In March 2011, a California newspaper predicted that the price of gasoline in two years would be $4.10. The newspaper claimed that the prediction would be within 2% of the actual price of gasoline in March 2013. Given the data in the table, determine the percent error of the prediction. Was the newspapers claim correct or incorrect. Provide work or an explanation to justify your answer.

Thus, the equation of a parallel line with the slope -3 and passing point (2,−1) is found as : y = -3x + 5.

Two or more lines that have been spaced the same apart, never merging but never diverging, are said to be parallel. Parallel lines run indefinitely in both directions because, as we mentioned earlier, lines are non-stop.

As long as they are consistently spaced at the same distance apart, they don't necessarily need to be straight lines.

equation of a line :  y = −3x−5

Comparing with slope-intercept form of line.

y = mx + c

m is the slope and c is the y intercept.

m = -3

Parallel lines have the same slopes:

m = -3 and passing points (2,−1).

Using the point -slope equation:

y - y 1 = m(x - x1)

y + 1 = -3(x - 2)

y = -3x + 6 - 1

y = -3x + 5

Thus, the equation of a parallel line with the slope -3 and passing point (2,−1) is found as : y = -3x + 5.

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Complete question:

Find the equation of a line parallel to y=−3x−5that passes through the point (2,−1).

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108[/tex]

By simplifying  the derivative of f(x) is:,[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^ 2 (x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2 )[/tex]

A derivative is a mathematical cοncept that represents the rate at which a functiοn changes with respect tο οne οf its variables. In οther wοrds, the derivative measures hοw much the οutput οf a functiοn changes when yοu change the input by a small amοunt.

Tο find the derivative οf f(x), we will use the quοtient rule οf differentiatiοn.

Let's begin by simplifying the expression:

[tex]f(x) = [5(x^2 + 2) cot(x)]/[2 - cos(x) csc(x)][/tex]

[tex]f(x) = [5(x^2 + 2) cos(x)/sin(x)]/[2sin(x) - cos(x)][/tex]

[tex]f(x) = [5(x^2 + 2) cos(x)]/[sin(x)(2sin(x) - cos(x))][/tex]

Now we can apply the quotient rule:

[tex]f'(x) = [(5(x^2 + 2) cos(x))'sin(x)(2sin(x) - cos(x)) - (5(x^2 + 2) cos(x))(sin(x)(2sin(x) - cos(x)))']/(sin(x)(2sin(x) - cos(x))^2)[/tex]

To simplify, let's find the derivatives of the individual terms in the numerator:

[tex][(5(x^2+ 2) cos(x))'] = 10xcos(x) - 5(x^2+ 2)sin(x)[/tex]

[tex][(sin(x)(2sin(x) - cos(x)))'] = 3cos^2 (x) - 4sin^2(x)[/tex]

Now we can substitute these back into our original equation for f'(x):

[tex]f'(x) = [(10xcos(x) - 5(x^2 + 2)sin(x))sin(x)(2sin(x) - cos(x)) - (5(x^2 + 2) cos(x))(3cos^2(x) - 4sin^2 x))]/(sin(x)(2sin(x) - cos(x))^2)[/tex]

Simplifying further:

[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 5(x^2 + 2)sin^2 (x)(2sin(x) - cos(x)) - 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^2x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]

[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2+ 2)sin^ 2(x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]

Therefore, the derivative of f(x) is:

[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^2(x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]

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Answer:

  d)  1/(4e)

Step-by-step explanation:

You want the value of the limit of 1/4f(x)^(1/x) as x approaches -1, where f(x) = x^2·e^(x^2).

The function is continuous and defined at x=-1, so the limit can be evaluated directly.

  [tex]\lim=\dfrac{1}{4}((-1)^2\cdot e^{(-1)^2})^{(1/-1)}=\dfrac{1}{4}(1\cdot e^1)^{-1}=\boxed{\dfrac{1}{4e}}[/tex]

Answer:

D

Step-by-step explanation:

If the triangles are similar, their side ratios are equal

[tex] \frac{54}{12} = \frac{x}{15} [/tex]

Cross-multiply to find x:

[tex]x = \frac{54 \times 15}{12} = 67.5[/tex]

The value of q is 16.

What is a quadratic equation?

Any equation can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation. An equation containing a single variable of degree 2.

Here, we have

Given: Equation: 3x²+18x–21 = 0 is written in the form (x–p)²=q.

We have to find the value of q.

