Answer:
Step-by-step explanation:
n = 400
Proportion p = 229/400= 0.5725
For 95% confidence interval we use Z value as 1.96
Std error = 0.025
margin of error = 1.96*0.025
Confidence interval 95% = 0.5725±Margin of error
= (0.524, 0.621)
b) When smiled x becomes 277
p = 0.6925
Std error = 0.023
Margin of error= 1.96*0.023
Confidence interval = (0.647, 0.738)
Smiling increases the chances of stopping since mean and conidence interval bounds are showing increasing trend.
Answer:
The correct answer is:
The graph will be the same width as the parent graph f(x) = x², but the vertex has been shifted to (1, 2).
Step-by-step explanation:
Since the value of a, the coefficient of x², is 1, this means the graph has not been stretched or shrunk. However, since the function is different than f(x)=x², we know that the vertex is not at (0, 0). We can write the function in vertex form to find the new vertex.
To write the function in vertex form, we find the value of b/2. The value of b in this function is -2; -2/2 = -1. We then square this: (-1)² = 1. This is what we add and subtract to the function (we must do both to preserve equality), giving us:
f(x) = x²-2x+1+3-1
The first three terms of this function can be written as the square (x+(b/2))²; this is (x-1)², and gives us f(x) = (x-1)²+3-1. Combining like terms, we have:
f(x) = (x-1)²+2
This is vertex form, f(x) = a(x-h)²+k, where (h, k) is the vertex. This means the vertex is at (1, 2) instead of (0, 0).
V^2 + 3v - 4 = 0 can be factored: (v+4)(v-1) = 0. Then v = -4 and v = 1.
<span>D) perpendicular bisector <em>I believe.
</em></span>
Answer:
Step-by-step explanation:
This is permutation, since order matters. The formula for us is
₁₈P₅ = 
which simplifies to
₁₈P₅ = 
The factorial of 13 cancels out on the top and bottom leaving you with
₁₈P₅ = 18 × 17 × 16 × 15 × 14
which comes to 1,028,160 ways
Another way to look at it is: the first 5 people of 18 finish and the others you don't care about. Once the first place person is first, there are only 4 of the 18 left to finish in second place. Then there are only 3 left to finish in third place, etc. So if we use that reasoning, we don't even need to use the formula, we can just say
18 * 17 * 16 * 15 * 14 and those are the first 5 people of 18 to finish.
