Are all equilateral triangles also isosceles triangles are all isosceles triangles also equilateral triangles explain?.

you get to keep whatever 6-digit dollar amount you want as long as no one else chooses it is $809,417

you choose a random number, but don't want to make it start with 9 as everyone will be picking nine as the first digit. So instead go with the next best, 8. Then making the next digit 0 since people would be unlikely to have the second number as 0, trying to max out their money while also picking the lowest first number. Then have the rest of the digits be random to maximize the odds of no one happening to select it.

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The total number of sides of the given polygon is 16.

What is the interior and exterior angle of a regular polygon?

In a regular polygon, all internal angles and exterior angles are equal. The formula for determining the amount of an interior angle is given:

Interior angle of a polygon = sum of interior angles/number of sides  

A polygon's exterior angles add up to 360°.

Given, each interior angle of a regular polygon = 157.5°

Then, each exterior angle of a regular polygon = 180° - 157.5° = 22.5°

the sum of the exterior angles of any n-gon = 360°

So, the total number of sides = 360°/22.5° = 16 sides

Hence, the total number of sides of the polygon is 16.

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Answer:

  0.253 m/s

Step-by-step explanation:

You want to know the horizontal component of motion of a passenger riding a Ferris wheel when they are 1/27 of the way around the circle and their rate of rise is 0.06 m/s.

The wheel makes one revolution in 27 minutes, so the angular displacement is changing at the rate of (360°)/(27 min) = 13 1/3°/min.

After 1 minute, the passenger is following a path that has an angle of elevation of 13 1/3°.

The ratio of vertical speed to horizontal speed will be the tangent of the angle of elevation:

  Vv/Vh = tan(13 1/3°)

Then the horizontal speed will be ...

  Vh = Vv/tan(13 1/3°) = (0.06 m/s)/0.237004

  Vh ≈ 0.253 m/s

The passenger's horizontal motion is about 0.253 m/s.

The mean and variance of C are 200 & 1960000 respectively.

What are the mean and variance?

The mean is the average of a set of numbers, whereas the variance is the average degree to which each number deviates from the mean.

y ~ Exponential with mean of 10 hours

P. d. f of y,

[tex]f_{y} (y) = { \left \{ {{\frac{1}{10}e^{\frac{-y}{10} } } \atop {0}} \right.\\\left {{y > 0} \atop { 0 \ otherwise}} \right.[/tex]

[tex]f_{y} (y) = \int\limits^{\infty}_{-\infty} {y^{k} f_{y} (y)} \, dy[/tex]

[tex]f_{y} (y) = \int\limits^{\infty}_{0} {y^{k} \frac{1}{10} . e^{-\frac{y}{10} } \, dy[/tex]

[tex]=\frac{1}{10} \int\limits^{\infty}_{0} {y^{k+1} . e^{-\frac{y}{10} } \, dy[/tex]

[tex]= \frac{10^{k+1} }{10} \ \Gamma(k+1)[/tex] ---------(1)

E(Y³) = 10³ Γ(3+1)   [putting k = 3 in (1)]

= 10³ Γ(4)

= 10³ 3!    ..........[Γ(n) = (n-1)!]

= 6000

E(Y⁴) = 10⁴ Γ(4+1)   [putting k = 4 in (1)]

= 10⁴ Γ(5)

= 10⁴ 4!    ..........[Γ(n) = (n-1)!]

= 240000

C = 100 + 40Y + 3Y²

Mean of C,

E(C) = E(100 + 40Y + 3Y²)

E(C) = 100 + 40E(Y) + 3E(Y²)

E(Y) = 10           .......[Given]

E(Y²) = 10² Γ(2+1)   [putting k = 2 in (1)]

= 10² Γ(3)

= 10² 2!

= 200

E(C) = 100 + 40(10) + 3(200)

E(C) = 1100

The variance of C,

Var(C) = Var[100 + 40Y + 3Y²]

= 1600var(Y) + 9(Y²)

= 1600[E(Y²) - E²(Y)] + 9[E(Y⁴) - E²(Y⁴)]

= 1600[200 -(10)²] + 9[240000 - (200)²]

= 1960000

Hence, the mean and variance of C are 200 & 1960000 respectively.

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If a triangle has an obtuse angle which measures more than 90 degrees but less than 180 degrees it is an obtuse angled triangle.

When one of the vertex angles of a triangle is greater than 90°, it is called an obtuse angle triangle

An obtuse triangle can either be an isosceles or a scalene triangle but not an equilateral triangle.

In an obtuse angle triangle, the sum of the squares of the two sides is always less than the square of the longest side.

Therefore,  if a triangle has an obtuse angle which measures more than 90 degrees but less than 180 degrees it is an obtuse angled triangle.

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Using compound interest  formula, the amount compounded at a rate of 3% quarterly for 5 years is $15,095.39

The compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The formula for compound interest can be derived from the formula for simple interest. The formula for simple interest is the product of the principal, time period, and rate of interest (SI = ptr/100). Before looking into to derivation of the formula for compound interest, let us understand the basic difference between simple interest, compound interest computation. The principal remains constant over a period of time, for simple internet computation, but for compound interest computation the interest is added to the principal, for compound interest computation. The compound interest formula is given below:

A = P(1 + r/n)^nt

plugging the values into the formula above

A = 13000(1 + 0.03/4)^4 * 5

A = 13000(1.0075)^20

A = $15,095.39

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The point slope formula is [tex]y-y_1=m(x-x_1)[/tex].

The point slope form is used to calculate the equation of a straight line that is inclined to the x-axis at a certain angle and passes through a particular point.

When we know the slope of a line and a point on it, we may use the point slope formula.

Point Slope Formula:

[tex]y-y_1=m(x-x_1)[/tex]

where,

(x, y) is a point on the line at random (which should be kept as variables while applying the formula).

(x1, y1) is the line's fixed point.

slope of the line is 'm'.

Thus, the point slope formula is [tex]y-y_1=m(x-x_1)[/tex].

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Dijkstra's algorithm should be executed twice, once from s and once from u.

Given,

We have to determine an effective algorithm that, provided it's not too inconvenient, will choose the best route from s to t based on your choice for stopping at u along the way. Either the shortest path from s to t or the shortest path from s to t that includes u should be returned.

Algorithm;-

An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially. All aspects of information technology employ algorithms extensively.

Here,

Run Dijkstra's algorithm two times, from s and u, respectively.

The shortest path from s to u and the shortest path from u to t make up the shortest path from s to t containing u.

Choose the path to return to based on their lengths by comparing this path's length to the path's length from s to t.

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The distance from (0, -4) to the line x + 5y = 10 is approximately 6 units.

To find the distance from a point to a given line, recall the following:

Step 1: Find the slope of the line, x + 5y = 10:

Rewrite the equation, x + 5y = 10 as y = mx + b, to find the value of the slope (m)

5y = -x + 10

y = -x/5 + 10/5

y = -1/5x + 2

The slope (m) = -1/5.

Step 2: Find an equation of the perpendicular line to the line x + 5y = 10 that passes through the point (0, -4):

Slope (m) = 5 [negative reciprocal of -1/5]

y-intercept (b) = -4

Substitute m = 5 and b = -4 into y = mx + b:

Equation of the line:  y = 5x - 4

Step 3:  Find the point of intersection of the lines y = 5x - 4 and y = -1/5x + 2:

Therefore, the lines intersect when 5x - 4 = -1/5x + 2

5x - 4 = -1/5x + 2

5x + x/5 = 4 + 2

26x/5 = 6

26x = 30

x = 30/26

x ≈ 1.2

Substitute x = 1.2 into y = 5x - 4:

y = 5(1.2) - 4

y = 2

Point of intersection is: (1.2, 2)

Step 4:  Find the distance between (0, -4) and (1.2, 2) using the distance formula:

d = √[(1.2 − 0)² + (2−(−4))²]

d = √[(1.2)² + (6)²]

d = √37.44

d ≈ 6 (nearest whole number)

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The number of ways for six ce majors and ten cs majors to stand in a line so that no two ce majors stand next to each other are 462.

We need to maintain one condition that no two ce majors stand next to each other.

So, what we can do firstly we allow ten cs majors to stand in a line as there are no restrictions on cs majors.

Total number of ways by which ten cs majors can stand=10!=3628800

Now, when 10 cs majors stand in a line then we have 11 spaces.

Now, we need to choose such  space for 6 ce majors so that no two ce majors stand next to each other.

So, it is equivalent to choose 6 spaces from 11 spaces which is given by [tex]^1^1C_6[/tex] ways =(11!)/(6!×5!)=11×2×3×8×7=462ways.

Hence, total number of ways are 462.

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The average, median and quartile of the figures 1,2,3 are:

Normal : Average= 1, median is 1 the first quartile is 1

Adjusted: Average=5.67, median is 5.62 and the quartile is 4.5

Quartile is defined as a type of quantile which divides the number of data points into four parts, Median is the middle data value, Mean is calculated by dividing the sum of the data values by the number of data values

The given figures are:

Normal 1,1,1

Adjusted: 5.82, 5.56, 5.62

Normal mean = 1+1+1 /3 = 3/3=1

Normal median= 5.56, 5.62, 5.85 =5.62

Lower quartile = [tex]n+1*\frac{1}{4}[/tex]

3+1*[tex]\frac{1}{4} =1[/tex]

Adjusted: mean [tex]\frac{5.82+5.56+5.62}{3}=\frac{17}{3}=5.67[/tex]

median: 5.56, 5.62, 5.85 = 5.62

Quartile: [tex]17+1*\frac{1}{4}[/tex]

=4.5

In the normal column, the wages remained constant but in the adjusted column, the wages were fluctuation as a sign of inflation

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a) The value of p₀=1

b)  The population in the year 2020 is 1.3 billion.

c)  The function f(x)=1.5 billion reaches India's population in the year 2030.

A function is a relationship between two or more inputs, each of which corresponds to exactly one output. A domain and a codomain or range are assigned to each function.

a) Given, The population of India after x years is f(x)=p₀(1.01355)ˣ⁻²⁰⁰⁰

Also in 2000, the population reached 1 billion.

That is when x=2000, f(x)=1

f(2000)=1

p₀(1.01355)ˣ⁻²⁰⁰⁰⁻²⁰⁰⁰=1

p₀×1=1

p₀=1

Hence p₀=1

b) Here the objective is we have to find the population in the year 2020

Then the value of f(x) when x=2020

Hence,

f(2020)=p₀(1.01355)ˣ⁻²⁰²⁰⁻²⁰²⁰

f(2020)=1(1.01355)²⁰

f(2020)=1.3

Therefore, the population in the year 2020 is 1.3 billion.

c) f(x)=1.5

p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5

1×p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5

p₀(1.01355)ˣ⁻²⁰⁰⁰=1.5

ln(p₀(1.01355)ˣ⁻²⁰⁰⁰)=ln(1.5)

(x-2000)ln(1.01355)=ln(1.5)

x-2000=ln(1.5)/ln(1.01355)

x=(ln(1.5)/ln(1.01355))+2000

x=30.12+2000

x=2030.12

Hence in the year 2030, the population might reaches to 1.5 billion.

Therefore, f(x)=1.5 billion

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The complete question is:

In 2000 , India's population reached 1 billion, and its projected to be \( 1.45 \) billion in 2025 . Use the function \( f(x

Show transcribed data

In 2000 , India's population reached 1 billion, and it's projected to be

1.45

billion in 2025 . Use the function

f(x)=P0(1.01355)

x−2000

find the help find the following a) What is p₀

​? billion b) Predict India's population in 2020 to the nearest tenth of a billion. billion c) Use the function to determine the year when India's population might reach

1.5

billion. (Round to the nearest year) Question 21 Out of pocket spending for healthcare in the United States increased between 2000 and 2008 . The function

f(x)=2572e

0.0359x

models the average annual expenditures per household, dollars, In this model,

x

represents the year,

x=0"

Answer:

25%

Step-by-step explanation:

you want to figure out how many % are 55 of 220.
To get this, you do:
percentage = (55 * 100) / 220 = 25
-> so 55 are 25% of 220. 25% of the total fatal accidents were on building sites.

Answer:

B. 1 > -2, C. 4 > 1, and D. -3 < -1

Step-by-step explanation:

B. 1 is larger than -2

C. 4 is larger than 1

D. -3 is less than -1

Greater inputs only result in the leading term becoming more and more positive if the leading coefficient is positive. The graph will incline rightward. Larger inputs will simply make the leading term more and more negative if the leading coefficient is negative. The rightward descent of the graph is planned.

The coefficient of the leading term is the leading coefficient in a polynomial. Because of the negative leading coefficient, the graph slants to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

The term with the largest power of x is the leading term in a polynomial. As an illustration, the leading word in 7+x3x2 is 3x2. A polynomial's leading coefficient is the coefficient of the leading term. The leading coefficient in the aforementioned illustration is 3.

The numbers placed in front of the variable with the largest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like regular coefficients.

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Answer:

First, know that [tex]csc(x)=\frac{1}{sin(x)}[/tex]:

[tex]\frac{1}{sin^{2}(x)} *cos^{2}(x)=\frac{cos^{2}(x)}{sin^{2}(x)}[/tex]

Remember that cos²(x) + sin²(x) = 1, so cos²(x) = 1 - sin²(x):

[tex]\frac{cos^{2}(x)}{sin^{2}(x)} =\frac{1-sin^{2}(x)}{sin^{2}(x)} =\frac{1}{sin^{2}(x)} -\frac{sin^{2}(x)}{sin^{2}(x)} =csc^{2}(x)-1[/tex]

Step-by-step explanation:

this might be the answer

If you wanted to save $30,000 you need to work 30 times .

Given:

if you wanted to save $30,000 to buy a new car. instead of focusing on saving the whole amount, you work to earn $1,000 at a time. this makes the process seem more manageable to you because you are using the heuristic.

Number of times to work = money to save / at a time money.

= $30000/$1000

= 30000/1000

= 3000/100

= 300/10

= 30 times

Therefore you need to work 30 times to earn $30,000.

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After the disk technique and the washer method, the cylindrical shell method of conducting a revolution is the third approach to determine the volume of the solid created by rotating about an axis. Technically, either of the first two approaches can find any revolution, but the cylindrical shell approach may be simpler to compute.

The cylindrical shell method's biggest drawback is that it necessitates more visualization of the regions where the cylinders are formed because you must determine both the cylinder's radius and height, whereas the other two methods only require the radius.

I'm going to start out by presuming that just the area in the first quadrant is rotating about the y-axis. Second, because the shell has a thickness of dx and the rotation revolves around a vertical axis, the integral must be expressed in terms of x. Third, the cylinder's height is and its height has a radius of [tex]36 - x^{2}[/tex]. Last but not least, the bounds are 0≤x≤6 since the area being rotated is constrained by the axes and the function. The integral can now be set up.

[tex]\int\limits {2\pi rh} \, dx = \int\limits^6_0 {2\pi x(36-x^{2} )} \, dx[/tex]                                          [Set Up the Integral]

               [tex]= 2\pi \int\limits^6_0 {36x - x^{3} } \, dx[/tex]                                                            [Distribute]                

               [tex]= 2\pi (\frac{36x^{2} }{2} - \frac{x^{4} }{4} )[/tex]  = [tex]2\pi ( (\frac{36(6)^{2} }{2} - \frac{6^{4} }{4} ) - (\frac{36(0)^{2} }{2} - \frac{0^{2} }{4} ) )[/tex]

               [tex]= 2\pi ( \frac{36(6)^{2} }{2} - \frac{6^{4} }{4} )[/tex]                                                                [Evaluate]

               [tex]= 1296\pi[/tex]                                                                                {Answer}

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The right Question is:

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

[tex]y = 36 - x^{2} \\y = 0[/tex]

The two properties of showing the graph of polynomial function are

i) Polynomial functions have graphs that do not have sharp corners

ii) Polynomial functions also display graphs that have no breaks

what is a polynomial ?

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. We can execute arithmetic operations on polynomial expressions, such as addition, subtraction, multiplication, and positive integer exponents, but not division by variables.

Polynomial functions of degree 2 or more have graphs that do not have sharp corners; recall that these types of graphs are called smooth curves. Polynomial functions also display graphs that have no breaks. Curves with no breaks are called continuous.

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When the negative exponent is outside the parentheses indicates that you need to take the inverse of the base number, or put it in the denominator.

Given:

when the negative exponent is outside the parentheses.

suppose (3)^-3 = 1/3^3.

Example:

(7)^-3

Take the inverse of base number and put it in denominator.

= 1/7^3

So the negative is outside the parenthesis is tells that the negative sign must be removed.

Therefore when the negative exponent is outside the parentheses indicates that you need to take the inverse of the base number, or put it in the denominator.

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the x-intercepts of the given graph are 12n - 3 where n is 0,±1,±2...

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The given straight line is y = sin πx/6 + 1

To find the x-intercepts we have to y=0 in the function.

So the equation become, 0 = sin πx/6 + 1

sin πx/6 = - 1

πx/6=nπ+(−1) n ( -π/2)

x = 12n - 3

So, the x-intercepts of the given graph are

12n - 3 where n is 0,±1,±2...

Hence the x-intercepts of the given graph are 12n - 3 where n is 0,±1,±2...

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The equation of a straight line passing through the given point and slope is y - y1 = m(x - x1).

Given:

Let the given point be (x1,y1).

slope be m.

we know that,

Line equation passing through point is:

y - y1 = m(x - x1)

where m = slope and (x1,y1) = given point.

Therefore The equation of a straight line passing through the given point and slope is  y - y1 = m(x - x1).

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The probability that the number on the second tag exceeds the number on the first tag is 0.5

A hat contains tags numbered 1, 2, 3, 4, 5, 6. two tags are selected.

The complete sample space is 6 x 6 = 36

the probability that the number on the second tag exceeds the number on the first tag...Let this event be L

when (a) the first tag is not replaced before the second tag is drawn

If the 1st tag is 1,

Then P(L) = 1/6 x 5/5

If the 1st tag is 2,

Then P(L) = 4/5 x 1/6

If the 1st tag is 3,

Then P(L) = 3/5 x 1/6

If the 1st tag is 4,

Then P(L) = 2/5 x 1/6

If the 1st tag is 5,

Then P(L) = 1/5 x 1/6

If the 1st tag is 6,

Then P(L) = 0/5 x 1/6 = 0

P(L) = 5/30 + 4/30 + 3/30 + 2/30 + 1/30

The probability that the number on the second tag exceeds the number on the first tag = (15/30) = 1/2 = 0.5

Therefore,  the probability that the number on the second tag exceeds the number on the first tag is 0.5

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Depreciation expenses using Straight line is $11,000

Depreciation expenses using Double-declining balance is $18,400

Depreciation expenses using Units of production is $12,500

Straight-line method of depreciation is regarded as the simplest form of depreciation

Given information

Purchase value of equipment = $115,000

Estimated residual value = $5,000

Estimated service life = 10

Deprecation expenses = ($115,000 - $5,000) / 10 years

Deprecation expenses = $110,000 / 10

Deprecation expenses = $11,000

Double-declining balance method is an accelerated depreciation method where asset are depreciated at twice the rate in the straight-line method

Depreciation rate = 1 / Estimated service life

Depreciation rate = 1 / 10

Depreciation rate = 10%

So, the rate is double = 10% * 2 = , 20%

in year 2, Depreciation =  ($115,000 - $23,000) * 20%

Depreciation = $18,400

Formulae for Units-of-production method is (Purchase value of equipment - estimated residual value) / Estimated production units

Units-of-production method = [$115,000 - $5,000] / $220,000 units

Units-of-production method = $110,000 /  220,000 units

Units-of-production method = $0.5 per units

For 2021, Depreciation = Production units in 2021 year * Depreciation per unit

Depreciation = 30,000 units × $0.5

Depreciation = $15,000

For 2022, Depreciation = Production units in 2022 year * Depreciation per unit

Depreciation = 25,000 units * $0.5

Depreciation = $12,500

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Full Question ;

On January 1, 2021, the Allegheny Corporation purchased equipment for $115,000. The estimated service life of the equipment is 10 years and the estimated residual value is $5,000. The equipment is expected to produce 220,000 units during its life. Calculate depreciation for 2021 and 2022 using each of the following methods. Round all computations to the nearest dollar.

1. Straight line

2. Double-declining balance

3. Units of production (units produced in 2021, 30,000; units produced in 2022, 25,000)

Depreciation expense value from different different methods are the following:

a)Using Straight line Method,

depreciation= $13,200

b) Using Double declined balance method,

depreciation=$26,800

c) Using Units of production,

depreciation for 2024 is $ 18,700 and for 2025 is

$ 15,950.

Straight line Method :

A linear basis is a method of calculating depreciation. A process in which an asset is consumed over a period of time longer than it was purchased.

The formula for straight-line depreciation is represented as :

a) Straight line depreciation = (cost of the asset – estimated salvage value) ÷ (estimated useful life of an asset)

We have given that,

Corporation purchased equipment or cost of asset = $134,000

Estimated residual value 0r salvage value

= $2,000

Estimated useful life of the equipment = 10 yr

Expected to produce = 240,000 units

Putting all known values in above formula we get ,

depreciation =( $134,000 - $2,000)/10

= $13,200 per annum

b) Double declined balance method :

It is an accelerated deprecation method where asset are deprecated at twice the rate in straight line Method

depreciated rate =(1 /Estimated useful life) ×100

Rate of deprecated =(2/Estimated useful life) ×100

= 2/10 ×100 = 20%

depreciation= cost of asset × rate of depreciated

= $134,000 × 20% = $26,800

c) Units of production :

Formula of deprecation based on units of production is

depreciation = ( purchased equipment or cost of asset - estimated residual or salvage value ) / ( excepted production units)

so, depreciation = ($134,000 - $2,000)/240,000

= $0.55

For 2024 ,

depreciation= production units in 2024 × depreciation per unit

=$ 34,000× 0.55 = $ 18,700

for 2025 ,

depreciation= production units in 2025 × depreciation per unit

=$ 29,000× 0.55 = $ 15,950

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Using PEMDAS rule , we can evaluate the provide expression . The required result is thirteen that's the value is L= 13.

