What is the value (Shown in the picture) of f(81)?

The maximum dimension of a rectangular microchip she can use is 12 mm and 24 mm.

A rectangular microchip, commonly known as an integrated circuit or chip, resembles a flat rectangle approximately small in size with a slew of wires designated by pins protruding from it.

The maximum dimension of a rectangular microchip can be determined by finding its length and width.

From the information given:

The surface area of the rectangle can be expressed by using the formula:

S = 2(lw + lh + wh)

where;

The surface area then becomes:

864 = 2(2x² + 8x + 4x)

Divide both sides by 2, and we have:

432 = 2x² + 12x

We can now have a quadratic expression as:

2x² + 12x - 432 = 0

x² + 6x - 216 = 0

using the  factorization method;

(x + 18) (x - 12) = 0

x = - 18 or x = 12;

Since x cannot be negative, then x = 12. Therefore, width = 12 mm, and the length = 2(12) = 24 mm. Therefore, we can conclude that the maximum dimension of the microchip she can use is 12 mm and 24 mm.

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Answer:

I went with B. 9 mm and 18 mm   PLATO

Step-by-step explanation:  mad maths skills

Answer:

To find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%, we can use the formula for the probability mass function of the binomial distribution:

P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)

Where:

X is the number of successes in the binomial experiment

n is the number of trials

p is the probability of success in any one trial

k is the number of successes we are interested in

So, in this case, we want to find the probability of X being equal to 0, 1, or 2 successes. We can do this by summing the probabilities of each of these events:

P(X = 0) + P(X = 1) + P(X = 2)

Plugging in the values from the problem, we get:

P(X = 0) = (5 choose 0) * (0.18)^0 * (1 - 0.18)^(5-0) = 0.3199

P(X = 1) = (5 choose 1) * (0.18)^1 * (1 - 0.18)^(5-1) = 0.4199

P(X = 2) = (5 choose 2) * (0.18)^2 * (1 - 0.18)^(5-2) = 0.2082

So the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18% is:

0.3199 + 0.4199 + 0.2082 = 0.948

Step-by-step explanation:

a) The linear equation for R(t) is given as follows: R(t) = -2.1t + 16.

b) The helium reserves in 2015 will be of: 5.5 billion.

c) The reserve will be depleted in the year of: 2018.

The linear function in this problem has the definition in slope-intercept format presented as follows:

R(t) = mt + b.

In which:

Considering the measures in billions, the parameters are given as follows:

m = -2.1, b = 16.

Then the equation is defined as follows:

H(t) = -2.1t + 16.

2015 is five years after 2010, hence the estimate is calculated as follows:

H(5) = -2.1(5) + 16 = 5.5 billion.

The reserve will be depleted in the year t + 2010 + 1, when R(t) = 0, hence:

-2.1t + 16 = 0

2.1t = 16

t = 16/2.1

t = 7.61 years.

Hence the reserves will be depleted during the year of 2018.

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The required null hypothesis of the given observation is μ1 = μ2 = μ3.

The null hypothesis is a typical mathematical theory that asserts that there is no statistical relationship and significance between two sets of observed data and measured phenomena for each set of specified, single observable variables.

The null hypothesis can be evaluated to determine whether or not there is a relationship between two measured phenomena, which makes it valuable.

It can let the user know if the outcomes are the product of random chance or deliberate manipulation of a phenomenon.

The null hypothesis, often known as "H-nought," "H-null," or "H-zero," is written as H0 to distinguish it from other hypotheses.

The null hypothesis of the given observation:

μ1 = μ2 = μ3

Therefore, the required null hypothesis of the given observation is μ1 = μ2 = μ3.

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Complete question:
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Treatment

Observations

A

20

30

25

33

B

22

26

20

28

C

40

30

28

22

The null hypothesis for this ANOVA problem is?

