Question

1. vocabulary how do you know if a situation represents a proportional relationship? lesson 2-3

1. ana runs \\(\frac{1}{4}\\) mile in 6 minutes. assuming she runs at a constant rate, what is her speed, in miles per hour? lessons 2-1 and 2-2

1. a trail mix recipe includes granola, oats, and almonds. there are 135 calories in a \\(\frac{1}{4}\\)-cup serving of the trail mix. how many calories are in 2 cups of trail mix? lesson 2-2

1. does this table show a proportional relationship? if so, what is the constant of proportionality? lessons 2-3 and 2-4

\\(\boldsymbol{\text{\textcircled{a}}}\\) yes; \\(\frac{1}{5}\\)
\\(\boldsymbol{\text{\textcircled{b}}}\\) yes; 5
\\(\boldsymbol{\text{\textcircled{c}}}\\) yes; 10
\\(\boldsymbol{\text{\textcircled{d}}}\\) the quantities are not proportional.

1. janet, rosi, and tanya buy postcards from their favorite souvenir shop. janet buys 3 postcards for $1.05. rosi buys 5 postcards for $1.75. tanya buys 8 postcards for $2.80. are the cost, \\(y\\), in dollars and the number of postcards, \\(x\\), proportional? explain your answer. write an equation to represent this relationship, if possible. lesson 2-4

1. four movie tickets cost $30.00. five concert tickets cost $36.50. does the movie or the concert cost less per ticket? how much less? lesson 2-1

Explanation:

Step1: Calculate the unit rate for each person

For Janet: \(\frac{1.05}{3}=0.35\)
For Rosi: \(\frac{1.75}{5}=0.35\)
For Tanya: \(\frac{2.80}{8}=0.35\)

Step2: Determine if it's proportional

Since the unit rate (constant of proportionality) is the same (\(0.35\)) for all three, the relationship is proportional.

Step3: Write the equation

The equation for a proportional relationship is \(y = kx\), where \(k\) is the constant of proportionality. So the equation is \(y = 0.35x\)

Answer:

Yes, the cost \(y\) and the number of postcards \(x\) are proportional. The equation is \(y = 0.35x\)