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DedPeter [7]
4 years ago
14

The probability that a train leaves on time is 0.4. The probability that the train arrives on time and leaves on time is 0.28. W

hat is the probability that the train arrives on time, given that it leaves on time?
0.4
0.12
0.28
0.7
Mathematics
1 answer:
Y_Kistochka [10]4 years ago
8 0
You need to use the conditional probability formula:
P(A|B) = P(A∩B) / P(B)
Key:
P(A|B): Probability of A given B
P(A∩B): Probability of A and B

If we say A is the event that the train arrives on time and B is the event that the train leaves on time, then according to the information:
P(B) = 0.4
P(A∩B) = 0.28
Just insert into the formula:
P(A|B) = 0.28 / 0.4 = 0.7
(or 70% as a percentage).
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just olya [345]

Answer:

It is a metaphor.

Step-by-step explanation:

Hope it helps

3 0
3 years ago
in a tidal river, the time between high and low tide is 7.6 hours. At high tide the depth of water is 17.2 feet, while at low ti
Lady_Fox [76]
Alright, so the difference between tidal heights is 12.6 ft. right? For every integer cos(x) is multiplied, say a*cos(x) the amplitude doubles. So then, (1/2)=(n/12.6) will gives us a value for a that will match the differences in tidal height. a=6.3. Now let's say that 2pi will give us a full cycle from high to low back to high again. If 12:00 noon is our high, it takes 15.2hrs to complete a cycle back to high again. 2pi = 6.28 roughly, and we know that is less than our midpoint in a whole cycle, 7.6 hrs. Also, for every value k>1 in cos(kx), this increases the frequency of waves in a given period. So it seems that we need a value of k less than 1. So we can lower the frequency to match the cycle we are looking for, which is to come back to 17.7 ft by 15.2hrs. So to find our value k we divide 2pi by 15.2. This is 0.41. We do it that way based on the ratio for the standard period to what we need, which is a number that can get us to 15.2. So far we have f(t) = 6.3cos(0.41x). Now the problem we have now is that we are not at our height for max, nor our min, even though our wave matches the difference between them, we are between 6.3 and -6.3 so far. so for every value of c in cos(x)+c, this adds to the height cos starts on the y-axis. Since we are at 6.3 already, all we need to do is subtract 6.3 from 17.6 to get c. So C is 11.3 and our final equation is f(t)=6.3cos(0.41x)+11.3. This gives our tides in 15.2 hr periods, starting at 12 noon = x=0, with extremes at intervals of 7.6 hours. Let me know if you have any more questions about it, it's kind of rough to explain. We transformed by f(t)=a*cos(kx)+c altogether, but I thought it might help to separate each value independently.
4 0
3 years ago
Read 2 more answers
The Ship It Anywhere Company bought a truck for $245,000. According to the company’s accounting department, the truck will depre
Svetradugi [14.3K]

Answer:

1. V(t) = -32500t + 245000

a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.

b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).

c. The formula is: V(t) = -32500t + 245000

2. t-intercept: t = 7.5385

The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.

3. Graph in the image attached.

4. The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].

5. V(8) = -15000

It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.

6. After 3.6 years.

7. Between 3.23 years and 5.63 years.

Step-by-step explanation:

1.

The inicial value is 245,000, and each year the value decreases 32,500, so we can write the equation:

V(t) = -32500t + 245000

a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.

b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).

c. The formula is: V(t) = -32500t + 245000

2.

To find the t-intercept we just need to use V(t) = 0 and then find the value of t:

0 = -32500t + 245000

32500t = 245000

t = 7.5385

The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.

3.

The graph of the function is in the image attached.

4.

The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].

5.

V(8) = -32500*8 + 245000 = -15000

It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.

6.

128000 = -32500t + 245000

32500t = 117000

t = 3.6

After 3.6 years.

7.

62000 = -32500t + 245000

32500t = 183000

t = 5.6308

140000 = -32500t + 245000

32500t = 105000

t = 3.2308

Between 3.23 years and 5.63 years.

5 0
3 years ago
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storchak [24]
You can combine the same numbers with the same variables using the operation sign for each. For example, using your equation, you would combine the 3n and 4n which is 7n. So your equation would be
7n - 2
5 0
4 years ago
Read 2 more answers
If the length of the 45° region of this circle is 10 inches, what is the radius of the circle? Use and round to the nearest tent
USPshnik [31]

Answer:

12.71in

step explanation:

The Length of an arc given is expressed as;

A = theta/360 * 2πr

10 = 45/360 * 2 * 3.14r

10 = 1/8 * 6.28r

Cross multiply

10 * 8 = 6.28r

80 = 6.28r

r = 80/6.28

r = 12.74in

Hence the radius is 12.71in

8 0
3 years ago
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