MATH C277: Finite Mathematics

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Free MATH C277: Finite Mathematics Questions

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)?

33 hours
21 hours
29 hours
25 hours

Explanation

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

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.

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(-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

Which property is illustrated?
( a(bc) = (ab)c )

Associative Property
Closure Property
Commutative Property
Distributive Property

Explanation

Explanation
The equation shows that when multiplying three numbers, the way the numbers are grouped does not change the result. In ( a(bc) ) and ( (ab)c ), the factors stay in the same order, but the grouping changes. This demonstrates that multiplication is associative, meaning parentheses can be moved without affecting the product.
Correct answer
Associative Property

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.

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.

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

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.

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:

$L . C . M (a, b) = \frac{a \times b}{GCF (a, b)}$

First, find the greatest common factor (GCF).

504 = 2³× 3² × 7

540 = 2²× 3³ ×5

GCF = 2²×3²= 36

Now calculate the LCM:

LCM = $\frac{504 \times 540}{36}$ =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.

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