Answer:
43 is equivalent to 215
Step-by-step explanation:
=420(1+0.03/12)^2 use the calculator to find the answer
Answer:
75
Step-by-step explanation:
N 1 FRONT LEFT TOWER
[surface area of a prism]=[area of the base]+perimeter*h------> only one base
[surface area of a prism]=[3*3]+[4*3]*50----> 609 units²
[surface area of a triangular pyramid]=[area of the 4 triangles]----> without base
[area of 1 triangle]=3*h/2
h²=3²+1.5²----> h²=11.25-----> h=√11.25 units
[area of 1 triangle]=3*√11.25/2-----> 5.03 units²
[surface area of a triangular pyramid]=[4*5.03]-----> 20.12 units²
surface area of the front left tower=609+20.12-----> 629.12 units²
[volume of a prism]=[3*3*50]=450 units³
volume of a triangular pyramid]=[area of the base]*h/3
volume of a triangular pyramid]=[3*3]*3/3-----> 9 units³
[volume of the front left tower]=450+9------> 459 units³
N 2 FRONT RIGHT TOWER
[surface area of a cylinder]=[area of the base]+perimeter*h--> only one base
[surface area of a cylinder]=[pi*3²]+[2*pi*50]--> 342.26 units²
[surface area of a cone]=pi*r*l------> without base
r=3 units
l²=r²+h²-----> 3²+3²-----> 18---------> l=√18 units
[surface area of a cone]=pi*3*√18------> 39.97 units²
surface area of the front right tower=342.26+39.97------> 382.23 units²
[volume of a cylinder]=pi*r²*h
[volume of a cylinder]=pi*3²*50-----> 1413 units³
[volume of a cone]=pi*r²*h/3
[volume of a cone]=pi*3²*3/3----> 28.26 units ³
[volume of the front right tower]=1413+28.26-----> 1441.26 units³
N 3 BACK LEFT TOWER
[surface area of a cylinder]=[area of the base]+perimeter*h--> only one base
[surface area of a cylinder]=[pi*3²]+[2*pi*50]--> 342.26 units²
[surface area of hemisphere]=2*pi*r²
[surface area of hemisphere]=2*pi*3²-------> 56.52 units²
surface area of the back left tower=342.26+56.52-----> 113.04 units²
[volume of a cylinder]=pi*r²*h
[volume of a cylinder]=pi*3²*50-----> 1413 units³
[volume of a hemisphere]=(4/6)*pi*r³
[volume of a hemisphere]=(4/6)*pi*3³-----> 56.52 units³
[volume of the back left tower]=1413+56.52-------> 1469.52 units³
N 4 BACK RIGHT TOWER
[surface area of a triangular prism]=[area of the base]+perimeter*h------> only one base
find the area of the base
h²=3²-1.5²-----> h=√6.75
[area of the base]=3*√6.75/2----> 3.90 units²
[surface area of a triangular prism]=[3.90]+[3*3*50]-----> 453.9 units²
[surface area of a triangular pyramid]=[area of the 3 triangles]----> without base
[area of 1 triangle]=3*h/2
h²=3²+1.5²----> h²=11.25-----> h=√11.25 units
[area of 1 triangle]=3*√11.25/2-----> 5.03 units²
[surface area of a triangular pyramid]=[3*5.03]-----> 15.09 units²
surface area of the back right tower=453.9+15.09-----> 468.99 units²
[volume of a triangular prism]=area of the base *height
find the area of the base
h²=3²-1.5²-----> h=√6.75
[area of the base]=3*√6.75/2----> 3.90 units²
[volume of a triangular prism]= 3.90*50------> 195 units³
volume of a triangular pyramid]=[area of the base]*h/3
volume of a triangular pyramid]=[3.90]*3/3------> 3.90 units³
[volume of the back right tower]=195+3.90------> 198.90 units³
N 5 CENTRAL BUILDING
[surface area]=2*[area of the base]+perimeter of the base *heigth
[surface area]=100*50*2+2*(150)*30-----> 10000+9000-----> 19000 units²
surface area of the central building=19000 units²
volume of the central building =100*50*30-----> 150000 units³
volume of the central building=150000 units³
N 6
total surface area=629.12+382.23+113.04+468.99+19000-----> 20593.38 unit²
total volume=459+1441.26+1469.52+198.90+150000------> 153568.68 units³
Answer:
16% probability that the facility needs to recalibrate their machines.
Step-by-step explanation:
We have to use the Empirical Rule to solve this problem.
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
What is the probability that the facility needs to recalibrate their machines?
They will have to recalibrate if the number of defects is more than one standard deviation above the mean.
We know that by the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% is more than 1 standard deviation from the mean. Since the normal distribution is symmetric, of those 32%, 16% are more than one standard deviation below the mean, and 16% are more than one standard deviation above the mean.
So there is a 16% probability that the facility needs to recalibrate their machines.
