MATH C277: Finite Mathematics

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Free MATH C277: Finite Mathematics Questions

Wildlife biologists tagged 68 fish and released them into a lake. Later, they caught 119 fish and found that 17 of them were tagged.
Approximately how many fish are in the lake?

7,956
476
1,156
204
85

Explanation

Correct Answer:

476

Explanation:

First calculating the ratio of the tagged fish that were caught to the total fish tagged.

119 ÷ 17 = 4

Hence there will be 4 times more fish in the lake compared to the one caught.

119 * 4 = 476.

Why Other Options Are Wrong:

7,956

This is far too high and would suggest a tagging rate that doesn’t match the 17 tagged fish found in the sample.

1,156

Also too high; it results from miscalculating the proportion or misusing the cross-multiplication step.

204

Too low; this would imply an unrealistically high tag rate in the sample, inconsistent with 17 out of 119 being tagged.

85

This is almost the number of tagged fish, not the total population estimate. It significantly underrepresents the lake population.

$3 \frac{3}{12} + 5 \frac{1}{8}$
Simplify the above expression.

$\frac{11}{8}$
$\frac{101}{12}$
$\frac{29}{12}$
$\frac{67}{8}$

Explanation

Correct Answer:

$\frac{67}{8}$

Explanation:

$3 \frac{3}{12} + 5 \frac{1}{8} = 3 \frac{1}{4} + 5 \frac{1}{8}$

= $3 \frac{2}{8} + 5 \frac{1}{8}$

= $8 \frac{3}{8}$

= $\frac{67}{8}$

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.

Simplify $\frac{5 \times 10^{2}}{2 \times 10^{5}}$

2.5 × 10³
2.5 × 10^-3
2.5 × 10⁷
2.5 × 10^-7

Explanation

Explanation
First divide the coefficients: 5/2 = 2.5. Next apply the laws of exponents by subtracting the exponents when dividing powers of ten: 10² ÷ 10⁵ = 10^2-5 = 10^-3. Combine the results to get 2.5 × 10^-3, which matches one of the answer choices.
Correct answer
2.5 × 10^-3

Which list of numbers is in order from least to greatest?

2.23565, 2.2356, 2.2359, √5
5, 2.23565, 2.2359, 2.2356
√5, 2.2359, 2.2356, 2.23565
2.2356, 2.23565, 2.2359, √5

Explanation

Correct Answer:

2.2356, 2.23565, 2.2359, √5

Explanation:

To determine the correct order from least to greatest, compare the decimal numbers and the square root of 5 (approximately 2.23607). Start with the decimals: 2.2356 is the smallest as its digits are 2.2356, followed by 2.23565 (which adds a 5 in the fifth decimal place), then 2.2359 (which has a 9 in the fourth decimal place, making it larger than the others). Next, compare these to √5 (2.23607), which is greater than 2.2359 because 2.23607 exceeds 2.2359 at the fourth decimal place. Thus, the order 2.2356, 2.23565, 2.2359, √5 is correct as it progresses from the smallest to the largest value.

Why Other Options Are Wrong:

2.23565, 2.2356, 2.2359, √5

This is incorrect because 2.2356 is listed before 2.23565, but 2.2356 is less than 2.23565 due to the additional 5 in the fifth decimal place of 2.23565. The sequence should start with the smallest number, 2.2356, making this order invalid as it reverses the correct progression.

5, 2.23565, 2.2359, 2.2356

This is incorrect because 5 is much larger than the other numbers, which are all around 2.23 to 2.24, including √5 (approximately 2.23607). Placing 5 first violates the least-to-greatest order, as it should be the last number if included, rendering this sequence incorrect.

√5, 2.2359, 2.2356, 2.23565

This is incorrect because √5 (approximately 2.23607) is greater than 2.2359, 2.2356, and 2.23565, so it should be last in the sequence. Starting with √5 places the largest value first, which contradicts the requirement for order from least to greatest.

The ratio of women to men at a certain college is 5 to 4. There are 2,480 men. What is the total population of the college?

4464
6944
3100
5580

Explanation

Explanation
The ratio shows that men represent 4 equal parts. If 4 parts equal 2,480 men, then 1 part equals 2,480 ÷ 4 = 620. Women make up 5 parts, so the number of women is 5 × 620 = 3,100. Adding men and women together gives a total population of 2,480 + 3,100 = 5,580.
Correct answer
5580

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

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.

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

$\frac{1}{1440}$

A survey of 85 college students is taken to determine participation in intramural sports. 44 students participate in soccer, 40 in basketball, and 30 in volleyball. 19 students participate in soccer and basketball, 13 in basketball and volleyball, and 11 in soccer and volleyball. 6 students participate in all 3 intramural sports.

Match the description with the correct number of students.
Answer options may be used more than once or not at all. Select your answers from the pull-down list.
The number of students who participated only in soccer
The number of students who participated in none of the 3 sports in the survey
The number of students who participated only in volleyball
The number of students who participated in both soccer and basketball, but not volleyball
The number of students who participated in both soccer and volleyball, but not basketball
The number of students who participated only in basketball

20, 8, 12, 13, 5, 14
44. 8, 12, 13, 5, 14
20, 77, 12, 13, 5, 14
20, 8, 17, 13, 5, 14

Explanation

Explanation:

The number of students who participated only in soccer is 20 since the rest who also participated in soccer participated in other games.

The number of students who participated in none of the 3 sports in the survey is 8 since in the diagram only 8 students are out of the three sets.

The number of students who participated only in volleyball is 12 since the rest who also participated in soccer participated in other games.

The number of students who participated in both soccer and basketball, but not volleyball, is 13 students.

The number of students who participated in both soccer and volleyball, but not basketball, is 5 students.

The number of students who participated only in basketball is 14 students.

Correct answer:

20, 8, 12, 13, 5, 14

Why other options are wrong:

44. 8, 12, 13, 5, 14: The first option is wrong since it assumes even players who participated in other games but still participated in soccer.

20, 77, 12, 13, 5, 14: The second option is wrong since it assumes all the players who played all sports rather than those who didn’t.

20, 8, 17, 13, 5, 14: The third option (17) is wrong since it includes both player plates who played volleyball only and those who played soccer and volleyball while the question ask only those who played volleyball only.

10.

Truncate 0.12345 to the fourth decimal place and explain your answer.

0.1235; Truncation rounds the fourth decimal place up from 4 to 5.
0.1235; Truncation leaves off digits after rounding the fourth decimal place.
0.1230; Truncation rounds the fourth decimal place from 4 to 0.
0.1234; Truncation leaves off digits past the fourth decimal place.

Explanation

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

How to Order

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