For Questions 28–37, refer to the following: From years of experience, a bagel shop has determined that at a price of p = $ 2.50 , they will sell x = 450 bagels each week. If they lower the price to p = $ 2.00 , they will sell x = 550 bagels each week. The revenue generated by selling these bagels is the product of the price p times the number of bagels sold, x. Write an equation that represents revenue by substituting your result from above into the equation R = x p .
For Questions 28–37, refer to the following: From years of experience, a bagel shop has determined that at a price of p = $ 2.50 , they will sell x = 450 bagels each week. If they lower the price to p = $ 2.00 , they will sell x = 550 bagels each week. The revenue generated by selling these bagels is the product of the price p times the number of bagels sold, x. Write an equation that represents revenue by substituting your result from above into the equation R = x p .
Solution Summary: The author calculates the equation for revenue in the form of R=xp.
For Questions 28–37, refer to the following: From years of experience, a bagel shop has determined that at a price of
p
=
$
2.50
, they will sell
x
=
450
bagels each week. If they lower the price to
p
=
$
2.00
, they will sell
x
=
550
bagels each week.
The revenue generated by selling these bagels is the product of the price p times the number of bagels sold, x. Write an equation that represents revenue by substituting your result from above into the equation
R
=
x
p
.
-
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Shading a Venn diagram with 3 sets: Unions, intersections, and...
The Venn diagram shows sets A, B, C, and the universal set U.
Shade (CUA)' n B on the Venn diagram.
U
Explanation
Check
A-
B
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