For tax reasons, i need to create a rectangular vegetable patch with an area of exactly 50 square feet. the fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. what are the dimensions of the vegetable patch with the least expensive fence?

Answer:

x = -3.75 or 4

Step-by-step explanation:

Multiply by 4x and solve the resulting quadratic in any of the usual ways.

... 4x² = 60 +x

... 4x² -x -60 = 0 . . . . . . . . . . . subtract 60+x

... (x -4)(4x +15) = 0  . . . . . . . . .factor the equation

... x = 4 . . . or . . . -15/4 . . . . . . the values that make the factors zero

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Comment on the graph

It is convenient to use a graphing calculator to find the zeros of a function, so it works well to rewrite the equation to be something that is equal to zero. Here, we've subtracted the right side, so we have ...

... f(x) = x - (15/x +1/4) = 0

Answer:

For a function to be decreasing over an interval, the outputs on the function are getting smaller as the inputs of the function are getting larger, but the outputs could be positive or negative. For a function to be negative over an interval, the  outputs must be negative, while the inputs could be positive or negative.

a. The elasticity of demand is 0.0225.

b. Demand is inelastic over this price range.

c. Total revenue would increase due to the more elastic demand resulting in a greater quantity demanded with a price decrease.

Let's first calculate the price elasticity of demand using the midpoint method:

a. Price elasticity of demand formula:

[tex]\[ E_d = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} \times \frac{\text{Average price}}{\text{Average quantity}} \][/tex]

Percentage change in quantity demanded:

[tex]\[ \text{Percentage change in quantity demanded} = \frac{300 - 100}{\frac{300 + 100}{2}} \times 100\% = \frac{200}{200} \times 100\% = 100\% \][/tex]

Percentage change in price:

[tex]\[ \text{Percentage change in price} = \frac{1.25 - 1.75}{\frac{1.25 + 1.75}{2}} \times 100\% = \frac{-0.5}{1.5} \times 100\% = -33.33\% \][/tex]

Average price and average quantity:

[tex]\[ \text{Average price} = \frac{1.25 + 1.75}{2} = \frac{3}{2} = 1.50 \]\[ \text{Average quantity} = \frac{300 + 100}{2} = \frac{400}{2} = 200 \][/tex]

Now, we can plug these values into the elasticity formula:

[tex]\[ E_d = \frac{100\%}{-33.33\%} \times \frac{1.50}{200} \]\[ E_d = -3 \times 0.0075 \]\[ E_d = -0.0225 \][/tex]

a. The elasticity of demand is 0.0225.

b. Since the elasticity of demand is less than 1, demand is inelastic over this price range.

c. If demand had the same elasticity for a price decline from $1.25 to $0.75 as it does for the decline from $1.75 to $1.25, cutting the price from $1.25 to $0.75 would increase Danny's total revenue because the demand would be more elastic, resulting in a greater increase in quantity demanded compared to the decrease in price.

Complete Question:

Danny “Dimes” Donahue is a neighborhood’s 9-year old entrepreneur. His most recent venture is selling homemade brownies that he bakes himself. At a price of $1.75 each, he sells 100. At a price of $1.25 each, he sells 300.

Instructions: Use the midpoint method and round your answer to 2 decimal places. Do not include a minus sign.

a. What is the elasticity of demand?

b. Is demand elastic or inelastic over this price range?

c. If demand had the same elasticity for a price decline from $ 1.25 to $ 0.75 as it does for the decline from $ 1.75 to $ 1.25, would cutting the price from $ 1.25 to $ 0.75 increase or decrease Danny's total revenue?

Answer:

I think its 30 as well

Step-by-step explanation:

Place value is the value of each digit in a number. 

The value of 43 ones x 3 tens is 129 tens

43 ones x 3 tens = 129 tens.

Place value is the value of each digit in a number. 

Example: 2345.67

2 – thousands place value

3 – hundreds place value

4 – tens place value

5 – ones place value

6 – tenths place value

7 – hundredths place value

We have,

43 ones x 3 tens

43 ones can be written as 43

3 tens can be written as 30

So,

43 ones x 3 tens = 43 x 30

43 x 30 = 1290

This means,

1290 = 129 tens

43 ones x 3 tens = 129 tens

Thus,

The value of 43 ones x 3 tens is 129 tens

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Answer:

The answer is actually 5.17 centimeters

Step-by-step explanation:

The question is asking you to calculate the minimum thickness so you have to find the lowest bounds.

The covers are 0.9 mm to 1 d.p so the minimum thickness is 0.85 because that is the lowest bound.

The pages are 0.13 mm to 2 d.p so the minimum thickness is 0.125 as that is the lowest bound.

0.85  x 2 = 1.7 and 0.125 x 400 = 50

50 + 1.7 = 51.7 which is the minimum length.

Final answer:

The minimum thickness of a book with 400 pages, each 0.13mm thick, and two covers, each 0.9mm thick, is calculated to be 53.8mm.

Explanation:

The minimum thickness of a book can be calculated by summing the thickness of the covers and all the pages. We are given that each cover is 0.9mm thick and each page is 0.13mm thick. To find the minimum thickness of the book, we multiply the thickness of each page by the total number of pages and then add the thicknesses of the front and back covers.

To calculate:

Thickness of all pages: 400 pages × 0.13 mm/page = 52 mm

Thickness of both covers: 2 covers × 0.9 mm/cover = 1.8 mm

Total minimum thickness: 52 mm + 1.8 mm = 53.8 mm

The minimum thickness of the book is therefore 53.8 mm.

Yes,[tex]\(30 \times 10^3\)[/tex] is equal to 30,000.

When we have a number written in scientific notation, such as [tex]\(10^3\),[/tex] it means we are multiplying the base (which is 10 in this case) by itself a certain number of times, indicated by the exponent (which is 3 in this case).

So, [tex]\(10^3\)[/tex] means [tex]\(10 \times 10 \times 10\)[/tex], which equals 1,000.

Therefore, when we multiply 30 by [tex]\(10^3\)[/tex], it's equivalent to multiplying 30 by 1,000, which results in 30,000.

The probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is (8/15).

Probability is the chance of happening an event or incident.

Given, the probability that Jinelle’s bus is on time is 2/3.

The probability that Mr. Corney is driving the bus is 4/5.

Therefore, the probability that on any given day Jinelle’s bus is on time and Mr. Corney is the driver is:

= (2/3) × (4/5)

= (8/15)

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Final answer:

The probability of shooting free throws in alphabetical order is 0.5.

Explanation:

Probability of shooting free throws in alphabetical order:

Determine the total number of ways the players can shoot. There are 2 players, so 2! (2 factorial) = 2 ways.

Calculate the number of ways they can shoot in alphabetical order. As they have different names, only 1 way exists.

Probability = (Number of ways shooting in alphabetical order) / (Total number of ways to shoot) = 1/2 = 0.5.

Subtract the first day of the month from the date of the last Wednesday and divide by 7 to find the remainder. Count backwards from Wednesday to determine the day of the week for the first day of the month, which is Saturday in this case.

The subject of this question pertains to dates and the calendar, which fall under the domain of Mathematics. To answer the question, we need to calculate how many days have passed from the 26th (the last Wednesday) to the 1st day of the same month. A week has seven days so we use the principles of modular arithmetic, a branch of number theory. The 26th day is a Wednesday, and for every seven days we go back, it will still be Wednesday. Thus, the difference from 26 to 1 is 25. Dividing 25 by 7, we get a quotient of 3 and a remainder of 4. This tells us that four days before the last Wednesday, which was the 26th, would be the first day of the month. Going backwards from Wednesday, we count Tuesday (1), Monday (2), Sunday (3), and Saturday (4). Therefore, the first day of that month falls on a Saturday.

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3/20, or 0.15 of the shirts each evening

1 - 1/4 = 3/4

(3/4) / 5 = (3/4) / (5/1) = (3/4) x (1/5) = 3/20 = 0.15