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2 years ago

Prove that using: X ∩ (Y ∪ Z ) =(X∩Y) ∪ (Y ∩ Z )

Mathematics

1 answer:

sertanlavr [38]2 years ago

5 0

There should be a typo in the question: the correct formula would be

$X\cap(Y\cup Z)=(X\cap Y)\cup (X\cap Z)$

Let's compute $X\cap (Y\cup Z)$ first. We have

$(Y\cup Z)=\{1, 4, 5, 6, 7, 8, 9\}$

If we intersect this set with X, we have

$X\cap (Y\cup Z) = \{5, 8, 9\}$

So, that would be the left hand side. For the right hand side, we have

$X\cap Y = \{8\},\quad X\cap Z = \{5,9\}$

And their union is again $\{5,8,9\}$

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The equation of the line which passes through the point (0,5) and has a gradient of 4 is

const2013 [10]

Answer:

y = 4x + 5

Step-by-step explanation:

slope = m = 4

y-intercept = b = 5

y = mx + b

y = 4x + 5

6 0

2 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 68-95-99.7 rule roughly states that in a normal distribution 68%, 95% and 99.7% of the values lie within one, two and three standard deviation(s) around the mean. The z-scores represent values from the mean in a standard normal distribution, 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 x is any value which can be transformed to a z-value.

Then, z = 1 and z = -1 represent values for one standard deviation 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 driest of all years 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 symmetrical, 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 x 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 x = 688mm and the smallest monsoons rains of all year are less than this value of x = 688mm, 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

A line passes through the points (2,-4) and (6,10). What is the equation of the line?

deff fn [24]

Answer:

y = $\frac{7}{2}$ x - 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (2, - 4) and (x₂, y₂ ) = (6, 10)

m = $\frac{10+4}{6-2}$ = $\frac{14}{4}$ = $\frac{7}{2}$ , thus

y = $\frac{7}{2}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, - 4) , then

- 4 = 7 + c ⇒ c = - 4 - 7 = - 11

y = $\frac{7}{2}$ x - 11 ← equation of line

7 0

2 years ago

A video game company is designing a game based on professional race cars. Professional race cars have a length of 570 cm and a w

siniylev [52]

Answer:

A) 1/45

B) 1/60

Step-by-step explanation:

Part A

The actual car has a length to width ratio of ...

length/width = (570 cm)/(180 cm) = 57/18 = 3 1/6

The rectangle on the screen has a length to width ratio of ...

length/width = (13 cm)/(4 cm) = 3 1/4

Relative to its width, the screen rectangle is longer than necessary for a model of the car. So, the scale factor will be determined by the width of the car relative to the width of the screen model.

For a model width of 4 cm, the scale factor is ...

model/life-size = (4 cm)/(180 cm) = 1/45

Part B

For a model width of 3 cm, the scale factor is ...

model/life-size = (3 cm)/(180 cm) = 1/60

7 0

2 years ago

We will use the values off(x) at the points 0.0,0.2,0.4,0.6,0.8. Generate the data set beforeyou start the numerical integration

leva [86]

Answer:

Check attachment for complete question and answer

8 0

2 years ago