the concept of hedonistic calculus is associated with

The proportion that could be used to find the width of Grace's model car is 1/2 = Model width / 12 inches.

To find the width of Grace's model car, a proportion can be set up using the lengths of the actual car and the desired model:

Proportion: Actual width / Actual length = Model width / Model length

Given values:

Actual length = 8 feet

Actual width = 4 feet

Model length = 12 inches

Converting the units:

12 inches = 1 foot (since 1 foot = 12 inches)

Substituting the values into the proportion:

4 feet / 8 feet = Model width / 12 inches

Simplifying the proportion:

1/2 = Model width / 12 inches

To find the model width, cross-multiply and solve for the unknown:

Model width = (1/2) * 12 inches = 6 inches

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an equation to represent the relation is,

⇒ y = 10/x

We know that,

Proportion is extensively explained. Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, while a ratio is represented as a:b, and a proportion states that two ratios are equal. In this case, a and b can be any two integers. The ratio and proportion are important foundations for understanding numerous ideas in mathematics and science.

Since, The relation represents an inverse variation because as the values of x is increasing the values of y is decreasing.

Hence, We can formulate;

y = k/x

Plug y = 5, x = 2;

5 = k/2

Solve for k;

k = 5 x 2

k = 10

Thus, The required equation is y = 10/x

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The complete question is :

does the relation in the table represent direct variation, inverse variation, or neither? if it is direct or inverse variation, write an equation to represent the situation. Explain your answer

x 5, 10, 15, 20

Y 2, 1, 2/3, 1/2

The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.

Solution:

When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, y reflection )'s across the x-axis is (x, -y).

the point (x , y)→ (x , -y).

In the question given 4 coordinates,

U(1 , -3)

V(4 , -3)

T(1 , -4)

W(5 , -4)

the reflection across x-axis

U(1 , -3) →U' (1, 3)

V(4 , -3) → V'(4 , 3)

T(1 , -4) → T'(1 , 4)

W(5 , -4) → W'(5 , 4)

so  after the reflection across the x axis the coordinates of the vertices becomes ,

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)

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complete question:

Find the coordinates of the vertices of each figure after the given transformation

3) reflection across the x-axis

Enter Question Text

A U'(1,3),V'(4,3), W'(5,4),T'(1,4)

B U'(3,1),V'(3,4,), W'(4,5),T'(4,1)

D U'(-1,3),V'(-4,3), W'(-5,4),T'(-1,4)

(3)(4-3);W(Sp-4)T(4)

U

T

X

Answer:

48m^2 + 56m

Step-by-step explanation:

-8m(-6m - 7)

Use the distributive property. (-8m*-6m & -8m*-7)

-8m*-6m = 48m^2

-8m*-7 = 56m

48m^2 + 56m

The value of the standardized test statistic for this significance test is -1.3

For the standardized test statistic for this significance test, we need to compare the sample proportion to the hypothesized population proportion.

The null hypothesis (H₀)  

H₀: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is equal to 30%.

The alternative hypothesis (H₁)

H₁: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is different from 30%.

The sample size is 25 and 5 of those files are missing a medical,

The sample proportion (p) can be calculated as

(p) hat = (Number of files missing justification) / (Total number of files)

(p) hat = 5 / 25

(p) hat = 0.2

The standard error is given by

SE = √[((p) hat × (1 - (p) hat)) / n]

SE = √[(0.2 × (1 - 0.2)) / 25] = √(0.16 / 25) = 0.08

For the standardized test statistic, we use the formula:

z = ((p) hat - p₀) / SE

where p₀ is the hypothesized population proportion.

p₀ = 30% = 0.3

z = (0.2 - 0.3) / 0.08 = -0.1 / 0.08 = -1.25 = -1.3

The value of the standardized test statistic for this significance test is approximately -1.3

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An ounce of the chemical cost in 2018 is $98.54.

Given:

The function c(x) = 72 ⋅ (1.04)ˣ models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory.

Exponential function, involves exponents. an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.

In mathematics, an exponential function is a function of form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

x represents the number of years since 2010.

An ounce of the chemical cost in 2018 is,

= 72 × (1.04)⁸

= $98.54

Therefore, the cost is $98.54.

