<h3>
Answer: Independent </h3>
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Reason:
The first marble was replaced, so the original state of the bag hasn't changed overall. The probability isn't changed either. We can treat the second selection entirely independent of the first one.
If the first marble wasn't replaced, then the marble count of course goes down by 1. That affects the probability of the second selection and we'd consider these events to be dependent.
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An example:
Consider a bag with 4 red marbles and 6 green ones. The chances of picking red on the first try are 4/10 = 2/5. The chances of picking red again would be 2/5 assuming we put that red marble back. We can see the second selection is independent of the first.
If the marble wasn't put back, then the chances of picking a 2nd red marble would be 3/9 = 1/3. I subtracted 1 from the numerator and denominator of 4/10 to get to 3/9. In this case, the 2nd selection's probability depends on the first event (whether red was picked or not).
Answer:
Option d. is the correct choice.
Step-by-step explanation:
8 can be written as √8 x √8 = √64
So, given expression will become:
= √64 x √6
= √384
Best Regards!
To find the vertex of a quadratic function, you need to 'complete the square';
Completing the square gives a quadratic in another form;
For quadratics that have an x² coefficient of 1 as is the case, it is a simple matter to complete the square:
For the quadratic x² + bx + c
Simply, put x added to half the coefficient of the x term (b/2) in a bracket and square the bracket;
Then add the constant (c) and the square of the half the coefficient of the x term (b/2), so:
(x + d)² + e, where d is a (rational) number to be identified;
d = b/2
e = d² + c
So, for f(x) = x² + 0x + 3:
Then the completed-the-square form is: f(x) = (x + 0)² + 3
As it happens, this quadratic function has a common normal form and completed-the-square form because the x-coefficient is 0.
The vertex coordinates are, according to the general format given above:
(-d, e).
So, looking at completed-the-square form for the function in question, we can tell the vertex is at the coordinates: (0, 3)
Quadratic functions always have symmetry about the vertical line with the x-coordinate of the vertex;
This makes sense if you think about how the graph looks (u-shaped);
Therefore for our function, the vertex is:
x = 0 (a vertical line with the x-coordinate of the vertex).
You can get this by using the quadratic equation with a = 7, b = -1, c = -9
I think this is just a simple addition problem to calculate the exact distance in kilometers.
So add 3.6+4.705+5.92=
14.225 kilometers that Andrea ran over the three days.
Hope this helps, have a good day. c;
