A teacher has two large containers filled with blue, red, and green beads. He wants his students to estimate the difference in the proportion of red beads in each container. Each student shakes the first container, randomly selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student sampled 13 red beads from the first container and 16 red beads from the second container. Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of red beads in each container? Find the z-table here.

(0.26 minus 0.32) plus-or-minus 1.96 StartRoot StartFraction 0.26 (1 minus 0.26) Over 50 EndFraction + StartFraction 0.32 (1 minus 0.32) Over 50 EndFraction EndRoot
(0.26 minus 0.32) plus-or-minus 1.65 StartRoot StartFraction 0.26 (1 minus 0.26) Over 50 EndFraction + StartFraction 0.32 (1 minus 0.32) Over 50 EndFraction EndRoot
(0.74 minus 0.68) plus-or-minus 1.96 StartRoot StartFraction 0.74 (1 minus 0.74) Over 50 EndFraction + StartFraction 0.68 (1 minus 0.68) Over 50 EndFraction EndRoot
(0.74 minus 0.68) plus-or-minus 1.65 StartRoot StartFraction 0.74 (1 minus 0.74) Over 50 EndFraction + StartFraction 0.68 (1 minus 0.68) Over 50 EndFraction EndRoot

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Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.