Pasha travels 62 miles in an hour (217 divided by 3.5 is 62). So, 62 times 4 hours is 248. So, in 4 hours, she would have traveled 248 miles
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Answer:
(c) dZ/dt = 11/√544, so moving away at about 0.47 m/s
Step-by-step explanation:
The (x, y) coordinates of the car are related by the fact that they are on a circle centered at (12, 7) with a radius of 5. Then their rates of change are related by the derivative of the circle equation with respect to time.
(x -12)^2 + (y -7)^2 = 25
2(x -12)x' +2(y -7)y' = 0
y' = -(x -12)/(y -7)x'
At the time and point of interest, we have ...
y' = -(15 -12)/(11 -7)(1) = -3/4
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The distance (z) to the observer is given by the Pythagorean theorem:
z^2 = (x -0)^2 +(y -2)^2
and its rate of change with time is ...
2z·z' = 2(x-0)x' +2(y -2)y'
The distance d at the point of interest is ...
z = √((15 -0)^2 +(11 -2)^2) = √(225 +81) = √306 = 3√34
So, the rate of change of distance to the observer at the time and point of interest is ...
z' = (x(x') +(y -2)y')/z
z' = ((15)(1) +(11-2)(-3/4))/(3√34) = (33/4)/(3√34)
z' = 11/√544 ≈ 0.47 . . . m/s
Answer:
15/56
Step-by-step explanation:
5 people have a license
3 people don't
? = Probability that first person has a license and second does not
We can divide the problem into two sections, the first being the probability of the first person having a license, and the second section is the probability that the second person doesn't have a license.
P1 = Probability of the first person having a license, there are 5 out of 8 person having a license, thus P1 = 5/8.
P2 = Probability of the second person having a license. There are 3 people not having a license, out of 8-1 = 7 persons available, since one is taken already from the first choice, therefore P2 = 3/7.
P1 and P2 are dependent events, thus P(1,2) = P1 * P2.
P(1,2) = P1 * P1 = 5/8 * 3/7 = 15/56
Answer:
See explanation
Step-by-step explanation:
<h3 /><h3>Step 1</h3>
Miguel wins $2 is if he pulls two chips with the number 1.
<u>Probability of winning is:
</u>
- 2/4 * 1/3 = 1/6 as there are 4 chips in total
<u>
Probability of loosing is:</u>
<h3 /><h3>Step 2</h3>
<u>Missing values we found in the step 1, can be populated in the table:</u>
- Xi === 2 === -1
- P(Xi) === 1/6 === 5/6
<u>Expected Value as per table data:</u>
Expected value is $1/2 loss each time he plays
<h3 /><h3>Step 3</h3>
To make the game fair, the expected value should be zero.
<u>Then as per the calculation above, let's replace 2, with x, and find its value.</u>
- 1/6x + 5/6*(-1) = 0
- 1/6x = 5/6
- x= 5
So the amount should be $5 to make the game fair.
I think it is A because i think it is the only one that makes sense