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Answer:

Down below

Step-by-step explanation:

2)(-6,3)

where h=-6&k=3

(x-h)²+(y-k)²=R²

(x-(-3)²+(y-6)²=11²

(x+3)²+(y²-6²)=11²

3)(x-3)²+(y+4)²=25

(x-h)²+(y-k)²=R²

h=3

k=-4

(

C(3,-4)

4)(x+1)²+(y-6)²=361

(x-h)²+(y-k)²=R²

R²=361

√R²=√361

R=19

The total recruiting expense is  $91,200 which includes Recruitment Cost, Interview Costs, Job Posting fee, Family travel cost and more

The total recruiting expense would be:

Recruitment Costs: $43,600

Interview Costs: $2,000 x 3

= $6,000

Job Posting fee: $1,000

1st year fee: 10% x $130,000

= $13,000

Real Estate Fee: 6% x $360,000

= $21,600

Shipping fee: $4,000

Family travel cost: $400 x 5

= $2,000

Total = $43,600 + $6,000 + $1,000 + $13,000 + $21,600 + $4,000 + $2,000

= $91,200

Hence, the total recruiting expense is  $91,200

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Answer:

what is 478/6 +7*25+78+123-568

The possible value of positive constant b for an absolute maximum value of function g(x), [tex]g(x) = xe^{-x} + be^{-x} [/tex] at x = [tex] \frac{2}{3} [/tex] is equals to the [tex] \frac{1}{3} [/tex].

An absolute maximum point is a point where the function acquires its largest possible value. To drive the max or min absolute value, we have to substitute the derivative value of function equals to zero. We have a function, [tex]g(x) = xe^{-x} + be^{-x} [/tex], where b is positive constant. We have to determine the possible value of b for absolute maximum of g at x= 2/3.

Differentiating the function g(x) with respect to x

=> [tex]g'(x) = - x e^{-x} + e^{-x} - be^{-x} [/tex]

[tex]= (1 - x - b )e^{-x}[/tex]

[tex]= \frac{1 - x - b }{e^{x}}[/tex]

For obtaining absolute maximum value put, g'(x) = 0

=> [tex]\frac{1 - x - b }{e^{x}} = 0[/tex]

Substitute x = 2/3, in above expression,

[tex] \frac{1 - \frac{2}{3} - b }{e^{\frac{2}{3}}} = 0[/tex]

=> [tex]1 - \frac{2}{3} - b = 0[/tex]

=> [tex] b = \frac{1}{3}[/tex]

Hence, the required value of b is [tex] \frac{1}{3} [/tex].

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Complete question:

Let g(x)=xe^(-x)+be^(-1), where b is a positive constant. For what positive value of b does g have an absolute maximum at x=2/3 .Justify your answer.

Hello !

Minimum = 6 (the smallest value)

First quartile = 8 (25% of 7 = 1,75    => 2nd value)

Median = 15 (the value in the middle)

Third quartil = 23 (75% of 7 = 5,25    => 6th value)

Maximum = 31 (the greatest value)

It's C

Answer:

C. The 3.rd Answer :)

We need to use some basic algebraic equations. Let's assume that the initial payment made by Frankie was x, and the total amount he has to pay for the computer is y. Also, let's assume that Frankie will make n monthly payments.

Now, we know that Frankie has already paid x, and he has to pay y-x more. Since he will pay this amount in n monthly installments, we can represent the monthly installment as (y-x)/n.

So, the equation that represents the relationship between n and y can be written as:

y = x + n*(y-x)/n

Simplifying this equation, we get:

y = x + y-x

y = y

This means that the equation is true for any value of n and y, as long as x is a valid initial payment amount. Therefore, the equation that represents the relationship between n and y is:

y = x + n*(y-x)/n

The equation we derived above is a simple but important concept in mathematics and finance. It shows us that we can calculate the total amount we need to pay for something by multiplying the monthly installment by the number of payments and adding the initial payment to it. This concept is used in many financial transactions, such as car loans, mortgages, and credit card payments.

Moreover, this equation also helps us to plan our finances and manage our budget effectively. We can use it to calculate how much we need to save every month to reach our financial goals, or to compare different payment options and choose the one that suits us best.

In conclusion, the equation that represents the relationship between the number of monthly payments and the total amount paid is an essential tool for anyone who wants to make wise financial decisions. By understanding this equation, we can save money, avoid debt, and achieve our financial goals more easily.

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Answer:

2.02

Explanation:

Each pail of plaster covers 97 Square feet of ceiling

The ceiling of the room is 14 ft long

= 14×14

= 196

Therefore the pail of plaster that will be needed to cover the rooms can be calculated as follows

= 196/97

= 2.02

Answer:

  B, D, F

Step-by-step explanation:

You want the diagrams that show lines through the center of enlargement, where the smaller triangle is enlarged to form the larger triangle.

Each point in an enlarged figure is moved toward or away from the center of enlargement along a line through that center. That is, corresponding vertices of a triangle and its enlargement will lie on a line through the enlargement center.

The diagrams of interest are those that show lines through corresponding vertices of the triangles.

Diagrams B, D, F show lines through the center of enlargement.

__

Additional comment

The center of enlargement is marked in the attachment by a blue dot. Enlargement is by a factor of 3.

Points are moved away if the scale factor is greater than 1; toward the center of enlargement for a scale factor less than 1.

<95141404393>

The research method that involves collecting data repeatedly on the same person as he or she ages is longitudinal.

Longitudinal research involves studying the same group of individuals over an extended period of time, typically years or even decades. This type of research allows researchers to collect data on changes in behavior, attitudes, or health outcomes over time, and can provide valuable information on the effects of age, development, or life events on these outcomes. Longitudinal research can be especially useful in studying developmental processes, as it allows researchers to track changes in individuals as they grow and develop.

However, longitudinal studies can also be expensive and time-consuming, as researchers must track and collect data from the same group of individuals over many years, and there is a risk of attrition or drop-out over time.

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Answer:

  q = 2

Step-by-step explanation:

You want to find q such that the difference between the two roots of 3x²-5x+q is 1/3.

In quadratic ax²+bx+c, the sum of the roots is (-b/a). For roots p and s, this tells us ...

  p + s = -(-5)/3 = 5/3

The problem statement tells us the difference is ...

  p - s = 1/3

Adding these two equations gives ...

  2p = (5+1)/3 = 2

  p = 1 . . . . . . . . . . . . . divide by 2

  s = p -1/3 = 2/3 . . . . find the smaller root

The product of the two roots is (c/a) = (q/3):

  ps = (1)(2/3) = q/3

  q = 2 . . . . . multiply by 3

The value of q is 2.

#95141404393

The steps to graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7) are given below.

To graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7), we need to apply the following steps:

Plot the original figure on a coordinate plane.

Draw a point at the center of dilation (2, −7).

Draw lines connecting the vertices of the original figure to the center of dilation.

Extend each line from the center of dilation by a factor of 3.

Plot the new vertices where the extended lines intersect.

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Answer:

The Correct answer is C

communicative property

Answer:

y = (1/3)x - 5

Step-by-step explanation:

x - 3y = 15

x - 15 = 3y

3y = x -15

y = (1/3)x - 5

Hello !

Answer:

[tex]\boxed{y=\frac{1}{3}x-5}[/tex]

Step-by-step explanation:

An equation in slope-intercept form is [tex]y=mx+b[/tex].

Let's isolate y in our equation :

[tex]x-3y=15\\-3y=-x+15\\3y=x-15\\y=\frac{1}{3}x-5[/tex]

Our equation is in the form [tex]y=mx+b[/tex] with [tex]m=\frac{1}{3}[/tex] and [tex]b=-5[/tex].

Have a nice day

Answer:

4/3

Step-by-step explanation:

Tan(x)=Opposite/adjacent

We need to find the opposite side.

We can use the Pythagorean theorem to help us:

5^2=3^2+x^2

25=9+x^2

16=x^2

x=4

4 is the measure of the opposite side

The adjacent side has measure of 3

Tan(theta)= 4/3

*theta is the weird 0 with a bar thingy at the angle, its some letter in the greek alphabet that denotes an unknown angle in geometry

The mean absolute deviation of the given data set, 94, 86, 95, 99, 88, 90, is 4

The values differ from the mean by an average of 4.

From the question, we are to calculate the mean absolute deviation of the given data

The given data

94, 86, 95, 99, 88, 90

To calculate the mean absolute deviation of the given data,

First, we will calculate the mean

Mean = (94 + 86 + 95 + 99 + 88 + 90) / 6

Mean = 552 / 6

Mean = 92

Now,

We will determine the absolute value of the difference between each data and the mean

|94 - 92| = 2

|86 - 92| = 6

|95 - 92| = 3

|99 - 92| = 7

|88 - 92| = 4

|90 - 92| = 2

Now,

We will determine the mean of these absolute differences

Mean absolute deviation = (2 + 6 + 3 + 7 + 4 + 2) / 6

Mean absolute deviation = 4

Hence,

The mean absolute deviation is 4

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The area of the banner is 24 square feet.

We have,

Since the spirit spanner is in the form of a triangle.

We can use the area of a triangle to calculate the area of the banner.

The area of a triangle is given by the formula:

Area = (1/2) x base x height

Substituting the given values.

Area = (1/2) x 8 feet x 6 feet

Area = 24 square feet

Therefore,

The area of the banner is 24 square feet.

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The length of y of the triangle is y = 9√2 units

Given data ,

Let the Triangle be ΔABC , such that

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

On simplifying , we get

From the trigonometric relations , we get

sin θ = opposite / hypotenuse

sin 45° = 9 / y

Multiply by y on both sides , we get

y = 9 / sin 45°

On simplifying , we get

y = 9√2 units

Hence , the length is y = 9√2 units

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Kyra will receive $125 USD when she converts £67.50 to USD.

Given that, Kyra wants to convert some Australian dollars to pounds she received £67.50.

Exchange rate =

Exchange rates are typically quoted as currency pairs, where one currency is the base currency and the other is the counter currency.

To convert £67.50 into USD using the exchange rate of $1 = £0.54, you can multiply the amount in pounds by the exchange rate.

Here's the calculation:

£67.50 x $1/£0.54 = $125

Therefore, Kyra will receive $125 USD when she converts £67.50 to USD.

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Answer:

x = 2, 6

Step-by-step explanation:

differentiate f(x) using the power rule

f'(a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and f'( constant) = 0

given

f(x) = x³ - 12x² + 6x - 8

f'(x) = 3x² - 24x + 6

equate f'(x) to - 30

3x² - 24x + 6 = - 30 ( add 30 to both sides )

3x² - 24x + 36 = 0 ( divide through by 3 )

x² - 8x + 12 = 0 ← in standard form

(x - 2)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 6 = 0 ⇒ x = 6

solution is x = 2, 6

Step-by-step explanation:

To find f(x + h), we substitute x + h for x in the function f(x):

f(x + h) = (x + h)^2 + 2(x + h) + 1

Now we simplify by expanding the square:

f(x + h) = x^2 + 2hx + h^2 + 2x + 2h + 1

We can combine like terms to simplify this expression:

f(x + h) = x^2 + (2h + 2)x + (h^2 + 2h + 1)

Therefore, f(x + h) = x^2 + (2h + 2)x + (h^2 + 2h + 1).

Answer:

[tex]f(x+h) = x^2 + 2xh + h^2 + 2x+2h + 1[/tex]

Step-by-step explanation:

In this question, we have to plug (x + h) into the given function and simplify.

[tex]f(x) = x^2 + 2x + 1[/tex]

↓ replacing all instances of x with (x + h)

[tex]f(x+h) = (x+h)^2 + 2(x+h) + 1[/tex]

↓ expanding the quadratic term (x + h)²

[tex]f(x+h) = (x^2 + 2xh + h^2) + 2(x+h) + 1[/tex]

↓ applying the distributive property ... [tex]2(x+h) = 2x + 2h[/tex]

[tex]\boxed{f(x+h) = x^2 + 2xh + h^2 + 2x+2h + 1}[/tex]

No further simplification can be done.

Answer:

12 hours

Step-by-step explanation:

1 3/4=1.75

21÷1.75=12