<span>There is 1 way to win 6 games in a row
wwwwww
There are 2 ways to win 5 games in a row
wwwwwl, lwwwww
There are 5 ways to win 4 games in a row
llwwww, wwwwll, lwwwwl, wlwwww, and wwwwlw.
There are 2^n to arrange 6 wins and losses which adds up to 2^(6) = 64
So the Probability they win all four games in a stretch is 5 + 2 + 1 ways = 8 ways.
So the probability = 8/64 = 1/8</span>
Answer:
53.33 meters
Step-by-step explanation:
Let AB represents the height of the cliff,
( where, A is top and B is bottom ),
Also, C and D represents the shadow of the cloud and cloud in the sky respectively,
Suppose E is a point in the segment CD,
Such that,
AB = DE = 40 meters,
According to the question,


Since,




Now,



Hence,
The height of the cloud above the lake = CE + ED

Let price of the Caleb's groceries was $x.
Given that tax rate is 2.5% or 0.025
Then sales tax is given by product of 0.025 and x.
which is 0.025x.
Given that tax paid is $1.60 so both must be equal

divide both side by 0.025


Hence final answer is $64.
To check if the student is correct, we are going to solve the equation step by step.
Step 1 divide both sides of the equation by 5:



Step 2 take square root to both sides of the equation:


or 
The equation has tow solutions,
and
.
I disagree with the student because
is just one solution and not the only one;
is also a valid solution of the equation.