Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:

Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.

The customer margin on sales to Interstate Trucking for the year is $33,581.

Indirect costs are expenses that cannot be directly linked to a specific product or service. Instead, they are costs that are incurred for the general operation of a business and are shared among different products or services produced by the business.

In the given question,

To calculate the customer margin on sales to Interstate Trucking, we need to use the activity-based costing system to allocate the indirect costs to the order and then subtract the total costs from the sales revenue. Here are the steps to follow:

Calculate the total indirect costs for the order:

Batch processing cost = Number of batches x Batch processing activity rate

Batch processing cost = 3 x $95 = $285

Order processing cost = Number of orders x Order processing activity rate

Order processing cost = 1 x $285 = $285

Customer service cost = Number of customers x Customer service activity rate

Customer service cost = 1 x $2,624 = $2,624

Total indirect costs = Supporting direct labor cost + Batch processing cost + Order processing cost + Customer service cost

Total indirect costs = Number of direct labor-hours x Supporting direct labor activity rate + Batch processing cost + Order processing cost + Customer service cost

Total indirect costs = 0.7 x 2,200 x $8 + $285 + $285 + $2,624

Total indirect costs = $20,289

Calculate the total costs for the order:

Total costs = Direct materials cost + Direct labor cost + Total indirect costs

Total costs = $110 x 2,200 + $13.70 x 2,200 + $20,289

Total costs = $147,739

Calculate the customer margin on sales:

Customer margin = Sales revenue - Total costs

Customer margin = $141.60 x 2,200 - $147,739

Customer margin = $181,320 - $147,739

Customer margin = $33,581

Therefore, the customer margin on sales to Interstate Trucking for the year is $33,581.

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The length of side z to the nearest tenth of a centimeter is approximately 261.8 cm.

What is the Law of Sines?

The Law of Sines is a mathematical formula used to relate the side lengths and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

a/sin(A) = b/sin(B) = c/sin(C)

To find the length of side z in triangle XYZ, we can use the Law of Sines, which states:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles.

In this case, we know the length of side x, and the measures of angles Y and Z.

We want to find the length of side z. So, we can use the Law of Sines as follows:

z/sin(180° - 141° - 25°) = 830/sin(141°)

z/sin(14°) = 830/sin(141°)

Cross-multiplying:

z = (830*sin(14°))/sin(141°)

z ≈ 261.8 cm

Therefore, the length of side z to the nearest tenth of a centimeter is approximately 261.8 cm.

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3/8 divided by 1 3/5 is 3/8 ÷ 1 3/5 = 15/64.

What is the fraction?

A fraction is a numerical quantity that represents a part of a whole or a ratio between two quantities. It is expressed as one integer divided by another integer, with a horizontal line separating the two numbers. The number above the line is called the numerator and the number below the line is called the denominator.

To divide a fraction by another fraction, you need to multiply the first fraction by the reciprocal of the second fraction.

First, we need to convert the mixed number to an improper fraction:

1 3/5 = (5*1 + 3)/5 = 8/5

Now we can find the reciprocal of 8/5:

reciprocal of 8/5 = 5/8

So, 3/8 ÷ 1 3/5 can be rewritten as:

3/8 ÷ 8/5 = 3/8 * 5/8

Multiplying the numerators and denominators:

3/8 * 5/8 = (35)/(88) = 15/64

Therefore, 3/8 divided by 1 3/5 is 3/8 ÷ 1 3/5 = 15/64.

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The equation of the circle after it is dilated by a scale factor of 2 is given as follows:

B. (x + 6)² + (y - 4)² = 36.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The equation of the circle in this problem is given as follows:

(x + 3)² + (y - 2)² = 9.

The features are:

After the dilation by a scale factor of 2, the features are given as follows:

Then the equation of the circle would be of:

(x + 6)² + (y - 4)² = 36.

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As per the curve, the area under the shaded region is = 0.4878.

The entire area covered by a flat (2-D) area or the form of an item is known as area. A plane figure's area is the space that is enclosed by its border. The area of a closed figure is the sum of the number of unit squares that cover its surface. Square units like cm² and m² are used to quantify area.

99.7% (or 0.997) of the standard normal curve's entire area, which is 1, is located within three standard deviations of the mean.

