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The speaker verbally says "greatest common denominator," but the mathematical notation on the board is "gcd," which conventionally stands for "greatest common divisor." The context of dividing integers to find a common factor confirms that the intended concept is the greatest common divisor, and the spoken word is a verbal slip.

Conditions: The video discusses finding the common factor of two integers.; The board displays the notation gcd(a;b).; The procedure involves repeated integer division.

The speaker verbally says "greatest common denominator," but the mathematical notation on the board is "gcd," which conventionally stands for "greatest common divisor." The context of dividing integers to find a common factor confirms that the intended concept is the greatest common divisor, and the spoken word is a verbal slip.

Conditions: The video discusses finding the common factor of two integers.; The board displays the notation gcd(a;b).; The procedure involves repeated integer division.

It means that in the worst case, the algorithm's output cost is at most twice the true optimal cost.

Conditions: The problem is a minimization problem.; The algorithm is a 2-approximation.

It means that in the worst case, the algorithm's output cost is at most twice the true optimal cost.

Conditions: The problem is a minimization problem.; The algorithm is a 2-approximation.

The probability density function (PDF) for a continuous uniform distribution on the interval [a, b] is a constant value given by the formula $f(x) = \frac{1}{b - a}$. The numerator 1 represents the total probability of 100%, while the denominator $b - a$ is the length of the interval, calculated as the upper bound minus the lower bound.

Conditions: The distribution is continuous and uniform.; The random variable is defined on the closed interval [a, b].; The lower bound a is strictly less than the upper bound b.

The probability density function (PDF) for a continuous uniform distribution on the interval [a, b] is a constant value given by the formula $f(x) = \frac{1}{b - a}$. The numerator 1 represents the total probability of 100%, while the denominator $b - a$ is the length of the interval, calculated as the upper bound minus the lower bound.

Conditions: The distribution is continuous and uniform.; The random variable is defined on the closed interval [a, b].; The lower bound a is strictly less than the upper bound b.

The present value is $55,839.48. This is calculated by discounting the future value of $100,000 back 10 years using the formula$PV = $\frac{FV}{(1+r)^n}$$, where$$r = 0.06$$and$$n = 10$$.

Conditions: The future value FV is $100,000.; The annual interest rate r is 6% (0.06).; The number of periods n is 10 years.; Compounding is annual.

The present value is $55,839.48. This is calculated by discounting the future value of $100,000 back 10 years using the formula$PV = $\frac{FV}{(1+r)^n}$$, where$$r = 0.06$$and$$n = 10$$.

Conditions: The future value FV is $100,000.; The annual interest rate r is 6% (0.06).; The number of periods n is 10 years.; Compounding is annual.

The value of the definite integral from 0 to 7 is 10.5. This is obtained by summing the signed areas of the three sub-intervals created by splitting at the breakpoints: 4.5, 6, and 0.

Conditions: The function is piecewise-linear.; The integration interval is from 0 to 7.; The graph consists of regions with signed areas 4.5, 6, and 0.

The value of the definite integral from 0 to 7 is 10.5. This is obtained by summing the signed areas of the three sub-intervals created by splitting at the breakpoints: 4.5, 6, and 0.

Conditions: The function is piecewise-linear.; The integration interval is from 0 to 7.; The graph consists of regions with signed areas 4.5, 6, and 0.