Answer:
Ans 1 is correct.
Step-by-step explanation:
We have given that,
p=0.85,
n=20.
we know that
1-P(x=1)=1-(0.85×0.15^19)=0.999
Ans 1 is correct.
It should be B because you have to have 2 angles to know for sure.
Consider this option:
C³₂₇=27!/(3!*24!)=25*13*9=2925 ways to select 3 students.
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work
EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same
For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y
For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4
Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.
Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the
x²y = -4 ... (I)
Condition 2: Real parts are the same
x² + y = -3 ... (II)
We have a system of equations since both conditions must be satisfied
x²y = -4 ... (I)
x² + y = -3 ... (II)
We can rearrange equation (II) so that we have
y = -3 - x² ... (II)
Substituting into equation (I)
x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0
Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.
Solve for y:
y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4
So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:
-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i
x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i
They result in conjugates
Answer:
Option A is correct.
The system of equation is inconsistent is;
2x+8y=6
5x+20y=2
Explanation:
* A system of equations is called an inconsistent system, if there is no solution because the lines are parallel.
* If a system has at least one solution, it is said to be consistent .
*A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.
(A)
2x+8y=6
5x+20y=2
This is inconsistent, because as shown below in the graph of figure 1 that the lines do not intersect, so the graphs are parallel and there is no solution.
(B)
5x+4y=-14
3x+6y=6
this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 2 and also it is independent.
(C)
x+2y=3
4x+6y=5
this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 3.
(D)
3x-2y=2
6x-4y=4
this is a consistent system and has an infinite number of solutions, it is dependent because both equations represent the same line. as shown below in the graph of Figure-4.
Therefore, the only Option A system of equation is inconsistent.