The distribution of mean is μ = 0

The distribution of standard deviation is σ = 1

We must determine the area of the shaded zone according to the curve.

That is as follows:

P (-2.25 < Z < 0)

The formula to determine:

= P (Z < 0) - P (Z < -2.25)

Substitute the values in the above equation.

= 0.5 - 0.0122

The value is,

= 0.4878

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Answer:

Answer: C. 40°

Step-by-step explanation:

The shape in the picture is an isosceles triangle. This is determined because two sides share the same length. This will mean that two angles will also share the same measurement, helping us to find our answer.

Step 2: Write an equation

Now that we have identified the type of triangle, we can write an equation to solve. Two angles will be equal to 70, so subtract 70 twice from 180. It will be taken away from 180, since in a triangle the three angles are equal to 180 degrees. Now we can write the equation!

X= 180-70-70

Step 3: Solve for ∠x

The final step will be to solve using the equation we have created before.

X= 180-70-70

X= 110-70

X= 40

There is the final answer. Hope this helps! Comment below for more questions.

The distance made good by the ship is approximately 259.5 nautical miles.

What is distance?

Distance is a measurement of how far apart two objects or points are, either numerically or rarely qualitatively. Distance can relate to a physical length in physics or to an estimate based on other factors in everyday language.

To find the distance made good, we need to calculate the total displacement of the ship. This can be found using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the 120 nm southward and 230 nm westward movements of the ship form the legs of a right triangle, and the hypotenuse represents the total displacement. Using the Pythagorean theorem, we get:

Total displacement = √((120²) + (230²)) nm

= √(14400 + 52900) nm

= √(67300) nm

≈ 259.5 nm

Therefore, the distance made good by the ship is approximately 259.5 nautical miles.

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Answer:

Step-by-step explanation:

But we know that √5 is an irrational number. So, {(a - 3b)/b} should also be an irrational number. Hence, it is a contradiction to our assumption. Thus, 3 + √5 is an irrational number.

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Answer:

[tex]2 \frac{8}{13} = 2.61[/tex]

Step-by-step explanation:

[tex]1. \: \frac{3 \times 5 + 2}{5} \div 1\frac{3}{10} \\ 2. \: \frac{15 + 2}{5} \div 1 \frac{3}{10} \\ 3. \: \frac{17}{5} \div 1 \frac{3}{10} \\ 4. \: \frac{17}{5} \div \frac{1 \times 10 + 3}{10} \\ 5. \: \frac{17}{5} \div \frac{10 + 3}{10} \\ 6. \: \frac{17}{5} \div \frac{13}{10} \\ 7. \: \frac{17}{5} \times \frac{10}{13} \\ 8. \: \frac{17 \times 10}{5 \times 13} \\ 9. \: \frac{170}{5 \times 13} \\ 10. \: \frac{170}{65} \\ 11. \: \frac{34}{13} \\ 12. \: 2 \frac{8}{13} = 2.61[/tex]

An equation for the function graphed above is [tex]y = \frac{4(x - 1)}{(x + 1)(x - 4)}[/tex].

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function shown above, we can logically deduce that its vertical asymptotes include the following;

x = -1 ⇒ x + 1 = 0.

x = 4 ⇒ x - 4 = 0.

In this context, an equation that represent its denominator is given by the following quadratic function:

Q(x) = (x + 1)(x - 4)

Assuming the leading coefficient of the function P(x) is represented by a;

P(x) = a(x - 1)

By evaluating and solving for the leading coefficient "a" in this function, we have;

f(x) = P(x)/Q(x)

f(x) = a(x - 1)/[(x + 1)(x - 4)]

f(0) = a(0 - 1)/[(0 + 1)(0 - 4)]

f(0) = -a/[(1)(-4)]

f(0) = a/4

Since the y-intercept of this graph is located at (0, 1), the value of the leading coefficient (a) can be calculated as follows;

1 = a/4

1 = a/4

a = 4 × 1

a = 4

By substituting the value of the leading coefficient (a) into the function, we have the following;

f(x) = P(x)/Q(x)

f(x) = y = 4(x - 1)/[(x + 1)(x - 4)]

[tex]f(x) = y = \frac{4(x - 1)}{(x + 1)(x - 4)}[/tex]

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Therefore, the factored form of the expression [tex]-5x^3+10x^2-3x+6 is -(5x^2+3)(x-2).[/tex]

In mathematics, a factor refers to a number or an algebraic expression that is multiplied by another number or expression.

For example, in the expression 6 x 8 = 48, 6 and 8 are factors of 48 because they are both multiplied together to get the product 48. Similarly, in the algebraic expression 3x(x+2), 3x and (x+2) are both factors of the expression.

by the question.

Question 4:

To factor the expression. [tex]2x^5+4x^3-6x^2-12[/tex], we can first take out a common factor of 2 from all the terms:

[tex]2(x^5+2x^3-3x^2-6)[/tex]

Next, we can factor the expression in the parentheses by grouping the first two terms and the last two terms:

[tex]2(x^5+2x^3-3x^2-6) = 2(x^5-3x^2) + 2(2x^3-6)[/tex]

[tex]= 2x^2(x^3-3) + 4(x^3-3)= (2x^2+4)(x^3-3)[/tex]

Therefore, the factored form of the expression[tex]2x^5+4x^3-6x^2-12 is (2x^2+4)(x^3-3).[/tex]

Question 5:

To factor the expression [tex]3x^7-8x^6-9x^5+24x^4[/tex], we can first take out a common factor of [tex]3x^4[/tex] from all the terms:

[tex]3x^4(x^3-8x^2-3x+8)[/tex]

Next, we can factor the expression in the parentheses by grouping the first two terms and the last two terms:

[tex]3x^4(x^3-8x^2-3x+8) = 3x^4(x^2(x-8)-1(x-8))= 3x^4(x-1)(x-8)(x^2+1)[/tex]

Therefore, the factored form of the expression[tex]3x^7-8x^6-9x^5+24x^4 is 3x^4(x-1)(x-8)(x^2+1).[/tex]

Question 6:

To factor the expression. [tex]-5x^3+10x^2-3x+6[/tex], we can first take out a common factor of -1 from all the terms:

[tex]-1(5x^3-10x^2+3x-6)[/tex]

Next, we can factor the expression in the parentheses by grouping the first two terms and the last two terms:

[tex]-1(5x^3-10x^2+3x-6) = -1(5x^2(x-2)+3(x-2))= -(5x^2+3)(x-2)[/tex]

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The possible dimensions of the rectangular plot are 13 m by 13 m (a square) or 26 m by 6.5 m.

Perimeter is the total distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding up the lengths of all the sides of the shape. The perimeter is a measure of the distance that must be covered to go around the shape, and is typically expressed in units of length, such as meters or feet.

Let the length of the rectangular plot be L and the width be W.

We know that the perimeter of the rectangular plot is equal to the sum of the lengths of the three sides of the fence:

2L + W = 39

Also, the area of the plot is LW = 169.

From the second equation, we can solve for L or W in terms of the other variable:

L = 169/W or W = 169/L.

Substitute these expressions into the first equation:

2(169/W) + W = 39

Simplify and rearrange:

2(169) + W² = 39W

W² - 39W + 338 = 0

Solve for W using the quadratic formula:

W = (39 ± √(39² - 4(1)(338))) / 2

W = (39 ± 13) / 2

W = 26 or 13.

If W = 26, then L = (39 - 2W)/2 = -6, which is not possible. So, we can discard this solution.

If W = 13, then L = (39 - 2W)/2 = 13.

Therefore, the possible dimensions of the rectangular plot are 13 m by 13 m (a square) or 26 m by 6.5 m.

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Answer:

Step-by-step explanation:

You want the angular speed in RPM and in radians per minute for a truck wheel 38 inches in diameter traveling at 60 mph.

There are 60 minutes in an hour, so a speed of 60 mi/h is a speed of ...

  [tex]\dfrac{60\text{ mi}}{1\text{ h}}\times\dfrac{1\text{ h}}{60\text{ min}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}=5280\text{ ft/min}[/tex]

The distance traveled for 1 revolution of the wheel is equal to its circumference:

  C = πd

  C = π(38 in)/(12 in/ft) = (19/6)π ft ≈ 9.948 ft

Then the number of revolutions in 5280 ft is ...

