Business Mathematics & Statistics #3

The equation 2x-3y=-6 is a linear equation because it is a first-degree equation in both variables x and y. The variables are not raised to any powers, and there are no products or divisions involving the variables. Therefore, it represents a straight line when graphed.

The contribution of the company on account of gratuity to the Gratuity Trust Fund is Rs 636.36. This is calculated as 4.81% of the basic salary, which is Rs 7,000. Therefore, 4.81% of Rs 7,000 is Rs 336.70. However, since the contribution is made on a monthly basis, we need to divide this amount by 12 to get the monthly contribution. So, Rs 336.70 divided by 12 is equal to Rs 28.06. Finally, we multiply this monthly contribution by 22.72 to get the yearly contribution, which is Rs 28.06 multiplied by 22.72, equal to Rs 636.36.

Series trade discounts refer to the discounts that are applied one after the other from the list price. This means that multiple discounts are deducted sequentially to calculate the final price. In contrast, inconsequential trade discounts are small discounts that have little impact on the overall price. Spontaneous trade discounts are unplanned discounts offered on the spot, while earned trade discounts are discounts given based on a customer's loyalty or volume of purchases.

Markup is an amount added to the cost price while calculating a selling price. This means that when determining the selling price of a product or service, the cost price is increased by a certain percentage or fixed amount. The markup is the additional amount that the seller includes to cover expenses, overheads, and to make a profit. By adding the markup to the cost price, the seller ensures that they can cover their costs and make a profit when selling the item.

The accumulated value can be calculated by multiplying the initial investment amount with the accumulated factor. In this case, the accumulated value would be 1500 * 15 = 22500.

The list price will be $22 because the net price of the shirt is $20 and there is a 10% discount applied. To find the list price, we can use the formula: List price = Net price / (1 - Discount). Plugging in the values, we get: List price = $20 / (1 - 0.10) = $20 / 0.90 = $22.

To find x, we need to solve the equation 3x + 7 - x = 17. Combining like terms, we get 2x + 7 = 17. Subtracting 7 from both sides, we have 2x = 10. Finally, dividing both sides by 2, we find x = 5.

An annuity refers to a sequence of payments made at equal intervals of time. It can be a series of payments made monthly, quarterly, annually, or at any other consistent interval. Annuities are commonly used in financial planning and investment strategies, such as retirement savings or insurance policies. The payments can be either fixed or variable, depending on the terms of the annuity contract. The concept of annuity helps individuals and businesses in managing their cash flow and planning for future financial needs.

To find 45% of a number, we multiply the number by 0.45. In this case, we are looking for a number that, when multiplied by 0.45, equals 9. Dividing 9 by 0.45 gives us the number 20. Therefore, the answer is 20.

The DSUM function is used to add numbers based on criteria stored in a separate range. It allows you to specify the criteria in the form of a database table and then sum up the values that meet the specified criteria. This function is specifically designed for working with databases and is commonly used in Excel to perform calculations on large sets of data.

The percentage decrease can be calculated by finding the difference between the original price and the new price, dividing it by the original price, and then multiplying by 100. In this case, the difference is Rs 255.50 - Rs 230.25 = Rs 25.25. Dividing this by the original price Rs 255.50 gives 0.0989. Multiplying by 100 gives 9.89%. Rounding it to the nearest whole number, the percentage decrease is 9.9%.

The break even point is the point at which a company's total revenue equals its total costs, resulting in no profit or loss. At this point, the company is able to cover all of its expenses, including fixed costs and variable costs, but does not generate any additional profit. It is an important metric for businesses as it helps determine the minimum level of sales or units that need to be sold in order to cover costs and start making a profit.

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The sale price is the price at which a product is sold to the customer. The markdown is the reduction in price from the original selling price. Therefore, the correct answer is "Markdown" because it represents the amount by which the selling price is reduced.

To convert a number in percent from a fraction, we multiply the fraction by 100. This is because percent is a way to express a fraction as a portion out of 100. Multiplying the fraction by 100 scales it up to be out of 100, effectively converting it into a percent.

The given question states that 4/7 of a tank can be filled in 2 minutes. To find out how many minutes it will take to fill the whole tank, we can set up a proportion. Let X represent the number of minutes it will take to fill the whole tank. The proportion can be set up as 4/7 : 2 = 1 : X. To solve for X, we can cross multiply and divide. Cross multiplying gives us 4X = 7 * 2, which simplifies to 4X = 14. Dividing both sides by 4 gives us X = 14 / 4, which simplifies to X = 3.5 minutes. Therefore, it will take 3.5 minutes to fill the whole tank.

The IF and SUM functions are used to add numbers based on multiple conditions. The IF function allows us to specify a condition and return a value if the condition is true or false. The SUM function then adds up the values that meet the specified condition. By combining these two functions, we can add numbers based on multiple conditions.

The given expression, 3x2 + 5x - 7, is a binomial. A binomial is an algebraic expression that consists of two terms connected by either addition or subtraction. In this case, the expression has two terms, 3x2 and 5x, connected by addition. Therefore, it is classified as a binomial.

Arithmetic operations such as addition, subtraction, multiplication, and division are fundamental operations in mathematics. These operations are used to perform calculations and solve mathematical problems. They provide the basis for more complex mathematical operations and concepts. Therefore, the correct answer is 5 because arithmetic operations are the foundation for all mathematical operations.

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The correct answer is FV(0.08/2, 8*4, 20000, 0, 0). This function calculates the future value of an annuity given an interest rate of 8% compounded quarterly, a total of 8*4 = 32 periods, a payment of Rs. 20,000 made at the end of each period, and no initial investment or additional contributions. By using this function, we can determine the total amount accumulated at the end of 8 years.

The taxable income of the employee is Rs. 15,000. This is because the basic salary of Rs. 12,000 and the allowances of Rs. 9,000 are added together to get a total income of Rs. 21,000. However, not all of this income is taxable. The basic salary is always fully taxable, but only a portion of the allowances are taxable. In this case, it is assumed that the entire amount of the allowances is taxable, so the taxable income is equal to the total income of Rs. 21,000 minus the non-taxable portion of the allowances, which is Rs. 6,000. Therefore, the taxable income is Rs. 15,000.

The markup rate for the golf club is 87.5%. This means that the shop is selling the club for 87.5% more than what they paid the wholesaler for it.

John has 4 more blue marbles than Ani. This is determined by finding the ratio of red marbles to blue marbles for both John and Ani. By setting up a proportion using the given information, it is found that John has 12 blue marbles and Ani has 8 blue marbles. Therefore, John has 4 more blue marbles than Ani.

The given answer "Same number" suggests that the percentage of the ratio of the given number with the standard number is equal to the given number itself. In other words, the ratio is 100%.

In order to find the product of two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Since matrix A has 3 columns, the number of columns in matrix B must be 3 in order to perform the multiplication. Therefore, the correct answer is 3.

The markup of the goods item is equal to the selling price S. This is because the cost is given to be half of the selling price. Therefore, the markup, which is the amount added to the cost to determine the selling price, is equal to the selling price itself.