<h3>
Answer: 21600 </h3>
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Explanation:
There are 6 letters to pick from {A,B,C,D,E,F} and we have two slots to fill, where no repeats are allowed. This means we have 6*5 = 30 different ways to pick two letters.
There are 10 digits to pick from {0,1,2,...,9} and there are 3 slots to fill. This gives 10*9*8 = 720 different permutations for this portion.
Overall, we have 30*720 = 21600 different serial numbers possible.
<h3><u>
Answer:</u></h3>
![\boxed{\boxed{\pink{\bf \leadsto Hence \ option\ [d]\ \bigg(y = \dfrac{5}{2}x + 5\bigg) \ is \ correct }}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%5Cpink%7B%5Cbf%20%5Cleadsto%20Hence%20%5C%20option%5C%20%5Bd%5D%5C%20%5Cbigg%28y%20%3D%20%20%5Cdfrac%7B5%7D%7B2%7Dx%20%2B%205%5Cbigg%29%20%5C%20is%20%5C%20correct%20%20%7D%7D%7D)
<h3>
<u>Step-by-step explanation:</u></h3>
Here from the given graph we can see that the graph the graph intersects x axis at (2,0) and y axis at (5,0). On seeing options it's clear that we have to use Slope intercept form . Which is :-

We know that slope is
. So here slope will be ,
Hence the slope is 5/2 . And here value of c will be 5 since it cuts y axis at (5,0).

<h3>
<u>Hence</u><u> </u><u>option</u><u> </u><u>[</u><u> </u><u>d</u><u> </u><u>]</u><u> </u><u>is</u><u> </u><u>corre</u><u>ct</u><u> </u><u>.</u><u> </u></h3>
Answer:
46°
Step-by-step explanation:
You have to make a cos graph that starts its minimum and of -2, has an amplitude of 10, a period of 10 and a maximum of 18.
I decided to use a cos graph since cos graphs start at their minimum or maximum unlike a sine graph that starts halfway between the minimum and maximum. You also know the amplitude has to be 10 since 18+2=20 and 20/2=10. We were also told that the water wheel completels a rotation every 10 minutes which means the period is 10 minutes.
lets start of with a regular cos(x) graph. This starts on its maximum instead of minimum so we have to multiply it by -1 to get -cos(x) which does start on its minimum.
-cos(x) has an amplitude of 1 instead of 10, to fix that we multiply it by 10 to get -10cos(x) which has an amplitude of 10.
-10cos(x) has a period of 2π instead of 10, to fix this we multiply the x by 2π/10 to get -10cos((π/5)x) which now has a period of 10.
-10cos((π/5)x) has a minimum of -10 and maximum of 10 instead of a minimum of -2 and maximum of 18, to fix this we add 8 to -10cos((π/5)x) to get -10cos((π/5)x)+8 which does have a minimum of -2 and maximum of 18.
Therefore the answer is y=-10cos((π/5)x)+8. x being time in minutes and and y being the height in feet.
I hope this helps. Let me know if anything is unclear.