Answer:
Step-by-step explanation:
We have to make 5 place serial number with first two as alphabets and last three as digits.
The alphabets are bonded to first 6 ( A, B, C, D, E, F) where as digits are 10 (say 1 to 10).
Let the serial number be S1 S2 S3 S4 S5.
For Alphabets
For S1 we have 6 alphabets.
Now for S2 we are left with 5 alphabets since there is no repetition one alphabet will be fix for S1.
So the possible combination for S1 S2= 6x5=30.
For Digits
We did the same as we did for alphabets, for S3 we have 10 possibilities, and for S4 and S5 9 and 8 respectively due to the no repetition condition.
So the possible combinations for S3 S4 S5 = 10x9x8=720
So the total number of serial numbers are 30+720=750.
Let the number of children be c, and the number of adults be a.
c + a = 170 (total number of tickets)
Then the cost of each is: $5.90/child, $9.60/adult:
5.9c + 9.6a = 1269.40 (total sales)
Solving as 2 simultaneous equations, we first transform the first equation:
a = 170 - c
Substitute into the 2nd equation:
5.9c + 9.6(170 - c) = 1269.40
Solving gives c = 98, and a = 170 - 98 = 72. This means that 72 adult tickets were sold that day.
Answer:
21 ft²
Step-by-step explanation:
3*5 + 2*3 = 21
Answer:
option-C
Step-by-step explanation:
we are given
Let P(A)=0.5
P(B)=0.9
P(A and B)=0.15
we know that

now, we can plug values


but we have
P(A)=0.5
we can see that both are not equal

so, A and B are not independent
so, option-C........Answer
Answer:
The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.
Step-by-step explanation:
Geometrically speaking, the volume of the right circular cone (
), in cubic inches, is defined by the following formula:
(1)
Where:
- Radius, in inches.
- Height, in inches.
Then, we derive an expression for the rate of change of the volume (
), in cubic inches per second, by derivatives:
(2)
Where:
- Rate of change of the radius, in inches per second.
- Rate of change of the height, in inches per second.
If we know that
,
,
and
, then the rate of change of the volume is:

The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.