Step-by-step explanation:
Convert the exponential equation to a logarithmic equation using the logarithm base
(
e
)
of the right side
(
0.0025
)
equals the exponent
(
−
6
)
.
log
e
(
0.0025
)
=
−
6
Answer:
Probability that event will have both red marbles will be 2.3% or 0.023.
Step-by-step explanation:
Given:
Total red marbles=5
Total blue marbles=25
Total number of marbles =30
To Find:
The probability that both are red without replacement of marbles.
Solution:
Now
Total sample space is 30 and total red marbles are 5
For a event that getting red marble probability is ,
=Total red marbles /total marbles.
=5/30
=1/6
So probability if getting red marble is 1/6
<em>Now for second chance there will be 4 red marbles remaining and 29 total marbles so,</em>
In second chance probability if getting red marble will be
=total red marbles present/total marbles remaining
=4/29
Now ,
The required probability will be getting both at a time
i.e probability getting red AND red marble so here AND operator which means multiple both the probability.
Probability both will have red =1/6*4/29
=4/(29*6)=2/(29*3)
=0.022988
=0.023
=2.3 %
If <em>y</em> = <em>A</em> sin(<em>x</em>) + <em>B</em> cos(<em>x</em>), then
<em>y'</em> = <em>A</em> cos(<em>x</em>) - <em>B</em> sin(<em>x</em>)
<em>y''</em> = -<em>A</em> sin(<em>x</em>) - <em>B</em> cos(<em>x</em>)
Substitute these into the ODE:
4<em>y''</em> + <em>y'</em> + 5<em>y</em> = 2 cos(<em>x</em>)
4 (-<em>A</em> sin(<em>x</em>) - <em>B</em> cos(<em>x</em>)) + (<em>A</em> cos(<em>x</em>) - <em>B</em> sin(<em>x</em>)) + 5(<em>A</em> sin(<em>x</em>) + <em>B</em> cos(<em>x</em>)) = 2 cos(<em>x</em>)
(-4<em>A</em> - <em>B</em> + 5<em>A</em>) sin(<em>x</em>) + (-4<em>B</em> + <em>A</em> + 5<em>B</em>) cos(<em>x</em>) = 2 cos(<em>x</em>)
(<em>A</em> - <em>B</em>) sin(<em>x</em>) + (<em>A</em> + <em>B</em>) cos(<em>x</em>) = 2 cos(<em>x</em>)
Then
<em>A</em> - <em>B</em> = 0
<em>A</em> + <em>B</em> = 2
Adding these equation gives
(<em>A</em> - <em>B</em>) + (<em>A</em> + <em>B</em>) = 0 + 2
2<em>A</em> = 2
<em>A</em> = 1 → <em>B</em> = 1
The standard equation for a circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k) and r is the radius.
To investigate this, check first if the quadratic equations are a perfect square. This is determined by dividing the middle term by 2 and taking its square. If it equals to the third term, it is a perfect square.
For (x^2 - 10x +25): (-10/2)^2 = 25 (perfect square)
For (y^2 - 16y + 64): (-16/2)^2 = 64 (perfect square)
Then, we simplify the equation by factoring:
(x - 5)^2 + (y -- 8)^2 = 16
Thus, the center is at point (5,8)
Also, the radius is square root of 16, which is 4.
Answer:
Correct choice is b.
Step-by-step explanation:
Rafael is taking a test that contains a section of 12 true-false questions. Exactly 8 correct answers of false from 12 true-false questions have
possible groups.