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Practice Test 39 - ACT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

  1. A gym charges a one-time sign-up fee and then a monthly fee. The total cost after xx months is y=30x+80y = 30x + 80, where xx is months and yy is total cost (dollars). What is the meaning of the slope in this context?
  2. A chemist has two solutions: Solution A is 2020\\% acid and Solution B is 5050\\% acid. How many milliliters of Solution A must be mixed with 40 milliliters of Solution B to obtain a mixture that is 3030\\% acid?
  3. If A=[014−3]A = \begin{bmatrix} 0 & 1 \\ 4 & -3 \end{bmatrix}, what is −1A-1A?
  4. A right triangle has legs of lengths 99 and 4040 (the legs meet at the right angle). Angle θ\theta is opposite the side of length 99. What is sin⁡(θ)\sin(\theta)?
  5. A transformation scales every coordinate by −3-3. If A=[−1204],A=\begin{bmatrix}-1 & 2\\ 0 & 4\end{bmatrix}, what is −3A-3A?
  6. A set of 8 test scores is {50,60,60,70,70,70,80,90}\{50, 60, 60, 70, 70, 70, 80, 90\}. What is the median of the data set?​
  7. Two triangles △ABC\triangle ABC and △DEF\triangle DEF are shown. AB=5AB=5, AC=7AC=7, and BC=8BC=8. In the other triangle, DE=10DE=10, DF=14DF=14, and EF=16EF=16. Which statement is correct?
  8. What is the volume of a rectangular prism with length 7 units, width 3 units, and height 4 units?
  9. What is the value of xx if log⁡(x)=2\log(x) = 2?
  10. Which polynomial is equivalent to x2−4x+4x^2 - 4x + 4?
  11. Lines mm and nn are parallel and cut by a transversal. An alternate interior angle is 50∘50^\circ. What is the measure of angle xx if xx is the alternate interior angle to the 50∘50^\circ angle?
  12. A university wants to estimate the average amount of sleep per night among all its students. A researcher surveys only students in an 8 a.m. class because they are easy to reach, and then reports the result as the university-wide average. To reduce bias, the researchers should:
  13. Which vector represents x+y\mathbf{x} + \mathbf{y} if x=⟨2,3⟩\mathbf{x} = \langle 2, 3 \rangle and y=⟨4,−1⟩\mathbf{y} = \langle 4, -1 \rangle?
  14. A bar graph shows the number of apples picked from four trees. How many trees had more than 30 apples picked?
  15. A university wants to know how many students prefer online learning. They send a survey link to all students via email. What could be a potential source of bias?
  16. A wind vector is v=⟨3, −4⟩\mathbf{v}=\langle 3,\,-4\rangle. Which vector represents the same direction but with twice the magnitude?
  17. A fair coin is flipped and a fair six-sided die is rolled. What is the probability of getting tails and rolling a number greater than 4? (Assume independence.)
  18. A student evaluates log⁡9(3)\log_9(3). What is the value of log⁡9(3)\log_9(3)?
  19. A set of values is {4,4,5,6,6,7,20}\{4, 4, 5, 6, 6, 7, 20\}. Which best describes the shape of the distribution?
  20. Lines mm and nn are parallel and cut by a transversal. If a corresponding angle measures 120∘120^\circ, what is the measure of angle xx that is corresponding to it?

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