If surface , S is the part of the sphere, x² + y²+ z² =1 ,lies above the cone, x² + y² = z

a)| ⃗rᵩ × ⃗rθ| = ⟨sin²φ cosθ,sin²φsinθ, sinφcosφ⟩

b)∫∫ z² ds = ₀∫ˣ₀∫ʸcos²φ dφdθ,

S

where x = 2π and y = π/4

A surface in space given in Cartesian coordinates as f(x,y,z) = 0, can be parametrized as a vector function with two parameters,

r(u,v)= ⟨r₁(u,v) , r₂(u,v) , r₃(u,v)⟩ , (u,v)∈R²

We have, S is a part of Sphere , x² + y²+ z² =1 , lies above the cone, x² + y² = z and surface S parametrized by following vector equation ,

r(θ, φ) = ⟨sinφ cosθ , sinφsinθ,cosφ⟩ --(1)

⃗rᵩ = ∂r/∂φ =⟨cos φ cosθ,cos φ sinθ,-sin φ⟩

⃗rθ= ∂r/∂θ=⟨- sinφ sinθ , sinφ cosθ ,0⟩

| ⃗rᵩ × ⃗rθ| =| i j k |

|cosφcosθ cosφ sinθ -sinφ |

|- sinφsinθ sinφ cosθ 0 |

= i( 0 + sinφ cosθsinφ) -j(0- (- sinφsinθ)(-sinφ)) + k(sinφ cosθ cosφcosθ - (-sinφ sinθ ) cosφ sinθ)

= (sin²φcosθ )i + (sin²φsinθ)j + (sinφcosφ(sin²θ+cos²θ))k

= sin²φcosθ )i + (sin²φsinθ)j +(sinφcosφ)k

| ⃗rᵩ× ⃗rθ|=⟨sin²φcosθ ,sin²φsinθ,sinφcosφ⟩

b) from part (a) we get,

x = sinφ cosθ

y = sinφsinθ

z = cosφ

are spherical coordinates of S where, 0≤φ≤π/4 and 0≤ θ≤ 2π.

so, ∫∫ z² ds = ₀∫ˣ₀∫ʸcos²φ dφ dθ ,

S

where x = 2π and y = π/4

So,Surface integeral is equals to ₀∫ˣ₀∫ʸcos²φ dφ dθ.

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Complete question:

If Sis the part of the sphere x2 + y2 + x2 = 1 that lies above the cone z= x2 + y2, find the following: a)S can be parametrized by a vector equation

r(θ, φ) = ⟨sinφ cosθ , sinφsinθ , cosφ ⟩ then a)| ⃗rᵩ × ⃗rθ| = ?

b) ∫∫ z² ds = ?

S

The correct statement regarding the inverse function of f(x) = 4x^4 is given as follows:

[tex]f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}[/tex]; f^(-1)(x) is not a function.

The function in this problem is defined as follows:

f(x) = 4x^4.

To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:

x = 4y^4.

Isolating the variable y, we have that:

y^4 = (x/4).

The inverse operation of the fourth power is the fourth root, hence:

[tex]y = \pm \sqrt[4]{\frac{x}{4}}[/tex]

[tex]f^{-1}(x) = \pm \sqrt[4]{\frac{x}{4}}[/tex]

[tex]f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}[/tex]

The plus/minus symbol means that for each input of x, the inverse function gives two outputs, meaning that there are multiple outputs mapped to each input, and thus the inverse is not a function.

This means that the second statement is correct.

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Answer:

6 hundred thousand

Step-by-step explanation:

there is 6 numbers in total.Each number is 5.The next number should be 6.

If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.

linearly independent vectors : In the theory of vector spaces, a set of vectors is said to be linearly dependent if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be linearly independent. These concepts are central to the definition of dimension

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a linearly independent vectors in a vector space V.

If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent.

If we delete a vector {say 2k}, from the collection, yes, we will still have a linearly independent collection of vectors

Therefore, if we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.

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Answer:

5−10g+20h

Step-by-step explanation:

To distribute the 5 to the terms inside the parentheses, we can use the distributive property:

(1−2g+4h)⋅5 = 5⋅1−5⋅2g+5⋅4h

= 5−10g+20h

This is the simplest equivalent expression we can get, as there are no more terms that can be combined.

To calculate the number of pieces into which Oscar divided the 4/5 kilogram of clay, we need to divide the total weight of the clay by the weight of each piece. We can do this by first converting the weight of the clay to kilograms and then dividing it by the weight of each piece. The weight of the clay in kilograms is 4/5 * 1 kilogram = 0.8 kilograms. And the weight of each piece is 1/5 * 1 kilogram = 0.2 kilograms. So, to find the number of pieces into which Oscar divided the clay, we divide the total weight of the clay by the weight of each piece, giving us 0.8 kilograms / 0.2 kilograms/piece = <<0.8/0.2=4>>4 pieces. Thus, Oscar divided the 4/5 kilogram of clay into 4 pieces.

Answer:

y = 1/4x + 1

Step-by-step explanation:

Answer:

a. compounding by the day: A = $5967.17

b. compounding by the hour: A = $5967.29

c. compounding by the minute: A = $5967.30

d. compounding by the second: A = $5967.30

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

If the interest is compounding by the day then n = 365.

Given:

Substitute the values into the compound interest formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.04}{365}\right)^{365 \times 10}[/tex]

[tex]\implies A=4000\left(1.00010958...\right)^{3650}[/tex]

[tex]\implies A=4000(1.49179200...)[/tex]

[tex]\implies A=5967.16801...[/tex]

[tex]\implies A=\$5967.17[/tex]

If the interest is compounding by the hour then:

Given:

Substitute the values into the compound interest formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.04}{8760}\right)^{8760 \times 10}[/tex]

[tex]\implies A=4000\left(1.00000456...\right)^{87600}[/tex]

[tex]\implies A=4000\left(1.49182333...\right)[/tex]

[tex]\implies A=5967.29333...[/tex]

[tex]\implies A=\$5967.29[/tex]

If the interest is compounding by the minute then:

Given:

Substitute the values into the compound interest formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.04}{525600}\right)^{525600 \times 10}[/tex]

[tex]\implies A=4000\left(1.00000007...\right)^{5256000}[/tex]

[tex]\implies A=4000(1.49182466...)[/tex]

[tex]\implies A=5967.29867...[/tex]

[tex]\implies A=\$5967.30[/tex]

If the interest is compounding by the second then:

Given:

Substitute the values into the compound interest formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.04}{31536000}\right)^{31536000 \times 10}[/tex]

[tex]\implies A=4000\left(1.00000000...\right)^{315360000}[/tex]

[tex]\implies A=4000\left(1.49182390...\right)[/tex]

[tex]\implies A=5967.29562...[/tex]

[tex]\implies A=\$5967.30[/tex]

The more compounding periods throughout the year, the higher the future value of the investment.  However, the difference between compounding by the day and compounding by the second results in a difference of 13 cents over the year, which is negligible comparatively.

Answer:

To rent a car from this company, Aaliyah will be charged a base rate of $71.87 per day, plus $0.09 for every mile she drives. In total, she plans to drive 475 miles, so she will be charged an additional $0.09 * 475 = $42.75 for the miles she drives.

The total cost of renting the car for one day will therefore be $71.87 + $42.75 = $114.62.

Aaliyah has a budget of $320, so she can afford to rent a car for a maximum of $320 / $114.62 = 2.79 days. However, since she can only rent the car for whole number of days, the maximum number of days she can afford is 2 days.

The inequality that can be used to determine the maximum number of days Aaliyah can afford to rent while staying within her budget is:

dd <= 2

Where dd is the number of days she plans to rent the car for. This inequality states that the maximum number of days Aaliyah can afford is 2.

[tex]10+2a < 4[/tex]

Simplify:

[tex]2a+10 < 4[/tex]

Subtract 10 from both sides:

[tex]2a+10-10 < 4-10[/tex]

[tex]2a < -6[/tex]

Divide both sides by 2:

[tex]\dfrac{2a}{2} < \dfrac{-6}{2}[/tex]

[tex]a < -3[/tex]

[tex]\fbox{Second Option}[/tex]

The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.

An addition operation involves two addends added together to result in a number called the sum.

The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.

Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.

1204.2 + 4.72613

= 1208.92613

= 1208.93

Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.

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Answer:  The measure of the three angles is 23, 67, and 90.

Step-by-step explanation:

The sum of three angles is equal to 180. We set the equation as:

x + 23 + 90 = 180

       x + 113 = 180

                x = 67

The measure of the three angles is 23, 67, and 90.

Answer:

10 shirts, 6 pants

Step-by-step explanation:

Let y = the number of shirts

Let x = the number of pants

y + 2 = 2x

x + y = 16

y = 2x - 2

x + (2x - 2) = 16

3x = 18

x = 6

y + 6 = 16

y =  10

Answer:

[tex]\textsf{A.} \quad \begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]

[tex]\textsf{B. \quad 6 pants and 10 shirts}[/tex]

Step-by-step explanation:

Given variables:

If the number of shirts Sylvia packed was 2 fewer than twice the number of pants she packed:

[tex]\implies y=2x-2[/tex]

If the total number of pairs of pants and shirts was 16:

[tex]\implies x+y=16[/tex]

Therefore, the system of equations that represents the problem is:

