Answer: - 2.5
Step-by-step explanation:
Using the attached number line has reference, the distance between each integer on the number line attached is 1, and the numbers are ordered in ascending order from - 10 to + 10. The point R exists in between the point marked - 2 and - 3 respectively. This shows that that point R is a number between the two integers, a number greater than - 3 but less than - 2.
From the picture attached the blue dot sits directly at the midpoint between - 3 and - 2. Hence the position can be a obtained by averaging the two integers.
(-3 + - 2) / 2 = - 5/2 = - 2.5
Let x be the number of Standard Specials sold last Monday and y be the number of Deluxe specials sold last Monday.
The Standard special sells for $2, then x Standard Specials cost $2x.
The Deluxe special sells for $4.50, then y Deluxe specials cost $4.50y.
1. Last Monday, PB&P sold at least $200 worth of Standard and Deluxe peanut butter and pickle sandwich specials. This means that
2x+4.50y≥200.
2. When all related business expenses are included, the Standard special costs $0.50 to prepare, then x Standard Specials cost $0.50x.
When all related business expenses are included, the Deluxe special costs $1.25 to prepare, then y Deluxe specials cost $1.25y.
Expenses were no more than $100, then
0.50x+1.25y≤100.
3. At least 30 Standard special were sold, then x≥30.
4. Graph all these inequalities (see attached diagram). As you can see only point (60,70) doesn't belong to needed region.
Answer: all points except point (60,70)
Conditional probability formula is:P ( A and B ) = P ( A ) · P ( B / A )0.46 = P ( A ) · 0.31P ( A ) = 0.46 : 0.31P ( A ) = 1.48And this is impossible because 0 ≤ P ( A ) ≤ 1The student obviously made a mistake.
Answer:

Step-by-step explanation:
The pool are is divided into 4 separated shapes: 2 circular sections and 2 isosceles triangles. Basically, to calculate the whole area, we need to find the area of each section. Due to its symmetry, both triangles are equal, and both circular sections are also the same, so it would be enough to calculate 1 circular section and 1 triangle, then multiply it by 2.
<h3>Area of each triangle:</h3>
From the figure, we know that <em>b = 20ft </em>and <em>h = 25ft. </em>So, the area would be:

<h3>Area of each circular section:</h3>
From the figure, we know that
and the radius is
. So, the are would be calculated with this formula:

Replacing all values:

Remember that 
Therefore, 
Now, the total are of the figure is:

Therefore the area of the symmetrical pool is 
Parameterize the intersection by setting

, so that


The length of the path

is then given by the line integral along

,

where

. We have



and so the line integral is

This result is fortuitous, since we can write

and so the integral reduces to