Let y represent the gallons of water left in the barrel, and let x represent the minutes that have passed. Water escapes the barrel at a rate of 1 gallon for every 10 minutes. Consequently, the appropriate linear equation for this scenario is shown in the attached graph.
Answer:
Yes, the cost 
in dollars and the quantity of yogurt 
are indeed proportional.
The relationship can be expressed as: 
Step-by-step explanation:
1. If varies directly with , it can be represented as:
Here, 
represents the constant of proportionality.
2. We'll calculate the proportionality constant. Given that 
and 
, we have:
3. Thus, the equation becomes:
4. Now, we need to verify proportionality. Substituting 
, which is the quantity of yogurt purchased by Jonah, we should arrive at $0.48:
5. They are indeed directly proportional.
Response:
Detailed explanation:
Hello!
Stratified sampling involves the categorization of the population into subgroups based on pre-established criteria for the study. These subgroups consist of homogeneous units concerning the relevant characteristics. In this instance, individuals in the groups will represent only one of the two potential opinions (support or not support) and not both.
The researcher determines the sample size desired, considering several factors such as finances, material availability, and accessibility to experimental subjects (for instance, if they are endangered species, larger sample sizes may not be feasible).
One might conduct proportionate stratified sampling by selecting a proportion of respondents who answered "yes" along with those who answered "no."
In this sampling method, taking a specific proportion from each subgroup allows for a more straightforward extrapolation of results to the overall populations. For example, if you needed a sample size of n = 20, each stratum would ideally contain half, meaning 10 from the “yes” group and 10 from the “no” group.
I hope this is helpful!
Examining Talia's steps to derive the line equation, we identify the erroneous step as detailed below:
Step 1:
Select a point on the line, such as (2,5)
Step 2:
<span>Select another point on the line, such as (1, 3)
Step 3:
</span><span>Measure units to find the slope. The line moves 1 unit to the right and 2 units upward, resulting in a slope of
(5-3)/(2-1) = 2/1 = 2
Step 4:
</span><span>Apply these values in the point-slope form
y - y1 = m(x - x1)
y - 3 = 2(x - 1)
y = 2x + 1
Hence, the conclusion is:
</span><span>Step 4 is erroneous due to incorrect application of (1, 3) in the point-slope format.</span>
