Let a be a positive constant number. Draw the graph of a
catenary y=acosh(x/a). Calculate the...
Let a be a positive constant number. Draw the graph of a
catenary y=acosh(x/a). Calculate the arc length s from the point
(0,a) to the point (x,acosh(x/a)), and find the expression of the
curve in terms of the parameter s.
Let x be the number of different research programs, and
let y be the mean number of patents per program. As in any
business, a company can spread itself too thin. For example, too
many research programs might lead to a decline in overall research
productivity. The following data are for a collection of
pharmaceutical companies and their research programs.
x
10
12
14
16
18
20
y
1.9
1.4
1.6
1.4
1.0
0.7
Complete parts (a) through (e), given...
Let x be a fixed positive integer. Is it possible to have a
graph G with 4x + 1 vertices such that G has a vertex of degree d
for all d = 1, 2, ..., 4x + 1? Justify your answer. (Note: The
graph G does not need to be simple.)
Let X and Y be independent positive random variables. Let Z=X/Y.
In what follows, all occurrences of x, y, z are assumed to be
positive numbers.
Suppose that X and Y are discrete, with known PMFs, pX and pY.
Then,
pZ|Y(z|y)=pX(?).
What is the argument in the place of the question mark?
Suppose that X and Y are continuous, with known PDFs, fX and fY.
Provide a formula, analogous to the one in part (a), for fZ|Y(z|y)
in terms...
Let X be the event that the
first number is even. Let Y be the event that the second number is
even. Let Z be the event that the
sum of the two numbers is even.
Are the events X and Z independent? (
Are the events X ∩ Y and Z independent?
Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The point (0,
0) is a stationary point of f. For what values of k will f have a
local minimum at (0, 0)?
(a) |k| > 4
(b) k ≥ −4
(c) k ≤ 4
(d) |k| < 4
(e) none of the above
The point P : (2, 2) is a stationary point of the function f(x,
y) = 6xy − x ^3...
Let x be per capita income in thousands of dollars. Let y be the
number of medical doctors per 10,000 residents. Six small cities in
Oregon gave the following information about x and y. x 8.6 9.7 10.3
8.0 8.3 8.7 y 9.7 19.0 22.0 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 53.6, Σy = 85.4, Σx2 = 482.72, Σy2 =
1344.7, Σxy = 784.51, and r ≈ 0.963.
(b) Verify the given sums Σx, Σy,...
Let x be per capita income in thousands of dollars. Let
y be the number of medical doctors per 10,000 residents.
Six small cities in Oregon gave the following information about
x and y.
x
9.0
9.4
10.2
8.0
8.3
8.7
y
9.5
18.0
21.2
10.2
11.4
13.1
Complete parts (a) through (e), given Σx = 53.6,
Σy = 83.4, Σx2 = 481.98,
Σy2 = 1269.3, Σxy = 761.13, and
r ≈ 0.864.
(b) Verify the given sums Σx, Σy,...
Let x be per capita income in thousands of dollars. Let y be the
number of medical doctors per 10,000 residents. Six small cities in
Oregon gave the following information about x and y. x 8.4 9.1 9.8
8.0 8.3 8.7 y 9.8 18.4 21.2 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 52.3, Σy = 84.1, Σx2 = 457.99, Σy2 =
1289.65, Σxy = 747.71, and r ≈ 0.958. (a) Draw a scatter diagram
displaying the...
Let x be per capita income in thousands of dollars. Let y be the
number of medical doctors per 10,000 residents. Six small cities in
Oregon gave the following information about x and y. x 8.3 9.3 10.2
8.0 8.3 8.7 y 9.9 18.1 20.6 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 52.8, Σy = 83.3, Σx2 = 468, Σy2 = 1255.59,
Σxy = 750.81, and r ≈ 0.974. (a) Draw a scatter diagram displaying
the...