Scientists believe there is a link between ambient temperature and damage to a head gasket on a car. They perform a study recording daily temperature and the damage index to a head gasket on a car.

What is the domain?

Answer: 8 minutes

Step-by-step explanation:

Given equation: 24x + 64y = 384, that represents the canned goods order .

where x = number of minutes spent producing fruit cans,

and y = number of minutes producing vegetable cans.

If the vegetable assembly line runs for 3 minutes, then put y=3 in equation we get

[tex]24x+64(3)=384\\\Rightarrow24x+192=384\\\Rightarrow24x=384-192\\\Rightarrow24x=192\\\Rightarrow\ x=\frac{192}{24}\\\Rightarrow\ x=8[/tex]

Therefore,  the fruit assembly line need to run to complete the order of 384 cans in 18 minutes.

Answer:

Substitute 3 into the equation for y. Solve for x and find that x = 8. So if cans of vegetables are processed for 3 minutes, fruit needs to be processed for 8 minutes to complete the 384-can order.

Step-by-step explanation:

sample response on edge 2023

The divisor for simplifying the fraction 4/12 to 1/3 is 4. Dividing fractions typically involves using the inverse of the second fraction, and fractions are often expressed as percentages by converting the denominator to 100.

The question provided asks to write the divisor of the fraction 4/12 which has been simplified to 1/3. In the context of this fraction, the divisor is essentially the part of the fraction that we are dividing by, which, in this case, is the denominator.

When the fraction 4/12 is simplified, both the numerator (top number) and the denominator (bottom number) are divided by their greatest common divisor, which is 4. Therefore, the divisor used in the simplification process of 4/12 to 1/3 is 4.

To determine how many 1/6 yard pieces can be made from a 2/3 yard board, divide 2/3 by 1/6. After multiplying the reciprocal of 1/6, the result is 4, meaning there are 4 pieces of 1/6 yard each.

To find out how many pieces of 1/6 yard can be cut from a 2/3 yard long board, we need to divide the total length of the board by the length of each piece. This is a division of fractions problem.

The calculation is as follows:

Write down the length of the board: 2/3 yard.

Write down the length of each piece: 1/6 yard.

Divide the length of the board by the length of each piece: (2/3) \/ (1/6).

To divide fractions, we multiply by the reciprocal of the second fraction: (2/3) * (6/1).

Multiply the numerators together: 2 * 6 = 12.

Multiply the denominators together: 3 * 1 = 3.

Simplify the fraction: 12/3 = 4.

So, Jenna can cut the board into 4 pieces of 1/6 yard each.

The new mixture, combined from an 8 qt 2% sugar solution and a 6 qt 51% sugar solution, has a sugar concentration of approximately 22.86%.

To find the concentration of the new mixture, we first need to understand that the total amount of sugar in the solution is the sum of the sugar in the 2% solution and the 51% solution. We are mixing 8 qt of a 2% sugar solution and 6 qt of a 51% sugar solution.

First, to find the total amount of sugar in the 2% mixture, multiply 8 qt by 2% (or 0.02). This gives:8 qt * 0.02 = 0.16 qtof sugar.

Second, do the same for the 51% solution: 6 qt * 0.51 = 3.06 qt of sugar.

Add these two amounts to find the total quantity of sugar: 0.16 qt + 3.06 qt = 3.22 qt.

The total volume of the solution is the sum of both volumes, or 8 qt + 6 qt = 14 qt.

Finally, we find the concentration of sugar in the new solution by dividing the total quantity of sugar by the total volume of the solution, and then multiplying by 100 to get a percentage:

(3.22 qt / 14 qt) * 100 = 22.86%

So, the new mixture has a sugar concentration of about 22.86%.

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If Jaylan makes limeade using 3/4 cup of water per 1/5 cup of lime juice.

Given:

Jaylan's recipe: 3/4 cup of water per 1/5 cup of lime juice

Wanchen's recipe: 2/3 cup of water per 1/6 cup of lime juice

Jaylan's recipe:

Unit rate = (3/4 cup of water) / (1/5 cup of lime juice)

= (3/4) / (1/5) [dividing fractions is the same as multiplying by the reciprocal]

= (3/4) * (5/1)

= (3 * 5) / (4 * 1)

= 15/4

= 3 3/4 cups of water per cup of lime juice

Wanchen's recipe:

Unit rate = (2/3 cup of water) / (1/6 cup of lime juice)

= (2/3) / (1/6)

= (2/3) * (6/1)

= (2 * 6) / (3 * 1)

= 12/3

= 4 cups of water per cup of lime juice

Compare the unit rates:

A higher unit rate means there is more water per cup of lime juice which results in a weaker flavor.

