A professional basketball star who had a reputation for being a poor free throw shooter made 5210 of the 9721 free throws that he attempted, for a success ratio of 0.536. A simulation was developed to generate random numbers between 1 and 1000. An outcome of 1 through 536 was considered to be a free throw that is made, and an outcome of 537 through 1000 was considered to be a free throw that is missed. The list below shows the results for five generated numbers where 1 represents a free throw that was made and 0 represents a free throw that was missed. Complete parts (a) and (b). a. Is the proportion of successful free throws P from the simulation reasonably close to the value of 0.536? (Hint: A proportion is said to be "reasonably close" if it is within the given success ratio ± the probability of a single event.) O Yes, P is reasonably close to the value of 0.536. No, P is not reasonably close to the value of 0.536. 1 1 1 0 0 b. The simulation was conducted 10 times to generate five results R1, R2, R3, R4 and R5 each time, as shown in the table below. Determine the proportion of successful free throws P in each case. Case R1 R2 R3 R4 R5 P 1 1 1 1 2 1 1 1 3 1 1 1 4 1 1 1 1 1 1 1 1 7 1 1 1 8 1 1 9 1 1 1 10 1 1 1 1 (Do not round.)
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.
See photo for details...Need help with Part B
For case one the required proportion P is calculated as:
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