When they are both racing on hoverboards, Victoria is 3 times as fast as her brother Max. When she is on foot, she is 3 times sl
2 answers:
Answer:
The time taken from start to finish is 48 minutes.
Step-by-step explanation:
Given : When they are both racing on hoverboards, Victoria is 3 times as fast as her brother Max. When she is on foot, she is 3 times slower than Max on his hoverboard. They took off on hoverboards at the same time, but after 12 minutes, Victoria’s hoverboard broke and she immediately started to run.
To find : How long, in minutes, did it last from start to finish?
Solution :
Distance = Speed × Time
Let the speed of Max = s
Time taken = t
At 12 minutes,
Distance covered by Max =
Victoria is 3 times as fast as her brother Max.
Distance covered by Victoria =
After 12 minutes,
Victoria’s hoverboard broke and she immediately started to run.
When Victoria is on foot, she is 3 times slower than Max on his hoverboard.
Distance covered by Max =
Distance covered by Victoria =
Since the race was a tie, then
Total distance of Max = Total distance of Victoria
The time taken from start to finish is 48 minutes.
Answer:
The answer is 48 minutes.
Step-by-step explanation:
Let the speed of Max on hoverboard be = x
Then the speed of Victoria on hoverboard will be = 3x
Now its given that the speed of Victoria on foot is 1/3 of the speed of Max on hoverboard, this is = x/3
Formula of speed =
Let the time taken by both to complete the race be t minutes.
Hence, distance covered by Victoria in 12 minutes + distance covered by Victoria on foot = distance covered by Max on hoverboard. Now in equation form this becomes:
Simplifying this we get,
This gives t=48
Hence, t = 48 minutes.
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Answer:
2, 2, 4, 6, 4
Step-by-step explanation:
Fundamental Theorem of Algebra states that 'An 'n' degree polynomial will have n number of real roots'.
1. The polynomial is given by
So, on simplifying we get that, .
Since, degree of polynomial is 5, it will have 5 roots.
This gives us that the roots of the equation are x = 0, -2, 2, 4i and -4i
So, the number of complex roots are 2.
2. The polynomial is given by
Since, degree of polynomial is 4, it will have 4 roots.
Equating them both by zero, and
gives that the roots of the polynomial are x = 2i, -2i, -5, -5.
So, the number of complex roots are 2.
3. The polynomial is given by
Since, degree of polynomial is 6, it will have 6 roots.
On simplifying, we get that the real roots of the polynomial are x = -1.75 and x = 4.28.
So, the number of complex roots are 6-2 = 4.
4. The polynomial is given by
Since, degree of polynomial is 7, it will have 7 roots.
On simplifying, we get that the only real root of the polynomial is x = -2.
So, the number of complex roots are 7-1 = 6.
5. The polynomial is given by
Since, degree of polynomial is 5, it will have 5 roots.
Simplifying the equation gives
Equating each to 0, we get the real roots of the polynomial is
So, the number of complex roots are 5-1 = 4
<u>Answer-</u>
<em>The lines are two </em><em>coinciding lines</em><em> or the </em><em>same lines</em><em>.</em>
<u>Solution-</u>
The given line equations are
the first one,
the second one,
As we know two line equations and
will be,
- Parallel if,
- Coincide if,
- Intersect if,
As here,
(C₁ and C₂ aren't considered as they are 0)
Therefore, the lines are two coinciding lines or the same lines.
Answer:
The probability that the reporter made no typographical errors for the 3-page article is 5%.
Step-by-step explanation:
Let <em>X</em> = number of typographical errors made by the writer.
The average umber of mistakes mad by the writer every page is, <em>E </em>(<em>X</em>) = 1.
The random variable <em>X</em> is defined as finite number of occurrence of a certain activity in a fixed interval of time.
A Poisson distribution is used to describe the distribution of occurrences in a certain interval.
Thus, the random variable <em>X</em> follows a Poisson distribution.
It is provided that the writer has landed a 3-page article in an important magazine.
Then the average number of mistakes in the 3 pages is:
<em>λ</em> = 3 × E (X) = 3 × 1 = 3.
The probability mass function of the Poisson random variable <em>X</em> is:
Compute the probability that the writer makes no mistake in a 3-page article as follows:
The probability that the writer makes no mistake in a 3-page article is 0.05.
Thus, the probability that the reporter made no typographical errors for the 3-page article is 5%.