How can I find the scale factor of the two similar triangles and how can I use similarity and scale factor to find the length?

Step-by-step explanation:

you need to give us also some context.

because that sequence can be anything.

but I suspect you mean

4 : 5 = x : 480

0.8 = x / 480

x = 480 × 0.8 = 384

1. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:

                                      LIFO           FIFO      Weighted-Average

Ending inventory          $425          $691                $573

Cost of goods sold      $492          $226               $344

FIFO (First-in, First-out) assumes that the physical flow of goods sold follows the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

The weighted-average method uses the average cost of goods to compute the ending inventory and the cost of goods sold.

LIFO:

Ending inventory = $425 ($917 - $492)

Cost of goods sold = $492 (12 x $20 + 12 x $21)

FIFO:

Ending inventory = $691 (9 x $11 + 17 x $20 + 12 x $21)

Cost of goods sold = $226 ($917 - $691)

Weighted Average:

Ending inventory = $573 (40 x $14.33)

Cost of goods sold = $344 (24 x $14.33)

                                   Units  Unit Cost    Total Cost

Jan. 1      Beg. Inventory  20     $8.00           $160

May 10   Purchases          15     $11.00           $165

June 30 Purchases          17    $20.00         $340

Dec. 10  Purchases          12    $21.00          $252

Total                                64                          $917

Units sold                       24

Ending inventory           40 (64 - 24)

Average cost = $14.33 ($917/64)

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Answer: -4, -1, 1, 3, 3.9, 3.99, 3.999, 4

Step-by-step explanation:

That inequality symbol means less than or equal to. So that includes 4 and any number that precedes it on the number line.

Answer: Estimate : 1000    Exact : 942.83

Step-by-step explanation:

The estimate is 1000 because 96.8 is rounded to 100 and 9.74 is rounded to 10, so 100 times 10 is 1000. If you wanted the exact, then the exact is 942.83200, If you simplify this total, then the final answer is 942.83.

Answer:

The new value is $8,272

Step-by-step explanation:

8800 x (1 - 0.06) = 8272

The values of the different trigonometric functions are as follows:

Now, solve using trigonometry as follows:

Now, we have:

Then, calculate as follows:

Now, we obtain:

Therefore, the values of the different trigonometric functions are as follows:

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The calculation of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:

                           Ratio      Amount

Department A       1/5        $10,000

Department B      4/5       $40,000

The ratio is the relative value relationship shared by two or more numbers.

Ratios are fractional values depicted in fractions, decimals, and percentages.

Like proportions, ratios show how much a value or variable is contained in another.

Total overhead = $60,000

Department   Square Feet  Ratio    Amount of Overhead Allocated

Dept. A            10,000         A = 1      B = $15,000 ($60,000 x 1/4)

Dept. B            30,000         = 3     D = $45,000 ($60,000 x 3/4)

Ratios = 10,000:30,000

= 1:3

Sum of Ratios = 4

Thus, based on the ratios, Department A is allocated $15,000, while Department B will be allocated $45,000 of the distributable overhead costs.

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Answer:

30

Step-by-step explanation:

3/8 is less than 1.

30 is much greater than 1.

Answer: 30

Answer:30 is greater

Step-by-step explanation:

Answer:

[tex]y=12[/tex]

Step-by-step explanation:

The [tex]y[/tex]-axis has equation [tex]x=0[/tex], so the equation of a line perpendicular to the [tex]y[/tex]-axis would be of the form [tex]y=c[/tex].

The equation of this line given the point [tex](3,12)[/tex] is [tex]y=12[/tex].

Probability of (a) George winning is 0.1

                       (b) Julia winning is 0.05

Given in question,

Total ticket sold = 100

George bought tickets = 10

Julia bought tickets = 5

Winning ticket = 1

Selecting 1 ticket from 100 = [tex]\left[\begin{array}{ccc}100\\1\\\end{array}\right][/tex]

                                            = 100

Selecting 1 ticket from 10 = [tex]\left[\begin{array}{ccc}10\\1\\\end{array}\right][/tex]

                                         = 10

Selecting 1 ticket from 5 = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]

                                        = 5

Probability = favorable outcome/total outcome

Probability of George winning = [tex]\frac{10}{100}[/tex]

                                                  = 0.1

Probability of Julia winning = [tex]\frac{5}{100}[/tex]

                                             = 0.05

Hence, probabilities are 0.1 and 0.05 respectively.

