Questions: A calculator is allowed on this question. The 12th grade class is having a cookie sale every day after school for one week. They decide to offer samples of cookies to encourage customers to buy. The table below shows the number of samples that were given away and the amount of money they made in sales for each day. Approximately how much should the students expect to make if they hold a cookie sale for one more day and give away 25 samples? Number of Samples (x) Sales (f(x)) 12 30.25 20 52.50 18 50.00 13 38.75 16 42.00

A calculator is allowed on this question.
The 12th grade class is having a cookie sale every day after school for one week. They decide to offer samples of cookies to encourage customers to buy. The table below shows the number of samples that were given away and the amount of money they made in sales for each day. Approximately how much should the students expect to make if they hold a cookie sale for one more day and give away 25 samples?

Number of Samples (x) Sales (f(x))
12 30.25
20 52.50
18 50.00
13 38.75
16 42.00

Transcript text: A calculator is allowed on this question. The 12 th grade class is having a cookie sale every day after school for one week. They decide to offer samples of cookies to encourage customers to buy. The table below shows the number of samples that were given away and the amount of money they made in sales for each day. Approximately how much should the students expect to make if they hold a cookie sale for one more day and give away 25 samples? Number of Samples $(x)$ & Sales $(f(x))$ \\ 12 & $\$ 30.25$ \\ 20 & $\$ 52.50$ \\ 18 & $\$ 50.00$ \\ 13 & $\$ 38.75$ \\ 16 & $\$ 42.00$

Solution

Solution Steps

To estimate the sales for 25 samples, we can use linear regression to find the best-fit line for the given data points. This line will help us predict the sales for a given number of samples. We will use the least squares method to calculate the slope and intercept of the line, and then use the equation of the line to predict the sales for 25 samples.

Step 1: Organize the Data

We have the following data points for the number of samples given away and the corresponding sales:

\( (12, 30.25) \)
\( (20, 52.50) \)
\( (18, 50.00) \)
\( (13, 38.75) \)
\( (16, 42.00) \)

Step 2: Determine the Linear Regression Line

To find the best-fit line, we use the linear regression formula \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. From the calculations, we have:

Slope (\( m \)) = 2.5770
Intercept (\( b \)) = 1.9833

Thus, the equation of the line is: \[ f(x) = 2.5770x + 1.9833 \]

Step 3: Predict Sales for 25 Samples

To predict the sales for 25 samples, substitute \( x = 25 \) into the equation: \[ f(25) = 2.5770 \times 25 + 1.9833 \]

Calculating this gives: \[ f(25) = 64.425 + 1.9833 = 66.4083 \]

Final Answer

\(\boxed{66.41}\)

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Answered

where the road became a bridge over a dry riverbed, tangled with brush and clinging vines; the bridge of rustic logs, made for trysting, but virginal and untested by lovers; on up the road, past the buildings, with the southern verandas half-a-cityblock long, to the sudden forking, barren of buildings, birds, or grass, where the road turned off to the insane asylum. I always come this far and open my eyes. The spell breaks and I try to re-see the rabbits, so tame through having never been hunted, that played in the hedges and along the road. And I see the purple and silver of thistle growing between the broken glass and sunheated stones, the ants moving nervously in single file, and I turn and retrace my steps and come back to the winding road past the hospital, where at night in certain wards the gay student nurses dispensed a far more precious thing than pills to lucky boys in the know; and I come to a stop at the chapel. And then it is suddenly winter, with the moon high above and the chimes in the steeple ringing and a sonorous choir of trombones rendering a Christmas carol; and over all is a quietness and an ache as though all the world were loneliness. And I stand and listen beneath the high-hung moon, hearing "A Mighty Fortress Is Our God," majestically mellow on four trombones, and then the organ. The sound floats over all, clear like the night, liquid, serene, and lonely. And I stand as for an answer and see in my mind's eye the cabins surrounded by empty fields beyond red clay roads, and beyond a certain road a river, sluggish and covered with algae more yellow than green in its stagnant stillness; past more empty fields, to the sun-shrunk shacks at the railroad crossing where the disabled veterans visited the whores, hobbling down the tracks on crutches and canes; sometimes pushing the legless, thighless one in a red wheelchair. And sometimes I listen to hear if music reaches that far, but recall only the drunken laughter of sad, sad whores. And I stand in the circle where three roads

< Previous Next >

Thank you for your feedback.

Copied!