PLEASE HELP!!!
Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180° In a triangle, the measures of the three angles are x, x + 7, and x - 13. What is the measure of each angle?​

1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600.

1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200.

2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600.

2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200.

3a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.

3b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.

4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.

4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.

2a. Direct material cost per unit is $7.30.

2a. Direct labor cost per unit is $4.30.

2a. The Variable manufacturing overhead per unit is $1.80.

2a. The Fixed manufacturing overhead per unit is $5.30.

2a. The total manufacturing cost per unit is $18.70 ($13.40 + $5.30)

2a. The number of units produced and sold is 14,000 units.

2a. Total direct costs are $217,000 (14,000 x $13.40 + 14,000 x $2.10).

2b. Total indirect costs are $166,600 (14,000 x $5.30 + 14,000 x $6.60).

Relevant production range = 12,000 to 16,000 units

Production and sales units = 14,000 units

                                                  Average Cost

                                                       per Unit

Direct materials                                $ 7.30

Direct labor                                      $ 4.30

Variable manufacturing overhead  $ 1.80

Direct cost per unit                         $13.40

Fixed manufacturing overhead     $ 5.30

Total manufacturing cost per unit $18.70

Fixed selling expense                   $ 3.80    $53,200 ($3.80 x 14,000)

Fixed administrative expense      $ 2.80     $39,200 ($2.80 x 14,000)

Total fixed costs per unit               $6.60     $92,400 ($6.60 x 14,000)

Variable selling and admin:

Sales commissions                        $ 1.30

Variable administrative expense $ 0.80

Total variable selling and admin per unit = $2.10

1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600 ($13.40 x 14,000).

1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200 ($5.30 x 14,000).

2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600 ($13.40 x 14,000).

2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200 ($5.30 x 14,000).

3) Fixed selling expenses =  $53,200 ($3.80 x 14,000)

Advertising expenses = $39,200

Sales Compensation = $14,000 ($53,200 - $39,200)

Sales Commission = $18,200 ($1.30 x 14,000)

Total Salespersons' compensation = $32,200

a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.

b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.

4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.

4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.

2a. Direct material cost per unit is $7.30.

2a. Direct labor cost per unit is $4.30.

2a. The Variable manufacturing overhead per unit is $1.80.

2a. The Fixed manufacturing overhead per unit is $5.30.

2a. The total manufacturing cost per unit is $18.70 ($13.40 + $5.30)

2a. The number of units produced and sold is 14,000 units.

2a. Total direct costs are $217,000 (14,000 x $13.40 + 14,000 x $2.10).

2b. Total indirect costs are $166,600 (14,000 x $5.30 + 14,000 x $6.60).

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Answer:

y = -2x + 18

Step-by-step explanation:

Slope m = -2 with y = 8, x = 5

y = mx + b

8 = (-2)(5) + b

8 = -10 + b

b = 8 + 10 = 18

then y = -2x + 18

the first derivative of the given function is:

f'(x) = (2x²- 12x - 2)/( 2x² - 2)²

The quotient rule says that, if f(x) = g(x)/h(x), then:

f'(x) = ( g'(x)*h(x) - g(x)*h'(x) )/h(x)²

In this case we know that:

g(x) = x² + x - 2

h(x) = 2x² - 2

The derivatives are:

g'(x) = 2x + 1

h'(x) = 4x

Replacing that we get:

f'(x) = ( g'(x)*h(x) - g(x)*h'(x) )/h(x)²

      = ( (2x + 1)*(2x² - 2) - ( x² + x - 2)*(4x) )/( 2x² - 2)²

Expanding the denominator we get:

f'(x) = ( 4x³ - 4x + 2x² - 2 - 4x³ + 4x² - 8x)/( 2x² - 2)²

f'(x) = (2x²- 12x - 2)/( 2x² - 2)²

That is the first derivative of the given function.

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hi

"times " =  multiply by

B*T*4 =  4BT   (as it is the custom to put numbers before letters, and letters in alphabetic order)

enter the correct letters in the boxes on the left with the negative statements on the right

E    Apples make good pies      A  seven is not a prime number

F    the sun is hot today             B   a line does not contain at least two points

D    3+2=7                                   C a right angle does not measure < 90degre

C    a right angle measure < 90  D  3+2[tex]\neq[/tex]7

 A  seven is a prime number       E apples does not make good pies

 B   a line contain at least two points   F  the sun is not hot today

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Answer:

2 hours

Step-by-step explanation:

Rate_Sally=1/3, Rate_Steve=1/6, Rate_Together=Rate_Sally+Rate_Steve;

T_Together=1/Rate_Together

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

Due to length restrictions, we kindly invite to check the explanation of this question for further details on equations.

In this problem we find equations that have got to be cleared with respect to a given variable, this can be done by taking advantage of algebra properties:

14) b / c = a → c = b / a

15) k = a - y → y = a - k

16) d · f · g = h → f = h / (d · g)

17) 2 · x + 3 · y = 12 → 3 · y = 12 - 2 · x → y = 4 - (2 / 3) · x

18) 2 · n = 4 · x + 2 · y → n = 2 · x + y

19) a · b · c = 1 / 2 → b = 1 / (2 · a · c)

20) y = 3 / (5 · u) + 5 → y - 5 = 3 / (5 · u) → 5 · u = 3 / (y - 5) → 3 / [5 · (y - 5)]

21) 8 · (x - a) = 2 · (2 · a - x) → 8 · x - 8 · a = 4 · a - 2 · x → 10 · x = 12 · a → x = (6 / 5) · a

22) 12 · (m + 3 · x) = 18 · (x - 3 · m) → 12 · m + 36 · x = 18 · x - 54 · m → 66 · m = - 18 · x → m = - (3 / 11) · x

23) V = (π / 3) · r² · h → h = [3 · V / (π · r²)]

24) V = (π / 3) · r² · (h - 1) → h - 1 = [3 · V / (π · r²)] → h = 1 + [3 · V / (π · r²)]

25) y · (a - b) = c · (y + a) → a · y - b · y = c · y + a · c → (a - b - c) · y = a · c → y = (a · c) / (a - b - c)

26) x = [3 · (y - b)] / m → (m · x) / 3 = y - b → y = b + (m · x) / 3

27) F = - (G · m) / r² → G = - (F · r²) / m

28) The area formula of the baking sheet is l · w = 117.

29) The temperature formula is T = (7 / 30) · n + 40.

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Answer:

[tex]x=35[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{x}{5} =7[/tex]

When x is the numerator of the fraction you multiply each side by the denominator in order to isolate the variable.

[tex]\frac{x}{5} =7[/tex]
[tex]\frac{5x}{5} =x[/tex]
[tex]7\times5=35[/tex]
[tex]x=35[/tex]

Hope this helps.

Answer:

x = 35

Explanation and Chcek part below

Hope this helps :)

Step-by-step explanation:

x

Fraction bar/divide ---> --- = 7

5

1. Isolate the variable since it says dividing by 5 we must do the inverse operation which is multiplying by 5 to cancel them out. We are multiplying by 5 on one side of equation so we must multiply on the other side too. When a number is next to parenthesis it means to multiply the 2 numbers.

x

(5) -- = 7 (5)

5

x = 35

Check:

35

---- = 7

5

7 = 7

True statement.

Answer:

14

Step-by-step explanation:

B is the midpoint of AC, in other words it is the halfway point.

So A to B should be equal to B to C

Our expression is:

2x + 9 = 37

Subtract 9

2x = 28

Divide by 2

x = 14

Answer:just draw 6 apples up and down, then draw them 11 more times right next to each other, so draw 72 apples

Step-by-step explanation:

The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

Given two equations  1)6x-10<8 and 2) [tex]\frac{x}{3}[/tex]+6 > 12

Solving the above equations

1) 6x-10≤8

⇒6x ≤ 18

⇒X≤ 3

⇒x ≤ 3 i.e.  x ∈ (-infinity,3]

2)[tex]\frac{x}{3}[/tex]+6 > 12

⇒[tex]\frac{x}{3}[/tex] > 6

⇒x>18

⇒ x > 18 i.e.  x ∈ (18,infinity)

Therefore,The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

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Answer:

5.1

Step-by-step explanation:

Answer:

3.5 or [tex]\frac{7}2}[/tex]

Step-by-step explanation:

4(x+2)-2=6x-2(4+x)

4x + 8 - 2 = 6x - 8 + 2x

4x + 6 = 8x - 8

14 = 4x

x = 3.5 or [tex]\frac{7}2}[/tex]

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Answer:

0+26=26, 26+0=26

Step-by-step explanation:

When you add 0 to a number and get the same number, that's the Identity Property of Addition.

Answer:

1 pound (lb) is equal to 453.59237 grams (g)

Answer:

´the set of all values for which the function is defined´

Step-by-step explanation:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set.

The typical average price of gasoline should be $2.81 and not $2.69 because $2.69  is not the average of the sampled prices.

We are given the prices of a gallon of gasoline from 5 gas stations surveyed as; $2.79, $2.99, $2.69, $2.89, and $2.69.

Thus, to calculate the mean, we will use the formula;

Mean = ∑x/n

Mean = (2.79 + 2.99 + 2.69 + 2.89 + 2.69)/5

Mean = 14.05/5

Mean = $2.81

Thus, the typical average price of gasoline should be $2.81 and not $2.69

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Answer:

work is shown and pictured

Step-by-step explanation:

all real numbers greater than our equal to -1.

as the parabola function is y = something in x², the parabola opens up either up or down.

if the function would have been x = something in y², the parabola would open left or right.

but our parabola here opens therefore up and down.

the vertex is therefore the maximum or minimum of the parabola. y does not get larger or smaller than the y value of the vertex.

as we see that the curve goes through points with y value 0 (which is clearly larger than -1), it means the vertex is a minimum, and the parabola opens up.

therefore the answer at the beginning. any y value of the function can only be greater than or equal to -1.

Answer: 729x^6

Step-by-step explanation: I got this answer because I first multiplied the 3^3 which is 27

then the equation is 27x^3 times 3^3x^3. Then you do the same thing on the other side which is 27x^3. So 27x^3 times 27x^3. After that you multiple 27 and 27 which is 729, don’t forget your x^3 and x^3 which is x^6 so your answer is 729x^6.

The rate of discharge is 1,54,550 cubic meter/sec.

This is the problem related to conversion of units. We need to convert cubic feet into cubic meter here.

Also we know that 1 foot = 0.305 meter.

The rate of discharge of water is given as 5,500,000 cubic feet per second.

So, now to convert to cubic meter we need to divide the given rate by cube of 0.305.

Now discharge in cubic meter per second = [tex]5,500,000*(0.305)^{3}[/tex]

                                                                  = [tex]5,500,000*0.028[/tex]

                                                                  = 1,54,550 cubic meter/sec

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The interval on a number line (-∞, -6)​ using set-builder notation is;

{ x | x ∈ R, x ≤ -6 }

Set-builder notation is a mathematical notation for describing a set by representing its elements or explaining the properties that its members must satisfy.

Real numbers (R) include all rational and irrational numbers. Thus, If we need to write the interval on a number line (-∞, -6)​ using set-builder notation, we will write as:

{ x | x ∈ R, x ≤ -6 }

In words : "x such that x belongs to R, x is less than or equal to -6"

This shows that x is any real number less than or equal to -6

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54 grams of aluminium is present in aluminium sulphate Al₂(SO₄)₃.

A substance's molecular mass is the sum of the atomic masses of all of the atoms in the molecule of a substance.

For the given question, the expression is;

aluminium sulphate Al₂(SO₄)₃

As three of aluminium is present in the aluminium sulphate.

And, molecular mass of one aluminium atom is 27 grams;

Thus, for 2 aluminium atoms = 2×27 = 54  grams.

Therefore, the compound aluminium sulphate contains 54 gram of aluminium in it.

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Answer: 28 units

Step-by-step explanation:

A=area of parallelogram. h=height. b=base

A=h*b

7=1/4 *b

(7=1/4 *b)*4    ==>Multiply both sides by 4 to get rid of fractions

28=b

b=28 units

An equation that relates the number of bags, x, to the cost, y is y = 5x.

An equation is a mathematical statement that claims that the two sides are equal.

An equation involves two or more variables that require some mathematical operations to obtain their equivalent value.

Therefore, an equation contains numbers, variables, and operators, which show a value after the mathematical operations.

Let the number of bags for the class = x (number of students)

Let the unit cost of a bag = $5

Let y = the total cost

Equation, y = 5x

Thus, an equation that relates the number of bags, x, to the cost, y is y = 5x.

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====================================================

Explanation:

Imagine drawing a circle and splitting it into 3 equal slices. Repeat this process to get 12 identical such circles. We have 12*3 = 36 slices so far.

Then add a 13th circle that has 2 of the 3 slices shaded, to represent 2/3. So we add 2 extra slices to the 36 original to get 36+2 = 38 total slices.

Each slice represents 1/3 of a cup. So each full circle represents 1 full cup.

-------------

Another approach:

Let's convert the mixed number 12 & 2/3 into an improper fraction

We use the formula

a & b/c = (a*c+b)/c

So,

12 & 2/3 = (12*3+2)/3 = (36+2)/3 = 38/3

Then rewrite the 38/3 as 38*(1/3) to show we have 38 copies of the 1/3 cup.

Answer: 38 cups

Step-by-step explanation:

       We will divide 12 2/3 cups by our measurement, 1/3 cup, to find how many 1/3 cups will be needed.

(12 + 2/3) / (1/3) = 38 cups

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}y^2\stackrel{\stackrel{b}{\downarrow }}{-7}y\stackrel{\stackrel{c}{\downarrow }}{-9}=0 \qquad \qquad y= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ y= \cfrac{ - (-7) \pm \sqrt { (-7)^2 -4(1)(-9)}}{2(1)} \implies y = \cfrac{ 7 \pm \sqrt { 49 +36}}{ 2 } \\\\\\ y= \cfrac{ 7 \pm \sqrt { 85 }}{ 2 }\implies y= \begin{cases} \frac{ 7 + \sqrt { 85 }}{ 2 }\\[1em] \frac{ 7 - \sqrt { 85 }}{ 2 } \end{cases}[/tex]

Answer:

500 x 4

500 x 4

5 x 4 =

20

Add the two 00's from 500.

You get 2,000.

Step-by-step explanation:

Well, we can focus on the number 5 from 500 and multiply it by 4 to receive the answer of 20 because we can assume the person solving this question knows simple multiplication factors and how to solve 5 times 4. Then, we can add the two zeros from the 500. Thus, it's 2,000.

Hope this helps.

Answer:2,000

Step-by-step explanation:

500x4

take the zeros  

5x4=20

then add the zeros

it will be 2,000