MATH C277: Finite Mathematics

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Free MATH C277: Finite Mathematics Questions

2[18 - 6(3² - 5)/8 + 4]

-113/2
8
20
38

Explanation

Explanation
Start inside the parentheses: 3² = 9, and 9 - 5 = 4. Multiply to get 6 × 4 = 24, then divide by 8 to get 3. Substitute back into the expression: 18 - 3 + 4 = 19. Finally, multiply by 2 to get 2 × 19 = 38.
Correct answer
38

Round 35,325.738 to the nearest hundredth and explain your answer.

35,325.74; The 8 to the right of the 3 rounds the 3 up to a 4, and digits to the right of this decimal position are then left off.
35,300; To round, change the digits after the hundreds place to zeros.
35,300; The 2 to the right of 3 is less than 5, so 3 does not change.
35,330; The 5 to the right of the 2 rounds the 2 up to a 3, and digits to the right of this decimal position are then changed to zeros.

Explanation

Explanation
The hundredth place in 35,325.738 is the second digit to the right of the decimal, which is 3. The digit immediately to its right (the thousandth place) is 8. Since 8 is greater than or equal to 5, the hundredth digit increases from 3 to 4. All digits to the right are dropped.
Correct answer
35,325.74

p → q
Select the truth table that represents the statement above.

Explanation

Correct Answer:

The table that shows:

T → T = T

T → F = F

F → T = T

F → F = T

Explanation:

The statement p → q means "if p, then q." In logic, this implication is false only when p is true and q is false. In all other cases, the implication is considered true.

When p is true and q is true, the implication holds, so the result is true.

When p is true and q is false, the implication fails, so the result is false.

When p is false (regardless of q), the implication is considered true because nothing is required of q when p is false.

Therefore, both cases where p is false (F → T and F → F) yield true.

Why Other Options Are Wrong:

Option one: This option is incorrect because it fails to mark the statement as true when both p and q are true. In the case of p → q, if both are true, the implication is valid and the result must be true. The presence of any incorrect truth value makes the entire truth table invalid.

Option two: This option is incorrect because it shows the implication as false when both p and q are false. However, in logic, p → q is true when p is false, regardless of q’s value. Therefore, marking this case as false is logically incorrect.

Simplify the expression:
$\sqrt{\frac{4}{9} \times \frac{9}{4}}$
Reduce to lowest terms.

1
$\frac{13}{6}$
$\frac{\sqrt{13}}{6}$
$\frac{\sqrt{97}}{6}$

Explanation

Correct Answer:

$\frac{\sqrt{97}}{6}$

Explanation:

Step 1: Add the fractions under the square root

$\frac{4}{9} + \frac{9}{4} = \frac{(4 \times 4) + (9 \times 9)}{36} = \frac{16 + 81}{36} = \frac{97}{36}$

Step 2: Apply the square root

$\sqrt{\frac{97}{36}} = \frac{\sqrt{97}}{\sqrt{36}} = \frac{\sqrt{97}}{6}$

So actually, the simplified result is:

$\frac{\sqrt{97}}{6}$

Why Other Options Are Wrong:

1

This is far too small. The value under the square root is greater than 1, so the square root is also greater than 1.

$\frac{13}{6}$

This implies the square root of a rational number, but $\frac{\sqrt{97}}{6}$ ≠ $\frac{13}{6}$ . That would only be true if the value inside the radical were exactly $\frac{\sqrt{169}}{6}$ , which it isn’t.

$\frac{\sqrt{13}}{6}$

The expression under the radical is $\frac{97}{36}$ , not 13. So this doesn't match and is incorrect.

2(-3)² - 4(-5)²

82
436
−364
−82

Explanation

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

Truncate 348.856 to the nearest tenths place and explain your answer.

348.8; Truncation leaves off digits past the tenths place.
348.9; Truncation rounds and then leaves off digits past the tenths place.
349; Truncation rounds and then leaves off digits starting with the tenths place.
348; Truncation leaves off digits starting with the tenths place.

Explanation

Correct Answer:

348.8; Truncation leaves off digits past the tenths place.

Explanation:

Truncation means cutting off digits without rounding. To truncate 348.856 to the tenths place, we simply keep the tenths digit (which is 8) and remove everything after it (i.e., the hundredths and thousandths, which are 5 and 6). We do not round up based on those digits.

So, 348.856 truncated to the tenths place is 348.8.

Why Other Options Are Wrong:

348.9

This result involves rounding the tenths place (since the hundredths is 5), but truncation does not round — it only chops off digits.

349

This rounds the entire number up and drops all decimal digits, which is incorrect. Truncation at the tenths place does not affect whole numbers.

348

This removes everything from the tenths place onward, which is incorrect for truncation to the tenths place. This would be truncating to the ones place instead.

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.

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 = 1,942.51228,530 ≈ 0.0085 Rate ≈ 0.0085 Now use this rate to find the assessed value for the new tax amount: Assessed Value = 1,341.640.0085 ≈ 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.

9.
Place the following real numbers in increasing order:
$\frac{16}{\sqrt{32}}$ , $\frac{12}{\sqrt{8}}$ , $\frac{2}{\sqrt{2}}$ , $\frac{16}{\sqrt{8}}$

$\frac{2}{\sqrt{2}}, \frac{12}{\sqrt{8}}, \frac{16}{\sqrt{32}}, \frac{16}{\sqrt{8}}$

$\frac{16}{\sqrt{32}}, \frac{2}{\sqrt{2}}, \frac{12}{\sqrt{8}}, \frac{16}{\sqrt{8}}$

$\frac{2}{\sqrt{2}}, \frac{16}{\sqrt{32}}, \frac{12}{\sqrt{8}}, \frac{16}{\sqrt{8}}$

$\frac{2}{\sqrt{2}}, \frac{16}{\sqrt{8}}, \frac{12}{\sqrt{8}}, \frac{16}{\sqrt{32}}$

Explanation

10.
The following numbers are listed according to a pattern: $\frac{1}{2}, \frac{1}{4}, \frac{1}{12}, \frac{1}{48}, \frac{1}{240}$ … Which of the following could be the next number in the pattern?

$\frac{1}{480}$

$\frac{1}{960}$

$\frac{1}{1200}$

$\frac{1}{1440}$

Explanation

Explanation

Look at how the denominators change: 2 → 4 → 12 → 48 → 240. Each step multiplies by the next integer: 2 × 2 = 4, 4 × 3 = 12, 12 × 4 = 48, 48 × 5=240. So the next denominator should be 240 × 6 = 1440. Therefore, the next term is $\frac{1}{1440}$ .

Correct answer

$\frac{1}{1440}$

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