Answer:
There’s only one way to get 12 when 2 dice are tossed, both have to equal 6. There are 6 ways tossing a single die can come out (1,2,3,4,5,6), so if you toss dice, the second die could have any one of six values with each of the numbers that could result from the first toss (e.g., 1 from die 1 and 1,2,3,4,5, or 6 from die 2). So, considering there are 6 ways to fill each of two slots, there are 6 x 6 = 36 possible outcomes of tossing two dice. Only one of them equals 12, so p(12 given 2 dice tossed) = 1/36 = 0.02777777777778.
Answer:
1/21
Step-by-step explanation:
Cards: 2,3,4,5,6,7,8 7 cards
1st card :5
P(5) = number of 5's / total
= 1/7
Then we keep the card
Cards: 2,3,4,6,7,8 only 6 cards left
card less than 4: 2,3
P (card less than 4) = number of cards less than 4/ total cards
= 2/6 = 1/3
P (5, no replacement, card less than 4) = P(5) * P( less than 4)
= 1/7 * 1/3
=1/21
Answer:
CA = 13.5
Step-by-step explanation:
tan 64 = CA/6.6
2.05 = CA/6.6
CA = 13.5
It costs $3.63 more for the gold die than the gold plated die.
The volume of each half of the die is given by the formula
V=1/3s³.
This means the total volume is V = 2(1/3s³) = 2(1/3(2³)) = 16/3 = 5.33 mm³.
For the solid gold die, we know that it weighs 0.02g per mm³:
5.33(0.02) = 0.1066g
Gold costs $40.38 per gram:
40.38(0.1066) = $4.30
For the plastic die, plastic weighs 0.01 g per mm³:
0.01(5.33) = 0.0533g
Plastic costs $10 per gram:
0.0533(10) = 0.533 ≈ $0.54.
We also need to find the surface area, as it will be painted. Each face is an equilateral triangle; the area of a triangle is given by the formula
A = 1/2bh
We need to use the Pythagorean theorem to find the height. The height will be one leg and 1/2 of the base will be the other; the slanted side will be the hypotenuse:
h² + (1/2(2))² = 2²
h² + 1² = 2²
h² + 1 = 4
h² = 3
h = √3
The area of the triangle would then be A = 1/2bh = 1/2(2)(√3) = √3. There are 8 such faces on the die, so the total surface area would be 8√3 = 13.86mm².
Paint costs $0.01 per mm²:
13.86(0.01) = 0.1386 ≈ $0.14
Together the cost for the plastic is 0.14+0.53 = $0.67.
The difference between it and the cost for the gold die is 4.30 - 0.67 = $3.63.
