Welcome to our “Daily Math Practice Challenge: Preparing for the ACT Exam”! This challenge is designed to help you engage in targeted math practice every day, gearing up for the ACT exam. Through daily exercises, you will enhance your problem-solving speed, deepen your understanding of mathematical concepts, and strengthen your ability to tackle a variety of math problems.

1. Each student in Mrs. O’Malley’s first-period Civics class draws 1 tag at random from each of 2 bowls to determine seating location in the class. The tag drawn from the first bowl is the row number of a student’s seat; the 28 tags in the first bowl have an equal distribution of the numbers 1, 2, 3, 4, 5, 6, and 7. The tag drawn from the second bowl is the seat number within the row determined by the first tag; the 28 tags in the second bowl have an equal distribution of the numbers 1, 2, 3, and 4. What is the probability that the first student who draws will have a seating location that is in Row 5, but NOT in Seat 1 ?

F. \( \frac{1}{28} \)

G.\( \frac{3}{28} \)

H. \( \frac{6}{28} \)

J. \( \frac{9}{28} \)

K. \( \frac{18}{28} \)

2. The inequality 7x²y < 0 is true for 2 fixed real numbers x and y. Which of the following inequalities must be true?

F. x > 0

G. y > 0

H. x < 0

J. y < 0

K. xy < 0

3. . Given that c ≠ d, what are all the real values of b that make the inequality \( \frac{bc-bd}{6c-6d}<0 \) true?

A. 6 only

B. \( \frac{1}{6} \)only

C. \( -\frac{1}{6} \) only

D. All positive real numbers

E. All negative real numbers

4. For all negative values of k, what is the range of values of \( 2^k \)?

F. All negative numbers

G. All numbers less than 1

H. All rational numbers less than 1

J. All positive numbers less than 1

K. All positive numbers less than 2

5. For all triangles with sides of length a, b, and c opposite angles of measure A, B, and C, respectively, which of the following equations must be true?

A. \( \frac{a}{A}=\frac{b}{B} \)

B. \( \frac{sin A}{A}=\frac{sin B}{b} \)

C. \( \frac{a}{cos A}=\frac{b}{cosB} \)

D. b² = a² + c² − 2ab(sin B)

E. c² = a² + b² − 2ab(cos C)