Below is a two-column proof incorrectly proving that the three angles of ΔPQR add up to 180°: Statements Reasons
Draw line ZY parallel to segment PQ Construction
m∠ZRP + m∠PRQ + m∠QRY = m∠ZRY Angle Addition Postulate
∠ZRP ≅ ∠RPQ Alternate Interior Angles Theorem
∠QRY ≅ ∠PQR Alternate Interior Angles Theorem
m∠RPQ + m∠PRQ + m∠PQR = m∠ZRY Substitution
m∠ZRY = 180° Definition of a Straight Angle
m∠RPQ + m∠PRQ + m∠PQR = 180° Additive Property of Equality

Which statement will accurately correct the two-column proof?
The measure of angle ZRY equals 180° by definition of supplementary angles.
Angles QRY and PQR should be proven congruent before the construction of line ZY.
The three angles of ΔPQR equal 180° according to Substitution.
Line ZY should be drawn parallel to segment QR.

The size of a certain cell is 2.5*10^-9m. another cell is 1.5*10^3 times larger. how large is the larger cell in scientific notation?

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Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above