3x²+18x–21 = 0

3(x²+6x-7) = 0

x²+6x-7 = 0

(x+3)²-7-9 = 0

(x+3)² - 16 = 0

(x+3)² = 16

(x-p)² = q

Hence, the value of q is 16.

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The answer is 44.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

4*(12-1)

44

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Answer: D is correct.

Step-by-step explanation:

The economic system that has no government involvement in the market is d. No economic system is free from government involvement.

In reality, there is no government intervention because at some point the government will comes in , this could actually be minimal, only in the free market is where there is no government intervention.

It should be noted that in this free market, there is an unregulated system of economic exchange, where the act of taxes collection as well as quality controls,  has no economic interventions which can be attributed to the government. Because of this, option D is correct.

I hope this helped! Brainilist is highly appreciated! <333

Answer:

Step-by-step explanation:

We can use the DuPont model to calculate the ROE (Return on Equity):

ROE = Profit margin * Total assets turnover * Equity multiplier

Substituting the given values, we get:

ROE = 0.085 * 1.5 * 1.8 = 0.2295 or 22.95%

Therefore, Precision Aviation's ROE was 22.95%.

As a result, after fοur years οf depreciatiοn, the car is wοrth abοut $12,914.96.

Subtract the asset's cοst frοm its scrap value (what yοu anticipate it tο be wοrth just at end οf the useful life) tο determine depreciatiοn using the straight-line technique. The quantity that can be depreciated, οr the depreciable basis, is the οutcοme. Take this amοunt and deduct it frοm the lifespan οf the asset, which is expressed in years.

This fοrmula fοr expοnentially decaying can be used tο determine the value οf a vehicle after fοur years οf depreciatiοn:

[tex]A = P * e^{(-rt)} (-rt)[/tex]

where A represents a finaI vaIue, P represents its initiaI price, r represents the yearIy depreciatiοn rate in decimaI fοrm, and t is the periοd οf time.

Inputting the specified vaIues resuIts in:

P = $15,200 (the οriginaI vaIue) (the initiaI vaIue)

Given that the annuaI depreciatiοn rate is 5.8%, r is equaI tο 0.058.

t = 4 (because we want tο find the vaIue after 4 years)

When we enter these vaIues, we οbtain:

[tex]A = $15,200 * e^{(-0.058 * 4)}[/tex]

Hence, When we condense an expression, we get:

[tex]A = $15,200 * e^{(-0.232)} (-0.232)[/tex]

A = $12,914.96

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The measure of the sector that represents the probability of the medicine curing one person is 216°. So correct option is A.

In geometry, a sector is a region of a circle enclosed by two radii and an arc. The two radii form an angle, called the central angle, which defines the boundary of the sector.

The area of a sector can be calculated using the following formula:

Area of sector = (central angle / 360) * π * r²

where:

central angle is the angle formed by the two radii

r is the radius of the circle

π is the mathematical constant pi, which is approximately 3.14159

The perimeter of a sector is the sum of the length of the arc and the length of the two radii. The length of the arc can be calculated using the formula:

Length of arc = (central angle / 360) * 2 * π * r

Sectors are often used in real-world applications, such as calculating the area of a pizza slice or the distance traveled by a car in a circular racetrack. They are also used in trigonometry to calculate angles and side lengths of triangles formed by intersecting chords and tangents in circles.

The probability of the medicine curing one person is given by P(curing) = 3/5. Since the spinner is a circle of 360°, the measure of the sector that represents the probability of the medicine curing one person is:

360° × P(curing) = 360° × 3/5 = 216°

Therefore, the answer is A) 216 degrees.

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From the calculation that we have in the question, the volume of the rectangular prism is 30 cm^3.

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional shape that has six rectangular faces, where each pair of opposite faces are congruent and parallel. It can be thought of as a stretched cube, where the length, width, and height are all different.

We have that the volume of the rectangular prism is

V = lbh

V = 2 * 3 * 5

V = 30 cm^3

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Answer:

Step-by-step explanation:

the answer is 192

9hrs=$144

12hrs=X

you cross multiple

12x144/9

which give you $192

Answer:

Jenny made $144 for 9 hours of work so you divide 144 by 9 and you get 16.

$16 is the amount of money that Jenny makes in an hour. To check if it's correct you multiply 16 by 9 and you should get 144.

So, since the question wants you to find how much she makes for 12 hours of work, you multiply 16 times 12 and you should get 192.

In conclusion, Jenny makes $192 for 12 hours of work.