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answer:

10

step-by-step explanation:

easy: 100 ÷ 10 = 10. you need 10

explanation: you need 100 (on the left side) to equal the right side. each weight on the right side weighs 10, but you don't know how many you need. use x for the unknown amount. now, you have:

100 = 10x. solve by dividing each side by 10.

10 = x. verify by doing 10 x 10 = 100

Division of the monomial denominator by writing the fraction as the sum or difference of fractions is    [tex]8x+8 - \frac{1}{x^{3}}[/tex].

What is a polynomial equation?

Polynomial long division is a generalized variant of the well-known arithmetic operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.

We have,

                   [tex]\frac{8x^{4} + 8x^{2} - 1}{x^{3}}[/tex]

Break down the polynomial and divide:

                 [tex]= \frac{8x^{4} }{x^{3} } + \frac{8x^{2}}{x^{3}} + \frac{-1}{x^{3}}[/tex]

Calculating each division we get

                [tex]=8x+ 8x - \frac{1}{x^{3} }[/tex]

Therefore the final answer is

                 [tex]\frac{8x^{4} +8x^{3} −1}{x^{3}} = 8x+8 - \frac{1}{x^{3}}[/tex]

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Answer:

100

Step-by-step explanation:

x = 20

x ÷ 2

= 20 ÷ 2

= 10

y = 10

y ( x ÷ 2 )

= 10 x 10

= 100

The intercept reveals that the first loan amount was $1,560.00.

Every month, Michael's debt to his father drops by 290.

acc to our question-

The amount Michael owes is given by :

y = - 290x +18,560

x = number of months ; y = amount owed

Amount owed after 3 months :

Put x = 3 in the equation :

y= - 290(3) +18,560

y = - 870 + 18560

y = 17690

According to the general form of a linear equation :

y = mx + c

Where, m = slope ; c = intercept

The slope = - 290 ; Intercept = 18560

Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month

The intercept shows that the original amount borrowed is 18560.

Hence,The intercept reveals that the first loan amount was $1,560.00.

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The percent of error is 15%. The correct option is B.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Alton estimated that 230 people attended the band concert.

The actual count for attendance was 200 people.

To find the percent of error:

230 - 200 / 200

= 30 / 200

= 0.15

0.15 decimal to the percentage is 15%.

Therefore, the error is 15%

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The equation that relates x and y is given as y = 2.5x

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a.

The formula for direct variation is in the form of

y = kx

where we have the value of y = 5, the value of x = 2

we have to put this in the formula above

5 = 2k

to get the value of k we would have to divide through by 2

k = 5 / 2

k = 2.5

Hence we would have y = 2.5x

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The tip of his shadow moving when he is 50 ft from the pole is 10ft/s

The practical approach of differentiation may be performed utilizing just algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

The theory offers the following fundamental guidelines for differentiating the sum, product, or quotient of any two functions f(x) and g(x) whose derivatives are known (where a and b are constants) for functions constructed of combinations of these types of functions

I assume the man and pole are standing straight up, which means the 2 triangles are similar to each other.

(y-x)/y =6/15

15(y-x)=6y

9y=15x

y=(5/3)x

Differentiating both sides with respect to t,

dy/dt=(5/3)dx/dt

We know that, dx/dt= 6 ft/s

((5/3)*6=10 ft/s

Therefore, the tip of his shadow moving when he is 50 ft from the pole is 10ft/s

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Step-by-step explanation:

there are 18 dogs to choose 1 dog.

therefore, these are 18 options.

for each of these 18 options there are 24 cats to choose from.

so, altogether, there are

18×24 = 432

dog-cat options.

There are are 432 ways to choose dog-cat options are possible for the producer.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Total Number of Dogs= 18

Total Number of cats= 24

so, the number easy to select

= 18 x 24

= 432

Hence, there are 432 ways to choose dog-cat options are possible for the producer.

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Answer:

a little confused, but it should just be a horizontal line on -4 because of 4 times negative 1 = -4

Step-by-step explanation:

Answer:

5/14

Step-by-step explanation:

they subtract 1/14th each time
(You cant simplify)

The Claire's principal balance at the beginning of November is 32516.

Given that,

Vehicle purchase by Claire Russell. Her interest rate for the month of November was 210 percent at 7 3/4%. Employ 360 days. When calculating, do not round the numerator; instead, round your result to the nearest dollar.

We have to find how much was left on Claire's principal at the start of November.

We know that,

Principal= Interest / time× rate of interest

Here,

Interest is 210

Time is 30/360

Rate of interest is 0.0775

Principal = 210/(30/360)×0.0775

Principal= 210/ 0.00645833

Principal =32516

Therefore, The Claire's principal balance at the beginning of November is 32516.

