You are planning a sample survey of small businesses in your area. You will choose an SRS of businesses listed in the telephone book's Yellow Pages. Experience shows that only about half the businesses you contact will respond. (a) If you contact 142 businesses, is it reasonable to use the binomial distribution with n = 142 and p = 0.5 for the number X who respond? Explain why. O Each observation falls into a "success" or "failure." O There is a fixed number n of observations. O The n observations are all independent. O The probability of success p is the same for each observation. O None of the binomial conditions are met. (b) What is the expected number (the mean) who will respond? (c) What is the probability that 70 or fewer will respond? (Use the normal approximation.) (d) How large a sample must you take to increase the mean number of respondents to 100?

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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.