Answer:
x ∈ (- 9/2; 1/2), it can also be written as -9/2 <x< 1/2
Step-by-step explanation:
We have absolute value, so we will have2 inequalities.
2x + 4 < 5 and -(2x +4)< 5
2x < 1 -2x - 4 < 5
x < 1/2 -2x < 9
or x > -9/2
(-∞; 1/2) or (- 9/2; ∞)
(-∞; 1/2) ∩ (- 9/2; ∞) = (- 9/2; 1/2)
The answer is x ∈ (- 9/2; 1/2), it can also be written as -9/2 <x< 1/2.
Answer:
Step-by-step explanation:
Let x be the random variable representing the times a fire department takes to arrive at the scene of an emergency. Since the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 6 minutes
σ = 1 minute
the probability that fire department arrives at the scene in case of an emergency between 4 minutes and 8 minutes is expressed as
P(4 ≤ x ≤ 8)
For x = 4,
z = (4 - 6)/1 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
For x = 8
z = (8 - 6)/1 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.98
Therefore,
P(4 ≤ x ≤ 8) = 0.98 - 0.23 = 0.75
The percent of emergencies that the fire department arrive at the scene in between 4 minutes and 8 minutes is
0.75 × 100 = 75%
Step-by-step explanation:
ratios of lengths = 4/3
ratios of area = 16/9
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Subtract 87 from 700
700 - 87 = 613
You need 613 more points