Answer: ;)

The area of a circle is 64 square units

Step-by-step explanation:

Area of a circle a=64 square units in terms of

Step-by-step explanation:

Given that the diameter of a circle is 16

That is d=16

Therefore radius r=8

Now to find the area of a circle :Area of a circle square units

Substitute r=8 we get

Area of a circle

Therefore the area of a cicle is 64 square units

Area of a circle a=64 square units in terms of

Based on the given task content; the solution to the linear expressions 4(2b + 2) - 3 and -4 + 8p - 6p - 5 + 20p is 8b + 5 and -9 + 22p respectively.

11. 4(2b + 2) - 3

open parenthesis

= 8b + 8 - 3

= 8b + 5

12. -4 + 8p - 6p - 5 + 20p

combine like terms

-4 - 5 + 8p - 6p + 20p

= -9 + 22p

In conclusion, 8b + 5 and -9 + 22p is the solution to the linear expressions 4(2b + 2) - 3 and -4 + 8p - 6p - 5 + 20p respectively.

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Answer:

$84,220

Step-by-step explanation:

To calculate the taxable income, we need to subtract the allowable tax deductions from the annual salary:

Taxable income = Annual salary - Allowable tax deductions

Taxable income = $91,520 - $7,300

Taxable income = $84,220

Therefore, his taxable income is $84,220.

Answer:

75 square feet

Step-by-step explanation:

you will just multiply by 1 over 40 as it is the ratio that he works in one hour

(b) u₁e^λ₁t +u₂e^λ₂t (pI-A)⁻¹ f₀e^pt f for p ≠λ₁ orλ₂ as the coefficients can only be determined when the value of p is not equal to either of the eigenvalues  λ₁ or λ₂.

Eigenvalues are scalars associated with a linear transformation or a matrix. They can be used to determine the stability of the system and describe the behavior of the transformation.

In this case, the eigen values λ₁ and λ₂ are constants, and the solution to the differential equation y' + Ay = f₀e^pt can be solved by using the method of undetermined coefficients.

This method involves using a linear combination of the eigenvectors, which are associated with the eigenvalues  λ₁ and λ₂.

The solution for this differential equation is then given by u₁e^λ₁t +u₂e^λ₂t (pI-A)⁻¹ f₀e^pt f for p ≠ λ₁ or λ₂.

This is because the coefficients can only be determined when the value of p is not equal to either of the eigenvalues  λ₁ or λ₂. If p is equal to one of these eigenvalues, then the solution cannot be determined as the coefficients become indeterminate.

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Therefore, we cannot calculate the cost of an ounce of insulin in 2006 using this function. (a). the cost of insulin increases by 12% per year.

(b).Therefore, an ounce of insulin would have cost approximately $114.08 in 2018.

(c).Therefore, the cost of insulin increases by 12% per year.

What is function?

a function is a relationship between two sets of objects, where each object in the first set (called the domain) is associated with exactly one object in the second set (called the range). The domain and range can be any set, including numbers, geometric shapes, or other mathematical objects.

A function is typically represented by a rule or formula that describes how to map each element in the domain to an element in the range. For example, the function f(x) = 2x maps each value of x to its double, so that f(1) = 2, f(2) = 4, f(3) = 6, and so on.

The cost of insulin increases over time because the value of 1.12 is greater than 1, meaning the function's output grows with increasing t. To find the percentage increase per year, we can calculate the difference in cost between two consecutive years and divide it by the cost of the earlier year. For example, to find the percentage increase between 2010 and 2011:

[tex]c(1) - c(0) = 54(1.12) - 54 = 6.48[/tex]

Percentage increase = (6.48/54) x 100% = 12%

Therefore, the cost of insulin increases by 12% per year.

b. To find the cost of an ounce of insulin in 2018, we need to find the value of t for that year. Since t represents the number of years since 2010, we can subtract 2010 from 2018 to get:

[tex]t = 2018 - 2010 = 8[/tex]

[tex]c(8) = 54(1.12)^8 =$114.08[/tex]

Therefore, an ounce of insulin would have cost approximately $114.08 in 2018.

c. To find the cost of an ounce of insulin in 2006, we need to find the value of t for that year. Since t represents the number of years since 2010, we can subtract 2010 from 2006 to get:

[tex]t = 2006 - 2010 = -4[/tex]

However, a negative value of t is not meaningful in this context because the function assumes t represents the number of years since 2010. Therefore, we cannot calculate the cost of an ounce of insulin in 2006 using this function.

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Answer:

what type of a question is this man can send me the full question so i can answer to you??

Answer: 12 1/2

Step-by-step explanation:

thats the answer

Answer:

28x + 20

Step-by-step explanation:

you just need to distribute

4(7x + 5)

you multiply 4 X 7x which would give you 28 and because 7 has a variable and 4 doesn't have a variable the x stays there so it would be 28x.

45, you need to multiply 4 x 5 which would give you 20, and because neither 4 or 5 have a variable it will stay 20

So now you just 28x with 20

28x + 20.

Ronaldo therefore feeds his family 2 and 4/7 sandwiches as he eats sandwiches that are three and three-sevenths .

A mathematical strategy for resolving proportionality issues is the unitary method. Finding the value of one unit of a quantity and utilising that value to determine the value of a different number of units of the same quantity is what this process entails. The unitary technique can be used, for instance, to determine the cost of any quantity of apples if you know that 5 apples cost $10. $10/5 = $2 would be the price of one apple. By multiplying the quantity of apples by the price of one apple, you could then calculate the price of any other number of apples. For instance, 8 apples would cost 8 x $2, or $16, to purchase.

given

Ronaldo eats sandwiches that are three and three-sevenths of a sandwich, which is an incorrect fraction:

3 3/7 = (7*3 + 3)/7 = 24/7

He divides these sandwiches into thirds and fourths among his family, making a total of:

(3/4) * (24/7) = (324)/(47) = 18/7

We can change this incorrect fraction into a mixed number because:

18/7 = 2 and 4/7

Ronaldo therefore feeds his family 2 and 4/7 sandwiches as he eats sandwiches that are three and three-sevenths .

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Let the labeled price be 100x

20% discount, sale price = 80x

13% of 80x = 13x*4/5= 52x/5 = 10.4x

10.4x = 416

100x = ?

100/10.4 X416 = 41600/10.4 = Rs 4, 000 ANSWER

A graph of A(x) and B(x) in the interval 0 ≤ x 100 on a cartesian coordinate is shown below.

The solution of A(x) = B(x) to the nearest integer is (35, 8).

In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided about the two plans for speeding up its technical support time, we can logically deduce the following exponential functions;

[tex]A(x) = 15.7(0.98)^x \\\\B(x) = 11(0.99)^{x}[/tex]

By critically observing the graph of the two exponential functions, we can logically deduce that the point of intersection (solution) is in quadrant I, which is given by the ordered pair (35, 8).

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The solution for ‘d’ in the given equation is d = (ln(A) - ln(B))/ln(1+c/d).

Natural log is a logarithmic function commonly used in mathematics and in calculators to simplify equations. It is the inverse of the exponential function and is written as ln(x).

In order to solve for ‘d’ in the given equation, we need to isolate it on the left side of the equation.

To do this, we can begin by taking the natural log of both sides of the equation, as shown below.

ln(A) = ln(B) + d*ln(1+c/d)

We can now rearrange the terms in this equation such that ‘d’ is isolated on the left side of the equation.

d*ln(1+c/d) = ln(A)-ln(B)

We can now divide both sides of the equation by ln(1+c/d) in order to solve for ‘d’, as shown below.

d = (ln(A) - ln(B))/ln(1+c/d)

Therefore, the solution for ‘d’ in the given equation is

d = (ln(A) - ln(B))/ln(1+c/d).

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Answer:

2cos(3ẞ/2)(sin(7ẞ/2) + cos(19ẞ/2))

Step-by-step explanation:

We can use the identity for the sum of two sines to rewrite the expression as follows

sin 4ẞ + sin 10ẞ = 2sin(7ẞ/2)cos(3ẞ/2)

Similarly, we can use the identity for the sum of two cosines to rewrite the expression as follows

22ẞ + sin 16ẞ = 2cos(19ẞ/2)cos(3ẞ/2)

Therefore, we have

sin 4ẞ + sin 10ẞ + 22ẞ + sin 16ẞ = 2sin(7ẞ/2)cos(3ẞ/2) + 2cos(19ẞ/2)cos(3ẞ/2)

Factoring out the common factor of cos(3ẞ/2), we get

sin 4ẞ + sin 10ẞ + 22ẞ + sin 16ẞ = 2cos(3ẞ/2)(sin(7ẞ/2) + cos(19ẞ/2))

Therefore, the expression can be expressed as a product of 2cos(3ẞ/2) and the sum of sin(7ẞ/2) and cos(19ẞ/2).