High School

Use inductive reasoning to predict the next line in this sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct.

\[
9.3 + 5 = 32
\]
\[
99.3 + 5 = 302
\]
\[
999.3 + 5 = 3002
\]
\[
9999.3 + 5 = 30002
\]

Make a conjecture by predicting the correct numbers in the line below.

\[
99999.3 + 5 = \quad ?
\]

Is the conjecture correct?

A. Yes

B. No

Answer :

Answer and explanation:

Inductive reasoning is a method of reasoning whereby conclusion of an argument is based on specific observations or evidence that forms the premise of the argument. Inductive reasoning moves from observations to general conclusion unlike deductive reasoning.

B. The conjecture 0-3+5 -0 is incorrect

Given the above sequence of computations, we use inductive reasoning to predict the next computation

The correct next conjecture is

99999.3+5= 300002

The next number in the sequence is predicted to be 300007, and the conjecture is confirmed to be correct.

To predict the next line in the sequence, we can observe that the pattern is adding a sequence of 2s at the end of each number. The first number ends with 32, the second with 302, the third with 3002, and the fourth with 30002. Following this pattern, the next number in the line would be 300002. Calculating the sum, we get 300002 + 5 - 0 = 300007.

Therefore, the conjecture for the correct numbers in the next line is 300007.

By performing the arithmetic, we can confirm that the conjecture is indeed correct, as the sum of 9.3 + 5 - 0 equals 14.3, which matches the predicted number.

Learn more about Inductive reasoning here:

https://brainly.com/question/33871903

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