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The area that is watered as the sprinkler rotates 90° is 196,250.

What is the area of the circular plot?

The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = πr², where r is the circle's radius, is the formula for calculating a circle's surface area.

Here, we have

Diameter = 1000ft

Radius = 500

Then, we apply the area of a circle and get

= (90/360)× π×(500)²

= 62,500 × π

= 196,250

Hence, the area that is watered as the sprinkler rotates 90° is 196,250.

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Addition of the given polynomial functions (5a³ + 4a² - 3a + 2) and (a³ - 3a² + 3a - 9)​ gives 8a³ + a² - 7

A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.

Addition of polynomial is achieved term by term

= (5a³ + 4a² - 3a + 2) + (a³ - 3a² + 3a - 9)​

= 5a³ + 3a³+ 4a² - 3a²- 3a + 3a + 2 - 9

= 8a³ + a² - 7

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The length of the line segment will be 10 units.

What is Distance?

The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √( y₂ - y₁)² + (x₂ - x₁)²

Given that;

Two endpoints of the line segment are (6, -5) and (0, 3).

Now,

The length of the line segment is distance between two endpoints (6, -5) and (0, 3).

So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √(0 - 6)² + (3 - (-5))²

D = √36 + 64

D = √100

D = 10 units

Thus, The length of the line segment will be 10 units.

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Answer:

p = 20

Step-by-step explanation:

[tex]\rm \implies \dfrac{p}{2} - 9 = 1 \\ \\ \rm \implies \dfrac{p}{2} - 9 + 9 = 1 + 9 \\ \\ \rm \implies \dfrac{p}{2 } = 10 \\ \\ \rm \implies \dfrac{p}{ \cancel{2}} \times \cancel{2} = 10 \times 2 \\ \\ \rm \implies p = 20[/tex]

The distance and direction of the ship from the starting point is found using vectors as follows;

The ship is 48.03 nautical miles from the starting point at a directional bearing of N 18.53° E

A vector is a quantity that has a property of magnitude or size and direction.

The ship's speed = 36 nautical miles per hour

Direction of the ship = Due east

The duration the ship continues in the direction = 1 hour

The new direction of the ship = N32°E

The duration in which the ship continues in the new direction = Half an hour

The vector of the distances traveled by the ship are;

[tex]\overrightarrow{d_1}[/tex] = 36·i

[tex]\overrightarrow{d_2}[/tex] = 0.5 × 36×sin(32°)·i + 0.5 × 36×cos(32°)·j = 18×sin(32°)·i + 18×cos(32°)·j

The sum of the distances traveled by the ship is therefore;

36·i + 18×sin(32°)·i + 18×cos(32°)·j = (36 + 18×sin(32°))·i + 18×cos(32°)·j

(36 + 18×sin(32°))·i + 18×cos(32°)·j = 45.54·i + 15.26·j

The distance of the ship from the starting point, d, is therefore;

d ≈ √(45.54² + 15.26²) ≈ 48.03

The distance of the ship from the starting point is approximately 48.03 miles.

The direction from the North of the ship from its starting point, θ, is therefore;

[tex]\theta = arctan\left(\dfrac{15.26}{45.54} \right) \approx 18.53^{\circ}[/tex]

Then direction of the ship is N 18.53° E

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Answer:  12/0

Step-by-step explanation:  (5−3)(2)+8

(2)(3)−7+1

=

(2)(2)+8

(2)(3)−7+1

=

4+8

(2)(3)−7+1

=

12

(2)(3)−7+1

=

12

6−7+1

=

12

−1+1

=

12

0

=

1

0

;)

The value of the angle regarding the parallel lines are:

1. x = 14

2. x = 9

3. x = 17

4. x = 5

1. Lines 'l' and 'm' are the parallel lines and a transversal line is intersecting these  lines.

(9x + 13)° = (12x - 29)° [Alternate interior angles]

9x - 12x = -29 - 13

-3x = -42

Divide

x = 14

2). By substituting x = 14 in the box.

(13x + 5)° + (8x - 14)° = 180° [Consecutive interior angles]

21x - 9 = 180

21x = 189

Divide

x = 189/21

x = 9

3). By placing x = 9 in the box,

(5x + 52)° = (9x - 16)° [Corresponding angles]

5x - 9x = -52 - 16

-4x = -68

x = 17

4). By placing x = 17 in the box,

(10x + 17)° = (12x + 7)° [Alternate exterior angles]

10x - 12x = -17 + 7

-2x = -10

x = 5

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