We're going to "cut" the repeating part here in a few steps. First, we're going to put the number in a variable:
Next, to get rid of the negative, we can multiply either side by -1 to get
Now, we won't actually use this -x directly; instead, we want to create two new values, one by multiplying either side by 10:
and the other by multiplying either side by 1000:
Next, we can get rid of the repeated part of the number by subtracting -10x from -1000x:
And finally, we can divide either side of the equation by -990 to find that
Answer:
test statistic is 0.176
Step-by-step explanation:
Given Data
p>33
a=0.05
n=50
x=33.3
d(population deviation)=12
Test statistics=?
Solution
Test statistic z=(p-x)\(d/sqrt(50))
z=(33.3-30)\(12\sqrt(50))
z=0.176
The approximate width of Alice's backyard is 22.36 in.
Let l be the length of the rectangle and w be the width.
l = 2w
A = 1000 m2 = l*w
1000 m2 = 2w *w
500 m2 = w^2
√500 m2 = √w^2
w = <span>22.360679775 in or 22.36 in</span>
Since this is multiple choice ...
• check if B is correct:
x = 0, y = 4, z = 1 ⇒ 3x - y + 4z = -4 + 4 = 0 ≠ -10
(it's not)
• check if C is correct:
x = -2, y = 4, z = 0
⇒ 3x - y + 4z = -6 - 4 + 0 = -10
⇒ 3x - y + 4z = 2 + 4 + 0 = 6
⇒ 3x - y + 4z = -4 - 4 + 0 = -8
While this solution does satisfy the system, it can still have infinitely many other solutions that would work.
• check if D is correct:
Eliminate one of the variables from each equation. For instance,
(3x - y + 4z) + (-x + y + 2z) = -10 + 6
2x + 6z = -4
x + 3z = -2
and
(2x - y + z) + (-x + y + 2z) = -8 + 6
x + 3z = -2
but now it's impossible to eliminate one of the variables.
Therefore there are infinitely many solutions to the system [D].
