Answer:
critical value = 1.645
The 90% confidence interval = ( -22.62, -17.58)
Step-by-step explanation:
Given that:
the sample size 
= 178
the sample size 
= 226
the sample mean 
= 54.4
the sample mean 
= 74.5
population standard deviation 
= 18.58
population standard deviation 
= 9.52
level of significance ∝ = 1 - 0.90 = 0.10
The critical value for 
is 1.645
For the construction of our confidence interval, we use 90% since that is used to find the critical value.
∴
The margin of error = 
2.52
The lower limit = 
= ( 54.4-74.5) - (2.52)
= -20.1 - 2.52
= -22.62
The upper limit = 
= ( 54.4-74.5) + (2.52)
= -20.1 + 2.52
= -17.58
The 90% confidence interval = ( -22.62, -17.58)
Answer:
Jim can type 315 words in 3.5 minutes.
Step-by-step explanation:
90 x 3.5
The GCF of 24, 32, and 80 must be 8, since it is the largest number common to both lists. Example 1 Find the greatest common factor of each set of numbers by listing factors.
I think it would be Six
Because 30 divided by 5 = 6
because 5 times 6 = 30
C(x) = 200 - 7x + 0.345x^2
Domain is the set of x-values (i.e. units produced) that are feasible. This is all the positive integer values + 0, in case that you only consider that can produce whole units.
Range is the set of possible results for c(x), i.e. possible costs.
You can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y-intercept, the shape (it open upwards given that the cofficient of x^2 is positive). Also limit the costs to be positive.
You can substitute some values for x to help you, for example:
x y
0 200
1 200 -7 +0.345 = 193.345
2 200 - 14 + .345 (4) = 187.38
3 200 - 21 + .345(9) = 182.105
4 200 - 28 + .345(16) = 177.52
5 200 - 35 + 0.345(25) = 173.625
6 200 - 42 + 0.345(36) = 170.42
10 200 - 70 + 0.345(100) =164.5
11 200 - 77 + 0.345(121) = 164.745
The functions does not have real roots, then the costs never decrease to 0.
The function starts at c(x) = 200, decreases until the vertex, (x =10, c=164.5) and starts to increase.
Then the range goes to 164.5 to infinity, limited to the solutcion for x = positive integers.
