Answer:
PQ = 18
Step-by-step explanation:
If R is the midpoint of PQ, then PR = RQ
⇒ 6x + 7 = 3x + 8
⇒ 3x = 1
⇒ x = 1/3
So PR = 6x + 7 = 6(1/3) + 7 = 9
and RQ = 3x + 8 = 3(1/3) + 8 = 9
⇒ PQ = PR + RQ = 9 + 9 = 18
3x^2 - 8x + 5
3x^2 - 3x - 5x + 5
3x(x - 1) - 5(x - 1)
(x - 1)(3x - 5)
The answer is: (x - 1)(3x - 5).
Answer:
A) 12/37
B) 12/46
C) 25/54
D) 29/100
Step-by-step explanation:
Let event A = small-business owner selected economy,
event B = small-business owner selected finding qualified workers,
Thus, probabilities;
P(A)=46/100
P(B)=37/100
P(A∩B)=12/100
A) P(A ∩ B)/P(B) = (12/100)/(37/100) = 12/37
B) P(A∩B)/P(A) = (12/100)/(46/100)= 12/46
C) P(B∩A')= P(B) − P(A∩B) =
37/100 - 12/100 =25/100
P(B∩A')/P(A') =
(25/100)/(1-46/100) = 25/54
D) Using inclusion-exclusion principle;
P(A∪B) = P(A)+P(B)−P(A∩B)=
46/100 + 37/100 - 12/100 = 71/100
Hence, the probability that the owner believes neither that the economy is a challenge for growth nor that finding qualified workers is a challenge for growth is;
P( A' ∩ B') = 1 − P(A∪B)= 1− (71/100)= 29/100
Answer:
<h3>A. about 3.4 seconds</h3>
Step-by-step explanation:
Given the volume of air in liters in the human lungs described by the function V(t) = 0.173t +0.15t^2 - 0.035t^3 where t is the time in seconds,
The beginning of this respiratory cycle for the lungs to fill to their maximum volume of air occurs when dV/dt = 0
dV/dt = 0.173 + 0.3t - 3(0.035)t²
dV/dt = 0.173 + 0.3t - 0.105t²
Since dV/dt = 0
0.173 + 0.3t - 0.105t² = 0
multiply through by -1
-0.173 - 0.3t + 0.105t² = 0
0.105t² -0.3t-0.173 = 0
Factorize;
t = 0.3±√0.3²+4(0.105(0.173))/2(0.105)
t = 0.3±√0.09+0.07266/0.21
t = 0.3±√0.16266/0.21
t = 0.30±0.4033/0.21
t = 0.7033/0.21
t = 3.349secs
t ≈ 3.4secs
Hence it will take about 3.4secs for the lungs to fill to their maximum volume of air
The answer is that the width is 3 m and the length will be 14 m because 3•14 = 42m² and 3+11=14
