Find the surface area of the rectangular prism.
4 yd
3 yd
3 yd

Top company would accept the order as it increases the total profit of the corporation by $90000

As a company as a whole, Tops corporation will accept orders if the contribution margin increases by accepting orders.

a. The contribution margin will be:

= sales price - variable cost of manufacturing department - variable cost of marketing department

= $400 - [$2400*1000/10000units] - $70

= $400 - $240 - $70

= $90

Therefore, the increase in profit will be:

= $90 × 1000

= $90000

Top company would accept the order.

b. The marketing department will accept the order as it increases its profit by $400000-$370000 = 30000.

c. The manufacturing division manager would accept the order as it increases its profit by $60000. This was gotten as:

= (300 × 1000) - (240 × 1000)

= 300000 - 240000

= 60000

The other parts of the question include:

The company has just received an offer to buy 1,000 units of the product this month at a price of $400 per unit. The Marketing Division manager suggests that for the special order only, the transfer price be set at 50 percent of the sales price, or $200 per unit. Instead, assume the transfer price is unchanged from the current transfer price.

Required:

a. Does Tops Corporation want to accept this order?

b. Will the Marketing Division manager be willing to accept this order?

c. Will the Manufacturing Division manager be willing to accept this order?

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The answers to the problem are:

a) The value of x is : 8

b) ∠ZRB and ∠BTS are not supplementary angles.

c) ∠BST and ∠RSB are complementary angles.

d) ∠ABT is  an acute angle

e) SA is not the bisector of the angle ∠ZSY.

Angles are formed when two lines meet and they are of different types.

acute: this is an angle less than 90°

obtuse: this angle is greater than 90° but less than 180°

reflex: this angle is greater than 180° but less than 360°

Analysis:

∠BRS = 180 - (20X - 22) = 202 - 20X

a) To find x, sum of angles in the triangle = 202-20x + 2x+32 + 5x+10 + 120-10x = 180

364 -23x = 180

23x = 364-180

23x = 184

x = 8

b) ∠ZRB = 20x-22 = 20(8) - 22 = 138°

   ∠BTS = 2x+32 = 2(8)+32 = 48°

    138°+48° = 186° [tex]\neq[/tex] 180°

     They are not supplementary

c)  ∠BST = 120-10X = 120 - 10(8) = 40°

     ∠RSB = 5x+10 = 5(8)+10 = 50°

      50+40 = 90°. They are complementary

d)   ∠ABT = 180 - ∠ABR = 180 - 100 - x = 88°

      It is acute since it is less than 90°

e)   SA is not an angle bisector, since it dived the angles as 40° and 50° and not equal.

In conclusion, the solution to the questions are:

a) The value of x is : 8

b) ∠ZRB and ∠BTS are not supplementary angles

c) ∠BST and ∠RSB are complementary angles

d) ∠ABT is  an acute angle

e) SA is not the bisector of the angle ∠ZSY

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The slope within two sets of points is calculated using the slope equation [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

The slope of a line or points is the rate of change of the line.

This in other words means that, the vertical change per unit horizontal change

Assume that the points are given as:

(x1, y1) and (x2, y2)

The slope (m) of the points is:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

Hence, the equation of two sets of points is [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

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Answer:

I was unable to do no. 10 hope others solution can help you

Answer:

Angle 2 = 150°

Step-by-step explanation:

▪︎ Measures of supplementary angles add up to 180°.

Therefore,

Angle 1 + Angle 2 = 180°

Angle 1 = 30°

30° + Angle 2 = 180°

Angle 2 = 180° - 30° = 150°

Answer:

The rule is increase by 5. That means the next term would be 26.

Probability of paYing in credit card

P(Not paying in credit card)

The probability that the next customer will pay with something other than a credit card is 0.87.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Layla owns a small business selling clothing. She knows that in the last week, 52 customers paid cash, 20 customers used a debit card, and 11 customers used a credit card.

Based on these results we have;

Total cards=52+20+11=83

Probability of paying in credit card;

11/83

0.13

Now, P(Not paying in credit card)

1-0.13

0.87

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Answer:

Medical Insurance

Step-by-step explanation:

Answer:

Medical Insurance

Step-by-step explanation:

serious car accident and broke both wrists.

Answer:

they look similar but one of them is upside down.

Answer:

-6, -6

Step-by-step explanation:

Given :

Solving :

The zeros are : -6, -6

Answer:

y=-2x

Step-by-step explanation:

should look like a straight line, that is going up to the left. crossing (0,0) and (1,-2)

It is also called Middle Term Splitting

Its a cool thing with which you can solve different orders of polynomials(or any algebraic expressions if you're a pro).

It is writing an expression as a product of 2 or more factors

Answer:

factorization is of writing a number or another mathematical use as a product of several factors, usually smaller of the same kind.

Step-by-step explanation

3 × 5 is a factorization of the integer 15, and is a factorization of the polynomial x² – 4.

5 (12 + x)

Step-by-step explanation:

Answer:

5(12+X)

Step-by-step explanation:

Answer:

BC = 17 - x

Step-by-step explanation:

Let AC be the line segment and B be some point on it,

AB + BC = AC

( 2x - 8 ) + BC = x + 9   ...............(1)

BC = x + 9 - ( 2x - 8 )
BC = 17 - x

Answer:

Step-by-step explanation:

8²p=8^4

64p=4096

p=64

p could also equal 2

8^2x2=8^4

Answer: P = ^2

Step-by-step explanation:

8^4= 4096

8^2= 64

4096/64=64

(8^2)^2= 8^4

4096 = 4096

I'm good how's life!

Answer:

terminal point is at (0, -1) and sin 0 = -1

Step-by-step explanation:

In a unit circle the radius of the circle is 1 so

- we know the points where the circle intersects the x-axis and y-axis as a (x , y) coordinates.

(1, 0) where we start on the positive x-axis and where angle is 0°

(0, 1) where we go counterclockwise and where angle is 90°

(-1, 0) where we go continue counterclockwise and where angle is 180°

(0, -1) where we stop in our problem because the angle is 270°

-we also know that x= cos O and y= sin O so the coordinates (x, y) are really

(cos O, sinO)

Given:

        0 = 270°

    sin 0 = sin 270°

sin 270°  =  -1

The terminal point is at (0, -1) and sin 0 = -1

Answer:

[tex]x \approx 9.823\ ft[/tex]

Step-by-step explanation:

Remember that the area of a sector is defined as:

[tex]A = \frac{\theta}{360^\circ}\times \pi r^2[/tex]

In this problem, we are given the area [tex]A[/tex], and the angle [tex]\theta[/tex]. We can set up an equation to solve for the radius, which is x:

[tex]A = \frac{\theta}{360^\circ}\times \pi r^2\\128 = \frac{152}{360}\times \pi r^2\\128 \times \frac{360}{152} = \pi r^2\\\frac{5760}{19} = \pi r^2\\r = \sqrt{\frac{5760}{19 \pi}}\\r \approx 9.823[/tex]

Answer:

r ≈ 9.8 feet

Step-by-step explanation:

Formula of A Sector

Substitute the given values in the formula to find r.

Answer:

$3.40

Step-by-step explanation:

10% of $34

= [tex]\frac{10}{100}[/tex] × $34

= 0.1 × $34

=$3.40

Answer:

240cm³

Step-by-step explanation:

To find our answer we will multiply the volume, width, and height.

4 · 20 · 3 = 240.  Therefore, 240cm³ is our answer.  

Have a good day!

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's calculate its volume ~

Volume of a rectangular prism is :

[tex]\qquad \sf  \dashrightarrow \:v = l \cdot w\cdot h[/tex]

[tex]\qquad \sf  \dashrightarrow \:v = 20 \cdot 4\cdot 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:v = 240 \: \: cm {}^{3} [/tex]

The amount of sheet metal needed to form the conical funnel is 5525 cm²

The given parameters are:

Start by calculating the slant height (l) of the cone using:

l = √(r² + h²)

This gives

l = √(30² + 50²)

Evaluate

l = 58.31

The lateral surface area of the conical funnel including the overlap is then calculated as:

A = πrl + Overlap * l

This gives

A = 3.142 * 30 * 58.31 + 0.5 * 58.31

Evaluate

A = 5525.4556

Approximate

A = 5525

Hence. the amount of sheet metal needed is 5525 cm²

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Answer:

8.9r + (5s + 10)

actually the parenthesis aren't necessary...

8.9r + 5s + 10

Step-by-step explanation:

You can change a subtraction to addition if you change the second term to the opposite sign. This problem is like advanced mode of "Add the Opposite"

8.9r - (-5s - 10)

= 8.9r + (+5s + 10)

= 8.9r + (5s + 10)

= 8.9r + 5s + 10

Answer:

341.25

Step-by-step explanation:

You first split the figure into 2 pieces the triangular prism and the rectangular prism now that we know the dimensions of each figure we can create an expression, we will start with the triangular prism. the expression will be 3/2 x 5/2 x 10.5. Then we solve the rectangular prism. 5 x 5 x 10.5.