Therefore, Wanchen's limeade has a weaker flavor compared to Jaylan's limeade as it has a higher unit rate of water per lime juice.

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The solution to the equation 4(2 + 3c) = 56 is c = 4.

To solve the equation 4(2 + 3c) = 56, we will follow the order of operations (PEMDAS) to simplify the expression and isolate the variable c.

First, we distribute the 4 to both terms inside the parentheses:

4 * 2 + 4 * 3c = 56

Simplifying further:

8 + 12c = 56

Next, we want to isolate the variable c by subtracting 8 from both sides:

8 + 12c - 8 = 56 - 8

Simplifying:

12c = 48

Finally, we divide both sides by 12 to solve for c:

12c/12 = 48/12

Simplifying:

c = 4

Therefore, the solution to the equation 4(2 + 3c) = 56 is c = 4.

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Lee's paper clip chain grew at a rate of 6 feet per hour.

The question is asking for the rate of growth of Lee's paper clip chain in feet per hour. To find the rate, we need to determine how much the chain grew and over what period of time. We know that the chain started at 32 feet and ended at 80 feet, an increase of 80-32 = 48 feet. This growth took place over 8 hours. The unit rate (or rate of growth) is therefore the growth in feet divided by the time in hours which is 48 feet ÷ 8 hours = 6 feet per hour. So, Lee's paper clip chain grew at a rate of 6 feet per hour.

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A problem that requires multiplying two decimals is "If length of a rectangle is 0.2 m and breadth of a rectangle is 0.5 m.Then what is the area of the rectangle ?

What is Multiplication?

Multiplication is an operation that represents the basic idea of adding the same number repeatedly. The multiplied numbers are called factors, and the result obtained after multiplying two or more numbers is called the product of those numbers. Multiplication is used to simplify the task of repeatedly adding the same number.

Manually multiplying numbers to more than a few decimal places is tedious and error-prone. Common logarithms were invented to simplify such calculations, since the addition of logarithms equals multiplication. The slide rule made it possible to quickly multiply the number to an accuracy of about three. Beginning in the early 20th century, mechanical calculators such as the Marchant multiplied numbers up to 10 digits automatically. Modern electronic computers and calculators have greatly reduced the need for manual multiplication.

Here we are taking two decimal numbers 0.2 and 0.5.

If length of a rectangle is 0.2 m and breadth of a rectangle is 0.5 m.Then what is the area of the rectangle ?

Solution: Area of a rectangle = Length × Breadth

[tex] = 0.2 \times 0.5 \\ = 0.10 \: {m}^{2} [/tex]

Here 0.10 is a two decimal number.

Therefore, required problem is A problem that requires multiplying two decimals is "If length of a rectangle is 0.2 m and breadth of a rectangle is 0.5 m.Then what is the area of the rectangle ?

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Final answer:

The dimensions of the closet are 2.5 feet in length by 2.5 feet in width, given the perimeter is 10 feet and the length is equal to the width.

Explanation:

To solve this problem, we start by understanding that the perimeter of a closet is the sum of all its sides. For a rectangular closet where the length (L) is equal to the width (W), we can express the perimeter (P) as:

P = 2L + 2W

Given that the perimeter is 10 feet and L = W, we can set up the equation:

10 = 2L + 2L

Combining like terms, we get:

10 = 4L

Divide both sides by 4 to find the length:

L = 2.5 feet

Since the width is equal to the length in this closet, W also equals 2.5 feet. Therefore, the dimensions of the closet are 2.5 feet by 2.5 feet.

Answer

Find out the what is the salesman's commission as a percent of his total monthly sales.

To prove

Formula

[tex]Percentage = \frac{Part\ value\times100}{Total\ value}[/tex]

As given

A furniture store salesman had $15,200 in total monthly sales last month.

He made $912 in commission from those sales.

Here

Part value = $912

Total value =  $15,200

put in the formula

[tex]Percentage = \frac{912\times 100}{15200}[/tex]

solve the above equation

[tex]Percentage = \frac{91200}{15200}[/tex]

Percenatge = 6 %

Therefore the  salesman's commission is 6% of his total monthly sales .