Hank cut a cake into 12 equal pieces. He ate 2/12 pieces. He has 10/12 of the cake left to serve on plates. What part of the cake did he put on each plate.

To find the length of Chad's rope, the ratio of 16:6 was simplified to 8:3, and using Joey's rope length of 112 cm, we found out that Chad's rope is 42 cm long.

The question asks to find out the length of Chad's rope given the ratio of Joey's rope to Chad's rope is 16:6 and Joey's rope is 112 cm long. To solve this, we should first simplify the given ratio to its lowest terms. The ratio can be simplified to 8:3, by dividing both numbers by 2. If Joey's rope is 112 cm (which corresponds to 8 parts of the ratio), then each 'part' of the ratio represents 112 cm divided by 8, which is 14 cm. Since Chad's rope corresponds to 3 parts of this ratio, the length of Chad's rope is 3 times 14 cm, which equals 42 cm.

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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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 .

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 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.

Answer:

No, she didn't use all of the balloons

Step-by-step explanation:

The following information is missing:

Alice is making balloon bunches from 6 red balloons and 15 blue balloons.

If she makes 2 bunches, there are 6/2 = 3 red balloons in each bunch and 15/2 = 7 (rounded to the lowest integer) blue balloons in each bunch. In this case, there is 1 blue balloon left

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.

To find the number of buttons per jar, divide the total number of buttons (2.134) by the number of jars (12). However, the count of 2.134 buttons is likely incorrect as you cannot have a fraction of a button, indicating a potential typo or miscount.

The question asks how many buttons will be in each jar if Lisa has to sort 2.134 buttons equally into 12 jars. To find this, we need to divide the total number of buttons by the number of jars.

First, let's set up the division equation: 2.134 buttons ÷ 12 jars = number of buttons per jar.

Now, we calculate the number of buttons per jar: 2.134 ÷ 12 = approximately 0.1778 buttons per jar. However, since we can't have a fraction of a button, Lisa likely made an error in counting, as the number of buttons needs to be a whole number. So, assuming there's a typo, and the actual number of buttons is a whole number, Lisa would need to recount her buttons before sorting them.

Once Lisa has the correct number of whole buttons, she could repeat the division process to find the exact number of buttons per jar.

Each jar will contain approximately 0.1785 buttons.

To determine how many buttons will be in each jar, you divide the total number of buttons (2.134) by the number of jars (12). The calculation is as follows: [tex]\( \frac{2.134}{12} \approx 0.1785 \)[/tex]. Therefore, each jar will contain approximately 0.1785 buttons.

In this scenario, the division represents the distribution of buttons into equal portions, with the quotient being the number of buttons per jar. It's crucial to understand the concept of division to solve such problems. In practical terms, if you were to distribute 2.134 buttons equally among 12 jars, each jar would have approximately 0.1785 buttons. This approach ensures a fair and even distribution of the given quantity among the specified number of containers.

Overall, understanding the basic arithmetic operation of division helps solve real-world problems like distributing items equally, and in this case, finding the number of buttons per jar in Lisa's scenario.

Complete question: "Lisa has 2,134 buttons that need to be sorted equally into 12 jars. How many buttons will be in each jar?"

Answer:

The real answer is D.

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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The fraction of Earth's crust that is silicon is 0.28, which can also be written as 28/100 or 28%.

To determine the fraction of Earth's crust that is silicon, we need to convert the percentages into fractions.

The percentages:

Oxygen: 47%

Silicon: 28%

Aluminum: 8%

Other: 17%

To convert these percentages into fractions, we divide each percentage by 100:

Oxygen fraction = 47/100 = 0.47

Silicon fraction = 28/100 = 0.28

Aluminum fraction = 8/100 = 0.08

Other fraction = 17/100 = 0.17

Now, to find the fraction of Earth's crust that is silicon, we divide the silicon fraction by the sum of all the fractions:

Silicon fraction / (Oxygen fraction + Silicon fraction + Aluminum fraction + Other fraction)

0.28 / (0.47 + 0.28 + 0.08 + 0.17)

0.28 / 1

Therefore, the fraction of Earth's crust that is silicon is 0.28, which can also be written as 28/100 or 28%.

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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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Answer:

D 423

Step-by-step explanation:

1269/3 = 423

The cost for 3 pounds of peanuts is found by first determining the cost per pound from the 5 pound price, which is $1.50 per pound. Multiplying this rate by 3 pounds gives us the total cost of $4.50.

If the cost of peanuts varies directly with the number of pounds bought, this means you can find the cost per pound and then use it to calculate the price for any amount of peanuts. Given that 5 pounds costs $7.50, first we calculate the cost per pound:

Cost per pound = Total cost / Number of pounds = $7.50 / 5 pounds = $1.50 per pound.

Now, to find the cost of 3 pounds of peanuts, we multiply the cost per pound by the number of pounds:

Cost of 3 pounds = $1.50 per pound * 3 pounds = $4.50.

Therefore, the cost of 3 pounds of peanuts is $4.50.