Alex has 70% of her weekly paycheck automatically deposited into a savings account

Compare the process of solving |x – 1| + 1 < 15 to that of solving |x – 1| + 1 > 15.

kicyunya [14]

In the first case we'd subtract 1 from both sides, obtaining |x-1|<14.

In the second case we'd also subtract 1 from both sides, and would obtain
|x-1|>14.

What would the graphs look like?

In the first case, the graph would be on the x-axis with "center" at x=1. From this center count 14 units to the right, and then place a circle around that location (which would be at x=15). Next, count 14 units to the left of this center, and place a circle around that location (which would be -13). Draw a line segment connecting the two circles. Notice that all of the solutions are between -13 and +15, not including these endpoints.

In the second case, x has to be greater than 15 or less than -13. Draw an arrow from x=1 to the left, and then draw a separate arrow from 15 to the right. None of the values in between are solutions.

4 0

2 years ago

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An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equ

kompoz [17]

Answer:

0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

Normal probability distribution.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 800, \sigma = 40, n = 16, s = \frac{40}{\sqrt{16}} = 10$

Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

This probability is the pvalue of Z when $X = 775$ . So

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

$Z = \frac{775 - 800}{10}$

$Z = -2.5$

$Z = -2.5$ has a pvalue of 0.0062. So there is a 0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

5 0

2 years ago

Kiran has $100 saved in a bank account. (The account doesn’t earn interest.) He asked Clare to help him figure out how much he c

iris [78.8K]

The answer would be 650

3 0

1 year ago

Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break duri

katrin [286]

For this case we have the following equation:
$d (t) = 12t + 20
$
The variables are:
t: time in hours
d (t): distance traveled in miles.
We evaluate the distance traveled after 4 hours.
So we have that for t = 4:
$d (4) = 12 (4) +20

d (4) = 48 + 20

d (4) = 68$
Answer:
d (4) = 68
This means that after 4 hours Joanna cycled for 68 miles total

6 0

2 years ago

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In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some poin

FrozenT [24]

Answer: The length of segments between this point and the vertices of greater base are $7\frac{5}{7}$ and 18.