Answer: a) 
b) 25165824000
Step-by-step explanation:
The exponential equation for growth is given by :-
, where a= initial value , b =multiplicative growth factor and t = time.
Given : A bacteria culture contains 1500 bacteria initially and doubles every hour.
i.e. a = 1500 and b= 2
Then, the function N that models the number of bacteria after t hours will be :
To find , the number of bacteria after 24 hours , we put t= 24 in above equation , we get
Hence, the number of bacteria after 24 hours is 25165824000.
12 inches go into one foot, so we can calculate the volume of the tank in inches to make the calculations that follow easier. Therefore, to calculate the volume of the tank, we use length x breadth x height = 4 x 2 x 2 = 16 square feet x 12 for square inches = 192 square inches.
Every 12 square inches Joseph can fit a one inch fish. The fish that he has are 3 inches long, therefore he can only fit one fish every 36 square inches.
That means that if we take the total volume of the tank and divide it by the space that a 3 inch fish will take up, we are left with 192/36 = 5.3 fish.
You cannot have a third of a fish, so we round off to the nearest whole number, and we determine that Joseph can put 5 fish in his new aquarium.
1/5...
This question should be relatively easy for a high schooler...
The given final course grade, 88%, is the average of Frank's four quarter grades. The average is the sum of all grades divided among the four quarters. Let x be the average,
(82.5 + 94.7 + 87.9 + x) / 4 = 88
The value of x is equal to 86.9. Thus, the answer is letter C. 87%.
Please note that dilation does not affect angles. Thus, if an image is dilated the angle remains the same and does not change.
Therefore, even if
is dilated to
by a factor of 1.5 (or by any factor for that matter), the linear dimensions of the original triangle
will either get stretched or get shrunk by a factor of 1.5 but the angles of the original triangle will not be affected in any case.
Please note that this is true for all two dimensional geometric shapes.