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
1. Your answer is correct. The symbols 3/4, 0.75, and 75% are all different ways to express the same number, which is three-fourths or three quarters.
2. Your answer is correct. Based on the pattern, the next number in the sequence would be 8, because each number after 1 is repeated twice.
3. The argument is an example of inductive reasoning. Inductive reasoning involves making conclusions based on a pattern or observations. In this case, the argument is based on the observation that the last four answers were false, therefore assuming that the next answer will also be false. However, this is not a valid deductive argument because it does not provide a logical reason to conclude that the next answer will be false.
4. The negation of "8 + 2 = 10" is "8 + 2 ≠ 10". The negation simply changes the equality sign to the inequality sign.
5. Your answer is correct. The deductive reasoning used is an example of affirming the hypothesis. The hypothesis states that if a number is divisible by 3, then the sum of the digits of that number is divisible by 3. The argument affirms this hypothesis by stating that a number is divisible by 3, and therefore concludes that the sum of the digits of that number is also divisible by 3.
6. Your answer is correct. If the population decreased by 400 people per year from 1970 to 1985, then the decrease would be 400 multiplied by the number of years, which is 15. Subtracting this decrease from the population at the beginning of 1970 gives the population at the beginning of 1985.
7. Your answer is correct. There is a one-to-one correspondence between the sets {a, b, c, d} and {A, B, C, D} because each element in one set corresponds to exactly one element in the other set, and vice versa. The correspondence is as follows: a corresponds to A, b corresponds to B, c corresponds to C, and d corresponds to D.
8. The sets {first, second, third} and {1, 2, 3} are both equal and equivalent. They are equal because they have the same elements. They are also equivalent because each element in one set corresponds to the corresponding element in the other set in terms of position or value.
9. Your answer is correct. The property of addition that has been applied is the zero property of addition. According to this property, when you add zero to any number, the result is that number itself.
10. Your answer is correct. If the delicatessen serves 13 kinds of sandwiches and 5 kinds of chips, and each lunch consists of one sandwich and one bag of chips, then the total number of different sandwich and chip lunches they can make is the product of the number of sandwich options and the number of chip options, which is 13 multiplied by 5, resulting in 65 different lunches.