1. What is the midpoint of AB?

Answer:

1. Using the cost-plus pricing method, the selling price = $5.25

2. The change in selling price from 2018 to 2019 is $3.69 or 33.5% reduction.

3. To break-even, unit sales = 4,000 units

To realize a target return of $200,000, the unit sales = 5,600 units

4. Units to break-even = 12,500 meals

Sales revenue at break-even point = $125,000

Step-by-step explanation:

a) Data and Calculations:

Fixed costs = $3,000

Variable costs per unit = $5

Units manufactured = 100 units

Total variable costs = $500 ($5 * 100)

Total costs = $3,500 ($500 + $3,000)

Cost per unit = $3.50

Markup percentage = 50%

Using the cost-plus pricing method, the selling price = $5.25 ($3.50 * 1.5)

b) Fixed costs per year = $150,000

Variable costs per unit = $3

Production units = 30,000

Total variable costs = $90,000 ($3 * 30,000)

Cost-based pricing with a profit margin = $3 per unit

Total costs = $240,000 ($90,000 + $150,000)

Cost per unit = $8 ($240,000/30,000)

Selling price per unit = $11 ($8 + $3)

Variable cost = $2 per unit

Production units = 65,000 units

Total costs = ($2 * 65,000 + $150,000)

= $280,000 ($130,000 + $150,000)

Unit cost = $4.31 ($280,000/65,000)

Selling price = $7.31 ($4.31 + $3)

Change in selling = $3.69 ($11 = $7.31) = 33.5%

c) Fixed costs = $500,000

Per unit costs = $75

Proposed price = $200

Contribution margin per unit = $125 ($200 - $75)

To break-even, unit sales = $500,000/$125 = 4,000 units

To realize a target return of $200,000, the unit sales = $700,000/$125 = 5,600 units

d) Kitchen and related equipment costs = $100,000

Other fixed costs per year = $50,000

Variable costs = $6 per platter

Price per meal = $10

Contribution margin per meal = $4 ($10 - $6)

Units to break-even = $50,000/$4 = 12,500 meals

Sales revenue at break-even point = $50,000/40% = $125,000

$560-$500

=$500

therefore, other roommate will be paying $500 per month

Step-by-step explanation:

[tex] \longrightarrow \sf{ \dfrac{ \cfrac{ - 2}{x} + \cfrac{ 5}{y}}{\cfrac{ 3}{y} -\cfrac{ 2}{x} }} \\ \\ \longrightarrow \sf{ \dfrac{ \cfrac{ - 2y + 5x}{xy}}{\cfrac{ 3x - 2y}{xy} }} \\ \\ \longrightarrow \sf{ \cfrac{ - 2y + 5x}{xy}} \times{\cfrac{ xy}{3x - 2y} } \\ \\ \longrightarrow \boxed{ \sf{ \cfrac{ - 2y + 5x}{3x - 2y}}}[/tex]

Option A is correct!

The expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

[-2/x + 5/y] / [3/y - 2/x]

This expression could also be given by;

[-2y + 5x /xy] / [3 x- 2y /xy]

Now, we know that x would cancel out;

[-2y + 5x ] / [3 x- 2y]

Hence, the expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]

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Answer:

It has 1 term and a degree of 4.

Step-by-step explanation:

3j⁴k-2jk³+jk³-2j⁴k+jk³

= 3j⁴k-2j⁴k-2jk³+jk³+jk³

= j⁴k

So, in this expression, there is 1 term, and it has a degree of 4.

Answer:

24 km/h

Step-by-step explanation:

Given:

Constant speed of submarine = 24 km/h

Depth under sea = 5 km

Distance of submarine from lighthouse = 13 km

Find:

Speed of the submarine

Computation:

At steady speed, the distance between both the submarine and the lighthouse base decreases at a rate of 24 km/hr.

So, when it is 13 kilometres from its starting point, the speed remains constant at 24 kilometres per hour.

Answer:

n = 112/13 = 8.615

Step-by-step explanation:

(3/8) n + 5n - 30 = (17/8)n - 2

(3/8)n +5n - (17/8)n = 30-2

(13/4)n = 28

n = 28 * 4/13

n = 112/13

n = 8.615

lim ( sinx-1)/(x-1)

x=>0

apply x=0

(sin(0)-1)/(0-1)

(0-1)/(-1)

=1

Answer:

X * 0.8 = $64

x = $80

Step-by-step explanation:

Answer:

$80 (D)

Step-by-step explanation:

If Richard is getting a discount and his final price is $64 that means the answer must be above 64. That eliminates A, B, and C.

Use the formula: 20% of x = $64 and substitute the other two options. 20 percent of 84 is 16.8. 84-16.8=67.2 (not the correct answer). 20 percent of 80 is 16. 80-16=64(The Correct Answer).The answer must be $80 (D)    

Answer:

average of the two observations in the center of the data array

Step-by-step explanation:

When there is an odd number, we use the middle

Example

1,5,9

The median is 5

When there is an even number

1,3,5,7

The middle is between the 3 and 5 so we average the middle number

(3+5)/2 = 4

Answer:

the answer is => observation in the center of the data array

Step-by-step explanation:

[tex]\sf{}[/tex]

Answer:          

35/5 (if you mean 10.6)    

1000000 (if you mean 10 to the sixth power)      

0.000001 (if you mean 10/6)

Answer:

There are 126 inches in 10'6

Step-by-step explanation:

take our feet and multiply the value by 12

9514 1404 393

Answer:

Step-by-step explanation:

The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.

