The blood type of an individual is classified according to the presence of certain antigens, substances that cause the immune system to produce antibodies. These antigens are denoted by A,B , and Rh . If an individual's blood contains either the A or B antigen, these letters are listed in the blood type. If neither A nor B is present, then the letter O is used. If the Rh antigen is present, the blood is said to be Rh positive Rh + ; otherwise, the blood is Rh negative Rh − . Under this system, a person with AB + blood has all three antigens, and group O − is absent all three antigens. The distribution of blood types for people living in the United States is given in the table. Refer to the table for Exercises 75-78. Round to 3 decimal places when necessary. a. If an individual is randomly selected from the population, find the probability that the individual will have the Rh factor, b. If three people are selected at random, find the probability that they all have the Rh factor.
The blood type of an individual is classified according to the presence of certain antigens, substances that cause the immune system to produce antibodies. These antigens are denoted by A,B , and Rh . If an individual's blood contains either the A or B antigen, these letters are listed in the blood type. If neither A nor B is present, then the letter O is used. If the Rh antigen is present, the blood is said to be Rh positive Rh + ; otherwise, the blood is Rh negative Rh − . Under this system, a person with AB + blood has all three antigens, and group O − is absent all three antigens. The distribution of blood types for people living in the United States is given in the table. Refer to the table for Exercises 75-78. Round to 3 decimal places when necessary. a. If an individual is randomly selected from the population, find the probability that the individual will have the Rh factor, b. If three people are selected at random, find the probability that they all have the Rh factor.
The blood type of an individual is classified according to the presence of certain antigens, substances that cause the immune system to produce antibodies. These antigens are denoted by
A,B
, and
Rh
. If an individual's blood contains either the
A
or
B
antigen, these letters are listed in the blood type. If neither
A
nor
B
is present, then the letter
O
is used. If the
Rh
antigen is present, the blood is said to be
Rh
positive
Rh
+
; otherwise, the blood is
Rh
negative
Rh
−
. Under this system, a person with
AB
+
blood has all three antigens, and group
O
−
is absent all three antigens.
The distribution of blood types for people living in the United States is given in the table. Refer to the table for Exercises 75-78. Round to
3
decimal places when necessary.
a. If an individual is randomly selected from the population, find the probability that the individual will have the
Rh
factor,
b. If three people are selected at random, find the probability that they all have the
Rh
factor.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY