Answer:
The answer to the question is
The theory of the hot hand is valid in my opinion.
Step-by-step explanation:
The phenomenon of a "hot hand" is that a person who achieves a successful outcome at an attempt has a higher probability of coming out successful in subsequent attempts at the same event.
Based on evidence from the sampled statistics, the likelihood of achieving an increased probability of success on subsequent attempt on the condition that previous attempts were successful in my opinion is plausible. This is because the ability to score points at a game is dependent on several variables, all of which are from previous occurrence, such dependent variables include
1. The inherent ability of the sport athlete to deliver the required input for success. This is a conditional probability for success as such this forms part of the increased acceptance level for the "hot hand" phenomenon
2. Conditions of play may favor a particular probability than others resulting in a change in the mean, and the standard deviation of the distribution resulting in a skewed outcome
3. Increased opportunity giving to the athlete that previously had a successful attempt possibly by the athlete himself by way of confidence, the audience by way of focus on the outcome of the athletes attempt, and the administrators by way of trying to make it achievable and hence easier within the rules for the athlete have a successful attempt
The "hot hand" (also known as the "hot hand phenomenon" or "hot hand fallacy") is the purported phenomenon that a person who experiences a successful outcome has a greater chance of success in further attempts. The concept is often applied to sports and skill-based tasks in general and originates from basketball, whereas a shooter is allegedly more likely to score if their previous attempts were successful, i.e. while having "hot hands.” While previous success at a task can indeed change the psychological attitude and subsequent success rate of a player, researchers for many years did not find evidence for a "hot hand" in practice, dismissing it as fallacious. However, later research questioned whether the belief is indeed a fallacy.[1][2] Recent studies using modern statistical analysis show there is evidence for the "hot hand" in some sporting activities.[2]
, such that s is the length of any side. You are given that the volume of the carton is 1000 cubic inches, because each 1 by 1 by 1 cube has a volume of one cubic inch. If you put your given v into the equation, you get 
. If you take the cube root of both sides, you get that s=10 because 10^3=1000