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The reserve ratio is a crucial aspect of banking that determines how much money a bank must keep on hand compared to its total deposits. In this case, if a bank has a reserve ratio of 10% and total deposits amounting to $2000, we can calculate the reserves using a simple formula. The formula to … Read more

To find the sum of a geometric sequence, we first need to identify the first term and the common ratio. In the sequence you provided: First term (a) = 3 Second term = 15 Third term = 75 Now, we can find the common ratio (r). The common ratio can be found by dividing any … Read more

To solve the second-order differential equation y – 36y” = 0, we start by rewriting the equation in standard form: y” – rac{1}{36}y = 0 This is a linear homogeneous differential equation with constant coefficients. To solve it, we’ll assume a solution of the form: y(t) = e^{rt} where r is a constant that we … Read more

To solve the problem, we first need to determine the function values using the definitions provided: Given the function f(x) = x2 + 1, we can find f(10): f(10) = 102 + 1 = 100 + 1 = 101 Next, we have the second function g(x) = x + 4. However, we don’t need to … Read more

To find the value of y in the equation 5y = 12, we first need to isolate y. This involves using logarithms, which can help us solve equations involving an exponent. Starting with the equation: 5y = 12 To solve for y, we can express the equation in logarithmic form. First, we divide both sides … Read more

To convert the equation 3x + 10y = 7 into slope-intercept form, which is defined as y = mx + b (where m is the slope and b is the y-intercept), follow these steps: Start with the original equation: 3x + 10y = 7. Subtract 3x from both sides to isolate the term with y: … Read more

To determine the percentage discount offered on an item, you can use the following formula: Percentage Discount = (Discount Amount / Retail Price) × 100 In this case, the item has a retail price of $475 and a discount amount of $45. Now, let’s plug these values into the formula: Discount Amount = $45 Retail … Read more

The statement “if x = 3 and 3 = y, then x = y” illustrates the algebraic property known as the transitive property of equality. The transitive property states that if one quantity is equal to a second quantity, and that second quantity is equal to a third quantity, then the first quantity is also … Read more