Answer: x ≥ 3.2 OR x ≤ -0.75
Here's how to solve the compound inequality step-by-step: start by separating it into two inequalities. For the first one, 5x - 4 ≥ 12, add 4 to both sides to remove the constant, leaving 5x ≥ 16. Then divide both sides by 5 to isolate x, resulting in x ≥ 3.2.
Now for the second part, 12x + 5 ≤ -4, subtract 5 from both sides to obtain 12x ≤ -9. Dividing both sides by 12 gives x ≤ -9/12, which simplifies to x ≤ -0.75. So, combining both, the solution is x ≥ 3.2 OR x ≤ -0.75.
The tension does not approach infinity.
<span>Let's analyze free body diagrams (FBDs) for each mass, considering the direction of motion of m₁ as positive.
For m₁: m₁*g - T = m₁*a
For m₂: T - m₂*g = m₂*a
Assuming a massless cord and pulley without friction, the accelerations are the same.
From the second equation: a = (T - m₂*g) / m₂
Substitute into the first:
m₁*g - T = m₁ * [(T - m₂*g) / m₂]
Rearranging:
m₁*g - T = (m₁*T)/m₂ - m₁*g
2*m₁*g = T * (1 + m₁/m₂)
2*m₁*m₂*g = T * (m₂ + m₁)
T = (2*m₁*m₂*g) / (m₂ + m₁)
Taking the limit as m₁ approaches infinity:
T = 2*m₂*g
This aligns with intuition since the greatest acceleration m₁ can have is -g. The cord then accelerates m₂ upward at g while gravity acts downward, leading to a maximum upward acceleration of 2*g for m₁.</span>
Starting with the equation 4(3b + 2)² = 64, if we divide both sides by 4 we obtain
(3b + 2)² = 16. By taking the square root of both sides,
we derive two cases: (3b + 2) = 4 and (3b + 2) = -4.
Solving each equation for b yields:
3b = 2 or 3b = -6,
leading to b values of 2/3 and -2. Ultimately, the results specify that b = 2/3 and b = -2.
The likelihood of selecting one girl is calculated as 
. This is based on having 5 girls within a total of 12 students, and the probability of an event can be expressed as: 
.
Using the same reasoning, for the next student, we have reduced the number of students by 1, leading to 11 possible outcomes instead of 12, giving us:
, which represents the probability of selecting a boy as the second choice.
Lastly, the probability of choosing a girl for the third selection follows the same logic and is given as:
.
However, we must combine these individual probabilities to determine the likelihood of this specific sequence of selections occurring:
This simplifies to:
Answer:
Step-by-step explanation:
Cheapstore:
500p divided by 10 equals 50p, multiplied by 2 gives 100p or £1
£4 corresponds to 600g
Superstore:
600g divided by 10 results in 60g, which when multiplied by 3 yields 180g, added to 600g
£5 equals 780g
600 divided by 4 amounts to 150g for each pound
780 divided by 5 results in 156g for each pound
The box from the Superstore offers the best value