  (5280 ft/min)/(9.948 ft/rev) ≈ 530.7 rev/min

The wheels make about 530.7 revolutions per minute.

Each revolution is an angle of 2π radians, so the angular speed is ...

  ω = 530.7 rev/min × 2π rad/rev

  ω = 3334.7 rad/min

Answer:252

Step-by-step explanation:

14x18=252

Answer:

Answer: 4,772.8 cm2

Step-by-step explanation:

The company will need 3,583.2 square inches of paper to make 15 labels.

What is cylinder?

Traditionally, a cylinder was a three-dimensional solid, one of the most fundamental curvilinear geometric shapes. It is a prism with a circle as its base in elementary geometry.

The formula for circumference is:

Circumference = π × diameter

Circumference = 3.14 × 8in

Circumference = 25.12in

So the label will need to be 25.12 inches long.

The height of the label will be the same as the height of the can, which is 9 inches.

To find the total area of the paper needed for 15 labels, we need to multiply the length of each label by its height and then multiply that by the number of labels:

Total area = length × height × number of labels

Total area = 25.12in × 9in × 15

Total area = 3,583.2 square inches

Thus, the answer is 3,583.2 square inches.

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The value of the missing length indicated is 128 units.

Two or more triangles are said to be similar when on comparing their properties, they have some common relations. But similarity is not congruency.

Let the missing length indicated be represented by x. So that comparing the triangles, we have;

21/ 77 = 48/ (48 + x)

21(48 + x) = 48*77

1008 + 21x = 3696

21x = 3696 - 1008

      = 2688

x = 2688/ 21

  = 128

x = 128

The missing length indicated is 128 units.

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The probability that 2 particular health professionals will be selected in the subcommittee is 4/15. There are 210 ways to select a subcommittee of 4 health professionals from the 10 total health professionals.

Probability acts as an indicator of how likely an event is to occur.

It is a number between 0 and 1, with 0 indicating an impossible event and 1 suggesting a certain event.

The number of favorable outcomes divided by the total number of possible outcomes yields the probability of an event.

The number of ways to select a subcommittee of 4 health professionals out of the 10 total health professionals is given by the combination formula:

C(10, 4) = 10! / (4! * 6!) = 210

To calculate the probability that 2 particular health professionals will be selected in the subcommittee, we need to consider the number of ways that we can choose the other 2 health professionals from the remaining 8. The number of such combinations is given by the combination formula:

C(8, 2) = 8! / (2! * 6!) = 28

So the probability that the subcommittee will consist of the 2 particular health professionals we are interested in, as well as 2 other health professionals, is:

(2 choose 2) * (8 choose 2) / (10 choose 4) = 1 * 28 / 210 = 4/15

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The rectangle's perimeter is 42 inches as the rectangle's area is 80 square inches.

Perimeter = 2 (length + width)

given

The rectangle's area is 80 square inches, so this is the first known step.

The rectangle measures 5 inches long.

The rectangle's perimeter is unknown.

Step 2: To determine the width of the rectangle, we will utilise the variable "w."

The formula for calculating a rectangle's area is:

A = width x length

Inputting the values provided yields:

80 = 5w

With w solved, we obtain:

w = 16

Step 3: The equation for a rectangle's perimeter is:

P= 2 (length + width).

Inputting the values provided yields:

P = 2(5 + 16)

P = 2(21) (21)

P = 42

Step 4: The rectangle's perimeter is 42 inches as the rectangle's area is 80 square inches.

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Thus, the value of 'x' for the centroid of triangle ABC is found as: x = 3.

The intersection of the triangle's three medians is known as the centroid. The segments that join a vertex to the opposing side's midway are known as medians.

The centroid for triangle ABC in this image is located at point D. It is simplest to create all three medians and seek for the point of intersection to determine a triangle's centroid. The centroid is the point at which gravity is greatest for a triangle formed of a uniform material.

From the property of centroid of triangle:

BD = 2*DF

Put the given values:

6x+6 = 2(8x - 12)

6x + 6 = 16x - 24

10x = 30

x = 3

Thus, the value of 'x' for the centroid of triangle ABC is found as: x = 3.

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The functiοns are f(-3)=2,  f(1)=4 and f(4)= -2.

In mathematics, a functiοn is  a relatiοn between a set οf inputs having οne οutput each. We can explain that  a functiοn is a relatiοnship between inputs where each input is related tο exactly οne οutput. A functiοn is generally denοted by g(x) where x is the input. The general representatiοn οf a functiοn is y = g(x).

The given cοοrdinates are (-3,2); (1,4);(4,-2)

Frοm the given cοοrdinates the functiοns can be fοrmed.

Let the functiοn be y=f(x)

Frοm the given cοοrdinate system the first value is x- value and the secοnd value is y-cοοrdinate.

Sο cοnsidering the first cοοrdinate -3 is the x-cοοrdinate and 2 is the y cοοrdinate and similarly fοr οthers.

Hence the functiοn will be f(-3)=2

Similarly frοm the secοnd cοοrdinate the functiοn will be f(1)=4

[ As 1 is the x- cοοrdinate and 4 is the y-cοοrdinate]

Frοm the third cοοrdinate the functiοn will be f(4)= -2

Hence, the functiοns are

f(-3)=2

f(1)=4

f(4)= -2

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Answer:

0.4 hours

Step-by-step explanation:

or 24 minutes :D

Answer:

x could equal -5 or 3

Step-by-step explanation:

3x - 45 = 12x

-45 = 9x

x = -5

3x - 45 = -12x

x = 3

Answer:

If the radius of the pastry stamp Petra uses to stamp circles in the dough for the donuts is 4.25 inches, then the diameter is 2 * 4.25 = 8.5 inches. The area of each donut can be calculated using the formula for the area of a circle:

Area of a circle = π * radius^2

So, the area of each donut is:

π * (4.25)^2 = 56.75π square inches (rounded to two decimal places)

If the radius of the pastry stamp Petra uses to stamp out circles for the donut holes is 0.4 inches, then the diameter is 2 * 0.4 = 0.8 inches. The area of each donut hole can be calculated using the same formula:

Area of a circle = π * radius^2

So, the area of each donut hole is:

π * (0.4)^2 = 0.16π square inches (rounded to two decimal places)

Hope This Helps!

Answer:

numbers are in a pattern

like

1234

2168

3092

4926

5850

so the next number would be

6774

Answer:

62.37 in

Step-by-step explanation:

Hope this helped!

The length of a rectangle cannot be negative, hence the length of the rectangle is 7 units.

Based on the question given, the width (W) is the length (L) minus 3 units, which can be expressed as:

W = L - 3

The formula for the area (A) of a rectangle is:

A = Length × Width

We are given that the area is 28 square units, so:

A = 28

Now, we can substitute the expressions for width (W) and area (A) into the area formula:

28 = L × (L - 3)

Now, we need to solve this quadratic equation for L. First, expand the equation:

28 = L^2 - 3L

Now, rearrange the equation in standard quadratic form

L^2 - 3L - 28 = 0

To solve this quadratic equation, you can factor it:

(L - 7)(L + 4) = 0

Now, set each factor equal to zero and solve for L:

L - 7 = 0

L = 7

L + 4 = 0

L = -4

Since the length of a rectangle cannot be negative, hence the length of the rectangle is 7 units.

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The correct response is 4. We can consider the following construction to understand why: We drew a 3 cm radio circle with the center located at P. Llamemoso C1.

Half of a circle's diameter corresponds to its radius. The radius equals 5 cm for a 10 cm diameter.

So, in order for C2 to intersect C, the straight line connecting P and C's center must be contained within C2, that is, it must be separated from C's center by a distance less than r. In other words, we need that:

r > d + 3

the distance between the center of C and the straight line connecting P and the center of C is where d. Its distance, d, is same to that between P and the center of C, minus C1's radio. Defined as,

d = PC - 3

where PC denotes the distance between P and C's center.

Thus, we require that:

r > PC - 3 + 3 = PC

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Answer:

108.16 sq ft

Step-by-step explanation:

We know it is a square bedroom, meaning all sides are equal. So then we do 10.4*10.4 or 10.4^2 and get 108.16 sq ft