Answer: The Answer is "less than"
Step-by-step explanation:
To find the sum of a series, you find the difference between the first and last term, multiply that by the number of terms, then divide by 2.
For the even numbers, 2 is the first term and 200 is the 100th term (because 2+(100-1)2 is equal to 200). So, (100(2+202)/2 = 10100.
For the odd numbers, 1 is the first term and 201 is the 101th term (because 1+(101-1)2 is equal to 201). So, (101(1+202))/2 = 10251.5.
10100<10251.5 so the sum of the first 100 even numbers is less than the sum of the first odd 101 numbers.
Answer:
Since the diameter of the pool is 10 feet, the radius will be one-half of the diameter.
The radius will be 5 feet.
The circumference of the pool will be Pi times the diameter.
The circumference will be Pi (3.14) times 10 feet.
The circumference will be 31.4 feet.
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Answer:
The options provided do not have the correct answer. Read below.
Step-by-step explanation:
Given a 10 by 10 grid model means that there are exactly 100 individual squares present. This shows that each square is equal to 1%.
None of the options provided gives us 12% of the model.
The first option results in 50%, the second results in 5%, third option results in 0.5% and the last option results in 2%.
For 12% we can shade 12 squares completely, half of 24 squares etc.
I hope this answer helps.
Calculation:
(Length) (width) (height)
(2w+4) (w) (18-w) = 1152
(2w^2+4w) (18-w) = 1152
Distributive property:
36w^2 -2w^3+72w-4w^2 =1152
Remember to use FOIL method:
-2w^3 +32w^2+72w-1152 =0
Like terms:
-2(w^3-16w^2-36w+576) = 0
Factor it by 2:
w^3 -16w^2-36w+576 =0
Simplify:
w^2(w-16)-36(w-16) =0
(w^2-36) (w-16) = 0
w= -6,6,16
Width:
w = 6,16
Since width is 16, then the height should be less than the width (18-16=2)
Length of gift bag: 2(6)+4
=16 inches.
Width of the bag: 6
Height of the bag: 18-6
12 inches.
Answer: 16, 6 and 12 inches.
