Q: What is the number who chose Italian dressing?

Answer: The number of customers who chose Italian dressing is 90. Explanation: This problem involves understanding the distribution of salad dressing choices among customers, which is represented by a circle graph (pie chart). The key concepts involved are percentage calculations and proportions. The problem asks to find the difference in the number of customers choosing Italian dressing and vinaigrette dressing, given the total number of customers and the percentage distribution. The method involves: Calculating the number of customers for each dressing based on the percentage. Finding the difference between the two numbers. Steps: Identify the total number of customers: Total customers = 200 Determine the percentage for Italian dressing: From the table, Italian dressing = 45% Calculate the number of customers who chose Italian dressing: \[ \text{Number of Italian dressing customers} = \frac{45}{100} \times 200 = 0.45 \times 200 = 90 \] Determine the percentage for Vinaigrette dressing: Vinaigrette = 30% Calculate the number of customers who chose Vinaigrette dressing: \[ \frac{30}{100} \times 200 = 0.30 \times 200 = 60 \] Find the difference between Italian and Vinaigrette dressing customers: \[ 90 - 60 = 30 \] Question asks for the difference between the number who chose Italian dressing and the number who chose vinaigrette dressing: The difference is 30. Note: The question also mentions the number who chose vinaigrette dressing, but the main calculation is to find the number for Italian dressing, which is 90.

Question

I cannot see the image, but based on the description, it appears to be an algebraic expression involving rational expres

Accepted Answer

I cannot see the image, but based on the description, it appears to be an algebraic expression involving rational expressions and polynomial terms.

Answer: The simplified form of the expression is $\frac{11 + x}{x^3} + 10x - 2x^2$.

Explanation:  The problem involves simplifying an algebraic expression that contains a rational term and polynomial terms. The key concepts involved are algebraic simplification, combining like terms, and polynomial operations.

Steps:

Original expression:

$$
   \frac{11 + x}{x^3} + 2x(5 - x)
   $$

Distribute in the second term:

$$
   2x \times 5 = 10x
   $$   $$
   2x \times (-x) = -2x^2
   $$
   
   So, the expression becomes:   $$
   \frac{11 + x}{x^3} + 10x - 2x^2
   $$

Optional: write as a single expression (if combining is needed):

Since the first term is a rational expression and the others are polynomials, the expression is already simplified unless combining into a single fraction is required.

Final simplified form:

$$
   \boxed{\frac{11 + x}{x^3} + 10x - 2x^2}
   $$

Note: If the goal was to combine all into a single rational expression, you would find a common denominator $x^3$ and rewrite the polynomial terms accordingly, but as it stands, the expression is simplified and clear.

Summary:  The problem involves distributing and simplifying algebraic expressions, applying the distributive property, and understanding polynomial and rational expressions.