Now that we have acquired all the math that we need we can continue to simplify. 3 x 2 x 5/2 was derived from (3 x 5)/2 and we physically drew it out with properties of algebra (a later topic to study) anyways we get 15/2=7.5 and we multiply that by 10.5 giving us 78.75. the triangular prism is easier we just do 25 x 10.5 giving us 262.5. Now that we have succumbed both figures we can combine the to get the volume which is 341.25 (78.75 + 262.5).

Answer:

sequence

Step-by-step explanation:

Answer:

BC = 25 in

AN = 12 in

BN = 16 in

NC = 9 in

Formulas:

Pythagorean Theorem

[tex]c^2 = a^2 + b^2[/tex]

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Area of triangle

[tex]A = \frac{1}{2}bh[/tex]

A ... area of triangle

b ... base (one of the sides of the triangle)

h ... height perpendicular to base

Step-by-step explanation:

Given:

A = 90°

AB = 20 in

AC = 15 in

See attached picture.

1) BC

To find BC we can use Pythagorean theorem, since ABC is a right triangle. We have the lengths of two legs (AB, AC) and we are finding the hypotenuse.

[tex]c^2 = a^2 + b^2\\\text{BC}^2 = \text{AB}^2 + \text{AC}^2\\\text{BC}^2 = 20^2 + 15^2\\\text{BC}^2 = 625\\\sqrt{\text{BC}^2} = \sqrt{625}\\\text{BC} = 25 \text{ in}[/tex]

2) AN

AN is the height corresponding to base BC. To find it we can use formula for the area of the triangle. But first let's find the area of the triangle.

Notice how AB is perpendicular to AC. We can use AB as base and AC as height.

[tex]A = \frac{1}{2}bh\\\\A = \frac{1}{2} \times \text{AB} \times \text{AC}\\\\A = \frac{1}{2} \times 20 \times 15\\\\A = 150 \text{ in}^2[/tex]

Now that we have area, we can use BC as base and AN as height and solve for AN.

[tex]A = \frac{1}{2}bh\\\\A = \frac{1}{2} \times \text{BC} \times \text{AN}\\\\150 = \frac{1}{2} \times 25 \times \text{AN}\\\\\ 300 = 25 \times \text{AN}\\\\12 = \text{AN}\\\\\text{AN} = 12 \text{ in}[/tex]

3) BN

Let's use Pythagorean theorem in right triangle ABN. Hypotenuse is AB.

[tex]c^2 = a^2 + b^2\\\text{AB}^2 = \text{AN}^2 + \text{BN}^2\\20^2 = 12^2 + \text{BN}^2\\400 = 144 + \text{BN}^2\\256 = \text{BN}^2\\\sqrt{256} = \sqrt{\text{BN}^2}\\16 \text{ in} = \text{BN}[/tex]

4) NC

We know the lengths of BC an BN, so we can just subtract.

[tex]\text{NC} = \text{BC} - \text{BN}\\\text{NC} = 25 - 16\\\text{NC} = 9 \text{ in}[/tex]

Answer:

6

Step-by-step explanation:

that is because 6 is x and y is -3

Answer:

  62, 63, 64

Step-by-step explanation:

The middle integer of three consecutive integers will be the average of them. That is, it will be their sum, divided by 3.

__

The middle integer is 189/3 = 63.

The three consecutive integers are 62, 63, 64.

_____

Additional comment

If you'd like to write an equation that tells you the same thing, let x represent the middle integer. Then the lower one is x-1, and the upper one is x+1. Their sum is ...

  (x-1) +x +(x+1) = 189

  3x = 189 . . . . . . . . . . . . simplify

  x = 189/3 = 63 . . . . . . . divide by the coefficient of x

  (x-1) = 63-1 = 62 . . . . . . find the other two integers

  (x+1) = 63+1 = 64

Answer:

v = -3

General Formulas and Concepts:
Algebra I

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify given.

-6(v + 4) = -6

Step 2: Solve for v

∴ the value of v is equal to -3.

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Topic: Algebra I

Answer:

15%

Step-by-step explanation:

see the picture for explanation

Answer:

28%.

Step-by-step explanation:

That would be 100 * 7/25

= (100/25) * 7

= 4*7

= 28.

Answer:

Step-by-step explanation:

Conversion

A % can always be changed into a decimal by dividing by one hundred. In this case

decimal = 36.2/100 = 0.262 \\

Answer: 0.262

Answer:

181/500

Step-by-step explanation: