Ma 104 Midterm Examination Name 905154

Ma 104 Midterm Examination Name

Describe in your own words the meaning of the term linear model. List all the elements of B that are elements of the given set. Convert the mixed number to an improper fraction. Convert the improper fraction to a mixed number. Perform the indicated operation. Where possible, reduce the answer to its lowest terms. Express the rational number as a decimal. Find the absolute value. Perform the indicated subtraction. Perform the indicated multiplication. Evaluate the exponential expression. Evaluate the following expression. Simplify. Express the decimal as a percent. Express the percent as a decimal. What number is 4% of 200? Solve: The formula P = 0.45x – 69 describes profit for a certain vendor when the vendor sells x pretzels. Evaluate the algebraic expression when x = 1000 to find the profit that the vendor makes from selling 1000 pretzels. Evaluate the expression for a = -6, b = -2, c = . Find the slope passing through the points (3, -8) and (5, -2). State whether the line is increasing, decreasing, horizontal or vertical. Determine the slope and y-intercept of the equation below. Determine whether the below listed pair of lines is parallel, perpendicular, or neither. Let y be the cooking time of a turkey that weighs x pounds. A model of the situation is: y = 0.24x + 1.64. Estimate the cooking time of a 19-pound turkey. Determine whether the ordered pair is a solution of the given equation. ( -3, 2) y = x + . Use the graph to identify the x- and y- intercepts or state that there is no x- or y-intercept.

In addition, you will need to use vernacular common to the business culture to help you to relate to your audience, while simultaneously making the memo intelligible to the audience and the audience’s culture. For this Assignment, prepare a 350–500-word persuasive memo to your supervisor requesting that your company sponsor you individually in a business writing course that is available at the local university. If you are not currently working, you may create a fictitious company, supervisor, and position for yourself. In your memo, provide your supervisor with the following: Justify taking this course; include an outline of the benefits the company will receive from your participation in such an effort — persuade your supervisor. Include the amount of money you are seeking. Specify how long the course will take you to complete, and how your time spent completing the course will impact your performance at work. Complete the funding memo as a Microsoft® Word® document. Access instructions and an example of a memo. Access the rubric with grading criteria. Save your persuasive memo in a location with a title you will remember and that includes your name. Submit your memo to the Unit 1 Assignment Dropbox. Make sure that you save a copy of the paper you submit.

Paper For Above instruction

The term "linear model" is fundamental in understanding relationships in mathematics and statistics. A linear model describes a relationship between variables where the change in one variable is proportional to the change in another. Typically represented by an equation of the form y = mx + b, where m is the slope and b is the y-intercept, linear models are widely used in fields such as economics, engineering, and social sciences to predict and analyze data trends. Essentially, they assume a constant rate of change, making them straightforward yet powerful tools for modeling real-world phenomena.

Regarding the set elements, the symbols listed (, , , , ïƒ, , ï€ï€½) are a mixture of special characters and symbols. Elements of B that belong to the given set include those which are explicitly part of the set notation or symbols. For example, if the set includes integers such as 4, 1, 0, 18, 8, 7, then elements like 4, 1, 0, 18, 8, 7 are elements of B. The symbols such as , , etc., may represent special characters but are not standard numeric or algebraic elements unless specified by context. For the purpose of clarity, elements like 4, 1, 0, 18, 8, and 7 are clearly elements of B if B is a set of integers.

Conversion of mixed numbers to improper fractions involves multiplying the whole number by the denominator and adding the numerator, then placing over the original denominator. For example, 3 2/5 becomes (3×5 + 2)/5 = 17/5. Conversely, converting an improper fraction to a mixed number involves dividing the numerator by the denominator. For instance, 17/5 becomes 3 with a remainder of 2, so 3 2/5.

Performing operations such as multiplication and division with fractions requires converting and simplifying where necessary. For example, multiplying 9/7 by 6/1 involves straightforward multiplication of numerators and denominators, giving (9×6)/(7×1) = 54/7. Reducing answers to their lowest terms entails dividing numerator and denominator by their greatest common divisor (GCD).

Expressing rational numbers as decimals can be achieved through division; for instance, 8/7 as a decimal is approximately 1.142857. The absolute value of a number, such as |-17|, is the non-negative value of the number, which is 17. Subtraction of a negative number, like 12 - (-5), becomes addition: 12 + 5 = 17. Multiplication of negative numbers, such as (-32)×(-1), yields a positive result, 32.

Evaluating exponential expressions, such as 2^5, involves calculating 2 multiplied by itself five times, resulting in 32. Similarly, other expressions are evaluated based on order of operations and exponent rules. Converting decimals to percentages involves multiplication by 100, so 0.33 becomes 33%. Conversely, converting a percentage to a decimal involves dividing by 100, so 14% becomes 0.14.

To find a percentage of a number, such as 4% of 200, multiply the number by the percentage expressed as a decimal: 200×0.04 = 8. To analyze profit, using the formula P = 0.45x – 69, substituting x = 1000 yields P = 0.45(1000) – 69 = 450 – 69 = 381. This indicates that the vendor’s profit from selling 1000 pretzels would be $381.

Evaluating an algebraic expression with different values for variables allows for understanding relationships among variables. For example, with a = -6, b = -2, c unspecified, computing specific expressions provides insight into the behavior of formulas or functions.

The slope between two points, such as (3, -8) and (5, -2), is calculated using the formula (y2 - y1)/(x2 - x1). Substituting gives (-2 - (-8))/(5 - 3) = (6)/2 = 3. Since the slope is positive, the line is increasing. The y-intercept can be determined from the equation of the line or from the graph.

Determining whether lines are parallel, perpendicular, or neither involves comparing their slopes. Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals of each other.

Modeling the cooking time of a turkey based on its weight involves using a linear model, y = 0.24x + 1.64. For a 19-pound turkey, multiplying 19 by 0.24 and adding 1.64 estimates the cooking time: y = 0.24×19 + 1.64 ≈ 4.56 + 1.64 = 6.2 hours.

To verify if a pair of points satisfies a linear equation, substitute the coordinates into the equation to see if both sides are equal. For example, substituting (-3, 2) into y = x + 5 results in 2 = -3 + 5, which is true.

The questions span a broad range of basic algebra, arithmetic, coordinate geometry, and linear modeling concepts essential for foundational mathematics coursework.

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