distribution of expenses for sales of 240,000 ace manufacturing company how many dollars were spent for operating expenses

Answer:

14 inches and 21 inches

Step-by-step explanation:

sum the parts of the ratio , 2 + 3 = 5 parts

divide length of stick by 5 to find the value of one part of the ratio

35 inches ÷ 5 = 7 inches ← value of 1 part of the ratio , then

2 parts = 2 × 7 = 14

3 parts = 3 × 7 = 21

the 2 pieces are 14 inches and 21 inches long

Answer:

Step-by-step explanation:

Answer:

14 inches and 21 inches

Step-by-step explanation:

sum the parts of the ratio , 2 + 3 = 5 parts

divide length of stick by 5 to find the value of one part of the ratio

35 inches ÷ 5 = 7 inches ← value of 1 part of the ratio , then

2 parts = 2 × 7 = 14

3 parts = 3 × 7 = 21

the 2 pieces are 14 inches and 21 inches long

Answer:

Step-by-step explanation:

The given system of equations :

Multiply equation (1) with 3 and equation (2) with 2 , we get

Now subtract equation (4) from equation (3), we get

Substitute the value of y in equation (1), we get

Hence, the solution of the system : (x,y)=(2,6)

Now, consider   and substitute the value of x and y , we get

The solution to the equation is x - y = -4

Given data ,

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations equal:

(3)(2x-3y) = (3)(-14)

(2)(3x-2y) = (2)(-6)

Simplifying these equations gives:

6x-9y = -42

6x-4y = -12

Now, subtract the second equation from the first equation:

(6x-9y) - (6x-4y) = (-42) - (-12)

-5y = -30

Divide both sides by -5:

y = 6

Substitute this value of y back into one of the original equations, let's use the first equation:

2x - 3(6) = -14

2x - 18 = -14

2x = 4

x = 2

Now , the value of x - y is given by

A = x - y

A = 2 - 6

A = -4

Hence , the equation is solved

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Answer:

Let h = number of hours she worked on Monday

Given that she makes $9 per hour, it is 9 x h or 9h.

If her tips is a fixed $15 amount, then we simply add 15.

9h + 15

This expression above is the amount she made last Monday.

Since she made no less than $110, meaning she made more than $110 last monday.

The final inequality is: 9h + 15 > 110.

Step-by-step explanation:

Answer:

(a) The inequality for the number of items, x, produced by the labor, is given as follows;

250 ≤ x ≤ 600

(b) The inequality for the cost, C is $1,000 ≤ C ≤ $3,000

Step-by-step explanation:

The total time available for production = 1000 hours per week

The time it takes to produce an item on line A = 1 hour

The time it takes to produce an item on line B = 4 hour

Therefore, with both lines working simultaneously, the time it takes to produce 5 items = 4 hours

The number of items produced per the weekly labor = 1000/4 × 5 = 1,250 items

The minimum number of items that can be produced is when only line B is working which produces 1 item per 4 hours, with the weekly number of items = 1000/4 × 1 = 250 items

Therefore, the number of items, x, produced per week with the available labor is given as follows;

250 ≤ x ≤ 1250

Which is revised to 250 ≤ x ≤ 600 as shown in the following answer

(b) The cost of producing a single item on line A = $5

The cost of producing a single item on line B = $4

The total available amount for operating cost = $3,000

Therefore, given that we can have either one item each from lines A and B with a total possible item

When the minimum number of possible items is produced by line B, we have;

Cost = 250 × 4 = $1,000

When the maximum number of items possible, 1,250, is produced, whereby we have 250 items produced from line B and 1,000 items produced from line A, the total cost becomes;

Total cost = 250 × 4 + 1000 × 5 = 6,000

Whereby available weekly outlay = $3000, the maximum that can be produced from line A alone is therefore;

$3,000/$5 = 600 items = The maximum number of items that can be produced

The inequality for the cost, C, becomes;

$1,000 ≤ C ≤ $3,000

The time to produce the maximum 600 items on line A alone is given as follows;

1 hour/item × 600 items = 600 hours

The inequality for the number of items, x, produced by the labor, is therefore, given as follows;

250 ≤ x ≤ 600

(a) The inequality for the number of items, x, produced by the labor, is given as follows;

250 ≤ x ≤ 600

(b) The inequality for the cost, C is $1,000 ≤ C ≤ $3,000

What is inequality?

Inequality is a statement shows greater the, greater then equal to, less then,less then equal to between two algebraic expressions.

The total time available for production = 1000 hours per week

The time it takes to produce an item on line A = 1 hour

The time it takes to produce an item on line B = 4 hour

Therefore, with both lines working simultaneously, the time it takes to produce 5 items = 4 hours

The number of items produced per the weekly labor = 1000/4 × 5 = 1,250 items

The minimum number of items that can be produced is when only line B is working which produces 1 item per 4 hours, with the weekly number of items = 1000/4 × 1 = 250 items

Therefore, the number of items, x, produced per week with the available labor is given as follows;

250 ≤ x ≤ 1250

Which is revised to 250 ≤ x ≤ 600 as shown in the following answer

(b) The cost of producing a single item on line A = $5

The cost of producing a single item on line B = $4

The total available amount for operating cost = $3,000

Therefore, given that we can have either one item each from lines A and B with a total possible item

When the minimum number of possible items is produced by line B, we have;

Cost = 250 × 4 = $1,000

When the maximum number of items possible, 1,250, is produced, whereby we have 250 items produced from line B and 1,000 items produced from line A, the total cost becomes;

Total cost = 250 × 4 + 1000 × 5 = 6,000

Whereby available weekly outlay = $3000, the maximum that can be produced from line A alone is therefore;

$3,000/$5 = 600 items = The maximum number of items that can be produced

The inequality for the cost, C, becomes;

$1,000 ≤ C ≤ $3,000

The time to produce the maximum 600 items on line A alone is given as follows;

1 hour/item × 600 items = 600 hours

The inequality for the number of items, x, produced by the labor, is therefore, given as follows;

250 ≤ x ≤ 600

Hence the inequality for the number of items, x, produced by the labor, is 250 ≤ x ≤ 600 and the inequality for the cost, C is $1,000 ≤ C ≤ $3,000

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