The answer choices are sufficiently far apart that you can work this backward. The sum will be ...
236,196*(1 + 1/3 + 1/9 + 1/27 + ...)
so a reasonable estimate can be given by an infinite series with a common ratio of 1/3. That sum is
236,196*(1/(1 - 1/3)) = 236,196*(3/2)
Without doing any detailed calculation, you know the best answer choice is ...
354,292
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There are log(236196/4)/log(3) + 1 = 11 terms* in the series, so the sum will be found to be 4(3^11 -1)/(3-1) = 2*(3^11-1) = 354,292.
Using the above approach (working backward from the last term), the sum will be 236,196*(1-(1/3)^11)/(1-(1/3)) = 236,196*1.49999153246 = 354,292
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* If you just compute log(236196/4)/log(3) = 10 terms, then your sum comes out 118,096--a tempting choice. However, you must realize that the last term is larger than this, so this will not be the sum. (In fact, the sum is this value added to the last term.)
Answer:
x = 75
Step-by-step explanation:
Triangle BDH
The angle must add to 180 degrees
36+ 39 + DHB = 180
75 + DHB = 180
DBH = 180-75
DHB = 105
DBH + x = 180 since it is a straight line
105+ x = 180
x = 75
The answer would be 0.975 because 9.75/10=0.975
Answer:
3) B. 77 flowers
4) A. 62.8
Step-by-step explanation:
3) First find the area. The area of a circular flower bed is found using the formula for a circle A = πr². Here the diameter is 14 so r =7.
Substitute r = 7.
A = π(7)² = 49π = 153.86 square feet.
Each flower requires 2 square feet.
Divide the area by 2 for the number of flowers.
153.86 / 2 = 76.93 = 77
4) First find the area of the entire circle. The area is found using the formula for a circle A = πr².
Substitute r = 6.
A = π(6)² = 36π = 113.04 square feet.
Now find the area of the small circle inside. Then subtract the two areas.
The area is found using the formula for a circle A = πr².
Substitute r = 4.
A = π(4)² = 16π = 50.24 square feet.
The shaded area is 113.04 - 50.24 = 62.8.