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2 years ago

Simplify the expression. 3^-9 * 3^6 * 3^6 3^3 9^3 27^3 3^-324

Mathematics

1 answer:

kow [346]2 years ago

7 0

3^3. if you're simplifying then you keep the base the smae but add the exponents since you are "multiplying" the bases

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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

2 years ago

Determine the equation of the circle graphed below.

erica [24]

Answer: (-7,3)

Step-by-step explanation:

3 0

2 years ago

Pre-image ABCD was dilated to produce image A'B'C'D' .

LUCKY_DIMON [66]

14/8 = 1.75
The scale factor is 1.75 because 8* 1.75 = 14

3 0

2 years ago

Read 2 more answers

Use the information to answer the questions.

Anna71 [15]

Answer:

Part 1) The length of two sides and the measure of the included angle (Side-Angle-Side)

Part 2) $b^2=a^2+c^2-2(a)(c)cos(B)$

Part 3) $b=11.6\ in$

Step-by-step explanation:

we have

In the triangle ABC

$a=11\ in\\c=9\ in\\B=70^o$

Part 1) Which information about the triangle is given?

In this problem we have the length of two sides and the measure of the included angle (Side-Angle-Side)

see the attached figure to better understand the problem

Part 2) Which formula can you use ti find b?

I can use the law of cosines

$b^2=a^2+c^2-2(a)(c)cos(B)$

we have

$a=11\ in\\c=9\ in\\B=70^o$

substitute the given values

$b^2=11^2+9^2-2(11)(9)cos(70^o)$

$b^2=202-67.72$

$b=11.59\ in$

Part 3) What is b, rounded to the nearest tenth?

Remember that

To Round a number

a) Decide which is the last digit to keep

b) Leave it the same if the next digit is less than $5$ (this is called rounding down)

c) But increase it by $1$ if the next digit is $5$ or more (this is called rounding up)

In this problem we have

$11.59\ in$

We want to keep the digit $5$

The next digit is $9$ which is 5 or more, so increase the "5" by 1 to "6"

therefore

$b=11.6\ in$

4 0

2 years ago

How to know if a fraction is proportional

Murrr4er [49]

You can tell if two fractions are proportional by cross multiplying the fractions. If the fractions are equivalent, then they are proportional. If they are not equivalent, they are not proportional.

8 0

2 years ago

Read 2 more answers