Ratios, Proportions, and Basic Finance

Questions and Answers

What is the ratio of boys to girls in a class of 28 students with 13 boys and 15 girls?

13:15 (correct)

15:28

15:13

28:13

If a consumer makes a $400 down payment on a television that costs $1,570, how many months will it take to pay off the television with monthly payments of $100?

14 months

15 months

12 months (correct)

10 months

How many rooms are in a pediatric unit with 165 beds if each room holds 3 beds?

55 rooms

What is the length of a rectangle with a width of 4 inches and an area of 32 in²?

8 inches Signup and view all the answers

What is the net annual salary of an employee who withholds $468 from her gross paycheck of $2,350 each month?

$22,584 Signup and view all the answers

What is the solution to the equation -9(k-17)=-54?

23 Signup and view all the answers

Round the value 1782.96471 to the hundredths place.

1,782.96 Signup and view all the answers

What is the fractional representation equivalent to 0.897?

897/1000 Signup and view all the answers

What is the best decimal approximation for the positive square root of 7?

2.6 Signup and view all the answers

Simplify the expression 5/7 - 2/9.

31/63 Signup and view all the answers

What is the simplified value of (1/2)(10t) if it equals 50,000?

10,000 Signup and view all the answers

What percentage of students are enrolled in German if there are 1,020 students total, 269 in French, and 663 in Spanish?

65 Signup and view all the answers

If an investor owns 50 shares of stock worth $15.30 per share, how much money will he have if he cashes half of the shares?

$382.50 Signup and view all the answers

What is a good estimate of the length of a standard bed pillow?

0.5m Signup and view all the answers

What is the ratio of the width to length of a rectangle that is equivalent to 1:3?

21:63 Signup and view all the answers

Which equation represents 'five less than a number is greater than twenty'?

5-x>20 Signup and view all the answers

How many milliliters does a glass that holds 0.5 liters hold?

500ml Signup and view all the answers

Using the fractions (3/7), (2/5), (1/2), and (1/3), which number is the least?

1/3 Signup and view all the answers

Simplify the expression 4(1/6) + 1(1/3). Which of the following is correct?

41/2 Signup and view all the answers

How many runners completed a race in less than two hours if 548 runners participated and 26 did not finish?

261 Signup and view all the answers

Convert 95°F to degrees Celsius using the formula C=(5/9)(F-32).

35 C Signup and view all the answers

How many bags of sugar are needed for 300 people if a recipe for 50 people calls for 4 cups of sugar and each bag contains 6 cups?

4 bags Signup and view all the answers

How tall is a tree that casts a shadow of 12 meters if a vertical 1-meter stick casts a shadow of 0.4 meters?

30 m Signup and view all the answers

What is 27% of 54?

14.58 Signup and view all the answers

What is the discount percent of a textbook that is originally priced at $107.00 with a discount of $62.10?

45% Signup and view all the answers

If 0.0025 of all products in a factory contain defects, what percentage does this represent?

0.25% Signup and view all the answers

What is the simplified form of the expression (2x + 5)(4x-7)?

8x^2 + 6 - 35 Signup and view all the answers

What is the appropriate unit of measure for the mass of a pencil?

gram Signup and view all the answers

Which expression represents a rectangle where the length is 3 units greater than its width?

2w+2(w+3) Signup and view all the answers

Which equation represents the number of bicycles (x) in terms of snowmobiles (y) if x is 4 or more than 3 times y?

x=3y+4 Signup and view all the answers

What is the correct comparison of the two rational numbers 0.6 and 4/7?

0.6 > 4/7 Signup and view all the answers

Which fractional representations are equivalent to 1/4 and 2/5?

5/20, 8/20 Signup and view all the answers

How many survey respondents preferred white or red cars based on a survey of automobile color preference?

12 Signup and view all the answers

What is the student’s wage increase percentage if it goes from $12 per hour to $13.50 per hour?

12.5% Signup and view all the answers

Which number could be rounded to 12.9?

12.939 Signup and view all the answers

What percent is equivalent to 31/50?

62% Signup and view all the answers

How far does a patient drive round trip if they drive 19 miles one way for treatment over 22 days?

836 miles Signup and view all the answers

What is the simplification of the expression presented?

4 33/40 Signup and view all the answers

What is the independent variable in calorie expenditure while cycling?

speed Signup and view all the answers

How many more dimes does a child have than quarters if they have twice as many quarters as pennies and four times as many nickels and five times as many dimes as pennies?

10 times as many Signup and view all the answers

Which equation represents 'seven more than twice a number is equal to twenty-one'?

7 + 2x = 21 Signup and view all the answers

What is the simplified form of 2/7 + 3/5?

31/55 Signup and view all the answers

Study Notes

Ratios and Proportions

Ratio of boys to girls in a classroom with 13 boys and 15 girls is 13:15.
Width to length ratio of a rectangle can be expressed equivalently, for example, 1:3 is equivalent to 21:63.

Finance and Payments

A consumer pays a $400 down payment on a $1,570 television, resulting in 12 months of payments at $100 each.
A consumer's net annual salary is calculated at $22,584 after withholding $468 from a gross paycheck of $2,350 monthly.
A 20% down payment on a $20,000 house amounts to $4,000.

Measurements and conversions

1 meter is equivalent to 1,000 milliliters, so a 0.5L glass holds 500ml.
A bucket that can hold 3L can also hold 3,000ml.
95°F converts to approximately 35°C using the formula C=(5/9)(F-32).

Geometry and Area

A rectangle with a width of 4 inches and an area of 32 in² has a length of 8 inches.
The area of a basketball court is stated as 4,700 square feet.

Algebra and Equations

The equation -9(k-17)=-54 resolves to k=23.
The expression (½)(10t)=50,000 simplifies to t=10,000.
An equation expressing "seven more than twice a number is equal to twenty-one" is represented as 2x + 7 = 21.

Fractions and Decimals

5/7 - 2/9 simplifies to 31/63.
The decimal 0.897 is equivalent to the fraction 897/1000.
The best decimal approximation for the positive square root of 7 is 2.6.

Percentages and Statistics

In a high school with 1,020 students, if 663 are enrolled in Spanish and 269 in French, about 65% are enrolled in German.
The percentage discount for a textbook originally priced at $107, discounted to $62.10, is 45%.

Data Analysis and Problem Solving

In a race with 548 runners, 26 did not finish, with half of those who finished completing in less than two hours, resulting in 261 runners under two hours.
A customer who tips 8% leaving a $3.70 tip indicates a bill of approximately $46.25 before the tip.

Time and Rates

A child performs a daily task, and if she reads 15 pages in 10 minutes, it will take her 30 minutes to read 45 pages.
The average cooling rate of pasta salad dropping from 86°F to 38°F over 9 hours is approximately 5.33°F per hour.

Miscellaneous Calculations

An investor with 50 shares at $15.30 per share would receive $382.50 when cashing half of them.
If the length of a rectangular garden is 3 units greater than its width, represented by the expression 2w+2(w+3), indicates a relationship between width (w) and length.

Simplifications and Approximations

Simplifying the expression ( (x+3)(2x^2-3x+4) ) results in ( 2x^3 + 3x^2 - 5x + 12 ).
The expression ( \frac{6+9}{6 \times 9} ) simplifies down to ( \frac{5}{18} ).

These notes encapsulate the diverse math concepts and problem-solving strategies presented, providing a reference for key figures and equations.

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Description

This quiz covers various topics including ratios and proportions, basic finance calculations including down payments and salary deductions, measurement conversions, geometry for area calculations, and algebraic equations. Test your understanding and application of these fundamental concepts.