What word is used to name the perimeter of a circle
2 answers:
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Answer:
The question is giving you pairs of points in space which can be used to define lines. It is then asking you to determine if the lines defined by those points are parallel, perpendicular, or neither.
Step-by-step explanation:
Two key things you need to know to solve this is that the lines will be parallel if their slopes are the same, and perpendicular if one slope is the negative reciprocal of the other (i.e. )
Let's start with question 11. You are given two pairs of points, each of which describes a distinct line:
(3,5)-(1,1) and (0, 2)-(5, 12)
To find the slope of each pair, take the vertex with the lesser x co-ordinate, and subtract it from the vertex with the greater x co-ordinate. That will give us a valid Δx and Δy to get the slope.
In the first pair, 3 > 1, so we'll subtract the second point from the first:
So the first pair of vectors describe a line with a slope of 2. Let's look at the other pair:
That also gives us a slope of 2, meaning that the two lines are parallel.
This same process will need to be done for the other three questions. We can't answer questions 12 or 14 here, as the last point is cut off on the edge of the image. For question 3 though, one line has a slope of 7/3, and the other 3/7. That puts them in the "neither" category, as one is not the negative reciprocal of the other, but instead the positive reciprocal.
Answer:
a) σ/√n= 1.43 min
c) Margin of error 2.8028min
d) [30.1972; 35.8028]min
e) n=62 customers
Step-by-step explanation:
Hello!
The variable of interest is
X: Time a customer stays at a restaurant. (min)
A sample of 49 lunch customers was taken at a restaurant obtaining
X[bar]= 33 mi
The population standard deviation is known to be δ= 10min
a) and b)
There is no information about the distribution of the population, but we know that if the sample is large enough, n≥30, we can apply the central limit theorem and approximate the distribution of the sample mean to normal:
X[bar]≈N(μ;σ²/n)
Where μ is the population mean and σ²/n is the population variance of the sampling distribution.
The standard deviation of the mean is the square root of its variance:
√(σ²/n)= σ/√n= 10/√49= 10/7= 1.428≅ 1.43min
c)
The CI for the population mean has the general structure "Point estimator" ± "Margin of error"
Considering that we approximated the sampling distribution to normal and the standard deviation is known, the statistic to use to estimate the population mean is Z= (X[bar]-μ)/(σ/√n)≈N(0;1)
The formula for the interval is:
[X[bar]±*(σ/√n)]
The margin of error of the 95% interval is:
d= *(σ/√n)= 1.96* 1.43= 2.8028
d)
[X[bar]±*(σ/√n)]
[33±2.8028]
[30.1972; 35.8028]min
Using a confidence level of 95% you'd expect that the interval [30.1972; 35.8028]min contains the true average of time the customers spend at the restaurant.
e)
Considering the margin of error d=2.5min and the confidence level 95% you have to calculate the corresponding sample size to estimate the population mean. To do so you have to clear the value of n from the expression:
d= *(σ/√n)
= σ/√n
√n*()= σ
√n= σ* ()
n=( σ* ())²
n= (10*)²= 61.47≅ 62 customers
I hope this helps!