Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in casinos. a player is dealt two cards. face cards (jacks, queens, and kings) and tens have a point value of 10. aces have a point value of 1 or 11. a 52-card deck contains 16 cards with a point value of 10 (jacks, queens, kings, and tens) and four aces.

a. what is the probability that both cards dealt are aces or 10-point cards?
b. what is the probability that both of the cards are aces?
c. what is the probability that both of the cards have a point value of 10?
d. a blackjack is a 10-point card and an ace for a value of 21.
use your answers to parts
(a), (b), and (c) to determine the probability that a player is dealt blackjack.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

h * s * a

h = history teacher

s = science teacher

a =   art teacher.

i see no data table, but just multiply the number of history teachers, science teachers, and art teachers.

step-by-step explanation: