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The number of cups of flour required to make 1 dozen muffin is 2 1/3 cups.

To find out how many cups of flour are needed for every dozen muffins made, we'll use the information given that 3 1/2 cups of flour make 1 1/2 dozen muffins. We need to set up a proportion to scale the amount of flour down to the amount needed for 1 dozen muffins. First, we know that 1 1/2 dozens equals 18 muffins (since a dozen is 12), so we can express the known ratio as:

3 1/2 cups of flour / 18 muffins

To find out how many cups of flour make 12 muffins, we set up the proportion:

(3 1/2 cups / 18 muffins) = (x cups / 12 muffins)

We then cross-multiply and solve for x, which represents the cups of flour:

3 1/2 * 12 = 18 * x

7/3 or 2 1/3 = x

When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation.

In simpler terms, that means if A is always twice as much as B, then they directly vary. If a gallon of milk costs $3, and I buy 1 gallon, the total cost is $3. If I buy 10 gallons, the price is $30. In this example the total cost of milk and the number of gallons purchased are subject to direct variation -- the ratio of the cost to the number of gallons is always 3.

To be more "geometrical" about it, if y varies directly as x, then the graph of all points that describe this relationship is a line going through the origin (0, 0) whose slope is called the constant of variation. That's because each of the variables is a constant multiple of the other.Hope I helped

An equation in the slope-intercept form represents a direct variation only when the y-intercept is zero. For instance, y=3x is a direct variation while y=3x+9 isn't due to having y-intercept 9. The differentiation between a direct variation and a simple linear equation helps understand the relationship in algebra.

In mathematics, the slope-intercept form of an equation can represent a direct variation, but it's only sometimes true. An equation in the slope-intercept form represents a direct variation only when the y-intercept (the 'b' in the equation y=mx+b) is zero.

For example, the equation y = 3x represents a direct variation because the y-intercept is 0. Here, the value of y changes proportionately with x, which denotes a direct variation. However, in the equation y=3x+9 (represented in Figure A1), it does not represent a direct variation since the y-intercept is 9 (b ≠0).

Therefore, the direct variation depends on whether the y-intercept is zero or not in a slope-intercept equation. This relationship between the x and y variables in algebra helps scholars understand the difference between a direct variation and a simple linear equation.

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The mass of ether considering its density as 713 kg/m³ will be 0.09 kg.

Density or mass density is the mass of any object per volume.

For example, if the metal has a 100 kg mass and an area of 10-meter square then 100/10 = 10 kg/meter square will be the density of the given object.

Given the volume (V) of ether = 130 mL = 130 × 10⁻³ L

Since 1000 L = 1 m³

1 L =  10⁻³ m³

So, V = 130 × 10⁻³ × 10⁻³ m³

V = 130 × 10⁻⁶ M³

Now density of ether is 713 kg/m³

Thus, 713 = Mass / 130 × 10⁻⁶

Mass = 0.09 kg

Hence "The mass of ether considering its density as 713 kg/m³ will be 0.09 kg".

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The solution is 7000

The number 6,852 rounded to the nearest thousand is given by the equation A = 7,000

What is rounding up numbers?

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Non-zero digits are always significant

Zeros between non-zero digits are always significant

Leading zeros are never significant

Trailing zeros are only significant if the number contains a decimal point

Given data ,

Let the number be represented as A

Now , the value of A is

A = 6,852

The number 6,852 rounded to the nearest thousand is

You rounded to the nearest thousands place. The 6 in the thousands place rounds up to 7 because the digit to the right in the hundreds place is 8

And , when the digit to the right is 5 or greater we round away from 0

So , the rounded number is 7,000

Hence , the number is 7,000

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Answer:

Jon was a better shooter

Step-by-step explanation:

To compare the three players foul shot ratio, convert all of them in decimals as follows:

Jon: 18/19 = 0.947

Jim: 5/8 = 0.625

Joe ratio was: 0.94

The best shooter is Jon because his ratio is the greatest one.

The total area of two states is 2,27,696 square miles.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The state of Utah covers 82, 144 square miles.

The state of Montana covers 145, 552 square miles.

So, the total area of two states

= 145552 + 82144

= 2,27,696

Hence, the total area of two states is 2,27,696 square miles.

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To calculate the total of three employees' raises, each employee's current salary is multiplied by their respective raise percentage and then added together, resulting in the closest total of $4,790.

The question involves calculating the total amount of the raises given to three employees. We need to apply the given percentage raise to each employee's salary and then sum these amounts to find the answer.

Calculate Jane's raise: $41,100 * 0.04 = $1,644.

Calculate John's raise: $43,300 * 0.045 = $1,948.5.

Calculate Jack's raise: $39,900* 0.03 = $1,197.

Add the raises together to find the total: $1,644 + $1,948.5 + $1,197 = $4,789.5.

The closest amount to the total of all three raises is $4,790.

Answer:

8$

Step-by-step explanation:

The solution is, The blank is 1/2.

Here, we have,

given that,

if 4/5 times blank equals 2/5

Let x be the unknown

4/5 x = 2/5

Multiply each side by 5

4/5x * 5 = 2/5*5

4x = 2

Divide each side by 4

4x/4 = 2/4

x = 1/2

so, The blank is 1/2.

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All the solution of the expression are,

⇒ 223.6 ÷ 40 = 5.59

⇒ 8.14 ÷ 20 = 0.407

⇒ 361.5 ÷ 12 = 30.125

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

All the expressions are,

⇒ 223.6 ÷ 40

⇒ 8.14 ÷ 20

⇒ 361.5 ÷ 12

Now, We can divide all the expressions as;

⇒ 223.6 ÷ 40

⇒ 223.6 / 40

⇒ 5.59

⇒ 8.14 ÷ 20

⇒ 8.14 / 20

⇒ 0.407

⇒ 361.5 ÷ 12

⇒ 361.5 / 12

⇒ 30.125

Thus, All the solution of the expression are,

⇒ 223.6 ÷ 40 = 5.59

⇒ 8.14 ÷ 20 = 0.407

⇒ 361.5 ÷ 12 = 30.125

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The zoo orders 8 pounds of bananas each day, calculated by dividing the weekly amount (56 pounds) by the number of days in a week (7).

The question specifies that the zoo kitchen orders 56 pounds of bananas each week. To find out how many pounds of bananas are ordered daily, we need to divide this weekly quantity by the number of days in a week. Since there are seven days in a week, 56 pounds of bananas divided by 7 equals 8 pounds. So, the zoo kitchen orders 8 pounds of bananas each day.

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No, the flour is not enough to make the recipe; Katrina will still need 6/35 kilograms of flour.

To get the amount of kilogram that Katrina will still need, you should subtract the amount of flour Katrina needed from the amount she had.

This implies 3/5-3/7.

You have to find the smallest number that can divide the denominators (5 and 7) and since 35 is the smallest number that can divide both denominators, then it is the lowest common denominator or LCD.

You should now divide the denominators with 35, and also multiply the answer you get with the numerators.

This implies 3/5-3/7 = 21/35-15/35

= 6/35kg.

The final answer is 6/35, which means Katrina will still need 6/35 kilograms more of flour.

As you can see, we arrived at the final answer by subtracting the numerators (21-15) to have 6, and the lowest common denominator remains 35.

If you are faced with questions that require you to find the smallest number or LCD for large numbers, what you should do is to multiply the denominators together and reduces it if necessary.

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Answer:

1/10

Step-by-step explanation:

The place value of 3 in 6.832 is hundredth since 3 is located at the second position after the decimal point. Hundredth means 1/100

Similarly, The place value of 3 in 112.3 is a tenth since 3 is located at the first position in the value after the decimal from the back. Tenth means 1/10.

Since the value of 3 in 6.832 is 1/100, which is 1/10 of the place value of 3 in 112.3 i.e 1/10 of 1/10

The answer is therefore 1/10 since 1/10 of 1/10 gives 1/100

Answer:

A

Step-by-step explanation:

Let x be the number of cups needed for a cereal. Of the 15 cups, 5 cups are nuts and the rest is cereal:

[tex]=5/15=0.33[/tex]

33% of the mix is nuts and therefore:

[tex]100-33=67[/tex]

67% of the mix is cereal

To make 60 cup batch the cereal will be:

[tex]60\cdot{0.67}=40.2[/tex]

40 cups of cereal will make a 60 cup batch

The first digit of the quotient for 18.88 divided by 4 will be the ones place.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

WE need to find the first digit of the quotient for 18.88 divided by 4.

18.88 / 4 = 4.72

We know that Quotients are the number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

Therefore, the first digit of the quotient for 18.88 divided by 4 will be the ones place.

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To obtain a high score of 1500 points in the video game, you must beat at least 5 levels.

To find the number of levels you must beat in order to obtain the high score of 1500 points, we can set up an inequality. Let's denote the number of levels as 'x'. Each level gives you 300 points, so the total number of points you will earn is 300x. The inequality will be:

300x >= 1500

To solve this inequality, divide both sides by 300:

x >= 5

So, you must beat at least 5 levels to obtain the high score of 1500 points.