Step-by-step explanation:
fair coin is two sided Head H and Tail T
thrown 3 times
number of sample space n(s)=2³=>8
sample space (s)={HHH,HHT,HTH,HTT,THH,TTH,THT,TTT}
no of a head and two tails= 3/8
In order to prove Rathan wrong, we only need one counterexample. Take the number 6. 6 is even, but it has the odd number 3 as a factor, so clearly, not all factors of even numbers are even.
Answer:
B. 3(2^x)
Step-by-step explanation:
3(2^x) is the only function that yielded the given outputs when the inputs were plugged in.
Answer:
Height: 3/2 inches
Length: 12 inches
Width: 4 inches
Step-by-step explanation:
Let x is the side length of the square
The height of the box by cutting squares off :x
- The new length of the cardboard = 15 -2x (because we cut from 4 corners)
- The new width of the cardboard = 7 -2x (because we cut from 4 corners)
The new volume of it is:
V = (15 -2x) (7 -2x) x
<=> V =
To maximum volume, we use the first derivative of the volume
<=> 
<=> 
<=> 2x -3 = 0 or 6x -35 = 0
<=> x = 3/2 or x = 35/6
To determine which value of x gives a maximum, we evaluate
= 24x -88
= 24(3/2) -88 = -52
= 24(35/6) -88 = 52
We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.
So the dimensions (in inches) of the box is:
Height: 3/2 inches
Length: 15-2(3/2) = 12 inches
Width: 7 - 2(3/2) = 4 inches
Answer:
[ where
is number of months]

Step-by-step explanation:
Pool pass cost for first month =$30
Pool pass cost after first month = $15 for each month
The total amount charged by the pool can be expressed as a function
where
represents the number of months.

This can be simplified by using distribution.



Take 15 as greatest common factor.
∴ 
For 



∴ Amount charged by pool for 12 months = $195