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lidiya [134]
2 years ago
13

What is the following product? 3v2(5v6-7v3)

Mathematics
1 answer:
steposvetlana [31]2 years ago
6 0

Answer:

3v^2\left(5v^6-7v^3\right)=15v^8-21v^5

Step-by-step explanation:

Given the expression

3v^2\left(5v^6-7v^3\right)

Apply the distributive law

a\left(b-c\right)=ab-ac

a=3v^2,\:b=5v^6,\:c=7v^3

=3v^2\cdot \:5v^6-3v^2\cdot \:7v^3

=3\cdot \:5v^6v^2-3\cdot \:7v^3v^2

=15v^8-21v^5

Thus, we conclude that

3v^2\left(5v^6-7v^3\right)=15v^8-21v^5

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Samantha rose 22 kilometers on her bike . Which expression should be used to show how many meters she rode.
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m=km/0.0010000

Explanation:

There are 1000 meters in every kilometer.

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A customer at Lost Pastores placed an order for 3 burritos which was priced at x amount of dollars each. He also ordered a plate
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Answer:

3x +12.95 = 32.46

Step-by-step explanation:

3 burritos plus x + 12.95 = $32.46

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Write an equation of the line that has a slope of -5 and a y- intercept of 4 in a slope intercept form.
Anastasy [175]

Answer:

y=-5x+4

Step-by-step explanation:

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3 years ago
The summer monsoon brings 80% of India's rainfall and is essential for the country's agriculture.
Natasha_Volkova [10]

Answer:

Step 1. Between 688 and 1016mm. Step 2. Less than 688mm.

Step-by-step explanation:

The <em>68-95-99.7 rule </em>roughly states that in a <em>normal distribution</em> 68%, 95% and 99.7% of the values lie within one, two and three standard deviation(s) around the mean. The z-scores <em>represent values from the mean</em> in a <em>standard normal distribution</em>, and they are transformed values from which we can obtain any probability for any normal distribution. This transformation is as follows:

\\ z = \frac{x - \mu}{\sigma} (1)

\\ \mu\;is\;the\;population\;mean

\\ \sigma\;is\;the\;population\;standard\;deviation

And <em>x</em> is any value which can be transformed to a z-value.

Then, z = 1 and z = -1 represent values for <em>one standard deviation</em> above and below the mean, respectively; values of z = 2 and z =-2, represent values for two standard deviations above and below the mean, respectively and so on.

Because of the 68-95-99.7 rule, we know that approximately 95% of the values for a normal distribution lie between z = -2 and z = 2, that is, two standard deviations below and above the mean as remarked before.

<h3>Step 1: Between what values do the monsoon rains fall in 95% of all years?</h3>

Having all this information above and using equation (1):

\\ z = \frac{x - \mu}{\sigma}  

For z = -2:

\\ -2 = \frac{x - 852}{82}

\\ -2*82 + 852 = x

\\ x_{below} = 688mm

For z = 2:

\\ 2 = \frac{x - 852}{82}

\\ 2*82 = x - 852

\\ 2*82 + 852 = x

\\ x_{above} = 1016mm

Thus, the values for the monsoon rains fall between 688mm and 1016mm for approximately 95% of all years.

<h3>Step 2: How small are the monsoon rains in the driest 2.5% of all years?</h3>

The <em>driest of all years</em> means those with small monsoon rains compare to those with high values for precipitations. The smallest values are below the mean and at the left part of the normal distribution.

As you can see, in the previous question we found that about 95% of the values are between 688mm and 1016mm. The rest of the values represent 5% of the total area of the normal distribution. But, since the normal distribution is <em>symmetrical</em>, one half of the 5% (2.5%) of the remaining values are below the mean, and the other half of the 5% (2.5%) of the remaining values are above the mean. Those represent the smallest 2.5% and the greatest 2.5% values for the normally distributed data corresponding to the monsoon rains.

As a consequence, the value <em>x </em>for the smallest 2.5% of the data is precisely the same at z = -2 (a distance of two standard deviations from the mean), since the symmetry of the normal distribution permits that from the remaining 5%, half of them lie below the mean and the other half above the mean (as we explained in the previous paragraph). We already know that this value is <em>x</em> = 688mm and the smallest monsoons rains of all year are <em>less than this value of x = </em><em>688mm</em>, representing the smallest 2.5% of values of the normally distributed data.

The graph below shows these values. The shaded area are 95% of the values, and below 688mm lie the 2.5% of the smallest values.

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Molodets [167]

Answer:

(a)The amount of fuel in dollars = $1.62

(b)The rate equivalent to in U.S. dollars per gallon = $ 1.45

Step-by-step explanation:

Reid will be driving through Spain this summer. He did some research and knows that the average price of gas in Spain is approximately 1.12 euros per liter.

1 USD = 0.69 euros

We have to find the money that we should pay in order to get the same amount of fuel.

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1 euro = $1.45

So 1.12 euros = 1.12\times1.45 = $1.62

(a)The amount of fuel in dollars = $1.62

(b)The rate equivalent to in U.S. dollars per gallon = $ 1.45

5 0
3 years ago
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