(a) 1A 2A 3A 1B 2B 3B (6 possible outcomes
(b) Possible outcomes for A or 1 are 1A 2A 3A and 1B ( 4 outcomes) therefore:
Probabilty = 4/6 = 2/3
Answer:
Box b
Step-by-step explanation:
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Answer:
Option 3
Step-by-step explanation:
Since lines a and b are intersecting, x+5=2x-5. Because they are vertical angles.
x+5=2x-5
2x-x=5+5
x=10
Answer:
y = -2*x^3 - x + 2
Step-by-step explanation:
We want to solve the differential equation:
y'' + 12*x = 0
such that:
y(0) = 2
y'(0) = -1
We can rewrite our equation to:
y'' = -12x
if we integrate at both sides, we get:

Solving that integral we can find the value of y', so we will get:
y' = -12* (1/2)*x^2 + C = -6*x^2 + C
where C is the constant of integration.
Evaluating y' in x = 0 we get:
y'(0) = -6*0^2 + C = C
and for the initial value problem, we know that:
y'(0) = -1
then:
y'(0) = -1 = C
C = -1
So we have the equation:
y' = -6*x^2 - 1
Now we can integrate again, to get:
y = -6*(1/3)*x^3 - 1*x + K
y = -2*x^3 - x + K
Where K is the constant of integration.
Evaluating or function in x = 0 we get:
y(0) = -2*0^3 - 0 + K
y(0) = K
And by the initial value, we know that: y(0) = 2
Then:
y(0) = 2 = K
K = 2
The function is:
y = -2*x^3 - x + 2
The solution to the given system of equation is (3, 3, 3)
<h3>Solving system of equations</h3>
Given the following system of equation expressed as:
2x-y+5z=16
X-6у +2z=-9
3x+4y- z=32
Multiply equation 2 by 2 to have:
2x-y+5z=16
2X-12у +4z=-18
Subtract
10y+z = 34 .........4
Similarly
3X-18у +6z=-27
3x+4y- z=32
Subtract
-22y+7z = -59 ........... 5
Equate 4 and 5
10y+z = 34 .........4 * 7
-22y+7z = -59 ........... 5 * 1
_______________________
70y+7z = 238
-22y+7z = -59
Subtract
92y = 297
y = 3
Recall that
10y+z = 34
10(3) + z = 34
z = 3
Since x - 6y +2z = -9
x-6(3)+2(3) = -9
x - 18 + 6 = -9
x = 3
Hence the solution to the given system of equation is (3, 3, 3)
Learn more on system of equation here: brainly.com/question/25976025
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