Podcast
Questions and Answers
Which of the following numbers is not an integer?
Which of the following numbers is not an integer?
- 5
- 1/3 (correct)
- 3
- 1
The sum of 1/30 and 1/20 is?
The sum of 1/30 and 1/20 is?
1/12
What is 40% of 200?
What is 40% of 200?
80
18 is what percent of 90?
18 is what percent of 90?
What is the correct conversion of 8.6 dg to hg?
What is the correct conversion of 8.6 dg to hg?
What is the correct conversion of 60 c to qt?
What is the correct conversion of 60 c to qt?
What is 5,800,000 written in scientific notation?
What is 5,800,000 written in scientific notation?
When simplified, what is (82-16) = 8 - 2 + 1 × 3?
When simplified, what is (82-16) = 8 - 2 + 1 × 3?
What is the simplified product of 3 bu. 2 pk. and 5?
What is the simplified product of 3 bu. 2 pk. and 5?
The next term in the geometric sequence 4, -12, 36, -108 is?
The next term in the geometric sequence 4, -12, 36, -108 is?
When a = -1 and c = 4, what is the value of 4ac + 5c squared?
When a = -1 and c = 4, what is the value of 4ac + 5c squared?
Which expression correctly represents the phrase '5 less than x'?
Which expression correctly represents the phrase '5 less than x'?
Which is a pair of angles that share a common vertex and side between them?
Which is a pair of angles that share a common vertex and side between them?
Any polygon that has ten sides is a(n)?
Any polygon that has ten sides is a(n)?
Any parallelogram with all sides equal is a?
Any parallelogram with all sides equal is a?
From which situations can an infinite number of triangles be formed?
From which situations can an infinite number of triangles be formed?
The area between a central angle and its intercepted arc is a(n)?
The area between a central angle and its intercepted arc is a(n)?
Which polyhedron has two faces that are congruent and parallel?
Which polyhedron has two faces that are congruent and parallel?
Which three-dimensional figure is shaped like a donut?
Which three-dimensional figure is shaped like a donut?
A net made only of triangles is a?
A net made only of triangles is a?
The formula used to find the area of a circle is?
The formula used to find the area of a circle is?
Surface area of this figure is?
Surface area of this figure is?
The volume of a cube with an edge of 8 m is?
The volume of a cube with an edge of 8 m is?
The volume of a sphere with a radius of 3 cm is approximately?
The volume of a sphere with a radius of 3 cm is approximately?
The lateral surface area of the figure is approximately?
The lateral surface area of the figure is approximately?
What is the area of a trapezoid?
What is the area of a trapezoid?
What is the surface area of a square pyramid?
What is the surface area of a square pyramid?
What is the volume of a square pyramid?
What is the volume of a square pyramid?
What is the volume of a cone?
What is the volume of a cone?
What is the volume of a sphere?
What is the volume of a sphere?
What is 45 - 10 1/3?
What is 45 - 10 1/3?
Solve for X: X/8 = 10/25.
Solve for X: X/8 = 10/25.
What is -2 + (-6)?
What is -2 + (-6)?
What is -7 - (-13)?
What is -7 - (-13)?
What is 12(-4)?
What is 12(-4)?
-15 divided by -3 equals?
-15 divided by -3 equals?
Solve for X: 5x = 45.
Solve for X: 5x = 45.
Solve for X: 3x + 2 = 10 × -5.
Solve for X: 3x + 2 = 10 × -5.
Solve the inequality: -4x + 3 ≥ -9.
Solve the inequality: -4x + 3 ≥ -9.
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Study Notes
Fractions and Decimals
- 1/3: Not an integer; it is a fraction.
- 1/12: When summed with 1/30 and 1/20, find common denominators to add fractions.
- 0.0086: Conversion from 8.6 decigrams to hectograms.
Percentages
- 80: Calculation of 40% of 200, yielding 80.
- 20%: To determine what percent 18 is of 90, calculate the ratio and convert to a percentage.
Conversions
- 15: Conversion context where 60 cups equals a certain number of quarts.
- 60 c. = _ qt.: Ratio involves conversion of cups to quarts.
Scientific Notation
- 5.8 x 10^6: Scientific notation equivalent for the number 5,800,000.
Simplification and Operations
- 7: Result of the expression (82-16) = 8 - 2 + 1 × 3 after simplification.
- 17 bu. 2 pk: Resulting product of multiplying 3 bushels and 2 pecks by 5, simplified appropriately.
Sequences and Geometry
- 324: Next term in the geometric sequence: 4, -12, 36, -108.
- 64: Calculation involving values a = -1 and c = 4, leading to a computation of 4ac + 5c².
Algebraic Representations
- X-5: Represents the phrase "5 less than x" in algebraic form.
- X=3 1/2: Solution derived from the equation X/8=10/25.
Geometric Terms
- Adjacent angles: Defined as angles sharing a common vertex and an adjacent side.
- Decagon: Polygon with ten sides.
- Rhombus: Specific type of parallelogram where all sides are equal.
- Torus: Three-dimensional shape resembling a donut.
- Prism: Polyhedron with two parallel congruent faces.
Area and Volume Formulas
- Area of a circle: Calculated using the formula πr².
- Volume of a cube: For a cube with an edge of 8 m, volume is 512 m³.
- Volume of a sphere: Approximate volume for radius of 3 cm is 113.04 cm³.
- Lateral surface area: Measure approximating 69,080 mm² of a particular figure.
- Trapezoid area formula: A = 1/2 h (b1 + b2).
- Square pyramid surface area: Calculated as 4(1/2 bh) + b².
- Square pyramid volume: Given by 1/3 b² h.
- Cone volume: Formula is 1/3 πr² h.
- Sphere volume: Calculated using 4/3 πr³.
Integer and Arithmetic Operations
- -8: Result of -2 + (-6).
- 6: Result from operations -7 - (-13).
- -48: Product of 12 and -4.
- 5: The outcome of dividing -15 by -3.
- X=9: From the equation 5x = 45, solved via multiplication.
- X=1: From the equation 3x + 2 = 10× - 5, solved for x.
Inequalities
- X less than or equal to 3: Derived from the inequality -4x + 3 ≥ -9.
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