Question

directions: find or select the best answer. record your response on your answer sheet.

1. a graduated cylinder actually contains 7.5 milliliters of water. when han measures the volume of the water inside the graduated cylinder, his measurement is 7 milliliters. which of these is closest to the percent error for hans measurement?

a. 107.1%
b. 93.3%
c. 7.1%
d. 6.7%

1. on a coordinate plane, a line contains the point (4, 20) and models a proportional relationship. which of the following points are also on this line?

select all that apply.
a. (0, 0)
b. (5, 1)
c. (0, 5)
d. (2, 18)
e. (3, 15)

Explanation:

Question 8

Step1: Calculate the absolute error

Absolute error \(=\vert\text{Measured value}-\text{Actual value}\vert=\vert7 - 7.5\vert= 0.5\)

Step2: Calculate the percent error

Percent error formula is \(\text{Percent Error}=\frac{\text{Absolute Error}}{\text{Actual Value}}\times100\%\)
Substitute the values: \(\text{Percent Error}=\frac{0.5}{7.5}\times100\%=\frac{50}{7.5}\% \approx 6.7\%\)

A proportional relationship has the form \(y = kx\), where \(k\) is the constant of proportionality. Given the point \((4,20)\), we can find \(k\) as \(k=\frac{y}{x}=\frac{20}{4} = 5\). So the equation of the line is \(y = 5x\).

• For point \(A(0,0)\): Substitute \(x = 0\) into \(y=5x\), we get \(y=5\times0=0\). So \((0,0)\) is on the line.
• For point \(B(5,1)\): Substitute \(x = 5\) into \(y = 5x\), we get \(y=5\times5 = 25

eq1\). So \((5,1)\) is not on the line.

• For point \(C(0,5)\): Substitute \(x = 0\) into \(y=5x\), we get \(y=5\times0=0

eq5\). So \((0,5)\) is not on the line.

• For point \(D(2,18)\): Substitute \(x = 2\) into \(y=5x\), we get \(y=5\times2=10

eq18\). So \((2,18)\) is not on the line.

• For point \(E(3,15)\): Substitute \(x = 3\) into \(y=5x\), we get \(y=5\times3=15\). So \((3,15)\) is on the line.

Answer:

D. \(6.7\%\)

Question 9