MATH C277: Finite Mathematics

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Free MATH C277: Finite Mathematics Questions

Simplify the expression using the order of operations:
$10^{2} + 100 \div 5^{2} \times (- 2)$

Explanation

Correct Answer:

92

Explanation:

Using BODMAS

100 ÷ 5² = 100÷25 = 4

Next multiplication:

4 × (-2) = - 8

Finally:

102 + (-8) = 100 -8 = 92

Why Other Options Are Wrong:

0

This would result only if all terms cancel out, which they don’t.

100

This would be the result if the negative term were ignored.

108

This would occur if the multiplication was treated as positive (i.e., 4×2 instead of −2).

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.

Simplify the expression:
$\frac{\frac{\frac{2.4 \times 10^{- 7}}{8.0 \times 10^{- 7}}}{3.0 \times 10^{9}}}{6.0 \times 10^{- 3}}$

6.0 × 10³
6.0 × 10⁻¹³
1.5 × 10⁻¹³
1.5 × 10³

Explanation

Correct Answer:

6.0 × 10⁻¹³

Explanation:

Begin by simplifying the first part of the expression (the numerator):

$\frac{2.4 \times 10^{- 7}}{8.0 \times 10^{- 7}}$

$(2.4 \div 8.0) \times 10^{- 7 - (- 7)} = 0.3$

Next, simplify the second part (the denominator):

$\frac{3.0 \times 10^{9}}{6.0 \times 10^{- 3}}$

$(3.0 \div 6.0) \times 10^{9 - (- 3)} = 0.5 \times 10^{12}$

Now divide the simplified parts:

$\frac{0.3}{0.5 \times 10^{12}} = (\frac{0.3}{0.5}) \times 10^{12}$

$0.6 \times 10^{- 12} = 6 \times 10^{- 13}$

$6 \times 10^{- 13}$

Thus, the simplified expression is 6.0 × 10⁻¹³.

Why Other Options Are Wrong:

6.0 × 10³

This represents a very large number, which contradicts the result of dividing very small numbers by very large numbers. The actual operation yields a small value due to negative exponents, not a large one.

1.5 × 10⁻¹³

This value suggests a miscalculation in the base coefficient. The correct simplified result comes from 0.3 ÷ 0.5 = 0.6, not 1.5. The exponent may be close, but the base number is incorrect.

1.5 × 10³

This is incorrect both in magnitude and exponent direction. The correct simplification results in a very small number (negative exponent), not a large positive one. It also shows an incorrect coefficient of 1.5 instead of the accurate 0.6.

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.

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.

Which of the following are equivalent form of $\frac{22}{7}$ .

3.14
π
$3 \frac{1}{7}$
$2 \frac{11}{7}$
$1 \frac{15}{7}$
$\frac{- 1}{\frac{- 7}{22}}$

Explanation

Correct Answer:

$3 \frac{1}{7}$

$1 \frac{15}{7}$

$\frac{- 1}{\frac{- 7}{22}}$

Explanation:

To determine equivalent forms of $\frac{22}{7}$ , we evaluate each option:

$3 \frac{1}{7}$ is a mixed number equivalent to $\frac{22}{7}$ since 3 × 7 + 1= 22, and $\frac{22}{7}$ = $\frac{22}{7}$ .

$1 \frac{15}{7}$ equals $\frac{7 + 15}{7} = \frac{22}{7}$ , so it is also equivalent.

$\frac{- 1}{\frac{- 7}{22}} = \frac{22}{7}$ after simplifying double negatives and dividing by a fraction.

Why Other Options Are Wrong:

3.14

This is a rounded decimal approximation of π ≈ 3.1416, while $\frac{22}{7}$ ≠3.142 but ≈ 3.142 Meaning approximately. Although close, it isnot exactly equal to $\frac{22}{7}$ .

π

$\frac{22}{7}$ is a common approximation of π, but π is an irrational number with a non-repeating, infinite decimal expansion. Therefore, they are not exactly equal.

$2 \frac{11}{7}$

This mixed number equals $\frac{25}{7}$ , which is greater than $\frac{22}{7}$ and therefore not an equivalent form.

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.

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.

10.

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.

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MATH C277: Finite Mathematics

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