MATH C277: Finite Mathematics
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Free MATH C277: Finite Mathematics Questions
Truncate 0.12345 to the fourth decimal place and explain your answer.
- A. 0.1235; Truncation rounds the fourth decimal place up from 4 to 5.
- B. 0.1235; Truncation leaves off digits after rounding the fourth decimal place.
- C. 0.1230; Truncation rounds the fourth decimal place from 4 to 0.
- D. 0.1234; Truncation leaves off digits past the fourth decimal place.
Explanation
Truncation means cutting off digits beyond a specified place value without rounding. To truncate 0.12345 to the fourth decimal place, you keep the first four digits after the decimal point and remove everything that comes after. Since truncation does not consider the value of the next digit, the 5 in the fifth decimal place is simply dropped.
Correct answer
0.1234
Multiply 25.14 by 62.13.
Round your answer to the nearest hundredth and explain the answer.
-
1,561.948; because the 8 does not change because 2 is less than 5
-
1561.94; because digits to the right of 4 are dropped
-
1,561.95; because the 4 rounds up to 5
-
1,600; because the 5 rounds up to 6
Explanation
Correct Answer:
1,561.95; because the 4 rounds up to 5
Explanation:
Step 1: Multiply
25.14 × 62.13 = 1,561.9482
Step 2: Round to the nearest hundredth
The hundredth digit is 4 and the digit after it (the thousandths place) is 8, which is greater than 5.
So we round the 4 up to 5, giving:
1,561.95
Why Other Options Are Wrong:
1,561.948
This is the unrounded product. The question specifically asks for rounding to the nearest hundredth.
1561.94
This would be correct if the digit after the hundredths place were less than 5. But here it is 8, so we must round up.
1,600
This is a rough estimate, not a precise rounding to the hundredth. The correct rounding process requires attention to decimal places, not nearest hundred.
What is the least common multiple of 504 and 540?
-
272,160
-
7,560
-
50,400
-
4,540
Explanation
Correct Answer:
7,560
Explanation:
To find the least common multiple (LCM) of 504 and 540, use the formula:
First, find the greatest common factor (GCF).
504 = 23 × 32 × 7
540 = 22 × 33 ×5
GCF = 22×32 = 36
Now calculate the LCM:
LCM = =7,560
Why Other Options Are Wrong:
272,160
This is the product of 504 × 540 without dividing by the GCF. It is the maximum common multiple, not the least. It represents the numerator before simplification.
50,400
This is a multiple of both numbers but not the smallest one. It results from incorrect simplification and exceeds the correct LCM.
4,540
This number is neither a multiple of 504 nor 540. It is unrelated to the LCM calculation and likely included to mislead based on its similar digits.
A family goes on a road trip totaling 1,885 miles. If after 4 hours they have traveled 260 miles, how many hours more will it take to reach the destination (assuming the same rate of speed for the remainder of the trip)?
- A. 33 hours
- B. 21 hours
- C. 29 hours
- D. 25 hours
Explanation
First find the speed by dividing distance by time: 260 ÷ 4 = 65 miles per hour. Next determine the remaining distance: 1,885 - 260 = 1,625 miles. Divide the remaining distance by the speed: 1,625 ÷ 65 = 25. This gives the number of additional hours needed to complete the trip.
Correct answer
25 hours
Which property in the real number system is illustrated in this problem?
7⊕8=8⊕7
5 = 5
-
Associative Property
-
Closure
-
Commutative Property
-
Distributive Property
Explanation
Correct Answer:
Commutative Property
Explanation:
The commutative property states that changing the order of numbers in an operation does not affect the result. This applies to both addition and multiplication. In the expression shown, 7⊕8=8⊕7, the numbers are reversed in order, yet the equality remains true, demonstrating that the operation is commutative.
Why Other Options Are Wrong:
Associative Property
This property refers to changing grouping (parentheses), not order. It involves expressions like (a + b) + c = a + (b + c). Since no grouping is shown, it doesn’t apply here.
Closure
Closure means that performing an operation on two real numbers results in another real number. While true in general, it doesn’t explain the equality shown in this problem.
Distributive Property
The distributive property involves expressions like a (b + c) = ab + ac. This has nothing to do with reversing operands, so it is not applicable here.
2(-3)2 - 4(-5)2
- A. 82
- B. 436
- C. −364
- D. −82
Explanation
Apply the order of operations by evaluating exponents first.
(-3)2 = 9, so 2 × 9 = 18.
(-5)2 = 25, so 4 × 25 = 100.
Now subtract: 18 - 100 = -82.
This completes the simplification using exponents, multiplication, and subtraction in the correct order.
Correct answer
−82
The property tax on a house with an assessed value of $228,530 is $1,942.51.
What is the assessed value of a house whose property tax is $1,341.64, assuming the same tax rate?
Round your answer to the nearest dollar.
-
$156,972
-
$157,840
-
$114,039
-
$330,880
Explanation
Correct Answer:
$157,840
Explanation:
First, find the tax rate from the given values:
Tax Rate = ≈ 0.0085
Rate ≈ 0.0085
Now use this rate to find the assessed value for the new tax amount:
Assessed Value = ≈ 157,840
This matches the option $157,840 when rounded to the nearest dollar.
