Answer: 208.
Step-by-step explanation:
The formula to find the minimum sample size is given by :-
(1)
, where z* = critical z-value (two tailed).
= Standard deviation ( from prior study ) and E = Margin of error.
As per given , we have
Margin of error : E= 0.29
Confidence level = 85%
Significance level =
Using z-table , the critical value (two -tailed)=
As per previous study , Variance =

Now, the required minimum sample size =
[Substitute the values in formula (1)]

[ Round to the next integer]
Hence, the minimum number of third graders that must be included in a sample = 208.
Answer:

Step-by-step explanation:
The vertex form of a quadratic equation <em>y = ax² + bx + c :</em>
y = a(x - h)² + k
(h, k) - vertex
We have the equation

Convert to the vertex form:


<em>use (a + b)² = a² - 2ab + b²</em>

Step-by-step explanation:
1/2 * (6*5) = 6w
30=12w
w=2.5
Yes
Step-by-step explanation:
Full price for first course: £8.90
Half price: £4.45
One and one half times
full price is then: £13.35
Since this is less than Craig's £13.40, he can just barely afford to buy two main courses at these prices.