Answer:
option B
Step-by-step explanation:
We can see in the graph that the function has two values of x where the value of y goes to infinity: x = -6 and x = 6.
These points where the value of the function goes to infinity usually are roots of the polynomial in the denominator of a fraction (when the values of x tend to these values, the denominator of the fraction tends to 0, so we have a discontinuity in the function).
So the option that represents a function that have these points in x = -6 and x = 6 is the function in option B.
The other options show functions that have only one point that goes to infinity.
Answer:
0.1019
Step-by-step explanation:
Probability, p=12%=0.12
Sample size, n=130 students
Those writing with left=14 students
Using the formula for binomial distribution
P(X≤x)=![\left[\begin{array}{}n\\x\end{array}\right]p^{x}(1-p)^{n-x}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7B%7Dn%5C%5Cx%5Cend%7Barray%7D%5Cright%5Dp%5E%7Bx%7D%281-p%29%5E%7Bn-x%7D)
Substituting 0.12 for p, 130 for n, 14 for x we obtain
P(X≤x)=![\left[\begin{array}{}130\\14\end{array}\right]0.12^{14}(1-0.12)^{130-14}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7B%7D130%5C%5C14%5Cend%7Barray%7D%5Cright%5D0.12%5E%7B14%7D%281-0.12%29%5E%7B130-14%7D)
P(X≤x)=
P(X≤x)=0.1019
Answer:
84 cm²
Step-by-step explanation:
Surface area of the polyhedron = the sum of the areas of each parts of the net = area of 2 triangles + area of each of the 3 rectangles
Area of 2 triangles:
Base = 4 cm
Height = 3 cm
Area of the 2 triangles = 2(½*base*height)
= 2(½*4*3) = 4*3 = 12 cm²
Area of rectangle with the following dimensions:
Length = 6 cm
Width = 4 cm
Area = length * width = 24 cm²
Area of rectangle with the following dimensions:
Length = 6 cm
Width = 5 cm
Area = length * width = 30 cm²
Area of rectangle with the following dimensions:
Length = 6 cm
Width = 3 cm
Area = length * width = 18 cm²
Surface area of the polyhedron = 12 + 24 + 30 + 18 = 84 cm²
Answer:
a) 
With:


b) 

c) 

d) 


Step-by-step explanation:
For this case we know the following propoertis for the random variable X

We select a sample size of n = 81
Part a
Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

With:


Part b
We want this probability:

We can use the z score formula given by:

And if we find the z score for 89 we got:


Part c

We can use the z score formula given by:

And if we find the z score for 75.65 we got:


Part d
We want this probability:

We find the z scores:


