The probability of getting all heads is 1 / 2^6 = 1/64 as there is only 1 event where this happens in a possible 2^6 = 64 events. It is the same as the probability of getting all tails. The probability of getting at least 1 head is 1 - p(all tails) = 63/64.
Answer:
Third option: The graph moves left 18 units.
Step-by-step explanation:
Some transformations for a function f(x) are shown below:
If 
, the function is shifted up "k" units.
If 
, the function is shifted down "k" units.
If 
, the function is shifted left "k" units.
If 
, the function is shifted right "k" units.
In this case, we can observe that graph of 
is changed to 
Since:
We can conclude that the function is shifted left 18 units to get the function .
Answer:
Step-by-step explanation:
ST and WX
Answer:
isosceles
Step-by-step explanation:
9514 1404 393
Answer:
72
Step-by-step explanation:
The triangles are said to be similar. (ΔNPQ ~ ΔRSQ) That means corresponding sides have the same ratio:
NP/RS = NQ/RQ = PQ/SQ = 24/32 = 21/28 = 3/4
This ratio, or scale factor, also applies to the perimeters of the two triangles.
perimeter NPQ / perimeter RSQ = 3/4
Using the given expressions for the perimeters, we have ...
(7x +2)/(10x -4) = 3/4
We can solve this equation in the usual way to find the value of x. Then we can use that value to find the perimeter of ΔNPQ.
4(7x +2) = 3(10x -4) . . . . . multiply both sides by 4(10x -4)
28x +8 = 30x -12 . . . . . eliminate parentheses
20 = 2x . . . . . . . . . . . add 12-28x to both sides
10 = x . . . . . . . . . . . divide both sides by 10
The perimeter of ΔNPQ is ...
7x +2 = 7(10) +2 = 72
The perimeter of triangle NPQ is 72 units.
