Solution :
Alpha, α = 0.01
The sample proportion is :
= 0.636
Test statistics,
z = 7.727
The p value = 0.00001
Here we observe that p value is less than α, and so we reject the hypothesis .
Therefore, there is sufficient evidence,
Is 0.212121212121...a rational number because a irrational number does not terminate or repeat?
1 answer:
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Answer:
1) b =
2)m = -2.5
3)y = 15
4)x=2
Step-by-step explanation:
- subtract 8b from both sides
- subtract 2 from both sides
- divide both sides by 3
- Substitute this value into the equation and if both sides are equal then it is the solution.
2)Simplifying
7m + 32 = 12 + -1m
Reorder the terms:
32 + 7m = 12 + -1m
Solving
32 + 7m = 12 + -1m
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add 'm' to each side of the equation.
32 + 7m + m = 12 + -1m + m
Combine like terms: 7m + m = 8m
32 + 8m = 12 + -1m + m
Combine like terms: -1m + m = 0
32 + 8m = 12 + 0
32 + 8m = 12
Add '-32' to each side of the equation.
32 + -32 + 8m = 12 + -32
Combine like terms: 32 + -32 = 0
0 + 8m = 12 + -32
8m = 12 + -32
Combine like terms: 12 + -32 = -20
8m = -20
Divide each side by '8'.
m = -2.5
Simplifying
m = -2.5
3)Simplifying
16 + -5y = 1 + -4y
Solving
16 + -5y = 1 + -4y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '4y' to each side of the equation.
16 + -5y + 4y = 1 + -4y + 4y
Combine like terms: -5y + 4y = -1y
16 + -1y = 1 + -4y + 4y
Combine like terms: -4y + 4y = 0
16 + -1y = 1 + 0
16 + -1y = 1
Add '-16' to each side of the equation.
16 + -16 + -1y = 1 + -16
Combine like terms: 16 + -16 = 0
0 + -1y = 1 + -16
-1y = 1 + -16
Combine like terms: 1 + -16 = -15
-1y = -15
Divide each side by '-1'.
y = 15
Simplifying
y = 15
4)Simplifying
2x + -8x + 1 = 9 + -10x
Reorder the terms:
1 + 2x + -8x = 9 + -10x
Combine like terms: 2x + -8x = -6x
1 + -6x = 9 + -10x
Solving
1 + -6x = 9 + -10x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '10x' to each side of the equation.
1 + -6x + 10x = 9 + -10x + 10x
Combine like terms: -6x + 10x = 4x
1 + 4x = 9 + -10x + 10x
Combine like terms: -10x + 10x = 0
1 + 4x = 9 + 0
1 + 4x = 9
Add '-1' to each side of the equation.
1 + -1 + 4x = 9 + -1
Combine like terms: 1 + -1 = 0
0 + 4x = 9 + -1
4x = 9 + -1
Combine like terms: 9 + -1 = 8
4x = 8
Divide each side by '4'.
x = 2
Simplifying
x = 2
Answer:
The value of c that will result in a perfect square trinomial is (3)^2 or 9
The perfect square trinomial is:
Step-by-step explanation:
We need to determine the value of c that will result in a perfect square trinomial.
Perfect square trinomial are of form:
Now, the equation given is:
Looking at the term 6w, we can write it as 2(w)(3)
We are given: a = w, 2ab = 2(w)(3) so, b will be: (3)^2
So, we will be adding (3)^2 on both sides
So, The value of c that will result in a perfect square trinomial is (3)^2 or 9
The perfect square trinomial is: