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pls do dis

Here is a VERY similar post and answer....you should be able to apply the method to this Q for your answer.....

https://web2.0calc.com/questions/math-help-please_30

The equation of the function is:

First calculate the probability that he will have no spelling mistakes on any page.  This is p1 = 0.92¹¹.  

The probability that he will have at least one spelling mistake is then given by 1 - p1 = 1 - 0.92¹¹ ≈ 0.6004

not[A ∪ (B ∩ C)] = ( not A ∩ not B ) ∪ ( not A ∩ not C )

You did a good job here !!! 

volume of sphere= 4/3  pi r^3     must equal volume of cone = 1/3  pi r^2 h

4/3 pi r^3  =  1/3 pi r^2 h         remove pi r^2 from both sides (r is equal in the ice cream sphere and the cone)

4/3 r = 1/3 h       multiply both sides by 3

4r=h

4(2.5) = h = 10 cm

cot ^2   + 1   =    1/sin^2

cos^2/sin^2  + 1  = 1/sin^2      sub in     sin^2 / sin^2   for  1

(cos^2   + sin^2)/sin^2 = 1/sin^2        see the numerator?   Remember   cos^2 + sin^2 = 1  ?

1/sin^2  = 1/sin^2  = csc^2

Can't have x as an integer multiple of 180 because   sin is zero at those points and denominator 0 not defined.

Option A:  rolling a prime number:

     2  can be rolled only 1 way (1,1)

     3  can be rolled two ways (1,2) or (2,1)

     5  can be rolled four ways (1,4) or (2,3) or (3,2) or (4,1)

     7 can be rolled six ways (1,6) or (2,5) or (3,4) or (4,3) or (5,2) or (6,1)

   11 can be rolled two ways (5,6) or (6,5)

   There are 36 possible ways to roll two dice.

   The probability of rolling a prime number is:  (1 + 2 + 4 + 6 + 2) / 36  =  15/36

   Since rolling a prime number is worth 15 points, the expected value is  (15/36) x 15  =  6.25

Option B:  rolling a multiple of 3:

     3  can be rolled two ways (1,2) or (2,10

     6  can be rolled five ways (1,5) or (2,4) or (3,3) or (4,2) or (5,1)

     9  can be rolled four ways (3,6) or (4,5) or (5,4) or (6,3)

   12  can be rolled only 1 way (6,6)

   The probability of rolling a multiple of 3 is:  (3 + 6 + 9 + 12) / 36  =  12/36

   Since rolling a multiple of 3 is worth 12 points, the expected value is  (12/36) x 12  =  4

If you wish to maximize your expected point total choose Option A.

[I don't understand some of your expanation.]

If 2 lightest Roos weigh 25%of the total, that means each weighs on average =25% / 2 =12.5%

If 3 heaviest Roos weigh 60% of the total, that means on average each weighs =60%/3 =20%

But the total weight of the 5 animals =25% + 60% =85%. So, 100% - 85% =15% is the total weight of the remaining animal(s). But 15% cannot be split  among more than one animal, because they would be LIGHTER than the two light animals given.

Therefore, we must conclude that the remaining 15% belongs to one other Kangaroo. Or there must be 1 more Kangaroo for a total of 6.

a + b > c     or     a + c > b     or     b + c > a

You are choosing 3 out of 24 students = ₂₄C₃.

Either 2 of the 14 sociology students = ₁₄C₂ and 1 of the 10- non-sociology students = ₁₀C₁

or       3 of the 14 sociology students = ₁₄C₃ and none of the 10- non-sociology students = ₁₀C₀.

[ ₁₄C₂ x ₁₀C₁  +  ₁₄C₃ x ₁₀C₀ ] / ₂₄C₃

=  [ 91 x 10  +  364 x 1 ] / 2024 

=  [ 910 + 364 ] / 2024

=  1274 / 2024

A= 162

B= 18

supplementary means they sum to 180^o

^{B + 9B =} 180

b = 18    a = 162

1/w  + 1/a = 1/5

1/8   + 1/a =1/ 5

1/a = 3/40

a = 40/3 hr = 13 1/3 hr

I assume the 'n' means 'not'

find A     color it in       find the intersection of  B and C    (B ∩ C)    color it in

everything not colored is the    n[A ∪ (B ∩ C)]

L = 5 b + 2

A = 2 *L = 2 (5b+2) = 7b+22

          10b + 4 = 7b+22

             3b = 18

                 b = 6 pencils   

rate x time = distance

b = boat    c = current

(b-c)t  = 14          

 (b+c)t = 16           t is the same in both equations.    and c = 2 m/h

                      add these two equations

2 bt = 30

bt = 15      sub this into one of the equations

15 - ct = 14    (c=2)

-2t = -1

 t = 1/2

(b+2)(1/2) = 16

b = 30 m/hr

thanks!

thank you!(:

Thank you! and what blue box?

We can write a computer program:

for a in range(20)

for b in range(20)

for c in range(20)

if a + b + c = 30 then ++count

output: count = 298

Imagine 100 customers

40   want   reg           30% fill (12 customers)

35 want midgrade     60% fill (21 customers)

25 want premium      50% fill (12.5 customers)

plus gas and fill would be    12.5 %       ( but you mixed descriptions in your q  if PLUS gas is EXTRA gas , the answer would be 21 %)

next customer wants fill?    (12 + 21 + 12.5) = 45.5 %

Sorry I fixed the question is "What is the exact value of sin(cos^−1(-√2/2))+tan^−1(sin(π/2))?

What is the exact value of sin(cos^−1(−sqrt2/2))+tan^−1(sin(π/2))?

cos^-1  (-sqrt2/2)     =   3 pi/4   (or possibly 5 pi/4 I will use the first)        sin 3pi/4  = + sqrt2/2

sin pi/2 = 1

tan^-1 (1) = pi/4

sqrt2 / 2   + pi/4     = (2 sqrt2 + pi)/4