72. In 2012, MetricNet found that the average length of a phone call to a help desk was about ten minutes. Call times were strongly right skewed with a standard deviation around 3.5 minutes. Suppose we take a random sample of 50 calls to the help desk and find the average () call duration for the 50 calls. We repeat this process many times. (a) What do you expect the mean of the 's to be? (b) What do you expect the standard deviation of the r's to be? (c) What do you expect the shape of the r's to be? What guarantees this fact?

Q: held

A: 1. Existence of a virtual smooth controller \(y^* = a(z)\) that stabilizes the \(z\) dynamics…

Q: How many ways can you make a team of 4 from a roster of 8 players. discrete math

A:

Q: (x-5)" 1. 5"

A: since u have asked multiple questions in a single request so we will be answering only first…

Q: 1 a,b,c,d

A: Given below the detailed solution

Q: Vab

A:

Q: Need help with D and E. Already figured out a,b,c

A: Here x'(t) denotes the rate of change of position of a particle in t seconds. So, the value of the…

Q: 6. Suppose that P(E)=0.61, P(F) = 0.43, and P(EF) = 0.27. Find the following:

A: 6) Given,P(E) = 0.61P(F) = 0.43And 0.27Using formula,

Q: P (15. 1) P (11,7)

A:

Q: e,f,g

A: By using previous solution sign Table xf'(x)Positive zeroNegativeDNENegativezeroPositive

Q: ニ

A: To prove that,       x1+x=∑n=0∞-1nxn+1 if -1<x<1

Q: 7 pies 6 pies 4 pies O A. 17 pies3 B. 42 pies3 C. 168 pies D. 188 pies

A: The formula of  volume of a cuboid is…

Q: If a(0, –1, 3) + b(1, 1, 1) – c(1, 2, 5) = (-2, 3, –8), determine a, b and c.

A: If a0,-1,3+b1,1,1-c1,2,5=-2,3,-8determibe a,b,c

Q: e

A: We need to evaluate integral.

Q: What is the five-number summary for this data set? 4, 6, 10, 13, 18, 28, 34, 46, 50, 58 Assume the…

A: Given that: Data set  4,6,10 13,18,28,34,46,50,58. Five number summary is

Q: Random assignment signifies.

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.