which of the following equations represents a linear function?

x = 1
y equals one third times x squared
y equals one fourth times x minus 1
4x − 2 = 6

The index value for 5 years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, Year 5: 1,414.74 as it starts at 1000 index points.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement. Rather than being stated as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Here,

Market value of the stocks:

Year 1: 2,645 million

Year 2: 2,957 million

Year 3: 3,318 million

Year 4: 3,193 million

Year 5: 3,742 million

Value of Index in 5 years:

Year 1: 1,000

Year 2: 1,117.96

Year 3: 1,254.44

Year 4: 1,207.18

Year 5: 1,414.74

Calculations:

Year 1: 2,645 million / 2,645 million × 1,000 = 1,000.00

Year 2: 2,957 million / 2,645 million × 1,000 = 1,117.96

Year 3: 3,318 million / 2,645 million × 1,000 = 1,254.44

Year 4: 3,193 million / 2,645 million × 1,000 = 1,207.18

Year 2: 3,742 million / 2,645 million × 1,000 = 1,414.74

Since the index starts at 1,000 points, the values for the subsequent years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, and Year 5: 1,414.74.

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The Oregon Trail is a western route that runs 1,000 miles from Illinois to Utah Territory.

In American history, the Oregon Trail, also known as the Oregon-California Trail, was an overland route that connected Independence, Missouri, with Oregon City, which is located close to Portland, Oregon, today, in the Willamette River valley. In the nineteenth century, it was one of two major emigration routes to the American West, the other being the southerly Santa Fe Trail from Independence to Santa Fe (now in New Mexico). A spur of the northerly Oregon route, which was a component of the Oregon Trail, headed to the Great Salt Lake region of what is now northern Utah. Additionally, branches from each main trail provided links to places in California.

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Answer:

I can "Confirm" The answer is not Oregon Trail, I believe the answer is "The Mormon Trail "

Step-by-step explanation:

Or "A"

Have a Joyous Day

the role of auditor is in management skill.

What is accounting?

Accounting, conjointly referred to as business, is that the activity, processing, and communication monetary|of monetary|of economic} and non financial data concerning economic entities like businesses and companies.

Main body:

The role of the auditor or reviewer is to relinquish knowledgeable and freelance on these monetary statements. The review or audit of associate association’s monetary report will guarantee larger responsible to the members and supply associate assurance that every one funds received by the organisation are properly accounted for.

therefore the role of auditor is in management skill.

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The arc length of the curve is L= π^2/8

In order to get the length of the arc's curved line, an arc length formula is used (a segment of a circle). The arc length is the length of the circle's curved line, which can be expressed as a distance through the curve.

To find arc length of the curve on the given interval

X= sin t-cos t   y= cos t +t sin t

0≤ t ≤ π/2

On differentiating x and y w.r.t  t

dx/dt = cos t - [cos t+t (-sin t)]= cos t – cost + t sin t

dy/dt = sin t + [t cos t+sin t]= sin t+ sin t+ t cos t

So we have

dy/dt = t cost          and       dx/dt= t sin t

Arc length for parametric equation is given by

L= ∫_0^(π/2)▒〖√((〖dx/dt)〗^2+(〖dy/dt)〗^2  )  〗  dt

L= ∫_0^(π/2)▒〖√((t^2 〖cos〗^2 t+t^2 〖sin〗^2 t) )  〗 dt

L= ∫_0^(π/2)▒t  dt

L= [t^2/2]  (π/2)¦0 = π^2/4*1/2

L= π^2/8

Therefore the arc length of the curve is L= π^2/8

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The amount of money that Erica owes at the end of 6 years is $8,551.56.

The amount of money that  has in his account would increase at a compound rate each month. Compound growth is when both the amount that was invested and the interest that has already been earned increases at each compounding time.

The formula that can be used to determine the future value with monthly compounding is:

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

Where:

A = $5300 x (1 + 0.0067)^(6 x 12)

A = $5300 x 1.0067^72 = $8,551.56

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In an acute triangle, all the three angles are less than 90°.

How do triangles work?

The definition of an acute triangle?

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Answer:

The rate of decrement is given as: r = 4%. From the table, the initial population is. P (0) = 7900. So, the population in t years is. P (t) = P (0) * (1 - r)^t. This gives. P (t) = 7900 * (1 - 4%)^t. Evaluate the difference.

Population after 2 years = P (1 + 4/100)2 = 62500 X (104/100)2

= 62500 × 26/25 X 26/25 = 100 × 26 ×26 = 67600.

Hence, the population after two years will be 67,600.

A rectangle's area of 28cm2 (measured in cm2) is numerically equal to 4 times the rectangle's circumference (measured in cm). The rectangle's length to width ratio is 5:2.

Given,

l/b = 5/2

l = 5b/2

area = 4 times the rectangle's perimeter,

which equals 4*2(l+b)

= 8(l+b)

= 8(5b/2 + b)

= 28b cm2.

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For a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.

It is given to us that -

There is 95% confidence

The margin of error is 0.04

We have to do the estimation of the population proportion.

We know that in case of unknown population proportion, we can assume that the value of population proportion can be regarded as 0.5.

It is known that the formula of sample size is given by -

[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }[/tex] ----- (1)

where,

n = sample size

Z = critical value of Z-value

p = population proportion

E = margin of error

Also, we know that for a 95% confidence interval, Z = 1.960

From the given information, we have

p = 0.5

and E = 0.04

Substituting the values in equation (1), we have

[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }\\= > n = \frac{(1.960)^{2}*0.5(1-0.5) }{(0.04)^{2} }\\= > n = \frac{3.8416*0.25}{0.0016}\\ = > n = 600.25[/tex]

Since this is the value of minimum sample size, rounding up, we have the sample size as 601.

Therefore, for a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.

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Z test and the X² test (Chi squared) will be used to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2.

Any statistical test for which the test statistic's distribution under the null hypothesis may be roughly represented by a normal distribution is known as a Z-test. Z-tests examine a distribution's mean. To determine if a discovery or relationship is statistically significant or not, hypothesis testing uses a z-test. It specifically checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more can a z-test be applied.

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5o% of almost 1500 highway deaths in Pennsylvania each year are attributed to aggressive driving.

Aggressive driving is defined as any behind-the-wheel exertion that, without regard for safety, puts another person( or people) and/ or property in peril.

Aggressive driving can vary from potentially dangerous conduct to serious assault.

From the data attained the percentage of the nearly 1500 highway deaths in Pennsylvania each year attributed to aggressive driving will be 50%

5o% of almost 1500 highway deaths in Pennsylvania each year are attributed to aggressive driving.

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The fraction of Jonas age represent the age of nick after 6 years is 7/10.

Given that, present age of nick is 8 years and Jonas age is 14 years.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

After 6 years

Nick's age =14 years and Joan's age =20 years

So, the fraction =14/20

= 7/10

Therefore, the fraction of Jonas age represent the age of nick after 6 years is 7/10.

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The service life that appear to be out of control is 0.0456 as per the given sample service life.

The sample standard deviation is the root-mean square of the discrepancies between observations and the sample mean: A large divergence is defined as two or more standard deviations from the mean.

The sample standard deviation (s) is the square root of the sample variance and a measure of the deviation from expected values.

It is given that,

Rationale:

UCL=520

LCL=480

Mean [tex]\bar{x}[/tex]=500

The standard deviation of sample([tex]S_{n}[/tex])=11.55

Z(for UCL)=(UCL-Mean)/[tex]S_{n}[/tex]

=(520-500)/10

=2

Similarly, Z(for LCL)=(LCL-Mean)/[tex]S_{n}[/tex]

==(480=500)/10

=-2

Now, by using the z table for finding the confidence level between the Z value of -2 and 2.

Therefore, confidence level=0.4772+0.4772

=0.9544

Risk(alpha)=1-confidence level

=1-0.9544

=0.0456

The service life that appear to be out of control is 0.0456 as per the given sample service life.

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Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L

According to our question-

Qin = 4 000m3/day

Cin = 25mg/L

V = 20 000m3

k = 0.25/day

Find: Count = ?

outStarting from the mass balance equation for steady state 0 = QCin - QCount - kCountV

manipulate the equation to get:

\(Count=Cin(Q/Q+kV)\)  

Then simple plug in your givens:

Count = (25mg/L)((4000m3/day)/(4000m3/day + 0.25/day(20000m3))

Count = 11mg/L

Hence, Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L.

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The true statements are:

The function is given as D(x) = 2x

The function D(x) is a linear function, and it is also a proportional function

Proportional functions represent direct variation

This means that (b) and (e) are true

Also set x = 5, 6 and -2

D(5) = 2 x 5 = 10

D(6) = 2 x 6 = 12

D(-2) = 2 x -2 = -4

This means that (a) is true

Lastly, the function D(x) is dependent on x for its value

This means that x is the dependent variable.

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The third approximation is x3 = 19.6

The Newton's method allow to approximate the root of a function as:

Newton's method, commonly referred to as the Newton-Raphson method after Isaac Newton and Joseph Raphson, is a root-finding algorithm that generates progressively improved approximations to the roots (or zeroes) of a real-valued function. The most fundamental form begins with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial point x0 for the root of f.

xₙ = xₙ₊₁ + f(xₙ)/f'(xₙ)

For this function, it is:

f(x) = 1/3x³+1/2x²+8

f'(x) = 2/3x²+x

For x1=-3,

f(x1) = 1/3x³+1/2x²+8 = -9 + 4.5 + 8 =3.5

f'(x1) = 2/3x²+x = 3

x2 = x1 + f(x1)/f'(x1) = -1.8

Therefore, x2 = -1.8

Then, the third approximation is x_3 is

x3 = x2 + f(x2)/f'(x2) = -1.8+ (7.72/0.36)

x3 = 19.6

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The answer is regression equation.

