The difference between compound interest and simple interest for 2 years is given by SI * (r/100)^2. Setting this equal to $50 and solving gives Principal = $1200.

Rearranging the equation to y = -2/3x + 2 shows that the slope is -2/3.

To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, leading to y = 2.

'm' represents the slope of the line in the slope-intercept form of a linear equation.

'm' in the equation of a line represents the slope, which indicates the steepness and direction of the line.

The sum of the exponents in the term x^4y^3 is 4 + 3 = 7, hence n must be 7.

The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides can be calculated as 360 / 30 = 12.

Removing the first sentence would eliminate important context, weakening the argument presented.

The 6th term is given by 7 * 3^(6-1) = 7 * 243 = 1701.

The first term is 1, and the second term's reciprocal will be 1 + 2 = 3. Therefore, the second term is 1/3.

The reciprocals of the terms are 1, 3, and 1/x. The common difference is 2, so 1/x = 3 + 2 = 5, thus x = 1/5.

The first term in the arithmetic progression is 1/5, and the common difference is 2. Therefore, the second term in the harmonic progression is 1/(1/5 + 2) = 1/(2.2) = 5/11.

The reciprocals are 1/5 and 1/10. The common difference is -1/10. The fourth term's reciprocal will be 1/10 - 1/10 = 1/25, hence the fourth term is 25.

The reciprocals are 1/5 and 1/10. The common difference is -1/10. The third term's reciprocal will be 1/10 - 1/10 = 1/15, so the third term is 15.

The number of terms n can be calculated using the formula: n = (last - first) / difference + 1. Here, n = (50 - 10) / 5 + 1 = 9.

The last term can be expressed as a + (n-1)d. Here, 48 = 12 + 9d. Solving gives d = 4.

Using the formula for the nth term, a + (n-1)d = 7 + (8-1)(-2) = 7 - 14 = -7.

The nth term of an arithmetic sequence is given by a + (n-1)d. Here, a = 5, d = 3, n = 10. So, 5 + (10-1)3 = 32.

The reciprocals are 1, 2, and 3. The common difference is 2 - 1 = 1.

The reciprocals are 1, 2, and 3, which are in arithmetic progression. The next term in the sequence of reciprocals is 4, so the fourth term is 1/4.

In a harmonic progression, the reciprocals of the terms form an arithmetic progression, hence 1/a + 1/b = 1/c.

A function that is symmetric about the y-axis satisfies the property f(x) = f(-x) for all x.

A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).

Using the relation HCF * LCM = Product of the numbers, we have LCM = (24 * 36) / 12 = 72.

Using the relation HCF * LCM = Product of the numbers, we have LCM = 1000 / 5 = 200.

The product of the three numbers is equal to LCM * HCF^2. Therefore, 180 * 3^2 = 180 * 9 = 1620.

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 10 = 1200.

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 60 * 4 = 240.

The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.

The area of a rhombus can be calculated using the formula (1/2) × d1 × d2 = (1/2) × 10 × 24 = 120 cm².