The histogram that represents the data with the largest spread is Data Set B
This is so provided that the velocity changes continuously in which case we can apply the mean value theorem.
<span>Velocity (v) is the derivative of displacement (x) : </span>
<span>v = dx/dt </span>
<span>Monk 1 arrives after a time t* and Monk 2 too. </span>
<span>Name v1(t) and v2(t) their respective velocities throughout the trajectory. </span>
<span>Then we know that both average velocities were equal : </span>
<span>avg1 = avg2 </span>
<span>and avg = integral ( v(t) , t:0->t*) / t* </span>
<span>so </span>
<span>integral (v1(t), t:0->t*) = integral (v2(t), t:0->t*) </span>
<span>which is the same of saying that the covered distances after t* seconds are the same </span>
<span>=> integral (v1(t) - v2(t) , t:0->t*) = 0 </span>
<span>Thus, name v#(t) = v1(t) - v2(t) , then we obtain </span>
<span>=> integral ( v#(t) , t:0->t*) = 0 </span>
<span>Name the analytical integral of v#(t) = V(t) , then we have </span>
<span>=> V(t*) - V(0) = 0 </span>
<span>=> V(t*) = V(0) </span>
<span>So there exist a c in [0, t*] so that </span>
<span>V'(c) = (V(t*) - V(0)) / (t* - 0) (mean value theorem) </span>
<span>We know that V(0) = V(t*) = 0 (covered distances equal at the start and finish), so we get </span>
<span>V'(c) = v#(c) = v1(c) - v2(c) = 0 </span>
<span>=> v1(c) = v2(c) </span>
<span>So there exist a point c in [0, t*] so that the velocity of monk 1 equals that of monk 2. </span>
Answer:6.25 grams of protein is provided by this serving of raisins.
Step-by-step explanation:
The calorie count C for a serving of food can be computed using the formula,
C= 4h + 9f + 4p, where
h is the number of grams of carbohydrate contained in the serving,
f is the number of grams of fat contained in the serving, and
p is the number of grams of protein contained in the serving.
A serving of raisins contains 157 calories and 33 grams of carbohydrate. If raisins are a fat-free food, if means that f = 0
Therefore
157 = 4 × 33 + 9 × 0 + 4p
157 = 132 + 4p
4p = 157 - 132 = 25
p = 25/4 = 6.25
About 15.7, or 16 if you're looking for a whole number.