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Ann [662]
2 years ago
6

Independence and Exclusiveness are two topics which are important to probability and often confused. Discuss the difference betw

een two events being independent and two events being mutually exclusive. Use examples to demonstrate the difference. Remember to explain as if you are talking to someone who knows nothing about the topic
Mathematics
1 answer:
Pavlova-9 [17]2 years ago
7 0

Answer:

Independent means that one has no effect on the other. Exclusive means one cannot happen alongside the other. In simpler terms, independent events can be thought of as the chance it'll rain and how many people are flossing their teeth in the morning. Both happen, but neither one impacts the other.

Exclusive, on the other hand, means only one can happen. Lets say at nine in the evening your favorite show is on. However, you have an early morning and should be asleep by nine. You cannot both be asleep and watching your favorite show, and so these events are exclusive.

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The coordinates of a point satisfy the equation of a line if the point is on the line
solong [7]
This afirmation is true. A linear equation can be expressed in the form  y<span>=mx+b</span><span><span><span> </span></span> In this equation, x and y are coordinates of a point, m is the </span>slope, and b is the y-coordinate of the y-intercept. Because this equation describes a line in terms of its slope and its y-intercept, this equation is called the slope-intercept form. 

6 0
2 years ago
The gradient of the curve is given by the equation and a point on the curve is also given. Find the equation of the curve with w
IgorC [24]

Answer:

4 x^(3/2)         + 5x -32

Step-by-step explanation:

This problem involves definite integration (anti-derivatives).

If dy/dx = 6x^(1/2) - 5, then dy = 6x^(1/2)dx - 5dx.

                                        (1/2) + 1

This integrates to y = 6x                        

                                   ----------------                      

                                      (1/2) + 1             x^(3/2)

                                                      =  6 ------------ + C

                                                                 3/2

             

or:        4 x^(3/2) + C

and the ∫5dx term integrates to 5x + C.

The overall integral is:  

4 x^(3/2) + C + 5x + C. better expressed with just one C:

4 x^(3/2)         + 5x + C

We are told that the curve represented by  this function goes thru (4, 20).

This means that when x = 4, y = 20, and this info enables us to find the value of the constant of integration C:

20 = 4 · 4^(3/2)         + 5·4 + C, or:

20  =  4  (8)           + 20 + C

Then 0 = 32 + C, and so C = -32.

The equation of the curve is thus   4 x^(3/2)         + 5x -32

                   

           

                                      (1/2 + 1)

7 0
3 years ago
A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must
Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

  • (x) should be the width of the rectangle base;
  • (h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

  • the radius  \mathbf{r = \dfrac{x}{2}}  

and, the perimeter of the window can now be expressed as:

\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}

\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}

Given that the perimeter = 600 cm

∴

\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}

\mathbf{  h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}

Since h > 0, then:

\mathbf{  h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}

By rearrangement and using the inverse rule:

\mathbf{  x<  \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }

\mathbf{  x=  \dfrac{ 1200}{\Big( 2 +\pi \Big) } }

\mathbf{  x=  233.39 \ cm }

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}

\mathbf{A = x \Big [  300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ]  +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}

\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}

\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big)  \ =0}

Making x the subject of the formula, we have:

\mathbf{x = \dfrac{1200}{4 +\pi}}

x = 168.03 cm

Taking the second derivative:

\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}

\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

brainly.com/question/9964510?referrer=searchResults

6 0
3 years ago
57 divided by 592,346
dlinn [17]

Answer:

9.62 x 10⁻⁵

Step-by-step explanation:

57 / 592346 = 0.0000962275

Scientific notation: We moved the decimal 5 times to the right, and in order to put the number back in standard form, we have to move the decimal 5 times to the left. So the scientific way of saying this is 9.62 x 10⁻⁵

5 0
2 years ago
Read 2 more answers
What is the missing reason in the proof?
spayn [35]
Perpendicular bisector theorem
5 0
3 years ago
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