What is  regression equation?

The regression of y on x is that the algebraic expression of the regression lines. it's accustomed predict the values of the variable quantity from the given values of freelance variables.

Main Body:

When there is a relation between 2 variables , regression equation is used to describe the relation .

Hence regression equation is the result.

The actual question is like:

Given a collection of paired sample​ data, the​ ____________________ y with caret=b0+b1x algebraically describes the relationship between the two​ variables, x and y.

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The monthly utility bill (i.e. the x-value) that corresponds to a z-score of -0.75 is 64

Z-score gives you an idea of how far from the mean a data point is.

it’s a measure of how many standard deviations below or above the population mean a raw score is. A z-score can be placed on a normal distribution curve. Z-scores range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve).

The basic z score formula for a sample is:

z = (x – μ) / σ

According of the question,

Monthly utility bills in a city follows normal distribution

Mean of the monthly utility bills in a city : μ = $70

A standard deviation of monthly utility bills in a city : σ = $8

Z-score of utility bill = -0.75

z - score = x - μ / σ

=> - 0.75 = x - 70 / 8

=> -6 = x - 70

=> x = 70 - 6

=> x = 64

Hence , the x-value is 64

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Answer:

A Factor is a number that is multiplied. With another number to get a Product.

Step-by-step explanation:

Example  7 * 5 = 35

7 and 5 are factors of 35 that when multiplied give a product of 35

There is not enough money left to buy a card for $3.25 but they spend $ 5.88 to buy a gift.

What are combined earnings?

The term "Combined Earnings" refers to the total (without repetition) of (a) the aggregate (without repetition) Dividend Capacity of the Regulated Subsidiaries, (b) EBITDA, and (c) the aggregate (without repetition) tax provision, created in accordance with GAAP, for the Regulated Subsidiaries.

Here, we have

The earnings from Wednesday of Samuel and Jason are:

Samuel earnings = 12.5 x 0.40 = $5

Jason earnings = 7.1 x 0.40 = $2.84

The combined earnings from Wednesday are as follows:

Combined earnings = Samuel's earnings + Jason's earnings

Combined earnings = $5 + $ 2.84 = $ 7.84

The spended earnings are:

Spended earnings = combined earnings x ¾

Spended earnings = 7.84 x ¾ = $ 5.88

The leftover is:

 Leftover = combined earnings – spended earnings

 Leftover = 7.84 – 5.88 = $ 1.96

Hence, they spend $ 5.88 to buy a gift but not enough money to buy a card for $3.25.

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After choosing every proportion, if 24 people have the flu out of 360 people, then 60 people would have the flu out of 900.

We know very well that if any relation of one quantity is given with the second quantity at any instant of  time and same relation question is asking  at another instant of time, then always use unitary methods.

The unitary method is defined as a technique for solving a problem by first finding the value of a single unit, and then with the help of found value the necessary value can be find by multiplying the single unit value.

Here, In 360 people number of people would have flu=24

∴In 900 people number of people would have flu=(24×900)/360

                                                                                   =21600/360

                                                                                    =60people.

Hence, number of people would have flu is 60.

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One kilogram of mushrooms costs $2.90, whereas one kilogram of turnips costs $1.10.

An expression that describes the relationship between two or more numbers and variables is called an equation.

Dependent and independent variables are the two different categories. A dependent variable depends on another variable, whereas an independent variable does not depend on other variables.

Let x stand in for the price per kilogram of mushrooms, and y for the price per kilogram of turnips.

2 kg of mushrooms and 2.5 kg of turnips are priced at £8.55.

2x + 2.5y = 8.55  ________(1)

3 kg of mushrooms and 4 kg of turnips are priced at £13.10.

3x + 4y = 13.10   ________(2)

From both equations:

x = 2.9, y = 1.1

A kg of mushrooms costs $2.90, whereas a kg of turnips costs $1.10.

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Number of hours that Beth will take to catch up the Angie is 4.5 hours

The speed of Angie = 45 miles per hour

We know,

Speed = Distance / Time

Distance = Speed × Time

Substitute the values in the equation

In one hour the distance she traveled = 45 × 1

Multiply the numbers

= 45 miles

Beth leaves one hour later driving the same route

The speed of Beth = 55 miles per hour

The relative speed = 55 - 45

= 10 miles per hour

Then the time taken to catch up = 45/10

Divide the numbers

= 4.5 hours

Hence, the Beth will take 4.5 hours to catchup Angie

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None of the options are commutative for the given binary operations.

commutative property:

a*b = b*a

* is any binary operation.

