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Thepotemich [5.8K]
3 years ago
9

Find the slope of the line through the pair of points. A(2, –3), P(2, 9)

Mathematics
2 answers:
Flauer [41]3 years ago
6 0
The slope: m=\dfrac{y_2-y_1}{x_2-x_1}

A(2;-3)\to x_1=2;\ y_1=-3\\P(2;\ 9)\to x_2=2;\ y_2=9\\\\subtitute:\\\\m=\dfrac{9-(-3)}{2-2}=\dfrac{12}{0}!!!

<span>The denominator can not be <span>zero!

Conclusion: The slope is undenfined.
</span></span>
vladimir2022 [97]3 years ago
5 0
We are given with two points and is asked for the slope of the line formed by the two points. The formula of the slope is equal to change in y over change in x. In this case, the slope is (9+3)/(2-2) equal to 12/0 equal to infinity. This means the line connecting the two is a vertical line 
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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.

3 0
3 years ago
In the year 2003 a company made 8.8 million in profits. For each consecutive year after that their profits increased by 6%. How
yaroslaw [1]

Answer:

The company's profit in 2007 was 11.088 millions

Step-by-step explanation:

This is a compound interest problem where the initial amount is 8.8 million, the interest rate is 6% and the time period is 4 years and it gets compounded yearly. So we can use the compound interest formula, that is given by:

A = P*(1 + r/n)^(n*t)

Where A is the final amount, P is the initial amount, r is the rate, t is the total amount of time and n is the number of times it gets compounded in one year. We can now use all the values that were given to us to find out the profit of the company.

A = 8.8*(1 + (0.06))^(4) = 8.8*(1.06)^16

A  = 8.8*1.26 = 11.088 millions

So the company's profit in 2007 was 11.088 millions

6 0
3 years ago
Plz help as quick as possible!
kompoz [17]

average =65%

average = (60+70)/(100+100)*100

= 130/200*100

= 65%

6 0
3 years ago
Read 2 more answers
Given the figure below, find the values of x and z.
stepan [7]

Answer:

z = 96; x = 8.

Step-by-step explanation:

z = 96. This is because the angle measuring z degrees is a vertical angle of the angle measuring 96 degrees, which means that the two angles are congruent.

The angle measuring 5x + 44 degrees forms a straight angle with the 96 degree angle. That means that the measurements of the two angles will add to be 180 degrees.

5x + 44 + 96 = 180

5x + 140 = 180

5x = 40

x = 8

Hope this helps!

4 0
3 years ago
Bob sells part of a 50-acre rectangular plot of land he owns so that he can still own a smaller rectangular plot within the orig
Nuetrik [128]

Considering the area of a rectangle, it is found that the area of Bob's remaining plot of land is of 12.5 acres.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, that is:
A = lw.

In this problem, both the length and the width are divided in half, hence the proportion remaining is given by:

A = 0.5l x 0.5w = 0.25lw = 25% of the initial area.

Hence:

0.25 x 50 = 12.5.

The area of Bob's remaining plot of land is of 12.5 acres.

More can be learned about the area of a rectangle at brainly.com/question/10489198

#SPJ1

5 0
2 years ago
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