[tex]\begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]

System of equations:

[tex]\begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]

Substitute the first equation into the second equation and solve for x:

[tex]\implies x+2x-2=16[/tex]

[tex]\implies 3x-2=16[/tex]

[tex]\implies 3x=18[/tex]

[tex]\implies x=6[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\implies y=2(6)-2[/tex]

[tex]\implies y=12-2[/tex]

[tex]\implies y=10[/tex]

Therefore, Sylvia packed:

Answer:

Step-by-step explanation:

The value of y is unclear given the information provided. However, if BC intersects AD at E, then it stands to reason that y would be equal to the value of x. This is because, if BC intersects AD at E, then the two lines are parallel and therefore have the same value for y. Calculating the internal angles of triangle DEF, we can find the length of BW, CW and CE. Since BD=87 and WE=38, the remaining angle must be 55°. Therefore, using trigonometry and the known side lengths, we can calculate BW = 87 sin 55° = 77.5  , CW = 87cos55° = 48.5  and CE = 38sin55° = 33.2 . As you can see then, these are all easily calculable from the given data. In angle DEF, BD = 87 and WE = 38. Therefore, BW = 87 - 38 = 49, CW = 49 - 38 = 11, and CE = 11 - 1 = 10.

Raphael needs to run 3.9 miles on Friday so that he will have a total of 11 1/2 miles for the week.

What is Subtraction ?

An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction.

Raphael ran a total of 7 3/5 miles through Monday to Thursday.

We'll convert it from mixed fraction to simple fraction :

7 3/5 miles = [(7×5) + 3] / 5

                   = 38/5 miles.

He wants to have a total of 11 1/2 miles for the week.

Again, we will convert it into simple fraction :

11 1/2 miles = [(11×2) + 1 ] / 2

                  = 23/2 miles.

Let's he needs to run x miles to a total of 23/2 miles.

So, x + 38/5 = 23/2

     x = 23/2 - 38/5

        = [(23×5) - (38×2)] / 10

        =  (115 - 76)/10

        = 39/10 miles = 3.9 miles.

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Given the costs of 10 college math textbooks, we can calculate that:

a. The median is 70

b. The mean is 70.3

c. The variance is 2.01 and the standard deviation is 1.42

Median, mean, variance, and standard deviation

Median, mean, variance, and standard deviation are very basic but very important concepts of statistics.

Median is the middle value of the data that has been arranged sequentially from the smallest to the largest.

The median for the number of data (n) is odd:

[tex]M_{e} = x_{(\frac{n+1}{2} )}[/tex]

The median for the number of data (n) is even:

[tex]M_{e} = \frac{1}{2} (x_{(\frac{n}{2})} + x_{(\frac{n}{2} +1)} )[/tex]

Mean is the average of all data in a sample group, which is obtained by adding up all the data values, then dividing by the number of samples.

[tex]Mean = \frac{Sum of all data}{size of data (n)}[/tex]

Variance is a value that describes the variation of data, by measuring how far each piece of data is spread from the average of a data set.

[tex]Variance = \frac{sum (x_{i} - mean)^{2}}{n}[/tex]

Standard Deviation is a measure of the spread of observations in a data set relative to their mean. it measures how many observations in a data set differ from the mean and is the square root of the variance.

σ = [tex]\sqrt{variance}[/tex]

To do the problem, we first create a table for the given data.

Then we calculate the median as follows:

[tex]M_{e} = \frac{1}{2} (x_{(\frac{n}{2})} + x_{(\frac{n}{2} +1)} )\\= \frac{1}{2} (x_{5} + x_{6} )\\[/tex]

= 1/2 (70 + 70)

= 70

After that, we calculate the mean as follows:

[tex]Mean = \frac{Sum of all data}{size of data (n)}[/tex]

= (70 + 72 + 71 + 70 + 69 + 73 + 69 + 68 + 70 + 71) / 10

= 703 / 10

= 70.3

Now we calculate the difference between the data and the mean and put it into the table, and find the sum.

Then we can calculate the variance as follows:

[tex]Variance = \frac{sum (x_{i} - mean)^{2}}{n}[/tex]

= 20.1 / 10

= 2.01

Standard deviation can be calculated from the variance:

σ = [tex]\sqrt{variance}[/tex]

= [tex]\sqrt{2.01}[/tex]

= 1.42

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By applying vertical compression by a factor of 3, then vertical reflection and finally horizontal translation by 1 unit to the right we can transform into required graph.

