State the horizontal asymptote of the rational function. (5 points) worth lots of points!!!
f(x) = quantity three x squared minus four x minus three divided by quantity two x squared minus three x plus two

To determine if the inspector is justified in claiming that all the engine fan blades must be replaced, we can perform a hypothesis test using the sample variance and the given population variance threshold.

The null hypothesis (H0) is that the population variance is less than or equal to 0.18 mm2, and the alternative hypothesis (Ha) is that the population variance is greater than 0.18 mm2.

Using the chi-square distribution and a significance level of 0.01, we can calculate the critical chi-square value that corresponds to the upper tail area of 0.01.

Next, we calculate the chi-square test statistic using the sample variance, the sample size, and the population variance threshold. If the test statistic exceeds the critical chi-square value, we reject the null hypothesis and conclude that the fan blades must be replaced.

To find a 90% confidence interval for the population standard deviation, we can use the chi-square distribution and the degrees of freedom (n-1), where n is the sample size. The confidence interval will be constructed based on the chi-square values corresponding to the lower and upper tails of 0.05 each.

Performing these calculations will provide the necessary information to determine if the inspector is justified in claiming that all the engine fan blades must be replaced and to establish the confidence interval for the population standard deviation.

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Answer:

    (a, b) ∈ {(1, 729), (3, 243), (9, 81), (27, 27), (81, 9), (243, 3) (729, 1)}

Step-by-step explanation:

\(\sqrt{a\cdot b}=27\\\\(\sqrt{a\cdot b})^2=27^2\\\\a\cdot b=729\\\\\\729=27\cdot27=9\cdot81=3\cdot243=1\cdot729\)

So:

(a, b)∈{(1, 729), (3, 243), (9, 81), (27, 27), (81, 9), (243, 3) (729, 1)}

Answer:

F=2

Step-by-step explanation:

1.25f+2.75f=10-2

calculate like terms

4f=8

divide

F=2

Answer:

Step-by-step explanation:

f(5) = 2^8 - 5 +3

f(5) = 256-5+3

f(5) = 254

Answer:

A) 25 feet

Step-by-step explanation:

A sculptor uses the scale of 3 inches to represent 15 feet. Find the amount of feet represented by 1 inch by simply dividing 15 with 3:

15/3 = 5

1 inch represents 5 feet.

Next, it is given that the model of the airplane is 5 inches long. Multiply 5 inches with 5 feet to get the total measurement of the original airplane:

5 x 5 = 25 feet.

5 inches represent 25 feet.

A) 25 feet is our answer.

~

Answer:

2(x - 5)(x + 5)

Step-by-step explanation:

Common factor

2² − 50

2(² − 25)

Use the sum-product pattern

2(² − 25)

2(2² + 5 − 5 − 25)

Common factor from the two pairs

2(² + 5 − 5 − 25)

2(( + 5) − 5( + 5))

Rewrite in factored form

2(( + 5) − 5( + 5))

2( − 5)( + 5)

Solution

2( − 5)( + 5)

Answer:

$838.09

Details:

750.44 after one year.

771.45 after two years.

793.05 after three years.

815.26 after four years.

838.09 after five years.

Option c. is the correct answer.

Answer:

b^8

Step-by-step explanation:

When multiplying exponents with the same base, we can add the exponents

b^2 * b^6

b^ (2+6)

b^8

Answer:b8 x

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "b6"   was replaced by   "b^6".  1 more similar replacement(s).

STEP

1

:

Multiplying exponential expressions

1.1    b2 multiplied by b6 = b(2 + 6) = b8

Final result :

 b8x

Answer:

2125

Step-by-step explanation:

CP= x

MP= x+25%= 1.25x

SP= MP-15%= 1.25x*0.85= 1.0625x

SP- CP= 125

SP= 2000+125= 2125

------------

Cost price= 2000

Marked price= 2500

Selling price= 2125

Answer:

Subtract 15 from both sides.

5t > 35

Divide both sides by 5.

t > 7

(Sorry, I can't do the > with the _ under it.)

Please mark me Brainliest; I need it to move onto the next level. =D

Answer:

D, I think. Screenshot attached with the points.

Step-by-step explanation:

We have given two points (0, 6) and (-8, 0). The third point (8, -6) will make a complete right-angle triangle.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

We have given two points  (0, 6) and (-8, 0). we want to find Which of the following points would create a right triangle.

We have mentioned the points on the graph that represent a right-angle triangle. we know that the point (8, -6) will make a complete right-angle triangle.

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(i) To find the solution for yt in the given equation yt = yt−1 + εt + 0.3εt−1, we can rewrite it as yt - yt−1 = εt + 0.3εt−1. By applying the lag operator L, we have (1 - L)yt = εt + 0.3εt−1.

Solving for yt, we get yt = (1/L)(εt + 0.3εt−1). The solution for yt involves lag operators and depends on the values of εt and εt−1.  (ii) For the equation yt = 1.2yt−1 + εt, to find the s-step-ahead forecast Et[yt+s], we can recursively substitute the lagged values. Starting with yt = 1.2yt−1 + εt, we have yt+1 = 1.2(1.2yt−1 + εt) + εt+1, yt+2 = 1.2(1.2(1.2yt−1 + εt) + εt+1) + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to ensure that the coefficient on yt−1, which is 1.2 in this case, is less than 1 in absolute value. If it is greater than 1, the process will be explosive and not stationary. To achieve stationarity, we can either decrease the value of 1.2 or introduce appropriate differencing operators.

(iii) For the equation yt = yt−1 + t + εt, finding the solution for yt and the s-step-ahead forecast Et[yt+s] involves incorporating the time trend t. By recursively substituting the lagged values, we have yt = yt−1 + t + εt, yt+1 = yt + t + εt+1, yt+2 = yt+1 + t + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to remove the time trend component. We can achieve this by differencing the series. Taking first differences of yt, we obtain Δyt = yt - yt-1 = t + εt. The differenced series Δyt eliminates the time trend, making the model stationary. We can then apply forecasting techniques to predict Et[Δyt+s], which would correspond to the s-step-ahead forecast Et[yt+s] for the original series yt.

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Answer:

k = -18

Step-by-step explanation:

If x-3 is a factor, what this means is that if we substitute;

x = 3 into the equation, we should get 0

This is from the factor theorem

Thus ;

P(3) = 0 = 2(3)^3 -5(3)^2 + 3(3) + k

0 = 54 - 45 + 9 + k

k + 18 = 0

k = -18

Answer:

0.1 ounce

Step-by-step explanation:

5  cookies = 0.5 ounces

1 cookie = 0.5 / 5 = 0.1 ounce

The volume of the right prism with a base area of 10 square feet and a height of 6 feet is 60 cubic feet.

A prism is a polyhedron that has a base and a top face that are the same in size and shape, with sides connecting them that are rectangles in a right prism.

A right prism is a prism in which all of the side faces are perpendicular to the base.

Therefore, the height of the right prism is perpendicular to the base as well.

A right prism has a volume equal to the product of the base area and the height.

This formula can be represented as:

V = Bh

Here, B represents the area of the base, and h represents the height.

The volume of the right prism can be found by multiplying the area of the base by the height of the prism, according to the formula:

V = Bh.

In this problem, the area of the base of the prism is given to be 10 square feet.

The height of the prism is 6 feet.

We can simply substitute these values into the formula to obtain the volume of the right prism as follows:

V = BhV

   = 10 × 6V

   = 60

Therefore, the volume of the right prism is 60 cubic feet.

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Answer:

x = 4 .  x = 9 .    x= 9 .    n= 4 .    y= 3 .  y=2  

Step-by-step explanation:

Let x be the amount invested in the 5-yr CD and y be the amount invested in the 18-month CD.

We have the following equations:

0.044x + 0.03(x - 2000) = 1102.50 (total interest equation)

x + (x - 2000) = Total amount invested

Solving this system of equations will give the values of x and y

To determine how much was invested in each CD, we can set up a system of equations. Let x represent the amount invested in the 5-yr CD and y represent the amount invested in the 18-month CD.

The interest earned from the 5-yr CD can be calculated using the formula I = Prt, where I is the interest, P is the principal (amount invested), r is the interest rate, and t is the time in years. In this case, the interest equation for the 5-yr CD is 0.044x.

The interest earned from the 18-month CD can be calculated in the same way, using the formula I = Prt. However, since the time is given in months, we need to convert it to years by dividing by 12. The interest equation for the 18-month CD is 0.03(x - 2000).

The total interest earned from both CDs is $1102.50, so we have the equation 0.044x + 0.03(x - 2000) = 1102.50.

Additionally, the total amount invested is the sum of the amounts invested in each CD, which is x + (x - 2000).

By solving this system of equations, we can determine the values of x and y, representing the amounts invested in each CD. The solution to the system will provide the specific amounts invested in the 5-yr CD and the 18-month CD.

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If a model a rocket is used to test materials that will be used to build the body of the actual rocket. The limitation of this model is: D. It is smaller than the actual rocket.