__

a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).

The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)

These are equal, so we have ...

  16(AC -1.5) = 7(3 -AC)

  16AC -24 = 21 -7AC . . . . . eliminate parentheses

  23AC = 45 . . . . . . . . . . . add 7AC+24

  AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC

  AC ≈ 2.0 meters . . . . rounded to 1 dp

__

b) The torques in this scenario are ...

  M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m

  M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M

  M = 41.3 kg . . . . rounded to 1 dp

_____

Additional comment

Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.

The guidance director is conducting a sample poll in this experimental design.

Sample is a part of population. It does not comprises whole population. It is representatitive of whole population.

We are required to fill the blank with appropriate term among the options.

The correct option is sample poll because the guidance director collects data in his school only.

Census collects the whole population of the country.

Sample poll means collecting data from small population.

Random sample means collecting data from a part of popultion without identifying any variable.

Hence we found that he was doing sample poll.

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Answer:

Step-by-step explanation:

They travel 500 - 300 = 200 miles in 2 hours so their combined speed is

100 mph.

If their respective speed are x and y mph then we have the system

x + y = 100

x - y = 20

Adding the 2 equations

2x = 120

x = 60

and y = 40.

The other solution is that y = 60 mph and x = 40 mph.

Answer:

i) pi×4500 cm³

ii) pi×600 cm²

iii) 14 liters

Step-by-step explanation:

in general : the diameter is 30 cm, the radius is half of that (15 cm)

i)

the volume of a cylinder is base area times height.

Vc = pi×r²×h = pi×15²×20 = pi×225×20 = pi×4500 cm³

ii)

similar to volume, the side "mantle" area of the cylinder is the circumference of the base area times height.

surface area of the cylinder mantle is

Scm = 2×pi×r×h = 2×pi×15×20 = pi×30×20 = pi×600 cm²

iii)

for this we need now to do the multiplication with pi and then convert the cm³ to liters.

1 liter = a cube of 10 cm side length = 10×10×10 = 1000 cm³

pi×4500 = 14137.17 cm³ = 14.13717 liters or rounded 14 liters

Step-by-step explanation:

let's convert the statement into equation..

let the charge of 1st mechanic be x and second be y..

by the question..

10x+5y=750...(i)

x+y=105..(ii)

from eqn(ii)..

x+y=105

or, x=105-y...(iii)

substituting the value of x in eqn (i)..

10x+5y=750

or, 10(105-y)+5y=750

or, 1050-10y+5y=750

or, 1050-750=5y

or, y=300/5

•°• y=60

substituting the value of y in eqn(iii).

x=105-y

or, x=105-60

•°• x= 45..

the rate charged by two mechanics per hour was 60$ and 45$

no the square root of 113 is rounded to 56x2

Answer:

n=4

Step-by-step explanation:

f(x+n)=3(x+n)^2-7=3x^2+24x+41

3x^2+3n^2+6xn-7=3x^2+24x+41

Comparing and we will get, n=4

Answer:

2 3/10

Step-by-step explanation:

3/5x2=6/10

6/10-3/10=3/10

I think its A) (f+g)(z)=|2x+4|-2

Step-by-step explanation:

Whole numbers are natural numbers, and natural numbers do not include negatives, decimals, fractions, or roots, so all whole numbers can indeed satisfy the inequality.

Answer:

Step-by-step explanation:

Let L represent the length of the triangle.

Let W represent the width of the triangle.

The length of a rectangle is four more than three times the width. This means that

L = 3W + 4

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

If the perimeter of this rectangle is at least 70 square centimeters, an inequality that can be solved to find the width of the rectangle is

2(L + W) ≥ 70

L + W ≥ 70/2

L + W ≥ 35

Answer:

6w +8 ≥70

Step-by-step explanation:

Let w be the width

The length is then 3w+4 ("the length is 4 more than 3 times the width")

Since a rectangle has opposite sides equal, the perimeter would be 2(l+w) or 2(w+3w+4) which would be 6w +8.  If the perimeter is at least 70, that is, 70 or more, the inequality would be

  6w + 8 ≥ 70.  

The units, however, would not be SQUARE centimeters, just centimeters.  If the question were asking for area, the units would be square units, but since perimeter is a linear measurement,  the units would have to be linear.

Answer:

theres no question....

Step-by-step explanation:

???

Answer:

1.6 ft

Step-by-step explanation:

If you use the Pythagorean Theorem to solve for x, you get:

[tex]x=\sqrt{2.1^2-1.4^2}[/tex]

[tex]x=\sqrt{2.45} = 1.56524758425[/tex]

Rounded to the nearest tenth, the answer is 1.6

can you zoom in on my pic more or no does it say 1/z

Answer:

Option A. Reciprocal

Answered by GAUTHMATH

Answer:

200 kilometers and 150 kilometers

Answer:

t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks

S = V * t

V = S / t = 20 mi * 5280 ft/mi / 2800  sec  = 37.7 ft/sec

Since 88 ft/sec = 60 mph

the speed is 60 * 37.7 / 88 = 25.7 mph