Answer:
The 90% confidence interval is 
Step-by-step explanation:
From the question we are told that
The sample size is n = 1007
The sample proportion is 
From the question we are told the confidence level is 90% , hence the level of significance is
=> 
Generally from the normal distribution table the critical value of 
is
Generally the margin of error is mathematically represented as
=> 
=> 
Generally 90% confidence interval is mathematically represented as
=> 
=>
For the function to be differentiable, its derivative has to exist everywhere, which means the derivative itself must be continuous. Differentiating gives
The question mark is a placeholder, and if the derivative is to be continuous, then the question mark will have the same value as the limit as
from either side.
So the derivative will be continuous as long as
For the function to be differentiable everywhere, we need to require that
is itself continuous, which means the following limits should be the same:
So, the function should be
with derivative
Answer:
$121.82
Step-by-step explanation:
Okay, this is kind of complex, so let's go step by step.
First, we want to find the area of the rectangular lawn - we can do this by multiplying the length and width. The length is 100 and the width is 45 so 
m² is the area of the rectangle.
However, there are 3 ponds in which the grass seeds will not be going - so we need to find the area of all 3 of these circles and subtract it from 4500 (our rectangle area).
The area of a circle is represented by the formula 
The diameters are given here, which is double the radius, so to find the radius of each circle let's divide the diameters by 2.
First circle's radius: 
Second circle's radius: 
Third circle's radius: 
Now let's find the area of each circle.
<em>First Circle</em>: 
<em>Second Circle</em>: 
<em>Third Circle:</em> 
Adding all of these values gets us 412.125.
Now we can subtract from this from 4500 to get us 4087.875
If the grass seeds that cost £1.49 cover 50m² each, then we need 
bags.
Each bag costs £1.49, so the total cost is 
Hope this helped!!
Answer:
0.1 show be the answer.
Step-by-step explanation:
1/4 * 2/5 = 0.1 = 1/10
