Answer:
200 minutes
Step-by-step explanation:
14 + 0.09 x = 18 + 0.07 x
0.09 x - 0.07 x = 18 - 14
0.02 x = 4
x = 400/2 = 200
Answer:
the first one listed (y = - + 4)
Step-by-step explanation:
a 0 at an x-intercept means that when plugging in that number, you get a 0 as a y-value.
So, the easiest method to use is to plug x=2 into each equation listed, because we can see that (2,0) is a point on this graph
if y= - + 4
y = -2² + 4
y = -4 + 4
y = 0
This means that this graph has corresponding real zero(s) to the function y= + 4
(I chose which graph to test by looking to see which option seemed right)
Answer:
see explanation
Step-by-step explanation:
(1)
the sine of an angle =
(a)
here the opposite is 12 and the hypotenuse is 13
12 is the side opposite ∠DEF ← required angle
(b)
the tangent of an angle =
here the opposite is 5 and the adjacent is 12
∠DFE ← required angle
(2)
to calculate AB use Pythagoras' identity in the right triangle
AB² = 2² + 3² = 4 + 9 = 13, hence
AB = ≈ 3.6 ( to nearest tenth )
tanB = ⇒ B = 33.7°
tanA = ⇒ A = 56.3°
Answer:
Step-by-step explanation:
<u>Balls</u>
<u>Options of getting 3 balls</u>
- 1. White, black, black
- 2. Black, white, black
- 3. Black, black, white
Probability P(n) in each option
<u>1. WBB</u>
- P(w) = 6/(n + 6)
- P(b1) = n/(n + 6 - 1) = n/(n + 5)
- P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 1)
P(n) =
- P(w)P(b1)(P(b2) =
- 6/(n+6) × n/(n + 5) × (n - 1)/(n + 4) =
- 6n(n - 1)/(n + 6)(n + 5)(n + 4)
<u>2. BWB</u>
- P(b1) = n/(n + 6)
- P(w) = 6/(n + 6 - 1) = 6/(n + 5)
- P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 4)
P(n) =
- P(b1)P(w)(P(b2) =
- n/(n+6) × 6/(n + 5) × (n - 1)/(n + 4) =
- 6n(n - 1)/(n + 6)(n + 5)(n + 4)
<u>3. BBW</u>
- P(b1) = n/(n + 6)
- P(b2) = (n - 1)/(n + 6 - 1) = (n - 1)/(n + 5)
- P(w) = 6/(n + 5 - 1) = 6/(n + 4)
P(n) =
- P(b1)P(b2)(P(w) =
- n/(n+6) × (n - 1)/(n + 5) × 6/(n + 4) =
- 6n(n - 1)/(n + 6)(n + 5)(n + 4)
<u>Final equation is same for each case:</u>
- P(n) = 6n(n - 1) / (n + 6)(n + 5)(n + 4)
The easy way to find the maximum is to try the numbers or graph.
Both of the methods give the maximum integer n = 11 or n = 12
<em>See attached graph</em>
<u>At both values n we get P(n):</u>
- P(11) = 6*11*10 / 15*16*17 = 11/68 = 0.1618 (rounded)
- P(12) = 6*12*11 / 16*17*18 = 11/68 = 0.1618 (rounded)