Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8
Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?
Let's check it out:
Even-numbered lists of odd numbers:
1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .
Amazing ! The sum is always the square of the number of items in the set !
For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.
I slogged through it on my calculator, and it's true.
I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).
Answer:
C
Step-by-step explanation:
To find the area of a composite figure, separate it into the regular parts which make the irregular shape. This shape is composed of a semi-circle and a rectangle. Find the area by finding the area of each shape.
Semi-circle:
The semi-circle has a diameter of 2 + 4 + 2 = 8. The area this figure uses the radius which is half the diameter. The radius is 4. To find the area substitute r = 4 into 
. However the semi-circle has a smaller circle cut out of it with radius 2. The area of the smaller circle is 
. The semi circle in the shape is the areas subtracted which equals 12π.
Rectangle:
The area of the rectangle is found using A = b*h = 2*5 = 10.
The total area is 12π + 10 meters squared.
Answer:
C
Step-by-step explanation:
Here is the complete question
ack wants to fined out which can pineapples is the best buy. He has a choice of four different -sized cans. Which can has the lowest unit price per ounce?
A. 8 ounce for $ 1.44
B. 6 ounce for $ 1. 14
C. 18 ounce for $ 2.88
D. 10 ounce for $ 1.62
unit price = price / total ounces
$1.44 / 8 = $0.18
$1.14 / 6 = $0.19
$2.88 / 18 = $0.16
$1.62 / 10 = 0.162
the lowest is 18 ounce for $ 2.88
Answer:
x = 120 degrees
Step-by-step explanation:
Since the angle given is 30 and the four lengths given are equal corresponding the angles opposite to their given sides for the top left triangle and bottom right triangle, the corresponding angles are equal and also 30 degrees. Since x is where the top left triangle is, we need an equation to relate x. The sum of all the angles in the top left triangle is 180. So, x + 30 + 30 = 180.
Therefore,
x = 180-30-30 = 120
