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Juli2301 [7.4K]
3 years ago
13

4. Ten outcomes are all equally likely from an event and you choose one of them at random. What is the probability that the outc

ome you chose will be the outcome of the event?
0.50
0.10
0
0.90
Mathematics
2 answers:
Maksim231197 [3]3 years ago
7 0
1/10 because there are ten outcomes
photoshop1234 [79]3 years ago
6 0

Answer:  The correct option is (B) 0.10.

Step-by-step explanation:  Given that ten outcomes are all equally likely from an event and we choose one of them at random.

We are to find the probability that the outcome we chose will be the outcome of the event.

Since the outcomes are equally likely, so

let A denotes the event that any one of the outcome is chosen and S be the sample space for the experiment.

Then, n(A) = 1 and n(S) = 10.

Therefore, the probability  that the outcome we chose will be the outcome of the event is given by

P(A)=\dfrac{n(A)}{n(S)}=\dfrac{1}{10}=0.10.

Thus, teh required probability is 0.10.

Option (B) is CORRECT.

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damaskus [11]

Answer:

4,2,1

Step-by-step explanation:

7 0
3 years ago
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The graph shows a function.<br> Find the value of b and d.
True [87]

Answer:

<em>The required values are b=-6 and d=4</em>

Step-by-step explanation:

The graph corresponds to the function

r(x) =x^2+bx^2+8x+d

We are required to find the values of b and d.

They can be found by using two points that are clearly visible on the graph. For example, the points (0,4) and (2,0) belong to the function. Substituting their values in the function:

4 =0^2+b*0^2+8*0+d

Simplifying:

4 = d

d = 4

Now use the point (2,0):

0 =2^2+b*2^2+8*2+d

Since d=4, and calculating

0 =4+4b+16+4

Simplifying:

4b = -24

Dividing by 4:

b = -24/4 = -6

b = -6

The required values are b=-6 and d=4

5 0
3 years ago
The graphs of the quadratic functions f(x) = 6 – 10x2 and g(x) = 8 – (x – 2)2 are provided below. Observe there are TWO lines si
natta225 [31]

Answer:

a) y = 7.74*x + 7.5

b)  y = 1.148*x + 6.036

Step-by-step explanation:

Given:

                                  f(x) = 6 - 10*x^2

                                  g(x) = 8 - (x-2)^2

Find:

(a) The line simultaneously tangent to both graphs having the LARGEST slope has equation

(b) The other line simultaneously tangent to both graphs has equation,

Solution:

- Find the derivatives of the two functions given:

                                f'(x) = -20*x

                                g'(x) = -2*(x-2)

- Since, the derivative of both function depends on the x coordinate. We will choose a point x_o which is common for both the functions f(x) and g(x). Point: ( x_o , g(x_o)) Hence,

                                g'(x_o) = -2*(x_o -2)

- Now compute the gradient of a line tangent to both graphs at point (x_o , g(x_o) ) on g(x) graph and point ( x , f(x) ) on function f(x):

                                m = (g(x_o) - f(x)) / (x_o - x)

                                m = (8 - (x_o-2)^2 - 6 + 10*x^2) / (x_o - x)

                                m = (8 - (x_o^2 - 4*x_o + 4) - 6 + 10*x^2)/(x_o - x)

                                m = ( 8 - x_o^2 + 4*x_o -4 -6 +10*x^2) /(x_o - x)

                                m = ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x)

- Now the gradient of the line computed from a point on each graph m must be equal to the derivatives computed earlier for each function:

                                m = f'(x) = g'(x_o)

- We will develop the first expression:

                                m = f'(x)

                                ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

Eq 1.                          (-2 - x_o^2 + 4*x_o + 10*x^2) = -20*x*x_o + 20*x^2

And,

                              m = g'(x_o)

                              ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

                              -2 - x_o^2 + 4*x_o + 10*x^2 = -2(x_o - 2)(x_o - x)

Eq 2                       -2 - x_o^2 + 4*x_o+ 10*x^2 = -2(x_o^2 - x_o*(x + 2) + 2*x)

- Now subtract the two equations (Eq 1 - Eq 2):

                              -20*x*x_o + 20*x^2 + 2*x_o^2 - 2*x_o*(x + 2) + 4*x = 0

                              -22*x*x_o + 20*x^2 + 2*x_o^2 - 4*x_o + 4*x = 0

- Form factors:       20*x^2 - 20*x*x_o - 2*x*x_o + 2*x_o^2 - 4*x_o + 4*x = 0

                              20*x*(x - x_o) - 2*x_o*(x - x_o) + 4*(x - x_o) = 0

                               (x - x_o)(20*x - 2*x_o + 4) = 0  

                               x = x_o   ,     x_o = 10x + 2    

- For x_o = 10x + 2  ,

                               (g(10*x + 2) - f(x))/(10*x + 2 - x) = -20*x

                                (8 - 100*x^2 - 6 + 10*x^2)/(9*x + 2) = -20*x

                                (-90*x^2 + 2) = -180*x^2 - 40*x

                                90*x^2 + 40*x + 2 = 0  

- Solve the quadratic equation above:

                                 x = -0.0574, -0.387      

- Largest slope is at x = -0.387 where equation of line is:

                                  y - 4.502 = -20*(-0.387)*(x + 0.387)

                                  y = 7.74*x + 7.5          

- Other tangent line:

                                  y - 5.97 = 1.148*(x + 0.0574)

                                  y = 1.148*x + 6.036

6 0
3 years ago
5c+16.5=13.5+10c PLease answer quicly
frosja888 [35]
Remember you can do anything to an equation as long as you do it to both sides

5c+16.5=13.5+10c
minus 5c both sides
16.5=13.5+5c
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3=5c
divide both sides by 5
3/5=c
4 0
3 years ago
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tiny-mole [99]
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