Consider option a: subtraction of integers

Let a = 2,  b = 3

a - b = b - a (commutative property)

But

2 - 3  ≠ 3 - 2

-1  ≠ 1 not commutative

Option b: . division of nonzero real numbers

Let a = 2,  b = 3

a/b = b/ a (commutative property)

But

2/3  ≠ 3/2  not commutative

Option c. function composition of polynomials.

Let polynomial be a - b

Let a = 2,  b = 3

a - b = b - a (commutative property)

But

2 - 3  ≠ 3 - 2

-1  ≠ 1 not commutative

Thus, none of the options are commutative for the given binary operations.

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The general solution of equation y''+4y=sec(2z) is

y = c₁cos2z + c₂sin2z + [tex]\frac{cos2z}{4}[/tex] ln(cos2z) + [tex]\frac{z sin2z}{2}[/tex].

Given differential equation is,

y'' + 4y = sec(2z)

Characteristic equation of this equation is

(D²+4)=0

⇒ D² = -4

    D =  ±2i

Therefore the roots are imaginary.

D₁=2i ⇒ y₁ = e⁰cos2z = cos2z

D₂=-2I⇒ y₂ = e⁰sin2z = sin2z

yn= c₁cos2z + c₂sin2z

Noe to solve yp, first we need to solve Wronskian

y₁= cos2z ,   y₂=sin2z

y₁'= -2sin2z , y₂'=2cos2z

⇒ W = [tex]\left[\begin{array}{ccc}y1&y2\\y1'&y2'\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}cos2z&sin2z\\-2sin2z&2cos2z\\\end{array}\right][/tex]

                              = (cos2z)(2cos2z)-(-2sin2z)(sin2z)

                              = 2cos²2z + 2sin²2z

                              =2 (cos²2z + sin²2z)

                              = 2 ≠ 0

yp = - y₁[tex]\int\ {\frac{y2 g(z)}{W} } \, dz[/tex] + y₂[tex]\int\ {\frac{y1 g(z)}{W} } \, dz[/tex]

    = -(cos2z)[tex]\int\ {\frac{(sin2z)(sec2z)}{2} } \, dz[/tex] + (sin2z)[tex]\int\ {\frac{(cos2z)(sec2z)}{2} } \, dz[/tex]

    = - (cos2z)[tex]\int\ {\frac{sin2z/cos2z}{2} } \, dz[/tex] + (sin2z)[tex]\int\ {\frac{cos2z/cos2z}{2} } \, dz[/tex]

    = - [tex]\frac{cos2z}{2}[/tex][tex]\int\ {tan2z} \, dz[/tex] + [tex]\frac{sin2z}{2}[/tex][tex]\int\ \,dz[/tex]

    =  - [tex]\frac{cos2z}{2}[/tex](-[tex]\frac{1}{2}[/tex] ln (cos2z)) + [tex]\frac{sin2z}{2}[/tex] (z)

    =  [tex]\frac{cos2z}{4}[/tex]ln(cos2z) + [tex]\frac{zsin2z}{2}[/tex]

Now the general equation will become

y = yn + yp

y = c₁cos2z + c₂sin2z +[tex]\frac{cos2z}{4}[/tex]ln(cos2z) + [tex]\frac{zsin2z}{2}[/tex]    .

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After solving, the probability that we select a gold marble is 2/31.

In the given question,

A bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles.

So, Total marbles = 2+8+21

Total marbles = 31

As we know that, probability refers to the likelihood that an event will occur. If we don't know how such an event will end out, we can analyze the probability or likelihood of various outcomes. Statistic is the analysis of events that follow a probability distribution.

We have to randomly select one marble from the bag then we have to find the probability that we select a gold marble is

P(G) = Total number of gold marble/Total marbles

P(G) = 2/31

Hence, the probability that we select a gold marble is 2/31.

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If W(t) denotes the sumo wrestler's weight then the Function's formula will be w(t) = 5.5t + 79.5

Function formula: This relationship is often represented as y = f(x), or "f of x," and y and x are related in such a way that there is a unique value of y for every x; consequently, f(x) cannot have multiple values for the same x.

if we take y = mx + b,

the slope, m = 5.5, we need to find b,

at x = 11 and y = 14

14 = (5.5) (11) + b

b = 79.5

We plug in the qualities for x, y, and m. Then, we rearrange and deduct 60.5 from the two sides.

This makes the equation,

y = 5.5x + 79.5

or we can write as

w(t) = 5.5t + 79.5

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(complete question)

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms.Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).

Write the function's formula.

W(t)=?