Why Other Options Are Wrong:
$156,972
This is slightly below the correct computed value. It may result from a rounding or calculation error when estimating the tax rate or assessed value.
$114,039
This is too low and does not align with the tax amount provided. Using the correct tax rate, this amount would result in a much smaller tax.
$330,880
This value is too high. A house assessed this high at the same tax rate would owe over $2,800 in taxes, far above $1,341.64.
1, 1, 2, 4, 7, 13, 24, . . .
Find the next number in the sequence.
-
24
-
37
-
44
-
47
Explanation
Correct Answer:
44
Explanation:
From the sequence:
1 + 1 = 2
1 + 2 = 3 → Add 1 more to make 4 (next in sequence)
2 + 4 = 6 → Add 1 more to make 7 (next in sequence)
4 + 7 = 11 → Add 2 more to make 13
7 + 13 = 20 → Add 4 more to make 24
The extra numbers being added (1, 1, 2, 4) are themselves part of the original sequence: 1, 1, 2, 4. To continue this pattern, the next number to add is the next in the sequence after 4, which is 7. So:
13 + 24 = 37 → Add 7 more = 44
Why Other Options Are Wrong:
24
This number already appears in the sequence and does not follow the forward-moving additive pattern. Repeating it would break the logic that introduces a new number based on cumulative growth.
37
This is only the result of 13 + 24. The established pattern shows that we must also add a number from earlier in the sequence—specifically 7 in this case—making 44 the actual next number.
47
Although this seems like a plausible progression, it does not follow the underlying pattern. The logic requires adding a previous value from the sequence, not simply continuing numerical growth. 47 skips the required additive structure.
Let p and q represent the following simple statements:
p: They are eating lunch.
q: It is noon.
Match each English statement with its symbolic equivalent from the options below.
Each symbolic option corresponds to a logical expression involving p and q.
A. p→q
B. q→p
C. ∼p→∼q
D. ∼q→∼p
E. q↔p
F. p↔q
G. ∼p↔∼q
Match:
They eat lunch if and only if it is noon
If it is noon, then they are eating lunch
They are not eating lunch if it is not noon
If they are eating lunch, then it is noon
-
F, B, D, A
-
E, A, D, B
-
G, C, B, D
-
F, C, E, A
Explanation
Correct Answer:
F, B, D, A
Explanation:
1. They eat lunch if and only if it is noon
This is a biconditional statement, meaning both p and q must be either true or false for the statement to be true.
Symbolically: p ↔ q or q ↔ p — both are logically equivalent.
The matching option is F: p ↔ q
2. If it is noon, then they are eating lunch
This is a conditional statement where q → p.
The matching option is B: q → p
3. They are not eating lunch if it is not noon
This is another conditional statement written contrapositively as:
If ~q, then ~p → ~q → ~p
The matching option is D: ~q → ~p
4. If they are eating lunch, then it is noon
This is a standard conditional: p → q
The matching option is A: p → q
Why Other Options Are Wrong:
E, A, D, B:
Incorrect because option 1 ("They eat lunch if and only if it is noon") is matched with E, which uses q ↔ p. While this is logically equivalent to p ↔ q, the remaining matches do not align correctly: "If they are eating lunch, then it is noon" corresponds to A: p → q, but in this answer it's placed last, after a mismatch.
G, C, B, D:
Incorrect because option 1 is matched with G, which uses ~p ↔ ~q—this is the inverse, not logically equivalent to the biconditional p ↔ q. Also, the third match is B: q → p, which misrepresents "They are not eating lunch if it is not noon."
F, C, E, A:
Incorrect because C: ~p → ~q is not the correct contrapositive form of p → q. Additionally, E: q ↔ p in the third match is incorrectly matched to “They are not eating lunch if it is not noon,” which requires a conditional, not a biconditional.
Simplify the above expression.
Explanation
Correct Answer:
Explanation:
=
=
=
Why Other Options Are Wrong:
11/8
This is incorrect because 11/8 is a small fraction (1.375), far less than the sum of two mixed numbers like 3 3/12 and 5 5/8, which should exceed 8. The addition of whole numbers 3 + 5 = 8, plus fractional parts, results in a value much larger than 11/8, indicating this option likely stems from a division error or misinterpretation of the problem as a fraction division rather than addition.
101/12
This is incorrect because 101/12 (approximately 8.4167) is a fraction that does not reflect the sum of 3 3/12 and 5 5/8, which should be around 8 or 9 when considering the whole numbers and fractions. The numerator 101 suggests a miscalculation, possibly from adding numerators incorrectly or confusing the operation, making it an invalid result for this addition problem.
29/12
This is incorrect because 29/12 (approximately 2.4167) is too small to represent the sum of 3 3/12 and 5 5/8, which involves adding numbers greater than 8. This option might arise from an erroneous subtraction or division of the fractions rather than their addition, and it fails to account for the whole number components correctly.
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