The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form f ( x ) > 0 , f ( x ) < 0 , f ( x ) ≥ 0 , and f ( x ) ≤ 0 . That is, find the real solutions to the related equation and determine restricted values of x . Then determine the sign of f ( x ) on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. | x 2 − 4 | < 5
The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form f ( x ) > 0 , f ( x ) < 0 , f ( x ) ≥ 0 , and f ( x ) ≤ 0 . That is, find the real solutions to the related equation and determine restricted values of x . Then determine the sign of f ( x ) on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120. | x 2 − 4 | < 5
Solution Summary: The author explains how to find the value of variables in inequality, which is (-3,3).
The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the form
f
(
x
)
>
0
,
f
(
x
)
<
0
,
f
(
x
)
≥
0
, and
f
(
x
)
≤
0
. That is, find the real solutions to the related equation and determine restricted values of x. Then determine the sign of
f
(
x
)
on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109-120.
An airline owns an aging fleet of Boeing 737 jet airplanes. It is considering a major purchase of up to 17 new Boeing model 787 and 767 jets. The decision must take into account numerous cost and capability factors, including the following: (1) the airline can finance up to $1.6 billion in purchases; (2) each Boeing 787 will cost $80 million, and each Boeing 767 will cost $110 million; (3) at least one-third of the planes purchased should be the longer-range 787; (4) the annual maintenance budget is to be no more than $8 million; (5) the annual maintenance cost per 787 is estimated to be $800,000, and it is $500,000 for each 767; and (6) each 787 can carry 125,000 passengers per year, whereas each 767 can fly 81,000 passengers annually. Formulate this as an integer programming problem to maximize the annual passenger-carrying capability. What category of integer programming problem is this? Solve this problem
Consider the quadratic function.
f(x)=-(x+4)(x-1)
(a) What are the x-intercepts and y-intercept?
(b) What is the equation of the axis of symmetry?
(c) What are the coordinates of the vertex?
(d) Graph the function on the coordinate plane. Include the axis of symmetry.
Based on a poll of 1000 residents, a newspaper article claims that 62% of the residents in town favor the
development of a recreational park on the west side of town. A community action group interested in preserving
the environment claims that 45% of the town's residents favor the development of a recreational park.
To determine whether the sample supports the population proportion, a simulation of 100 trials is run, each with
a sample of 200, using the point estimate of the population. The minimum sample proportion from the simulation
is 0.46 and the maximum sample proportion is 0.76.
(a) What is the point estimate of the population?
(b) The margin of error of the population proportion is found using an estimate of the standard deviation.
What is the interval estimate of the true population proportion?
(c) The margin of error of the population proportion is found using the half the range.
What is the interval estimate of the true population proportion?
(d) Is the community action…
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