Step-by-step explanation:
The equation for the best fitting line is y = 2.599x + 105.08. When x is set to 20, the predicted height becomes y = 157.06. However, the actual height recorded is 160 cm, therefore, the residual is calculated as:
160 cm − 157.06 cm = 2.94 cm
The yearly sales total for mattresses equals 1,330.
The percentage of King size mattresses sold is 30% = 30/100 = 0.3
Now, we need to find the actual sales number using the following formula:
King size mattresses sold = Total mattresses sold in a year * Percentage of King size mattresses sold
King size mattresses sold = 1,330 * 0.3 = 399
King size mattresses sold = 399
To achieve a positive profit p(x)>0, we start with:

Next, we solve for x:

The parameters are:
a = -2
b = 7
c = -3
We will apply the quadratic formula:

This yields two results—one a fraction, the other a whole number. We focus on the whole number since the muffins sold must be a complete unit. Thus we conclude:
x>3
Answer:

Step-by-step explanation:
Step 1
Calculate the slope of the dashed line
The slope between two points is computed with the formula:

We consider
(-3,1) and (0,3)
and substitute into it:


Step 2
Determine the equation of the dashed line in slope-intercept form:

The equation we established is:

---> associated problem
Substituting yields:

Step 3
Establish the inequality corresponding to the graph
Given that it is represented by a dashed line, the area to the left of this line is shaded.
Thus,

Refer to the attached diagram for enhanced understanding of the problem.
Answer:
y=4x+7.75; continuous
Step-by-step explanation:
Let’s first establish the equation. Julie requires one segment of yarn measuring 7.75 inches: that's already known.
y = 7.75
Now, for the four pieces of yarn, each will be of equal length x. If she wants them to measure 1 inch, she'd need 4 inches of yarn. Therefore, the calculation would be:
y = 7.75 + 4x
Now, is this graph discrete or continuous? Continuous indicates there's a smooth line without gaps, while discrete has interruptions or spaces. In this scenario, x is continuous, as Julie can cut the yarn to any size for the four pieces. She is not limited to whole numbers; each piece could be, for instance, 2.5 inches or 3.1415 inches.