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lora16 [44]
3 years ago
8

Subtract (x+8)-(-3x-5)

Mathematics
1 answer:
sattari [20]3 years ago
4 0

\bold{Hey\ there!}\\ \\\bold{(x+8)-(-3x-5)} \\ \bold{Distribute\downarrow} \\ \bold{x(-3x)=-3x^2} \\ \bold{x(-5)=5x} \\ \bold{8(-3x)=-24x} \\ \bold{8(-5)=-40} \\ \\ \bold{We\ get:x+8+3x+5} \\ \bold{Combine\ the\ like\ terms\downarrow} \\ \bullet \ \bold{x \& 3x} \\ \bullet \ \bold{8\&5} \\ \\ \bold{Substitute\ the\ x\ by \ itself\ is\ 1}

\bold{1x+3x=4x} \\ \bold{8+5=13} \\ \\ \\ \boxed{\boxed{\bold{Answer:4x+13}}}\checkmark \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy \ your\ day!} \\ \\ \\ \\ \frak{LoveYourselfFirst:)}

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The time taken to assemble a laptop computer in a certain plant is a random variable having a normal distribution of 20 hours an
ludmilkaskok [199]

Answer:

a) 40.13% probability that a laptop computer can be assembled at this plant in a period of time of less than 19.5 hours.

b) 34.13% probability that a laptop computer can be assembled at this plant in a period of time between 20 hours and 22 hours.

Step-by-step explanation:

When the distribution is normal, we use 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 question:

\mu = 20, \sigma = 2

a)Less than 19.5 hours?

This is the pvalue of Z when X = 19.5. So

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

Z = \frac{19.5 - 20}{2}

Z = -0.25

Z = -0.25 has a pvalue of 0.4013.

40.13% probability that a laptop computer can be assembled at this plant in a period of time of less than 19.5 hours.

b)Between 20 hours and 22 hours?

This is the pvalue of Z when X = 22 subtracted by the pvalue of Z when X = 20. So

X = 22

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

Z = \frac{22 - 20}{2}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 20

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

Z = \frac{20 - 20}{2}

Z = 0

Z = 0 has a pvalue of 0.5

0.8413 - 0.5 = 0.3413

34.13% probability that a laptop computer can be assembled at this plant in a period of time between 20 hours and 22 hours.

4 0
3 years ago
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