Math Flashcards

If a truck travels 360 kilometers in 5 hours, how far will it travel in 9 hours if the same speed is maintained?

Answer: 648

To solve this, first calculate the truck's speed: 360 kilometers / 5 hours = 72 kilometers per hour. Then, multiply this constant speed by the new time to find the distance: 72 km/hour * 9 hours = 648 kilometers. Thus, the truck will travel 648 kilometers in 9 hours.

What is equivalent to 3x(2 + 5y)?

Answer: 6x + 15xy

To simplify the expression 3x(2 + 5y), apply the distributive property by multiplying 3x by each term inside the parentheses. This yields (3x * 2) + (3x * 5y), which simplifies to 6x + 15xy. This is the equivalent expression.

A box contains four yellow marbles and eight blue marbles. What is the probability that Emma will choose a yellow marble at random from the box?

Answer: 1/3

To find the probability, first determine the total number of marbles: 4 yellow + 8 blue = 12 marbles. The number of favorable outcomes (choosing a yellow marble) is 4. The probability is then the number of yellow marbles divided by the total number of marbles: 4/12, which simplifies to 1/3.

Jennie wants to paint a room's walls. She is aware that each can of paint holds one gallon. A half gallon of paint will completely cover a 55 square foot wall. The room's four walls are each 10 feet tall. Two of the walls are 10 feet wide, while the other two are 15 feet wide. How many 1-gallon buckets of paint does Jennie need to paint the entire room?

Answer: 5

First, calculate the total wall area: (2 walls * 10ft * 10ft) + (2 walls * 10ft * 15ft) = 200 sq ft + 300 sq ft = 500 sq ft. Since a half gallon covers 55 sq ft, one gallon covers 110 sq ft. To cover 500 sq ft, Jennie needs 500 sq ft / 110 sq ft/gallon = 4.54 gallons. As paint is sold in whole gallons, she must purchase 5 gallons.

What was Jelly's tip percentage if she left a $10.16 tip on a breakfast that cost $86.89?

Answer: 12%

To calculate the tip percentage, divide the tip amount by the original cost of the breakfast and then multiply by 100. So, ($10.16 / $86.89) * 100% = 0.1169 * 100% ≈ 11.69%. Rounded to the nearest whole percent, Jelly's tip percentage was 12%.

Factor: 4y(3x + 2) − 2(3x + 2)

Answer: (4y − 2)(3x + 2)

The expression 4y(3x + 2) − 2(3x + 2) has a common binomial factor, (3x + 2). To factor it, pull out this common factor, leaving the remaining terms (4y - 2) in another set of parentheses. This results in the factored form (4y − 2)(3x + 2).

Robert makes $8.10 per hour and works 40 hours per week. John's hourly wage is $10.80. How many hours would John have to work to earn the same as Robert over 40 hours?

Answer: 30

First, calculate Robert's total earnings for 40 hours: $8.10/hour * 40 hours = $324.00. To find out how many hours John needs to work to earn the same amount, divide Robert's total earnings by John's hourly wage: $324.00 / $10.80/hour = 30 hours. Therefore, John would have to work 30 hours.

Angel was three times Brian's age five years ago. How old is Angel now that Brian is 10 years old?

Answer: 20

If Brian is currently 10 years old, then five years ago, Brian was 10 - 5 = 5 years old. At that time, Angel was three times Brian's age, meaning Angel was 3 * 5 = 15 years old. To find Angel's current age, add 5 years to her age from five years ago: 15 + 5 = 20 years old.

How many outfit combinations are possible with six shirts, three slacks, and five ties?

Answer: 90

To find the total number of possible outfit combinations, multiply the number of choices for each item. With 6 shirts, 3 slacks, and 5 ties, the total combinations are 6 * 3 * 5 = 90. This is a fundamental principle of counting in probability.

A circular form with no beginning or end.

Answer: Circle

A circle is a fundamental geometric shape defined as a set of all points in a plane that are equidistant from a central point. It is characterized by its continuous, round form with no distinct beginning or end, fitting the description perfectly.

A triangle with one right angle and two acute angles.

Answer: right triangle

A right triangle is a specific type of triangle that is defined by having one interior angle that measures exactly 90 degrees. The other two angles in a right triangle must be acute, meaning they are each less than 90 degrees.

An angle produced by connecting lines that has two opposite congruent angles.

Answer: vertical angles

Vertical angles are a pair of non-adjacent angles formed when two straight lines intersect. A key property of vertical angles is that they are always congruent, meaning they have equal measures. This definition accurately describes vertical angles.

A dot-based graphical representation of data.

Answer: Dot plot

A dot plot is a simple graphical display of data where each data point is represented by a dot placed above a number line or category axis. It is used to quickly visualize the distribution, clustering, and outliers within a dataset.

Finding which prime numbers multiply together to make the original number.

Answer: Prime Factorization

Prime factorization is a fundamental concept in number theory. It is the process of breaking down a composite number into its prime factors, which are prime numbers that multiply together to produce the original number. This method helps in understanding the unique building blocks of any given integer.

The side of a right triangle opposite the right angle.

Answer: Hypotenuse

In a right triangle, the hypotenuse is defined as the side that is directly opposite the right (90-degree) angle. It is always the longest side of the triangle. This term is crucial for understanding the properties of right triangles, especially in relation to the Pythagorean theorem.

less than 90 degrees

Answer: Acute angle

An acute angle is a basic geometric classification for an angle that measures less than 90 degrees. This distinguishes it from a right angle (exactly 90 degrees) and an obtuse angle (greater than 90 degrees but less than 180 degrees). Understanding these classifications is foundational in geometry.