Answer:
16
Step-by-step explanation:
Subtracting the 2 expressions
3b² - 8 - b(b² + b - 7) ← distribute parenthesis
= 3b² - 8 - (b³ + b² - 7b) ← distribute parenthesis by - 1
= 3b² - 8 - b³ - b² + 7b ← collect like terms
= - b³ + 2b² + 7b - 8 ← substitute b = - 3 into the expression
= - (- 3)³ + 2(- 3)² + 7(- 3) - 8
= - (- 27) + 2(9) - 21 - 8
= 27 + 18 - 21 - 8
= 16
Answer:
a) <u>0.4647</u>
b) <u>24.6 secs</u>
Step-by-step explanation:
Let T be interval between two successive barges
t(t) = λe^λt where t > 0
The mean of the exponential
E(T) = 1/λ
E(T) = 8
1/λ = 8
λ = 1/8
∴ t(t) = 1/8×e^-t/8 [ t > 0]
Now the probability we need
p[T<5] = ₀∫⁵ t(t) dt
=₀∫⁵ 1/8×e^-t/8 dt
= 1/8 ₀∫⁵ e^-t/8 dt
= 1/8 [ (e^-t/8) / -1/8 ]₀⁵
= - [ e^-t/8]₀⁵
= - [ e^-5/8 - 1 ]
= 1 - e^-5/8 = <u>0.4647</u>
Therefore the probability that the time interval between two successive barges is less than 5 minutes is <u>0.4647</u>
<u></u>
b)
Now we find t such that;
p[T>t] = 0.95
so
t_∫¹⁰ t(x) dx = 0.95
t_∫¹⁰ 1/8×e^-x/8 = 0.95
1/8 t_∫¹⁰ e^-x/8 dx = 0.95
1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t = 0.95
- [ e^-x/8]¹⁰_t = 0.96
- [ 0 - e^-t/8 ] = 0.95
e^-t/8 = 0.95
take log of both sides
log (e^-t/8) = log (0.95)
-t/8 = In(0.95)
-t/8 = -0.0513
t = 8 × 0.0513
t = 0.4104 (min)
so we convert to seconds
t = 0.4104 × 60
t = <u>24.6 secs</u>
Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is <u>24.6 secs</u>
Answer:
(0,0)
Step-by-step explanation:
We have,
U = { (x,y) : x,y belong to real numbers }
A = { (x,y) : (x,y) is a solution of y=x }
B = { (x,y) : (x,y) is a solution of y=2x }
We need to find the ordered pair (x,y) that belong to A
B.
Let, (x,y) belong to A
B
i.e. (x,y) belong to A and (x,y) belong to B
i.e. y = x and y = 2x
i.e. x = 2x
i.e. x = 0
Now, substitute x= 0 in any of the equation say y = x, we get y = 0.
Hence, the ordered pair satisfying A
B is (0,0).
Ok so
24=30%
find 100%
24=30%
diivde by 3
8=10%
multiply 10
80=100%
answe ris 80 coins
Answer:
$88.00
Step-by-step explanation: