The axis of symmetry is at x = -3.
This can be found by looking at the basic form of vertex form:
y = (x - h)^2 + k
In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = -4. This means the vertex is at (-3, -4).
It is a fact that the axis of symmetry is a vertical line of x = (vertex value of x). So we can determine that the axis of symmetry is at x = -3
75 1/3 = 75.33
75.33% = 75.33/100
= 7533/10000
not sure if it can be simplified more than this
Answer:
12/30
Step-by-step explanation:
Here is the complete question
Three of these fractions are equivalent A.30/70 B.12/30 C.9/21 D.6/14 which one is the odd one out
to determine the equivalent fractions, convert the fractions to percentage
× 100 = 42.86%
× 100 = 40%
× 100 = 42.86%
x 100 = 42.86%
Another method is to convert the fraction to its simplest form
30/70
To transform to the simplest form. divide both the numerator and the denominator by 10 = 3/7
12/30
To transform to the simplest form. divide both the numerator and the denominator by 6 = 2/5
9/21
To transform to the simplest form. divide both the numerator and the denominator by 3 = 3/7
6/14
To transform to the simplest form. divide both the numerator and the denominator by 2 = 3/7
Using either methods, 12/30 is the odd one out
Using the z-distribution, it is found that the 95% confidence interval is (0.46, 0.526), and it does not provide strong evidence against that belief.
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:

In which:
is the sample proportion.
In this problem, we have a 95% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
We have that a random sample of 864 births in a state included 426 boys, hence the parameters are given by:

Then, the bounds of the interval are given by:


The 95% confidence interval estimate of the proportion of boys in all births is (0.46, 0.526). Since the interval contains 0.506, it does not provide strong evidence against that belief.
More can be learned about the z-distribution at brainly.com/question/25890103
Answer:
see explanation
Step-by-step explanation:
The perimeter (P) of a rectangle is calculated as
P = 2l + 2w ( l is the length and w the width )
perimeter of rectangle A = 2(7) + 2(5) = 14 + 10 = 24 in
perimeter of rectangle B = 2(4x - 3) + 2x = 8x - 6 + 2x = 10x - 6 in
Equating the two gives
10x - 6 = 24 ( add 6 to both sides )
10x = 30 ( divide both sides by 10 )
x = 3
Thus
length of rectangle B = 4x - 3 = 4(3) - 3 = 12 - 3 = 9 in
Width of rectangle B = x = 3 in