PEMDAS order of operations: The order of operations is a rule that tells the correct sequence of steps for evaluating a given mathematical expression. We can remember the order using "PEMDAS" where

P --> Parentheses

E --> Exponents (2⁵ is 2 raised to the power of 5)

M------> Multiplication and

D---->Division (from left to right)

A--->Addition

S--->Subtraction (from left to right).

We have given that

3/4 ( 2³ + 4² )

let given expresion equal to L i.e

L = 3/4 ( 2³ + 4² )

Now, we have to solve it

Using "PEMDAS" rule ,

L = 3/4 ( 2³ + 4²)

= 3/4 ( 8 + 4²)

= 3/4 ( 8 + 16 )

= 3/4 ( 24)

= 3/4 ×24

= 24×3/4

= 72/4

L = 1 3

Hence, the given expresion is equal to 13 .

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Median for the given data 17, 2 ,7 is  12.

What is median?

The median is that the value that’s precisely within the middle of a dataset once it's ordered. It’s a live of central tendency that separates the bottom 50% from the very best 50% of values.

Main body :

First of all to find the median data should be arranged in ascending order.

Aranging data in ascending order

2, 5 , 7 , 7 , 8 , 8 , 10 , 10 , 14 , 15 , 17 , 18 , 24 , 27 , 28 , 48

Now there are even number of terms i. e 16

So,

M1 = n / 2 and M2 = ( n / 2 ) + 1

= 16 / 2 = 8 + 1

= 8th term = 9th term

M1 = 10 M2 = 14

Median, M = ( M1 + M2 ) / 2

= ( 10 + 14 ) / 2

= 24 / 2

= 12

Hence median of observation is 12.

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If the function f(x) [tex]=[/tex] x [tex]+[/tex] 3 and g(x) = x² + 2x - 3, then the value of the composite function [gof](x) is =  x² + 8x + 12  .

In the question ,

it is given that

the function f(x) is [tex]=[/tex] x [tex]+[/tex] 3

and the function g(x) is [tex]=[/tex] x² [tex]+[/tex] 2x - 3 ,

we have to find the value of composite function , (gof)(x)

(gof)(x) = g(f(x))

substituting the value of f(x) = x + 3,

we get ,

g(f(x) = g(x + 3)

Substituting the (x+3) in place of x in the function g(x) , we get

= (x+3)² + 2(x+3) - 3

= x² + 6x + 9 + 2x + 6 - 3

= x² [tex]+[/tex] 8x [tex]+[/tex] 9 + 3

= x² [tex]+[/tex] 8x + 12

Therefore , If the function f(x) = x + 3 and g(x) = x² + 2x - 3, then the value of the composite function [gof](x) is =  x² + 8x + 12  .

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The number line we can see that 1.5 is less than 1.75.

Mark two points 1.75  and 1.5 on number line  and make a number line from -1 to 2 where each point is 0.25 units away

Then compare 1.75  and 1.5 on number line

Given :

Nico wants to use a horizontal number line to compare 1 3/4 and 1.5

Lets write the fraction in decimal form to compare and mark it on number line [tex]1\frac{3}{4}[/tex] = 1.75

Now mark two points 1.75  and 1.5 on number line

Make a number line from -1 to 2 where each point is 0.25 units away

Mark a number line that are 0.25 units away using below numbers

-1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2

On the number line ,

1.5 comes first

1.75 is next to 1.5

From this number line we can see that 1.5 is less than 1.75.

1.5 <       [tex]1\frac{3}{4}[/tex]

Hence the answer is the number line we can see that 1.5 is less than 1.75.

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47 cm is the perimeter of the figure

Perimeter is the distance around the edge of a shape. It can be found by adding up the side lengths of the shapes

Given: radius (r)  = 8 cm

First, we need to find the side length of the pentagon using the formula: Side length (a) = 2r × Sin(180/n)

where n is the number of sides. In this case n = 5

Side length (a) = 2(8) × Sin(180/5) = 16×Sin(36) = 9.4 cm

The perimeter of the regular pentagon can be determined using the formula:

Perimeter = 5a

Perimeter =  5 × 9.4 = 47 cm

Therefore, the perimeter of the figure is 47 cm

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