Suppose that a commercial bakery produces chocolate chip cookies. Based on extensive testing, the bakery has determined that the ideal number of chocolate chips per cookie is 18. In the past, master bakers mixed the dough and spooned it onto sheet pans by hand, but the owners have decided to test a new machine. The machine extrudes dough onto baking sheets at a uniform rate. It runs continuously from 4:30 a.m. until 12:30 p.m. The number of chips per cookie depends on the viscosity of the dough, and because the dough stiffens as it sits in the machine, the machine produces cookies that contain the optimal number of chips, 18 per cookie, between the hours of 5:00 a.m. and 11 a.m. The distribution of cookies is shown in the graph below
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Suppose that a commercial bakery produces chocolate chip cookies. Based on extensive testing, the bakery has determined that the ideal number of chocolate chips per cookie is 18. In the past, master bakers mixed the dough and spooned it onto sheet pans by hand, but the owners have decided to test a new machine.
The machine extrudes dough onto baking sheets at a uniform rate. It runs continuously from 4:30 a.m. until 12:30 p.m. The number of chips per cookie depends on the viscosity of the dough, and because the dough stiffens as it sits in the machine, the machine produces cookies that contain the optimal number of chips, 18 per cookie, between the hours of 5:00 a.m. and 11 a.m. The distribution of cookies is shown in the graph below.
![### Understanding Proportions of Optimal Cookies
The graph shown is a visual illustration representing the proportion of cookies produced that contain exactly 18 chocolate chips. Below is a detailed description of the graph and how to interpret it:
#### Graph Explanation
- **Horizontal Axis (Time):** This axis represents the time period starting from 4:00 and extends to 1:00. Major time intervals are marked at 4:00, 5:00, 6:00, 7:00, 8:00, 9:00, 10:00, 11:00, 12:00, and 1:00.
- **Shaded Area:** The area shaded in red represents the proportion of all cookies that contain exactly 18 chocolate chips. This shaded region spans from 5:00 to 11:00 on the time axis.
#### Calculation
To compute the proportion of cookies produced each day that contain the optimal number of chocolate chips, express it as a percentage with one decimal of precision:
Here, the provided proportion is:
\[
\text{Proportion} = 0.625 \%
\]
This means that 0.625% of all cookies produced each day contain exactly 18 chocolate chips.
By understanding this representation, one can assess and ensure the quality control of cookie production by monitoring the proportion of cookies that meet the desired chocolate chip criteria.
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Educational takeaway: This exercise helps students grasp the concept of proportions, visual data interpretation, and quality control metrics in a production scenario.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febcd0f3a-05e1-4ffe-9e2c-b3b8c058b0ac%2F2ebee64e-0d0b-441a-9278-20d02e6df704%2Ffeaxzob.jpeg&w=3840&q=75)
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