Answer:
The prizes can be given in 1320 ways.
Los premios se pueden otorgar en 1320 maneras.
Step-by-step explanation:
The order in which the swimmers are ranked is important. That is, A, B and C is a different finish than C, B and A. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
In this question:
3 prizes for 12 swimmers. So
The prizes can be given in 1320 ways.
Los premios se pueden otorgar en 1320 maneras.
9514 1404 393
Answer:
-7/4 < x < 8
Step-by-step explanation:
The value of y can be determined from the sum of the angles, so you know each of the angles exactly. That means you know the ratio of side lengths exactly, which lets you solve for x exactly.
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Setting that aside, we observe that angle C is greater than angle A, so side AB will be longer than side BC.
3x +15 > 4x +7
8 > x . . . . . . . . . . subtract 3x+7
We also know that the lengths of these sides must be positive. Since BC is the shorter side, we require ...
4x +7 > 0
4x > -7
x > -7/4
So, the allowable values of x are ...
-7/4 < x < 8
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<em>More complete solution</em>
If we read the figure correctly, the sum of angles is ...
(2y +12) +(4y +12) +(y -18) = 180
7y +6 = 180
y = (180 -6)/7 = 24 6/7°
Then (in degrees) ...
∠A = 2(24 6/7) +12 = 61 5/7, and ∠C = 4(24 6/7) +12 = 111 3/7
The Law of Sines tells us ...
AB/sin(C) = BC/sin(A)
sin(A)(3x +15) = sin(C)(4x+7)
x(4sin(C) -3sin(A)) = 15sin(A) -7sin(C)
x = (15sin(A) -7sin(C))/(4sin(C) -3sin(A))
x ≈ 6.1872652
Answer:
y = 5 x=4
Step-by-step explanation:
Answer:
P = 1 / 40320 or P = 2.48*10⁻⁵
Step-by-step explanation:
The total number of outcomes To is:
To = 8! To = 8*7*6*5*4*3*2
To = 40320
Of all these outcomes there is only one proper outcome, therefore the probability of having all men and women in alphabetical order is:
P = 1 / 40320 or P = 2.48*10⁻⁵
Answer:
Cone or Cylinder, Sphere
Step-by-step explanation:
