us that the estimated intercept is -106.13 and the estimated slope for X3 is 1.968. The R2-value is 0.8047‚ mean square error is 76.87. The second predictor entered into the stepwise model is X1. The estimated intercept is -127.596‚ the estimated slope for X1 is 0.3485 and the slope for X3 is 1.8232. The R2-value is 0.933 and the mean square error is 27.575. The final predictor entered is X4. The estimated intercept is -124.20‚ the estimated slope for X4 is 0.5174‚ the slope for X1 adjusts to 0.2963
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14/09/2013 Important Formulae_for website_for CAT2012 students RATIO – PROPORTION – VARIATION 1. If a : b : : c : d‚ then ad = bc 2. If a : b : : c : d‚ then a + b : b : : c + d : d 3. If a : b : : c : d‚ then a - b : b : : c - d : d 4. If a : b : : c : d‚ then a + b : a - b : : c + d : c - d 5. If then k = NUMBERS 1. a 3 + b 3 + c3 – 3abc = (a + b + c) (a 2 + b 2 + c2 – ab – bc – ca) 2. The product of n consecutive integers is always divisible by n! (n factorial) 3. The sum
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symmetry: The vertical line that passes through the vertex is called the axis of symmetry. Every parabola is symmetrical about its axis of symmetry. Axis of symmetry are the x value of the vertex. Axis of symmetry can be obtained through the following formula: x=- b/2a Symmetry is a very important mathematical concept. Symmetry is vital in the construction or designing of different applications including roller coasters. As Dobre and Daniel state in their paper on symmetry‚ engineers design machines
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Tutorial 11 A11.1 Data on manatee deaths due to powerboats was used to construct a linear regression model relating these deaths to the number of registered powerboats. Year 1977 1978 1979 1980 1981 1982 1983 Power boats (thousands) 447 460 481 498 513 512 526 Manatee Deaths 13 21 24 16 24 20 15 Year 1984 1985 1986 1987 1988 1989 1990 Power boats (thousands) 559 585 614 645 675 711 719 Manatee Deaths 34 33 33 39 43 50 47 The
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3√x y = 6 x3/2 = 16 Slope-Intercept Form The most common form is the slopeintercept equation of a straight line : http://www.mathsisfun.com/algebra/linear-equations.html 2/6 2014/9/16 Linear Equations Slope (or Gradient) Y Intercept Example: y = 2x + 1 (Our example from the top‚ which is in SlopeIntercept form) Slope: m = 2 Intercept: b = 1 Play With It ! You can see the effect of different values of m and b at Explore the Straight Line Graph Point-Slope Form Another common one is the
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the volume formula {fig.1} for a cylinder. Fig.1 Formula for the volume of a
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points is (5‚ - 5) and (4‚ 1). Equation of a line =? We know that‚ the equation of line is y = mx + c. m = slope‚ c = y-intercept. To find the equation of line‚ find out the m – slope and y-intercept values. Given points are (5‚- 5) and (4‚ 1). (x1‚ y1) is (5‚- 5) (x2‚ y2) is (4‚ 1) Slope m = (y2 - y1)/(x2 - x1) = (1 - (-5)) / (4 -5) = (1 + 5) / (-1) = 6 / (-1) Slope m = -6 Here we are. You’re actually going to take on your mathematics essay‚ you brave soul. You’ll want to
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2) b. 2(x - 3)(x - 4) or (2x - 3)(x - 4) Discriminant • Quadratic formula: If ax2 + bx + c‚ a ≠ 0‚ x = • The value contained in the square root of the quadratic formula is called the discriminant‚ and is often represented by ∆ = b2 – 4ac. * b2 – 4ac > 0 → There are 2 roots x1‚2= * b2 – 4ac = 0 * b2 – 4ac < 0 → → There is 1 real root‚ x = -b/2a. There are no real roots. . Using Quadratic Formula • A general formula for solving
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1. A line passes through the points (–3‚ –3) and (–1‚ 3). What is the slope of the line that passes through the two points? Hint X -3 -1/3 3 1/3 2. A line passes through the points (3‚ –4) and (7‚ 12). What is the y-intercept of the line? Hint X (0‚ 4) (4‚ 0) (0‚ –16) (–16‚ 0) 3. Consider the following system of equations. y = 8x - 8 y - 8x = 7 What can you conclude about the system of equations? Hint X The system of equations is inconsistent. The system
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of Y must be Response: 40 * Edit Question 5 Let I be the income of the consumer‚ Px be the price of good x and Py be the price of good y. If good is measured along the horizontal axis and good is measured along the vertical axis‚ then the “ -intercept” measures the maximum amount of good that the consumer can afford‚ which can be expressed as Response: Px/Py * Edit Question 6 Suppose a consumer has an income equal to I which he/she spends on either food or clothing. The price of food is given
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