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Mathematics

1 answer:

sesenic [268]2 years ago

3 0

Answer:

$z = \frac{5}{8} \\$

Step-by-step explanation:

$9z + (7z-4)=6 \\ 9z + 7z - 4 = 6 \\ 16z = 6 + 4 \\ 16z = 10 \\ z = \frac{10}{16} \\ \\ z = \frac{5}{8}$

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What is a rational number and how do you know?

Andreas93 [3]

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational.

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2 years ago

Question Help Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 5656 hours and a

koban [17]

Answer:

a)3.438% of the light bulbs will last more than 6262 hours.

b)11.31% of the light bulbs will last 5252 hours or less.

c) 23.655% of the light bulbs are going to last between 5858 and 6262 hours.

d) 0.12% of the light bulbs will last 4646 hours or less.

Step-by-step explanation:

Normally distributed problems can be solved by the z-score formula:

On a normaly distributed set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a value X is given by:

$Z = \frac{X - \mu}{\sigma}$

After we find the value of Z, we look into the z-score table and find the equivalent p-value of this score. This is the probability that a score will be LOWER than the value of X.

In this problem, we have that:

The lifetimes of light bulbs are approximately normally distributed, with a mean of 5656 hours and a standard deviation of 333.3 hours.

So $\mu = 5656, \sigma = 333.3$

(a) What proportion of light bulbs will last more than 6262 hours?

The pvalue of the z-score of $X = 6262$ is the proportion of light bulbs that will last less than 6262. Subtracting 100% by this value, we find the proportion of light bulbs that will last more than 6262 hours.