Hopefully you were able to find some time and a quiet place this weekend to try our Five Problems for Your Weekend (5/1/15). Below you’ll find the fully worked-out solutions to those problems.

7. D

Of the 20 people surveyed, 5 said their favorite color was purple. You can write this as a fraction: 5/20. Equivalently 5/20 = .25 = 25%.

8. K

Of the 20 people surveyed, 7 said their favorite color was red. As a fraction this is 7/20 of those surveyed, which is equivalent to 35% of the class. This sector should they take up 35% of the circle graph, which would be 360 x .35 = 126 degrees.

You also could have set up and solved a proportion for this problem: 7/20 = *x*/360.

27. C

Sean’s path around the track would include two “straightaways” and two semicircles, which together would be the circumference of a circle. You can compute his total distance using the circumference formula. Note that if the diameter of the circle is 100 feet, its radius is 50 feet.

*d* = 2(300) + 2π*r*

*d = *2(300) + 2π(50)

*d* ≈ 600 + 314

*d* ≈ 914

42. J

You can use what you know about 30-60-90 right triangles to label the other two side of triangle *ABC*.

Because segment *BC* is 8 inches long, the area of the shaded square must be 8² = 64 square inches.

55. B

The conjugate of 7 + 3*i* is 7 – 3*i*. Multiplying these two complexes number looks very much like a FOIL (binomial times binomial) problem.

(7 + 3*i*)(7 – 3*i*)

49 – 21*i + *21*i *– 9*i**²*

49 – 9*i*²

49 – 9(-1)

49 + 9

58

If you have questions about these problems or anything to do with the ACT, send us an email at info@cardinalec.com.

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