Answer:
0.321, 0.32...(Line means it is repeated), 2.52, 2.5...
Answer:
x = 33
<C = 81
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+ 2x+ 2x+15 = 180
Combine like terms
5x+15 = 180
Subtract 15 from each side
5x +15-15 =180-15
5x = 165
Divide by 5
5x/5 =165/5
x = 33
<C = 2x+15 = 2(33)+15 = 66+15 = 81
Count the number of multiples of 3, 4, and 12 in the range 1-2005:
⌊2005/3⌋ ≈ ⌊668.333⌋ = 668
⌊2005/4⌋ = ⌊501.25⌋ = 501
⌊2005/12⌋ ≈ ⌊167.083⌋ = 167
(⌊<em>x</em>⌋ means the "floor" of <em>x</em>, i.e. the largest integer smaller than <em>x</em>, so ⌊<em>a</em>/<em>b</em>⌋ is what you get when you divide <em>a</em> by <em>b</em> and ignore the remainder)
Then using the inclusion/exclusion principle, there are
668 + 501 - 2•167 = 835
numbers that are multiples of 3 or 4 but not 12. We subtract the number multiples of 12 twice because the sets of multiples of 3 and 4 both contain multiples of 12. Subtracting once removes the multiples of 3 <em>and</em> 4 that occur twice. Subtracting again removes them altogether.
Let x be the number of adults (under 50 years old) after a 12-hour fast where X ~ N(85,25)
The problem is missing some parts but here are the answers:
(a) x is more than 60
z(60) = (60-85)/25 = -1
P(x > 60) = P(z > -1) = 0.158655
(b) x is less than 110
z(110) = (110-85)/25 = 1
P(x < 110) = P(z < 1) = 0.841345
