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Monica [59]
3 years ago
15

What is the product (3a2b4)(-8ab3)

Mathematics
1 answer:
Alexus [3.1K]3 years ago
7 0

Answer:

-3a²2b²96

Step-by-step explanation:

(3a2b4)(-8ab3)

= (3a×2b×4)(-24×a×b)

multiply together

= (-96)(3a²)(2b²)

= -3a²2b²96

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8. Write the equation of the line that is parallel to the line 2x + 5y = 15 and passes through the
marissa [1.9K]

Answer:

\sf y = \bold -\frac{2}{5} x -3

Explanation:

part A identification for slope:

\sf 2x + 5y = 15

\sf 5y = -2x + 15

\sf y = \frac{-2x + 15}{5}

\sf y = -\frac{2 }{5} x+3

comparing with slope intercept form: y = mx + b

we can find that here the slope is \bold -\frac{2}{5}

part B, solving the equation:

if the line is parallel, then the slope will be same.

given coordinates: ( - 10, 1 )

using the equation:

y - y₁ = m( x - x₁ )

\sf y - 1 = \bold -\frac{2}{5} (x --10)

\sf y = \bold -\frac{2}{5} x -4 + 1

\sf y = \bold -\frac{2}{5} x -3

Extra information:

check the image below. this proves that the line is parallel and passes through point (-10, 1). the blue line is question line and red the answer line.

3 0
2 years ago
Read 2 more answers
CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars
velikii [3]

Answer:

P(939.6 < X < 972.5) = 0.6469

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that \mu = 965, \sigma = 113

Sample of 57:

This means that n = 57, s = \frac{113}{\sqrt{57}} = 14.97

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

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

By the Central Limit Theorem

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

Z = \frac{972.5 - 965}{14.97}

Z = 0.5

Z = 0.5 has a pvalue of 0.6915

X = 939.6

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

Z = \frac{939.6 - 965}{14.97}

Z = -1.7

Z = -1.7 has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

So

P(939.6 < X < 972.5) = 0.6469

3 0
2 years ago
Uche pumps gasoline at a rate of 18\,\dfrac{\text{L}}{\text{min}}18 min L ​ 18, start fraction, start text, L, end text, divided
Fiesta28 [93]

Answer:

Uche's pumping rate is <u>300 mL/s</u>.

Step-by-step explanation:

Given:

Uche pumps gasoline at a rate of 18 L/min.

Now, to find Uche's pumping rate in mL/s.

The rate at which Uche pumps gasoline = 18 L/min.

So, to get the pumping rate in mL/s we use convert L/min to mL/s by using conversion factor:

<u>1 L/min = 16.6667 mL/s.</u>

18 L/min = 16.6667 × 18 mL/s.

18L/min = 300 mL/s.

Therefore, Uche's pumping rate is 300 mL/s.

8 0
3 years ago
What is the Domain and Range of the function f(x)<img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx-7%7D%20%2B9" id="TexFormula1" tit
omeli [17]

For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}

<h3>How to get the domain and range?</h3>

Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:

x - 7 ≥ 0.

Solving for x we get:

x ≥ 0 + 7

Then the domain is:

x ≥ 7

To get the range, we evaluate in the minimum of the domain:

f(7) = √(7 - 7) + 9 = 9

Then the range is the set of all values larger than 9, because the function is increasing.

So the range is R: y ≥ 9.

If you want to learn more about domain and range:

brainly.com/question/10197594

#SPJ1

5 0
2 years ago
Convert the following fraction to a decimal.
Nookie1986 [14]
I think it’s C but I could be wrong but I don’t think I am
6 0
3 years ago
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