1.
What is the result of 15 divided by 3 times 2 plus 5?
Answer:
20
2.
Which term describes a polygon with all sides and angles equal?
Answer:
Regular
Explanation:
A regular polygon is defined as having all sides and all angles equal. This is distinct from an equilateral polygon, which specifically refers to equal sides, and a regular shape fulfills both conditions, having equal sides and angles.
3.
Simplify: (-3)^2
Answer:
9
Explanation:
When you square a negative number, such as -3, the result is positive because a negative multiplied by a negative gives a positive. Thus, (-3) times (-3) equals 9.
4.
What is the prime factorization of 60?
Answer:
2^2 x 3 x 5
Explanation:
Divide 60 by the smallest prime number 2, giving 30. Divide 30 by 2 again, giving 15. Then divide 15 by 3, giving 5, which is a prime number. The prime factors of 60 are thus 2 squared (because 2 is used twice), 3, and 5.
5.
Calculate the area of a triangle with a base of 10 cm and a height of 14 cm.
Answer:
70 cm squared
Explanation:
The area of a triangle is found using the formula: area = (base x height) / 2. Plugging in the values, (10 x 14) / 2 equals 70. Therefore, the area is 70 square centimeters.
6.
Solve for x if 4x + 5 = 21.
Answer:
4
Explanation:
To isolate x, first subtract 5 from both sides of the equation, giving 4x = 16. Then divide both sides by 4, resulting in x = 4. This value satisfies the original equation when checked.
7.
What is the volume of a cube with side length 3 cm?
Answer:
27 cm cubed
Explanation:
The volume of a cube is calculated by raising the side length to the power of three. For a cube with side length 3 cm, the volume is 3 x 3 x 3, which equals 27 cubic centimeters.
8.
If the circumference of a circle is 31.4 cm, what is its diameter? (Use pi approximately equal to 3.14)
Answer:
10 cm
Explanation:
The formula for the circumference of a circle is pi times the diameter. Rearrange to find the diameter: diameter = circumference/pi. Thus, 31.4 / 3.14 equals 10 cm.
9.
Convert 1500 milliliters to liters.
Answer:
1.5 liters
Explanation:
Since 1000 milliliters make up one liter, to convert milliliters to liters, divide by 1000. Therefore, 1500 milliliters divided by 1000 equals 1.5 liters.
10.
What is the probability of rolling an even number on a standard six-sided die?
Answer:
1/2
Explanation:
A standard six-sided die has three even numbers: 2, 4, and 6. With six possible outcomes, the probability of rolling an even number is the number of favorable outcomes divided by the total outcomes, which is 3/6 or simplified to 1/2.