Please check my answers:
How are the symbols 3/4, 0.75, and 75% related?
They are all different ways to express the same number.
2.(4pts)
Use inductive reasoning to predict the next number in the sequence.
1, 2, 2, 4, 4, 8, . . .8 because each number after 1 is repeated twice.
3.(4pts)
Decide whether the argument is an example of inductive or deductive reasoning. Why?
The last four answers were false, therefore the next will be false.
4.(4pts)
Write the negation of the following:
8 + 2 = 10
8+2�‚10
5.(4pts)
Indicate whether the deductive reasoning used is an example of affirming the hypothesis or denying the conclusion.
If a number is divisible by 3, then the sum of the digits of that number is divisible by 3. A number is divisible by 3. Therefore sum of the digits of that number is divisible by 3
Affirming the hypothesis
6.(4pts)
The population of a town was 35,700 at the beginning of 1970. If the population decreased 400 people per year, how many people lived in the town at the beginning of 1985?
400�~15=6000
35,700-6000=29,700
Determine whether there is a one-to-one correspondence between the two sets. Why or Why not?
{a, b, c, d} and {A, B, C, D} Yes there is a one to one correspondence because there are the same number of items in each set
Determine whether the sets are equal only, equivalent only, both equal and equivalent, or neither equal nor equivalent.
{first, second, third} and {1, 2, 3}
They are equivalent only because they do not have the same exact thing in both sets which is required for them to be equal.
Name the property of addition that has been applied.
0 + 5 = 5
Zero property of addition
A delicatessen serves 13 kinds of sandwiches and 5 kinds of chips. How many different sandwich and chip lunches can they make if each lunch has one sandwich and one bag of chips?
13�*5=65
Let's check your answers:
1. How are the symbols 3/4, 0.75, and 75% related?
Your answer is correct. They are all different ways to express the same number.
2. Use inductive reasoning to predict the next number in the sequence:
Your answer is incorrect. The correct answer would be 8, because each number after 1 doubles the previous number, so the pattern is 1, 2, 4, 8, ...
3. Decide whether the argument is an example of inductive or deductive reasoning:
Your answer is incorrect. The argument is an example of inductive reasoning because it is based on observations of previous answers, rather than a logical deduction.
4. Write the negation of the following:
Your answer is correct. The negation of "8 + 2 = 10" is "8 + 2 ≠ 10".
5. Indicate whether the deductive reasoning used is an example of affirming the hypothesis or denying the conclusion:
Your answer is correct. The deductive reasoning used is an example of affirming the hypothesis.
6. The population of a town was 35,700 at the beginning of 1970. If the population decreased 400 people per year, how many people lived in the town at the beginning of 1985?
Your answer is incorrect. The correct calculation would be:
35,700 - (400 * 15) = 29,700
For the remaining questions:
- There is a one-to-one correspondence between the sets {a, b, c, d} and {A, B, C, D} because each item in the first set corresponds to exactly one item in the second set.
- The sets {first, second, third} and {1, 2, 3} are equivalent only because they have a matching order and number of elements, but the actual elements are different.
- The property of addition applied in the equation 0 + 5 = 5 is the Zero property of addition, or the identity property of addition.
- The delicatessen can make a total of 65 different sandwich and chip lunches because for each of the 13 sandwich options, there are 5 chip options, giving us 13 * 5 = 65 possible combinations.
I hope this helps clarify your answers! Let me know if you have any further questions.