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OLEGan [10]
3 years ago
7

You are trying to cast four roles for a play. 12 actors try out, including sir Ian McKellen and Patrick Stewart. the director te

lls you that in order to bring the crowds, you must include at least one of sir Ian and Patrick in the cast. How many casts are possible?
Mathematics
1 answer:
Komok [63]3 years ago
8 0

Answer:

6,840 casts

Step-by-step explanation:

Assuming that every actor can play each of the 4 roles and that each role is different, the number of possible casts including at least one of sir Ian and Patrick is given by the total number of possible casts (permutation of 4 out of 12 actors), minus the number of casts without sir Ian and Patrick (permutation of 4 out of 10 actors):

n=\frac{12!}{(12-4!)} -\frac{10!}{(10-4)!}\\n=(12*11*10*9)-(10*9*8*7)\\n=6,840\ casts

There are 6,840 possible casts.

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(19) Geometry pls help
gogolik [260]
Yes it is possible to prove this is a parallelogram.

XN = NZ means the diagonal XZ has been bisected
The same goes for diagonal WY (because NY = NW)

Furthermore, we have the pair of vertical angles XNY and ZNW which are congruent

Through SAS, we can say that triangles XNY and ZNW are congruent

Using CPCTC, we can get to the fact that angle NWZ = angle NYX which are alternate interior angles leading to proving that XY || WZ

----------------------

If you repeat those steps above, but focus on triangles WNX and YNZ, we can prove that XW || YZ

----------------------

After proving that XY || WZ and XW || YZ, this is enough to prove we have a parallelogram as the opposite sides are parallel.

3 0
3 years ago
a farmer uses 1/3 of his land to plant cassava 3/5 of the remaining land to plant Maize and the rest vegetables if vegetables co
Rzqust [24]

Answer:

37.5 acres.

Step-by-step explanation:

Fraction of his land  where vegetables are grown

= 1 - 1/3 - 2/3 *3/5

(after taking away 1/3 we get 2/3 and the farmer uses 3/5 of this 2/3 to grow Maize.

= 1 - 1/3 - 6/15              LCD of 3 and 15= 15  so we write:

= 1 - 5/15 - 6/15

= 1 - (5+6)/16

=  1 - 11/15

= 4/15.

4 /15 is equivalent to  10 acres

so  total  area (= 1)  =   10 / 4/15     Invert the 4/15 and multiply:

= 10 * 15/4

=  150/4

= 37.5 acres.

3 0
3 years ago
There are 3 times as many students participating in the hiking trip this year than last year. There are 42 students on the trip
dalvyx [7]

Answer:

14

Step-by-step explanation:

42 divided by 3 is 14

8 0
3 years ago
Read 2 more answers
A number increased by 5 is less than or equal to 26
blagie [28]

Answer:

Equation: x + 5 ≤ 26

Solved: x ≤ 21

3 0
3 years ago
Clear parenthesis and combine like terms.<br><br> -2(x-4) -3(x+2y)<br><br> Show all the work.
Helen [10]

Answer:

-5x - 6y + 8

Step-by-step explanation:

-2(x - 4) -3(x + 2y)

-2x + 8 - 3x - 6y

-5x - 6y + 8

Hope this helps!

4 0
3 years ago
Read 2 more answers
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