Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.Use the Principle of Mathematical Induction to show that the statement "5 is a factor of 7n - 2n" is true for all natural numbers. (Hint: 
What will be an ideal response?
When 
, so the statement is true when 
. Assume the statement is true for some natural number k. That is, 
for some integer m. Then,
.
So the statement is true for 
. Conditions I and II are satisfied; by the Principle of Mathematical Induction, the statement is true for all natural numbers.
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Solve the problem. Round your answer to the nearest tenth, if necessary.A jet plane traveling at a constant speed goes 1200 mi with the wind, then turns around and travels for 1000 mi against the wind. If the speed of the wind is a constant 50 mph, and the total flight took 4 hours, find the speed of the plane.
A. 550 mph B. 435 mph C. 525 mph D. 605 mph
Find the product.(x - 11)(x2 + 8x - 6)
A. x3 - 3x2 - 94x + 66 B. x3 + 19x2 + 94x + 66 C. x3 + 19x2 + 82x - 66 D. x3 - 3x2 - 82x - 66
Find the probability.The table lists the eight possible blood types. Also given is the percent of the U.S. population having that type.
Let E be the event that a randomly selected person in the U. S. has type B blood. Let F be the event that a randomly selected person in the U. S. has RH-positive blood.Find P(F|E).
A. 0.818 B. 0.340 C. 0.720 D. 0.107
Graph the function.f(x) = 2 - e-0.64x
A. 
B. 
C. 
D. 