A model rocket is a scaled-down version of an actual rocket, which means it is smaller than the actual rocket. While a model rocket can be used to test materials that will be used to build the body of the actual rocket, there are limitations to using a model rocket for this purpose.

One of the main limitations is that the smaller size of the model rocket may not accurately represent the effects of a full-scale rocket launch on the materials.

In addition, there may be other differences between the model rocket and the actual rocket, such as the types of engines used, the payload carried, and the environmental conditions during the launch, which can also limit the applicability of the results obtained from testing the materials on the model rocket to the actual rocket.

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Answer:

87.92 rounded to the nearest tenth would be 87.9 because you wouldn't round up unless the number after the 9 was 5 or higher.

Step-by-step explanation:

Step-by-step explanation:

87.9

......

hope it helps!

Answer:

Your answer would be D!

Step-by-step explanation:

Answer:

Choose 3y^2-8y

Step-by-step explanation:

Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

Given that, height of the right-angled triangle = 4m. Width of the right-angled triangle = 1m. Let's assume that the rectangular enclosure will be built at the base of the right-angled triangle. The area of the rectangular enclosure can be obtained using the formula, Area of rectangle = length × breadth. Length of the rectangle = height of the right-angled triangle = 4mLet the breadth of the rectangle be x, then the length is the width of the right-angled triangle + x = 1 + x Hence, the area of the rectangular enclosure is given by: Area = Length × Breadth= (1+x)×4= 4x + 4m²Now, the maximum area can be obtained by differentiating the above expression with respect to x and equating it to zero: dA/dx = 4 = 0x = -1. This is not a valid solution since we cannot have a negative breadth, hence we conclude that the area is maximum when the breadth of the rectangular enclosure is equal to the width of the right-angled triangle, i.e., when x = 1m. Thus, Area of the rectangular enclosure = Length × Breadth= (1+1)×4= 8 m². Hence, the largest the area of Gottfried’s enclosure can be is 8 m².

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(a) The value of derivative dy/dx = 2x.
(b) The value of derivative dy/dx = 2y/x - 1/x².
(c) The value of derivative dy/dx = xˣ * ln(x).
(d) The value of derivative dy/dx = (y - xy cos(xy))/(1 - x²y² cos(xy)).
(e) The value of derivative dy/dx = (x-1)(3x²-2x(y-1))/(x³(x-1)+y-1).

a)  This is because the derivative of x² is 2x.

b) This can be found using implicit differentiation, which involves taking the derivative of both sides of the equation with respect to x and using the chain rule as dy/dx= 1/x(2y-1/x)

c)  This can be found using the power rule and the chain rule and the statndard derivative value is xˣ * ln(x)..

d)  This can be found using the chain rule and the product rule.

e) This can be found using the product rule and simplifying the expression.

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Answer:

Step-by-step explanation:

x^2+14x+45=0

x^2+(9+5)x+45=0

x^2+9x+5x+45

x(x+9)+5(x+9)=0

(x+9)(x+5)=0

either x+9=0                           Or,x+5=0

x+9=0

x=0-9

x=-9

x+5=0

x=0-5

x=-5

therefore x=-9,-5

The total amount of Greta's debt payments (including the proposed new loan) should not exceed $13,600.

What is Total cost?

Average total cost is referred to as the sum total of all production costs divided by the total quantity of output.

According to this rule, the maximum amount of debt payments (including the proposed new loan) should not exceed 40% of the borrower's gross income.

To apply the banker's rule to Greta's situation, we can calculate her maximum affordable debt payments as:

Maximum affordable debt payments = 40% of gross income

Maximum affordable debt payments = 0.4 x $34,000

Maximum affordable debt payments = $13,600

This means that the total amount of Greta's debt payments (including the proposed new loan) should not exceed $13,600.

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Each person living in the Sighet ghetto would have had an estimated personal space of 12.8 square feet, which is extremely cramped and overcrowded.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

First, we need to calculate the total number of rooms in the ghetto:

Number of people = 13,000

Number of people per room = 20

Total number of rooms = Number of people / Number of people per room = 13,000 / 20 = 650

Next, we can calculate the total area of all the rooms:

Total area of all the rooms = Number of rooms x Average room size = 650 x 256 = 166,400 square feet

Finally, we can calculate the amount of personal space each person had by dividing the total area of all the rooms by the number of people:

Personal space per person = Total area of all the rooms / Number of people = 166,400 / 13,000 = 12.8 square feet

Therefore, each person living in the Sighet ghetto would have had an estimated personal space of 12.8 square feet, which is extremely cramped and overcrowded.

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