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Andreyy89
2 years ago
12

Solve the inequality. -1/3w ≤ -5​

Mathematics
1 answer:
omeli [17]2 years ago
3 0

Answer:

\frac{ - 1}{3} w \leqslant  - 5

w \leqslant  - 5 \div  \frac{ - 1}{3}

w \leqslant  - 5 \times  - 3

w \leqslant 15

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What is the midpoint between the points (1, 4) and (-3, 2)?
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3 years ago
The annual rainfall (in inches) in a certain region is normally distributed with = 40 and = 4. What is the probability that star
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Answer:

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Step-by-step explanation:

Solution:-

- Denote a random variable "X" The annual rainfall (in inches) in a certain region . The random variable follows a normal distribution with parameters mean ( μ ) and standard deviation ( σ ) as follows:

                          X ~ Norm ( μ , σ^2 )

                          X ~ Norm ( 40 , 4^2 ).

- The probability that it rains more than 50 inches in that certain region is defined by:

                          P ( X > 50 )

- We will standardize our test value and compute the Z-score:

                          P ( Z > ( x - μ )  / σ )

Where, x : The test value

                          P (  Z > ( 50 - 40 )  / 4 )

                          P (  Z > 2.5 )

- Then use the Z-standardize tables for the following probability:

                          P ( Z < 2.5 ) = 0.0062

Therefore,          P ( X > 50 ) = 0.0062

- The probability that it rains in a certain region above 50 inches annually. is defined by:

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                           1 - q = 0.9938

                           n = 10 years   ..... Sample of n years taken

- The random variable "Y" follows binomial distribution for the number of years t it takes to rain over 50 inches.

                          Y ~ Bin ( 0.9938 , 0.0062 )

- The probability that it takes t = 10 years for it to rain:

                         =  10C10* ( 0.9938 )^10 * ( 0.0062 )^0

                         = ( 0.9938 )^10

                         = 0.93970

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