Provide the proper response.How many vertices must there be in order to draw a connected planar network with 14 edges that separates the plane into 10 regions?
A. 22
B. 6
C. 26
D. Cannot be drawn
Answer: B
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Solve the differential equation.y ' + y tan x = cos x, -?/2 < x < ?/2
A. y = x sin x + c sin x, -?/2 < x < ?/2 B. y = x sin x + c cos x, -?/2 < x < ?/2 C. y = x cos x + c sin x, -?/2 < x < ?/2 D. y = x cos x + c cos x, -?/2 < x < ?/2
Solve the problem.The demand for tickets at a concert hall can be approximated by 
where p is the price (in dollars) and q is the quantity demanded. Use implicit differentiation to find and interpret 
when 
A. 
= -4 means that if the price is increased by $1, the quantity demanded decreases by approximately 4 tickets.
B. 
= - 
means that if the price is increased by $1, the quantity demanded decreases by approximately 
tickets.
C. 
= -4 means that if the price is decreased by $4, the quantity demanded increases by 1 ticket.
D. 
= - 
means that if the price is decreased by $0.25, the quantity demanded increases by 1 ticket.
The probability that exactly k successes occur when a binomial trial is repeated independently n times and the probability of success on any given trial p is
A. 1 - p.
B. 
pn-k (1 - p)k.
C. 
.
D. pk (1 - p) n-k.
E. none of these
Find the volume of the described solid.The solid lies between planes perpendicular to the x-axis at 
and 
. The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the parabola 
to the parabola 
.
A. 800 B. 100 C. 400 D. 768