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.
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%.
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.
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) + 2πr
d = 2(300) + 2π(50)
d ≈ 600 + 314
d ≈ 914
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.
The conjugate of 7 + 3i is 7 – 3i. Multiplying these two complexes number looks very much like a FOIL (binomial times binomial) problem.
(7 + 3i)(7 – 3i)
49 – 21i + 21i – 9i²
49 – 9i²
49 – 9(-1)
49 + 9
If you have questions about these problems or anything to do with the ACT, send us an email at firstname.lastname@example.org.