Question

1. a box-and-whisker plot is made to show the gas prices per gallon. identify the median, upper and lower quartiles, upper and lower extremes, and the interquartile range. gasoline prices box plot with axis 2.2, 2.4, 2.6, 2.8, 3.0, 3.2 26. probability what is the probability that a data value will fall into the interquartile range? 27. verify use a graphing calculator to find the solution to the linear system. check your answer. ( y = -\frac{1}{2}x + 4 ) ( y = \frac{1}{4}x - 2 ) 28. multiple choice what is the solution of the linear system below? ( y = \frac{3}{4}x + 1 ) ( y = -\frac{1}{4}x - 3 ) a (4, −2) b (−2, 4) c (−4, −2) d (4, 0)

Explanation:

Question 27:

Step1: Set the equations equal

Since both equations are solved for \( y \), set \( -\frac{1}{2}x + 4=\frac{1}{4}x - 2 \).

Step2: Solve for \( x \)

Add \( \frac{1}{2}x \) to both sides: \( 4=\frac{1}{4}x+\frac{1}{2}x - 2 \). Combine like terms: \( 4=\frac{3}{4}x - 2 \). Add 2 to both sides: \( 6=\frac{3}{4}x \). Multiply both sides by \( \frac{4}{3} \): \( x = 8 \).

Step3: Find \( y \)

Substitute \( x = 8 \) into \( y=\frac{1}{4}x - 2 \): \( y=\frac{1}{4}(8)-2 = 2 - 2 = 0 \).

Step1: Set the equations equal

Set \( \frac{3}{4}x + 1=-\frac{1}{4}x - 3 \).

Step2: Solve for \( x \)

Add \( \frac{1}{4}x \) to both sides: \( \frac{3}{4}x+\frac{1}{4}x + 1=-3 \). Combine like terms: \( x + 1=-3 \). Subtract 1 from both sides: \( x=-4 \).

Step3: Find \( y \)

Substitute \( x = -4 \) into \( y=\frac{3}{4}x + 1 \): \( y=\frac{3}{4}(-4)+1=-3 + 1=-2 \).

Answer:

The solution is \( (8, 0) \).

Question 28: