Answer:
Remember that:
Speed = distance/time.
Then we can calculate the average speed in any segment,
Let's make a model where the average speed at t = t0 can be calculated as:
AS(t0) = (y(b) - y(a))/(b - a)
Where b is the next value of t0, and a is the previous value of t0. This is because t0 is the middle point in this segment.
Then:
if t0 = 100s
AS(100s) = (400ft - 0ft)/(200s - 0s) = 2ft/s
if t0 = 200s
AS(200s) = (1360ft - 50ft)/(300s - 100s) = 6.55 ft/s
if t0 = 300s
AS(300s) = (3200ft - 400ft)/(400s - 200s) = 14ft/s
if t0 = 400s
AS(400s) = (6250s - 1360s)/(500s - 300s) = 24.45 ft/s
So for the given options, t = 400s is the one where the velocity seems to be the biggest.
And this has a lot of sense, because while the distance between the values of time is constant (is always 100 seconds) we can see that the difference between consecutive values of y(t) is increasing.
Then we can conclude that the rocket is accelerating upwards, then as larger is the value of t, bigger will be the average velocity at that point.
Answer:
Expected pay winning $50= $0.585
Expected pay winning $25= $2.36
Expected pay for anything else= $-4.35
Expected returns=3.59
Expected value for one play= $(-1.41)
Do not play this game because you will lose $1.41
Step-by-step explanation:
Probability P(3 hearts) = (13/52)×(12/51)×(11/50) = 0.013
Probability P(3black)= (26/52)×(24/51)×(23/50) = 0.118
Probability P(drawing anything else)= 1 - 0.013 - 0.118= 0.869
Expected pay($50)= 0.013$(50-5)= $ 0.585
Expected pay($25)= 0.118(25-5)$ = $2.36
Expected pay for anything else= 0.869(0-5)$ =$(-4.347)
Expected value of one play=$ (0.585 + 2.353 -4.347) = -$1.41
c) Do not play the game.
There are a few ways you can go about solving this question. One way is to use the given information to find how many tons of flour can be processed in one hour. If 27 tons can be processed in 3 hours, we can do 27 divided by 3 to find that 9 tons of flour can be processed per hour. Then, if we want to see how many tons of flour can be processed in 8 hours, we can multiply 9 tons by 8 hours to get a total of 72 tons of flour.
I hope this helps.
Width = x
Length = x+18
Assuming the table is rectangular:
Area = x(x + 18)
Therefore:
x(x + 18) <span>≤ 175
x^2 + 18x </span><span>≤ 175
Using completing the square method:
x^2 + 18x + 81 </span><span>≤ 175 + 81
(x + 9)^2 </span><span>≤ 256
|x + 9| </span><span>≤ sqrt(256)
|x + 9| </span><span>≤ +-16
-16 </span>≤ x + 9 <span>≤ 16
</span>-16 - 9 ≤ x <span>≤ 16 - 9
</span>-25 ≤ x <span>≤ 7
</span><span>
But x > 0 (there are no negative measurements):
</span><span>
Therefore, the interval 0 < x </span><span>≤ 7 represents the possible widths.</span><span>
</span>
Answer: In the beginning he was given 27 sweets.
Step-by-step explanation: The most logical thing to do is to solve it backwards, that is, from what he had at the end of the third day up till the beginning of the first day.
On the third day he ate one-third and had 8 sweets left over. To determine how many he started with on the third day, let the total on day three be called a. If one-third of a is eaten, then the left over which is two-thirds is 8. That is;
8/a = 2/3
By cross multiplication we now have
8 x 3 = 2a
24/2 = a
a = 12
Let the number of sweets he had on day two be called b. If he ate one-third of b and he had 12 left over, then the two-thirds left over is 12 and we now have;
12/b = 2/3
By cross multiplication we now have
12 x 3 = 2b
36 = 2b
36/2 = b
b = 18
Let the number of sweets he had on day one be called x. If he ate one-third of x and he had 18 left over, then the two-thirds left over is 18, and we now have;
18/x = 2/3
By cross multiplication we now have
18 x 3 = 2x
54 = 2x
x = 27
Therefore Tim was given 27 sweets at the beginning.
