Answer: a. 1.981 < μ < 2.18
b. Yes.
Step-by-step explanation:
A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.
First, we calculate mean of the sample:


2.08
Now, we estimate standard deviation:


s = 0.1564
For t-score, we need to determine degree of freedom and
:
df = 12 - 1
df = 11
= 1 - 0.95
α = 0.05
0.025
Then, t-score is
= 2.201
The interval will be
± 
2.08 ± 
2.08 ± 0.099
The 95% two-sided CI on the mean is 1.981 < μ < 2.18.
B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.
<span> A line that never changes, so you can choose whatever two points you want and you will always get the same slope.
</span>
<span>Given:
x g(x)
−3 17
−1 −3
0 −4
2 13
The true statement for the given function is:
</span><span>The function is decreasing from x = −3 to x = −1.
</span><span>
As you can see, when x = -3 the corresponding value of the function is 17 but when x = -1 the corresponding value is -3. There is a decrease of 20. </span>→<span> 17 - 20 = -3
</span>
Answer:
-80
Step-by-step explanation:
We have to do the parentheses first because it's part of PEDMAS.
-2x-5= 10
Next, we take 10 times -8
-8 x 10= -80
There you go! Hope this helps!
Answer:
84.5 m
Step-by-step explanation:
It is often helpful to draw a diagram for word problems involving geometric relationships. One for this problem is shown below.
The mnemonic SOH CAH TOA reminds you of the relationship between sides of a right triangle:
Tan = Opposite/Adjacent
Here we're given angles of depression measured from the horizontal (as shown in the diagram), but it is more convenient to use angles measured from the vertical. In particular, ∠BAO is the complement of 60°, and its tangent is the ratio OB/OA:
tan(30°) = OB/OA
OB = (200 m)·tan(30°) ≈ 115.47 m . . . . . . multiply by OA, use OA=200 m
Likewise, we have ...
OC = (200 m)·tan(45°) = 200 m
Then the width of the river is the difference between these values:
BC = OC -OB = 200 m - 115.47 m = 84.53 m