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How many flat surfaces does a rectangular prism have?

A rectangular prism belongs to a family of shapes known as cuboids. A cuboid is any three-dimensional figure that has six sides that are all quadrilaterals. Along with rectangular prisms, square prisms and cubes are also cuboids. A special type of cuboid is the right square prism. The right square prism must have at least two faces that are square. There are many figures that can be considered right square prisms, including cubes and square prisms.

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If two vectors have unequal magnitudes, can their sum be zero?

According to Buffalo State Physics, two vectors of unequal magnitudes cannot add up to zero. If two vectors A = ax + ay and B = bx + by are added together, the sum is (ax + ay) + (bx + by). To have a magnitude of zero, it requires (ax + ay) + (bx + by) = 0x + 0y. However, this only holds true if ax = -bx and ay = -by; therefore, the magnitudes of A and B must have the same positive value.

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What does "effect size" mean?

The correlation coefficient "r" is commonly used in statistics to measure effect size because it can be used to indicate any possible relationship strength between variables. An "r" value of zero indicates that the variables have no relationship at all, while if the absolute value of "r" is 1, the variables are in perfect correlation.\nIn terms of effect size, if the absolute value of "r" is 0.1, then the variables have a small effect size. If it is 0.3, then the variables have a medium effect size. If it is 0.5, then the variables have a large effect size.

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How can you find an online dictionary of mathematics terms?

While many of the entries on Mathwords.com are only definitions of mathematical terms, several terms give a brief overview and explanation of the concepts that define the words. Some entry pages have links to mathematical topics relevant to the current entry. For example, the entry defining "arithmetic mean" provides links to other key characteristics of number sets such as median and mode.\nMany of these links are very helpful for mathematics students learning new subjects. For instance, in the calculus section, the main entry for the term "derivative" gives both a plain language and mathemat..

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What is a list of perfect square roots?

Websites and textbooks often publish perfect square-root charts. When looking at a multiplication table, the perfect squares form a diagonal line beginning at zero. Students who are familiar with their multiplication tables have the ability to recognize the perfect squares of the integers from zero to ten and the perfect square roots of numbers zero to 100.\nPerfect square roots include both positive and negative integers. Multiplying two negative numbers always produces a positive number. When the square-root symbol or radical is used, this indicates the positive square root. However, the per..

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What is the sum of two cubes?

The difference of two cubes also has a special factoring formula: a^3 - b^3 = (a - b) (a^2 + ab + b^2).\nFor example, x^3 - 8 factors to (x - 2)(x^2 + 2x + 4).\nBefore factoring, rewrite the original problem as the sum or difference of two cubes. For the example above, rewrite x^3 - 8 as x^3 - 2^3. This facilitates applying the special factoring formulas.

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What are some real life applications of the pythagorean theorem?

The Pythagorean Theorem can be usefully applied because the relationship between the lengths of the sides in any right triangle is consistent. For example, in a baseball field, if the distance between each base is known, then the shortest distance to throw the ball from first base to third base can be calculated using the Pythagorean Theorem. When purchasing a television, the size advertised refers to the length of the diagonal of the television. If an old TV was being sold, the lengths of two of its sides can be used to calculate the length of the diagonal and thereby determine the size of th..

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What is a monotonic sequence?

To establish whether or not an equation in a series is monotonic, the differential must be found. If the differential value is always decreasing (positive) or increasing (negative), then the sequence is monotonic. However, if some of the differential values are positive while others are negative, then the series is not monotonic. The sequence is most often used in probability theory as it has a limit at either the negative or positive infinity of a real number.

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What is the fourth root of 16?

Roots are usually written in mathematics using the radical symbol. Any expression that contains a radical is referred to as a radical expression. Roots are important in various theories, particularly the theory of infinite series. The origin of roots is mostly speculative, but it is believed Arabic mathematicians started to use it as early as the 13th century. The square root is the most common root operation.

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What are some ways to simplify square root problems?

Removing perfect squares from an expression containing square roots is the most common way to simplify the expression. Combine multiple square root terms to one large term, then search for the largest factors of that term that are perfect squares. For example, combining the terms in the expression sqrt(2) * sqrt(3) * sqrt(48) into a single term yields sqrt(288). Its largest factor, 144, is a perfect square of 12. Moving 12 outside the square root creates 12 * sqrt(2).

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