Answer:
The variable x lies within the interval of all positive real numbers less than 5 cm.
Detailed solution:
Problem statement:
Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.
Refer to the provided diagram for clarity.
Define:
x → length in centimeters of each square cutout side
The volume of the box with open top can be written as:
Given this, we have:
By substitution:
Determine the domain of x:
Because:
Therefore:
Domain is the interval (0,5)
That means all real numbers strictly greater than zero and less than 5 cm are valid for x.
Hence, the volume V as a function of x is:
Response:
Option B is correct
Step-by-step breakdown:
(One-tailed test at a significance level of 5%)
n = 16 and x̄ = 1.97
s = 0.1
Standard error of the mean = 
Difference in means = 
t statistic = Difference in means/se = -1.2
degrees of freedom = 16 - 1 = 15
p-value = 0.124375
(B) do not reject the null hypothesis since the test statistic (-1.2) is > the critical value (-1.7531).
To solve the equation 3x^2-4x=0 graphically, Amber will begin by plotting the graph of y=4x, and the x-coordinate points where the graphs intersect will provide the solutions.
Imagine a right triangle where vertex B is at the base of the hill, vertex S is at the top of the statue, and vertex Y represents your position. This triangle has a right angle at B, and angle Y measures 13.2°. Let h denote the height of the statue, making the lengths of sides YB and BS equal to 77 ft and 16+h ft, respectively.
With the lengths of two sides and one angle known, the height h can be determined using the tangent function:
ft.
Result: the height of the statue calculates to be 2.0565 ft.
