Write 63 As An Equivalent Decimal Point Number

Write 63 As An Equivalent Decimal Points 163 0063

Engaging with basic mathematical conversions and solving various algebraic expressions is essential for developing quantitative literacy. The tasks above involve converting whole numbers to decimal forms, percentages to decimals, decimals to fractions, and solving algebraic equations including linear and quadratic forms. These exercises encompass foundational skills necessary for more advanced mathematical understanding and practical applications in everyday contexts, such as calculating percentages, proportions, and profit margins.

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The initial question asks to express the number 63 as a decimal. Since 63 is a whole number, its equivalent decimal form is simply 63.0, which indicates the decimal point followed by zero, reaffirming the value's integrity across different formats. Understanding that whole numbers can be represented with a decimal point and trailing zeros is fundamental in fields like finance, engineering, and data analysis, where uniform formatting of numerical data is crucial.

Next, converting a percentage to a decimal involves dividing the percentage value by 100. For example, 6.3% as a decimal is 0.063. This conversion is vital in financial calculations, probability, and statistical data analysis, where percentages often need to be represented in decimal form to perform operations like multiplication or to input into formulas.

Similarly, converting a decimal to a percentage entails multiplying the decimal by 100. For instance, 0.382 as a percentage is 38.2%. Precise conversion between these forms supports numerous practical applications, including setting recipes, adjusting financial figures, and interpreting statistical data.

Calculating what percentage one number is of another involves dividing the part by the whole and multiplying by 100. In the case of finding what percent of 60 is 15, we compute (15/60) × 100 = 25%. This skill is useful in budgeting, assessing proportions, and understanding statistical relationships.

The addition of fractions, such as (-1/3) + (-5/6), necessitates finding common denominators. The sum, after converting to a common denominator, results in -7/6. Mastery of fraction operations underpins most algebraic manipulations, and it's essential for solving equations and understanding ratios.

Subtracting numerical expressions, such as 32 – 22 and 52 – 42, yields straightforward results: 10 and 10, respectively. When expressed as decimals, these are 10.0. Recognizing simple differences forms the basis for more complex operations like derivatives, integrals, and modeling real-world phenomena.

Evaluating quadratic expressions, such as -8x² + 7x – 1 for x = -2, involves substituting the value of x and performing the arithmetic operations. The calculation yields 1.0, demonstrating the importance of substituting values correctly and performing order of operations accurately.

Given a linear function F(x) = 7.50x – 20, calculating F(1000) involves substituting x with 1000, resulting in F(1000) = 7,500 – 20 = 7,480. Such evaluations assist in forecasting, cost analysis, and predicting outcomes based on linear models.

The compound interest formula A = P(1 + r/k)ⁿ is essential in finance. Substituting P=2000, r=0.06, k=365, and n=365 yields A ≈ 2,123.66, demonstrating how investment growth is modeled over time, with significance in savings and loan calculations.

Solving for x in linear equations like x – 15 = 200 involves straightforward algebraic manipulation: x = 200 + 15 = 215. Such skills are fundamental in solving practical problems involving unknown quantities.

Calculating salary increases is a typical application of percentage increase calculations. For Sam earning $31,400, a 4% raise results in a new salary of approximately $32,656, demonstrating how percentage increases influence earnings.

Estimating the number of defective bulbs in a larger batch based on a known defect rate involves setting up a proportion: (7/42) = (x/2,682), giving an estimated 451 defective bulbs out of 2,682. Proportional reasoning supports quality control and production planning.

Solving for x in x – 7/5 = 2 entails isolating x: x = 2 + 7/5 = 2 + 1.4 = 3.4, or simplified as x=17/5 if precision is kept as a fraction.

Addressing inequalities like 8 - 3x -5. Such inequalities are central in optimization and decision-making processes.

The slope of the line given by 3x + 5y = 16 is calculated by rewriting in slope-intercept form: y = (-3/5)x + 16/5, yielding a slope of -3/5. Understanding slope helps interpret the rate of change between variables.

The characteristics of the line y=2x - 3 include a slope of 2 and a y-intercept at (0, -3). Recognizing these allows graphing and analysis of linear relationships.

Deriving the equation of a line passing through points (0, 9) and (-3, 0) involves calculating the slope: (0 - 9)/(-3 - 0) = 3, and then applying point-slope form to find the line's equation: y=3x+9.

Graphing the equation 4x - y = -4 involves converting it to slope-intercept form and plotting the line based on calculated slope and intercepts.

Finding the x-coordinate of intersection between y=x-6 and y=3x-14 involves solving x - 6 = 3x - 14, which simplifies to x=4, indicating the intersection point occurs at x=4.

The profit function P(x) = 10x - 2000 models profit based on quantity sold. To generate a $63,000 profit, set P(x)=63000 and solve for x: 10x - 2000=63000, resulting in x=6500. This demonstrates the calculation of required sales volume to meet profit goals.

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