) The points (1, 0, 3), (1, 1, 1), and (−2, −1, 2) lie on a unique plane a1x1 + a2x2 + a3x3 = b. Using your previous answers, fi

The table is included below

Based on the table, we can observe that the cost of lemons contributes to 35% of the expenses.

Let x represent the expenses; hence, the lemon cost is 70.

The lemon cost is 35% of x.

So, 70 = 35% of x (where 35% = = 0.35).

Thus, 70 = 0.35 * x.

Solving that gives us x =

x = 200, meaning the expense is $200.

Given that the profit margin is 15% = = 0.15,

we calculate profit as the product of the profit percentage and expenses.

Profit equals 0.15 * 200 = 30.

Therefore, the profit amounts to $30

Answer:

a.[144;158]$

b. The parameter being estimated is the average weekly food expenses of American families.

Step-by-step explanation:

Hello!

The variable studied here represents "Weekly food expenses incurred by an American family"($)

From a sample of n=1014 American families, the sample mean is x[bar]=$151

It is indicated that for the 95% confidence interval, the margin of error is ±$7

a.

The estimated confidence interval for the population mean is formed as "estimator ± margin of error." In a Standard Normal distribution, the confidence interval formula is:

[x[bar]±*(δ/√n)]

For the provided sample, we have:

[151±7]

The lower limit equates to 144$

The upper limit amounts to 158$

b.

The parameter being contemplated is the average weekly food expenses of American families.

The confidence level for this interval reflects the likelihood that if 100 such intervals were constructed, approximately 95 would encompass the true value of the population mean we aim to estimate.

Wishing you a wonderful day!

Answer:

Part a) Your budget is $40.

Part b) The price for one gallon of gasoline is $3.55, while a car wash costs $8.

Part c)

Part d) Refer to the explanation below.

Step-by-step explanation:

Please see the complete question in the attached image.

Part a) The budget is expressed by the equation

y = 40

therefore,

Your budget amounts to $40.

Part b) In terms of costs, how much is a gallon of gasoline and what is the car wash price?

Let

y ------> denote the total cost for a gallon of gasoline along with a car wash

x -----> define the volume of gasoline in gallons

We can express the relationship as

y = 3.55x + 8

For calculations, when x = 0, we have:

y = 3.55(0) + 8 = 8

The y-intercept signifies the cost of the car wash, being $8.

Now, to identify the price of one gallon of gasoline:

We know the slope of the linear function is

m = $3.55 per gallon

This confirms that a gallon of gasoline costs $3.55.

Part c) Formulate an inequality representing the potential quantity of gasoline you can purchase:

We have:

Now, solve for x:

Part d) Utilize the graph to determine the solution of the inequality from part c)

We can set up the system:

y = 40

y = 3.55x + 8

The solution lies at the intersection of both graphs. By observing the graph, the intersection appears to be around (9, 40).

This indicates that the maximum volume of gasoline purchasable within your budget is approximately 9 gallons.