Answer:
The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Step-by-step explanation:
Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.
The random variable <em>X</em> is exponentially distributed with mean 7 minutes.
Then the parameter of the distribution is,
.
The probability density function of <em>X</em> is:
Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:
![=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148](https://tex.z-dn.net/?f=%3D%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7B%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7Be%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5B-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%5D%5E%7B9%7D_%7B6%7D%5C%5C%5C%5C%3De%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%206%7D-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%209%7D%5C%5C%5C%5C%3D0.424373-0.276453%5C%5C%5C%5C%3D0.14792%5C%5C%5C%5C%5Capprox%200.148)
Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Answer:
I don't know why this always happens to me it looks black can u ask the question and I will answer
Answer:
B I'm pretty sure
Step-by-step explanation:
We want to write an inequality that tells how much Hannah should walk this week. The inequality will be:
x ≥ (3 + 3/4) mi
<h3>
Finding the inequality:</h3>
We know that she already did walk 2 3/4 miles this week, and she wants to walk at least 6 1/2 miles.
So to reach that minimum, she needs to walk:
(6 1/2)mi - (2 + 3/4) mi = (3 + 3/4) mi
And she can walk that or more, so the inequality is:
x ≥ (3 + 3/4) mi
Where x represents how much she will walk this week.
If you want to learn more about inequalities, you can read:
brainly.com/question/11234618
Answer:
Step-by-step explanation:
Perpendicular means that the slopes of the "old" line and the "new" line are opposite reciprocals; bisector means that the "new" line goes directly through the center of the "old" line. This perpendicular bisector, then, will go directly through the center of the "old" line, cutting it directly in half and leaving in its wake a 90 degree angle. To write this equation, then, of the perpendicular bisector, we need the slope of the old line and the midpoint of the old line. Let's work on the midpoint first:
So the "new" line will go through this point.
Onto the slope:
so the slope is
m = -4. That means that the perpendicular slope is
Now we're ready to write the equation:
and
and finally,
