Until a train is a safe distance from the station it must travel at 5 m/s. Once the train is on open track it can speed up to 45
2 answers:
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Answer:
6%
Step-by-step explanation:
Step 1
The fist step is to define the probabilities.
The events are independent from each other. Each team wins with probability and looses with probability
Let
be probability that Roses win and
be the probability that Roses loose.
Step 2
The second step is to calculate the probabilities by multiplying the probabilities with the first 3 terms in the product being the probability of a win and the last term being the probability of a loss.
The calculation is shown below,
Step 3
The last step is to convert this probability into a percentage. Converting this probability to a percentage is done as shown below,
Step 4
The next step is to round down the percentage . The value of 6.25% rounded down is 6%. The correct answer is 6%.
Answer: The pattern is x^2+2
where x is the term number
Example: the 5th term is 27 because x = 5 leads to x^2+2 = 5^2+2 = 27
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Explanation:
- The jump from 3 to 6 is +3
- The jump from 6 to 11 is +5
- The jump from 11 to 18 is +7
- The jump from 18 to 27 is +9
- The jump from 27 to 38 is +11
The pattern of jumps is: 3, 5, 7, 9, 11
Those increments are going up by 2 each time.
Since we have a consistent pattern of increments, this means that the sequence follows a quadratic model.
Quadratics are stuff like x^2+7x+10 or 3x^2-7. The leading term has an exponent of 2.
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If x is the term number and y is the term itself, then we have these points
(1,3)
(2,6)
(3,11)
(4,18)
(5,27)
(6,38)
The x coordinates increase by 1 each time. The y coordinates are the terms given by your teacher.
Pick exactly 3 of those points. I'll pick the first 3.
Why 3? Because we'll have 3 unknowns to solve for, in which we'll need 3 equations.
- Plug (x,y) = (1,3) into y = ax^2+bx+c, then simplify. You should get the equation a+b+c = 3
- Repeat for (x,y) = (2,6) and you should get 4a+2b+c = 6
- Repeat for (x,y) = (3,11) and you should get 9a+3b+c = 11
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We have this system of equations
There are a number of methods to solve this system. Substitution is what I'll go for.
Solve the first equation for c
a+b+c = 3
c = 3-a-b
Then use substitution.
4a+2b+c = 6
4a+2b+(3-a-b) = 6
3a+b+3 = 6
3a+b = 6-3
3a+b = 3
and
9a+3b+c = 11
9a+3b+(3-a-b) = 11
8a+2b + 3 = 11
8a+2b = 11-3
8a+2b = 8
We now have this reduced system of equations.
I'll skip the steps as this solution is getting very lengthy as it is. The basic idea is to use substitution again. You should find that a = 1 and b = 0 form the solution set here.
Use those values to find c
c = 3-a-b
c = 3-1-0
c = 2
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To summarize the previous section, we have these solutions:
a = 1, b = 0, c = 2
Therefore the equation y = ax^2+bx+c becomes y = 1x^2+0x+2 aka y = x^2+2. This lets us find any term.
Let's test it out.
- If x = 1, then y = x^2+2 = 1^2+2 = 3
- If x = 2, then y = x^2+2 = 2^2+2 = 6
- If x = 3, then y = x^2+2 = 3^2+2 = 11
And so on. I'll let you test the other x values (4 through 6).
Another way to confirm the answer is to subtract 2 from each item in the original set {3,6,11,18,27,38} and you'll end up with {1,4,9,16,25,36}. This is the list of perfect squares. It shows that term x is simply x^2 but add on 2 so things are adjusted accordingly.
Side note: you can use a tool like GeoGebra or WolframAlpha to quickly solve the system of equations. However, I recommend it only as a means to check your answer rather than do the work for you.
<u>Answer: </u>
When you buy 2 , 3 and 4 tees , price you pay are 10.33 unit price , 13 unit price and 15.667 unit price respectively.
<u>Solution: </u>
Information provided in the question seems to be less . so assuming following two things.
1)Given function p = n + 5 do not include shipping cost as shipping cost is also dependent on number of tees.
2)If shipping charges for 3 tees is 5 , then shipping charges of 1 tee is
When you buy 2 tees , n = 2
Price = p = n+5 = 2+5 = 7
Shipping charges =( ) x 2 =
So total price you pay for two tees = 7 + () = 7 + 3.3333 = 10.3333 unit price.
When you buy three tees , n = 3
Price = p = n+5 = 3+5 = 8
Shipping charges =( ) x 3 = 5
So total price you pay for two tees = 8 + 5 = 13 unit price.
When you buy four tees, n = 4
Price = p = n+5 = 4+5 = 9
Shipping charges =( ) x 4 =
So total price you pay for two tees = 9 + () = 47/3 = 15.667 unit price.
Hence when you buy 2 , 3 and 4 tees , price you pay are 10.33 unit price , 13 unit price and 15.667 unit price respectively.