I'm sorry, I don't know the answer but wish I did.
Answer:
and 
expressed in interval notation.
Step-by-step explanation:
A compound inequality 
has been provided. Our task is to determine the solution for this inequality.
Initially, we will address each inequality independently, followed by merging the findings by combining the overlapping intervals.
By dividing with a negative number, it is necessary to reverse the inequality sign:
Again, dividing by a negative requires flipping the inequality sign:
In combining both intervals, we will arrive at:
Thus, the solution for the inequality provided is and in interval notation.
Answer:
The charge for the first three hours is $4 per hour.
Subsequently, the rate decreases to $2 per hour until the sixth hour.
Between the sixth and tenth hours, the cost is reduced further to $1 per hour.
The maximum charge for renting the bike is $30.
Step-by-step explanation:
The incline on the graph indicates the hourly rate for the bike rental.
During the initial three hours, the rental fee rises by $4 for each hour.
From the third to the sixth hour, the graph’s slope indicates a rate of $2 per hour for the rental.
The charge drops to $1 per hour from the sixth to the tenth hour.
After the tenth hour, the price, P, remains constant. The highest fee for the bike rental is $30.
In certain cases, a function necessitates multiple formulas to achieve the desired outcome. An example is the absolute value function \displaystyle f\left(x\right)=|x|f(x)=∣x∣. This function applies to all real numbers and yields results that are non-negative, defining absolute value as the magnitude or modulus of a real number regardless of its sign. It indicates the distance from zero on the number line, requiring all outputs to be zero or greater.
<pwhen inputting="" a="" non-negative="" value="" the="" output="" remains="" unchanged:="">
\displaystyle f\left(x\right)=x\text{ if }x\ge 0f(x)=x if x≥0
<pwhen inputting="" a="" negative="" value="" the="" output="" is="" inverse:="">
\displaystyle f\left(x\right)=-x\text{ if }x<0f(x)=−x if x<0
Due to the need for two distinct operations, the absolute value function qualifies as a piecewise function: a function defined by several formulas for different sections of its domain.
Piecewise functions help describe scenarios where rules or relationships alter as the input crosses specific "boundaries." Business contexts often demonstrate this, such as when the cost per unit of an item decreases past a certain order quantity. The concept of tax brackets also illustrates piecewise functions. For instance, in a basic tax system where earnings up to $10,000 face a 10% tax, additional income incurs a 20% tax rate. Thus, the total tax on an income S would be 0.1S when \displaystyle {S}\leS≤ $10,000 and 1000 + 0.2 (S – $10,000) when S > $10,000.
</pwhen></pwhen>
Answer: E. The sizes of shoes available for sale in a department store
Step-by-step explanation:
A continuous variable is characterized by:
- a quantitative variable capable of taking an infinite number of values between any two points.
- a measurement of a quantity such as height, weight, length, etc.
In this scenario, options A through D represent discrete variables that can be counted.
Only option E describes the measurement pertaining to shoe sizes.
Thus, "The sizes of shoes available for sale in a department store" defines a continuous variable.
Therefore, the correct choice is "E".
