=> (2x + 1) log (25) = log (144) (As )
=> 2x + 1 =
=> 2x + 1 =
=> 2x + 1 = 1.544
=> 2x = 0.544
=> x = 0.272
Hence, => x = 0.272, by properties of logarithm.
To learn more about logarithms, refer to the link: brainly.com/question/25710806
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Answer:
The designed life should be of 21,840 vehicle miles.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles.
This means that
Find its designed life if a .97 reliability is desired.
The designed life should be the 100 - 97 = 3rd percentile(we want only 3% of the vehicles to fail within this time), which is X when Z has a p-value of 0.03, so X when Z = -1.88.
The designed life should be of 21,840 vehicle miles.