Answer:
a
b
Step-by-step explanation:
From the question we are told that
The mean value is
The standard deviation is
Considering question a
The sample size is n = 9
Generally the standard error of the mean is mathematically represented as
=>
=>
Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as
=>
From the z table the area under the normal curve to the left corresponding to 2.5 is
=>
=>
Considering question b
The sample size is n = 40
Generally the standard error of the mean is mathematically represented as
=>
=>
Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as
=>
=>
From the z table the area under the normal curve to the left corresponding to 5.2715 and
=>
So
=>
Given:
Current revenue = $6000
<span>R(f)= -100f^2 + 400f + 6000
where f is a whole number of $5 fee increases
We are told to find f, when R(f) </span><span>< 6000
Since </span>R(f)= -100f^2+400f+6000
R(f) < 6000 ⇒ -100f^2+400f+6000 < 6000
Subtract 6000 from both sides
-100f^2 + 400f + 6000 - 6000 < 6000 - 6000
-100f^2 + 400f < 0
⇒ 400f - 100f^2 < 0
Divide the equation by 100
400f/100 - 100f^2/100 < 0/100
4f - f^2 < 0
Add f^2 to both sides of the equation
4f - f^2 + f^2 < 0 + f^2
4f < f^2
Divide both sides by f
4f/f < (f^2)/f
4 < f
⇒ f > 4
⇒ f ≥ 5
Therefore, <span> for 5 or more numbers of $5 fee increases, the revenue from fees will actually be less than its current value.</span>
Consider this population data set: 4,6,7, 11, 12, 18, 26, 23, 14, 31, 22, and 12. The values 11, 31, 22, and 12 constitute a ran
Andrej [43]
Answer:
The population mean is the sum of the 12 data set values divided by 12:
4 + 6 + 7 + 11 + 12 + 18 + 26 + 23 + 14 + 31 + 22 + 12 = 186.
Therefore the population mean = 186/12 = 15.5.
The sample mean is the sum of the 4 sample values divided by 4:
11 + 31 + 22 + 12 = 76.
Therefore the sample mean = 76/4 = 19.
The sample mean is more than the population mean by 19 - 15.5 = 3.5.
hope it helped
Step-by-step explanation:
Answer:
(3x - 3)(x - 2)
Step-by-step explanation:
3x² - 9x + 6
3x² - 6x - 3x + 6
3x(x - 2) - 3(x - 2)
<em><u>(3x - 3)(x - 2)</u></em>