Professors Han and Groman dabble in chemical engineering in their spare time. They have developed a plastics additive(S2009) that will make super balls bounce even higher. They believe this new additive may even have application in the space program. For example, if the shuttle were coated in it, space junk would simply bounce off. Han and Groman have tested the performance of their S2009additive by varying the amount they mix in plastic, molding the plastic into 0.5 in. diameter balls, then measuring how high (in feet) each ball bounces when dropped from a height of 3 feet. They conducted their test on 60 different balls (one each for 60 different additive levels), and used regression analysis to estimate the relationship between bounce, the dependent variable, and S2009, the independent variable, as reflected in the following model: Bounce; =Bo + B1 S2009; +ɛi A partial output of the regression is given below. Use this information to answer the following questions. SUMMARY OUTPUT Regression Statistics Multiple R 0.6121 K R Square Adjusted R Square Standard Error 5.4414 Observations 60 ANOVA df SS H MS F Significance F Regression 34.7451 Residual 1717.3069 29.6087 Total 2746.0660 Coefficients 1.0260 P-value Standard Error 0.7044 0.1909 t Stat Lower 95% Intercept A $2009 1.1251 D.

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.