Step-by-step explanation:
The height of the swipe card is given by :
.....(1)
We need to find the maximum height of the swipe card and the time to reach the maximum height.
For maximum height, put dh/dt = 0
So,
It will take 1.67 seconds to reach the maximum height.
Now, put t = 1.67 s in equation (1).
Hence, the maximum height of the swipe card is 34.68 feet and the time to reach this height is 1.67 s.
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Explanation:
If you graphed the equation 2x-5y = 14, you'll find it has a positive slope. It turns out the slope in this equation is 2/5, which is positive. A positive slope means the line goes uphill as you move from left to right. This means we can rule out choice because of this (since we want the line to slope downward).
Now let's turn to choice D. If we multiply both sides of the first inequality by -1, then we go from to
. Note the inequality sign flips. This always happens when we multiply both sides by any negative number. The inequality
implies that the shaded region will be above the boundary line, but this contradicts the drawing which shows the shaded region is below the diagonal boundary line. We can rule out choice D because of this. Choice A can be ruled out for similar reasoning.
You should find that only choice B is left. The diagonal line is 2x+5y = 14, and we shade below this boundary line, as well as shading to the right of the y axis (to indicate all values have positive x coordinates). Values on the boundary count as solution points as well.
Answer:
There is 1.98% of probability of being dealt a flush in 5-card Poker
Step-by-step explanation:
To know the probability of a flush being dealt, we can calculate the number of cases when that happens and divide it by the total number of cases of poker hands that exist, naming A the event of a flush.
We will use combinations (nCr button on a calculator) to count the number of cases, because we don't care about the order (it is the same to be dealt a 2, 4, 6, 7 and 8 of hearts than the opposite order), being a flush the event when we take 5 cards out of 13 of the same suit, times 1 out of 4 possible suits and the total number of cases is taking 5 random cards out of 52.
That means there is about a 2% of probability of being dealt a flush.
In other words, of every 16660 plays, 33 will be, on average, a flush
Answer:
Step-by-step explanation:
Using foil method, Multiply the first term
Next, Multiply the Outer term in each parenthesis. (2x^2 and 7
Then, Multiply the Inner Terms (-3x,-4,7) in each parenthesis
Then multiply the last term (-4 and 7).
Combine it you have
which simplify to