Mathematical Induction Questions and Answers
![A political scientist surveys 21 of the current 98 representatives in a state's congress.
What is the size of the sample:
What is the size of the population:](https://media.kunduz.com/media/sug-question/raw/84474258-1657981473.10181.jpeg?w=256)
Math - Others
Mathematical InductionA political scientist surveys 21 of the current 98 representatives in a state's congress.
What is the size of the sample:
What is the size of the population:
![A true-false test contains 10 questions. In how many different ways can this test be completed? (Assume we don't care about our scores.)
This test can be completed in different ways.](https://media.kunduz.com/media/sug-question/raw/84473664-1657977270.1446266.jpeg?w=256)
Math - Others
Mathematical InductionA true-false test contains 10 questions. In how many different ways can this test be completed? (Assume we don't care about our scores.)
This test can be completed in different ways.
![Circle the polynomials below that are in P2.
x²+x+2
x³ -x²+x-1
x²+x+1
5
Show that every polynomial in P2 can be written as a linear combination of the following three
polynomials.
x²+2x+1
(x-1)³ - (x + 1)³
x² + 4x +4](https://media.kunduz.com/media/sug-question/raw/84430280-1657653826.3941932.jpeg?w=256)
Math - Others
Mathematical InductionCircle the polynomials below that are in P2.
x²+x+2
x³ -x²+x-1
x²+x+1
5
Show that every polynomial in P2 can be written as a linear combination of the following three
polynomials.
x²+2x+1
(x-1)³ - (x + 1)³
x² + 4x +4
![Given its time to maturity the duration of a zero coupon bond is
O the same regardless of the discount rate
O lowest when the discount rate is equal to the risk free rate
O higher when the discount rate is lower
O higher when the discount rate is lower](https://media.kunduz.com/media/sug-question/raw/84334762-1657400793.2170234.jpeg?w=256)
Math - Others
Mathematical InductionGiven its time to maturity the duration of a zero coupon bond is
O the same regardless of the discount rate
O lowest when the discount rate is equal to the risk free rate
O higher when the discount rate is lower
O higher when the discount rate is lower
![For each of the following differential equations, determine whether it is an exact equation or
not. If it is, find a general solution.
a. 2y²e²xy dx + ((2xy + 1)e²xy + 2y) dy = 0
b. (xy² - 4y³) dx + (x²y — 12x²y) dy = 0](https://media.kunduz.com/media/sug-question/raw/84219407-1657015950.211017.jpeg?w=256)
Math - Others
Mathematical InductionFor each of the following differential equations, determine whether it is an exact equation or
not. If it is, find a general solution.
a. 2y²e²xy dx + ((2xy + 1)e²xy + 2y) dy = 0
b. (xy² - 4y³) dx + (x²y — 12x²y) dy = 0
![Perform the given calculations mentally from left to right. Write down a sequence of numbers indicating intermediate steps in your thought process.
(a) 647-382
(b) 3.173
(c) 56+36+41+4+75+32
(a) Select the choice below that shows a left to right thought process for 647-382 and fill in the final answer in the answer box in your choice.
A. 9, 120,
B. 9, 129,
C. 200, 182,
D. 300, 260,](https://media.kunduz.com/media/sug-question/raw/84212465-1657015816.9265597.jpeg?w=256)
Math - Others
Mathematical InductionPerform the given calculations mentally from left to right. Write down a sequence of numbers indicating intermediate steps in your thought process.
(a) 647-382
(b) 3.173
(c) 56+36+41+4+75+32
(a) Select the choice below that shows a left to right thought process for 647-382 and fill in the final answer in the answer box in your choice.
A. 9, 120,
B. 9, 129,
C. 200, 182,
D. 300, 260,