How do you solve for x in the equation 5x + 12 = 37?To solve for x in the equation 5x + 12 = 37, first subtract 12 from both sides to get 5x = 25. Then, divide both sides by 5 to find x = 5.
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How can you use a chi-square test to determine whether there is a significant association between categorical variables in a contingency table?
How can you use a chi-square test to determine whether there is a significant association between categorical variables in a contingency table?To use a chi-square test to determine if there is a significant association between categorical variables in a contingency table, follow these steps: (1) Formulate the null and alternative hypotheses. (2) Calculate the expected frequencies for each cell. (3) Compute the chi-square statistic using the formula χ² = Σ[(O-E)²/E], where O is the observed frequency and E is the expected frequency. (4) Determine the degrees of freedom (df) as (rows-1)*(columns-1). (5) Compare the chi-square statistic to the critical value from the chi-square distribution table at the desired significance level. If the calculated χ² exceeds the critical value, reject the null hypothesis, indicating a significant association.
How do you find the domain and range of a function in precalculus?
How do you find the domain and range of a function in precalculus?To find the domain of a function, determine all possible input values (x-values) that do not cause division by zero or other undefined operations. The range is the set of all possible output values (y-values) that result from using the domain values. Analyze the function’s behavior, considering restrictions like square roots, logarithms, and rational expressions.
How do you prove that the sum of the interior angles of a triangle equals 180 degrees using parallel lines and transversals?
How do you prove that the sum of the interior angles of a triangle equals 180 degrees using parallel lines and transversals?To prove the sum of the interior angles of a triangle equals 180 degrees using parallel lines and transversals, extend one side of the triangle and draw a line parallel to the opposite side through the third vertex. The alternate interior angles formed are congruent to the triangle’s angles, and the linear pair formed with the exterior angle sums to 180 degrees.
How do you solve a quadratic equation using the quadratic formula?
How do you solve a quadratic equation using the quadratic formula?To solve a quadratic equation using the quadratic formula, follow these steps: For a quadratic equation in the form ax^2 + bx + c = 0, the quadratic formula is x = (-b ± √(b² – 4ac)) / (2a). Substitute the values of a, b, and c into the formula, then calculate the discriminant (b² – 4ac). Finally, solve for x by completing the operations indicated in the formula.
How do you find the vertex of a parabola given in standard form?
How do you find the vertex of a parabola given in standard form?To find the vertex of a parabola in standard form y = ax^2 + bx + c, use the vertex formula: x = -b/(2a). Substitute this x-value back into the equation to find the y-coordinate. The vertex is at (x, y).
How do you find the derivative of a function using the chain rule when dealing with composite functions?
How do you find the derivative of a function using the chain rule when dealing with composite functions?To find the derivative of a composite function using the chain rule, identify the outer function f(u) and the inner function u=g(x). The chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x). Differentiate the outer function with respect to the inner function, then multiply by the derivative of the inner function.
Prove that the sum of the interior angles of a regular polygon can be calculated with the formula (n-2)×180°, where n is the number of sides.
Prove that the sum of the interior angles of a regular polygon can be calculated with the formula (n-2)×180°, where n is the number of sides.To prove that the sum of the interior angles of a regular polygon is (n-2)×180°, consider dividing the polygon into (n-2) triangles. Each triangle has an angle sum of 180°. Thus, the total interior angle sum is (n-2)×180°.
What is the difference between the derivative and the integral of a function?
What is the difference between the derivative and the integral of a function?The derivative of a function measures the rate at which the function’s value changes with respect to a change in its input value, often interpreted as the slope of the function. The integral of a function, on the other hand, measures the total accumulation of the function’s values over an interval, often interpreted as the area under the curve of the function. While the derivative focuses on local behavior and instantaneous rates of change, the integral focuses on global behavior and cumulative quantities.
How do you calculate the height of a triangle given its base length and area?
How do you calculate the height of a triangle given its base length and area?To calculate the height of a triangle given its base length and area, use the formula: height = (2 * area) / base. This formula derives from the basic area formula for a triangle, which is area = 0.5 * base * height. Rearrange it to solve for height.
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