A transformation is a mathematical operation that changes the position, size, or shape of a geometric object. In other words, it is a way to manipulate the object by moving, scaling, rotating, or reflecting it.

Reflection is a transformation that flips an object over a mirror line, or line of reflection. It creates a mirror image of the object on the other side of the line.

In mathematics, reflection is often represented by a matrix called the reflection matrix. This matrix encodes the rules for reflecting points in a particular direction.

To transform the graph of y = x^2 into y = -3(x+1)^2, we can apply the following transformations:

Vertical stretch or compression by a factor of 3: This transformation stretches or compresses the graph vertically by a factor of 3. To apply this transformation, we need to multiply the y-values of the points on the graph by 3.

Vertical reflection: This transformation reflects the graph across the x-axis. To apply this transformation, we need to multiply the y-values of the points on the graph by -1.

Horizontal translation by 1 unit to the right: This transformation shifts the graph 1 unit to the right. To apply this transformation, we need to add 1 to the x-values of the points on the graph.

Applying these transformations to the graph of y = x^2, we get the graph of y = -3(x+1)^2.

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Answer:

1,208.92613

Step-by-step explanation:

this is the answer

Answer:

Step-by-step explanation:

the following standards for variable manufacturing overhead havebeen established for a company that makes only one product:standard hours per unit of output.. 5.6 hoursstandard variable overhead rate. $19.15 per hourthe following data pertain to operations concerning the productfor the last month:actual hours .. 5,100

When t is that value, American men earned 2.8 more PhDs than women.

The given equation for h(t) is h(t) = f(t)/g(t), where f(t) models the number of PhDs awarded to men and g(t) models the number of PhDs awarded to women.

Since h(t) = 2.8 for some value of t, this means that the number of PhDs awarded to men is 2.8 times the number of PhDs awarded to women. Therefore, for that value of t, men in the U.S. earned 2.8 more PhDs than women.

The equation h(t) = f(t)/g(t) models the ratio of the number of PhDs awarded to men compared to women in the U.S., where f(t) models the number of PhDs awarded to men and g(t) models the number of PhDs awarded to women. Thus, if h(t) = 2.8 for some value of t, it means that the number of PhDs awarded to men is 2.8 times the number of PhDs awarded to women. In other words, for that value of t, men in the U.S. earned 2.8 more PhDs than women. This indicates that more men have received PhDs than women in the U.S. over the past few decades. The National Center for Education Statistics has kept track of this data and it is clear that men are receiving more degrees than women in the U.S.

h(t) = f(t)/g(t)

h(t) = 2.8

f(t) = 2.8g(t)

Therefore, for that value of t, men in the U.S. earned 2.8 more PhDs than women.

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The parameters of the exponential function in this problem are given as follows:

The standard format of an exponential function is given as follows:

y = c(1 - a)^t.

This is the case for a decaying exponential function, and the meaning of each parameter is given as follows:

In this problem, the function is given as follows:

f(x) = 1.1(0.44)^x.

Hence the values for the parameters are given as follows:

Then the percent of change is of -56%, as it is a decaying exponential function with a = 0.56.

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According to the given statement the positive exponent is [tex]\frac{16}{625}[/tex].

Exponents are a method of expressing enormous magnitudes in terms of their respective powers. The amount of times some number has already been multiplied in itself is the exponent, so to speak. For instance, the result of multiplying the number 6 on it's own four times is 6 6 6 6. This may be expressed as 64. Here, the exponent and base are 4 and 6, respectively.

The exponent is the exact quantity of times that base would be compounded on its own. As a result, if two powers have the same foundation, they can be multiplied. Whenever two powers are multiplied, exponents are added. If necessary, we can also divide the abilities.

= [tex]( \frac{2}{5} )^{4}[/tex]

= [tex]\frac{2}{5} \times\frac{2}{5} \times\frac{2}{5} \times\frac{2}{5} \\\\\frac{16}{625}[/tex]

Hence, the required exponent is [tex]\frac{16}{625}[/tex].

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1

The answer is 1 because if u use your brain you'd understand

The cost of the fixed assets will be $64258. The correct option is 1.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the data is, 36,000; - machinery and equipment - 18,600; - spare parts for repair - 608; - raw materials and materials - 7020.

The cost of the fixed assets will be calculated by adding all the values,

Cost = 36000 + 608 + 18600 + 7020

Cost = 62228 ≈ 64258

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