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 one by one:

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 correct. The pattern shows that each number after 1 is repeated twice, so the next number is 8.

3. Decide whether the argument is an example of inductive or deductive reasoning. Why?
Your answer is correct. This argument is an example of inductive reasoning because it is based on past observations and assumes that the pattern will continue in the same way.

4. Write the negation of the following: 8 + 2 = 10
Your answer is correct. The negation of the equation "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 because it starts with the hypothesis that if a number is divisible by 3, then the sum of the digits of that number is divisible by 3, and concludes that the sum of the digits is indeed divisible by 3 based on the given information.

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. To find the population at the beginning of 1985, you need to subtract the total decrease in population from the initial population. Since there are 15 years between 1970 and 1985, the population would have decreased by 400 x 15 = 6000 people. Therefore, the population at the beginning of 1985 would be 35,700 - 6000 = 29,700 people.

Now let's move on to the next set of questions:

7. Determine whether there is a one-to-one correspondence between the two sets. Why or Why not?
Your answer is correct. There is a one-to-one correspondence between the two sets because each element in the "a, b, c, d" set corresponds to exactly one element in the "A, B, C, D" set and vice versa.

8. Determine whether the sets are equal only, equivalent only, both equal and equivalent, or neither equal nor equivalent.
Your answer is incorrect. The given sets {first, second, third} and {1, 2, 3} are both equal and equivalent. They are equal because they contain the same elements, and they are equivalent because each element in one set corresponds to exactly one element in the other set.

9. Name the property of addition that has been applied.
Your answer is correct. The property of addition that has been applied is the zero property of addition, which states that adding zero to any number does not change its value.

10. 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?
Your answer is incorrect. To find the total number of different sandwich and chip lunches, you need to multiply the number of sandwich options (13) by the number of chip options (5). Therefore, the delicatessen can make 13 x 5 = 65 different sandwich and chip lunches.

Overall, you did a good job, but make sure to double-check your calculations in question 6 and question 10.