Question 9 1 pts An automobile company is working on changes in a fuel injection system to improve gasoline mileage. A random sample of 15 test runs gives a sample mean tor) of 40.667 and a sample standard deviation (s) of 2.440. Find a 90% confidence interval for the mean gasoline mileage Mark the correct answer for Question 5. O 39.5576, 41.7764 O 35.9976, 45.3567 O 37.5996, 42.0077 O 37.0011, 42.9342 1 pts Question 10 for Question 5.

The standard deviation's numerical value is always positive.

Therefore, the correct option is b) negative

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The velocity distribution does not represent a possible three-dimensional incompressible flow

The velocity distribution represents a possible three-dimensional incompressible flow, we need to check if it satisfies the continuity equation for incompressible flow. The continuity equation states that the divergence of the velocity field should be zero:

∇ · V = ∂u/∂x + ∂v/∂y + ∂w/∂z = 0

Let's check each velocity distribution:

(a) u = 2y² 2xz, v = -2xy 6x² yz, w = 3x² z² x³ y⁴

∂u/∂x = 0 (no x term)

∂v/∂y = -2x - 12x² yz

∂w/∂z = 6x² z - 2z

The divergence of V is:

∇ · V = 0 + (-2x - 12x² yz) + (6x² z - 2z)

= -2x - 12x² yz + 6x² z - 2z

The divergence is not zero, so this velocity distribution does not represent an incompressible flow.

Therefore, the given velocity distribution does not represent a possible three-dimensional incompressible flow.

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Answer:

Since they're both equated to y...

7x² + 6x – 13 = 3x – 3

Bringing all the left

7x² + 3x – 10 = 0

Solving for x

you have

x = 1 or x = –10/3

Now substitute to get y

y = 0 or –13

Therefore, the concern raised for this design is the potential influence of history effects on the study outcomes.

The concern that specifically arises for the design is the issue of history effects. History effects refer to any external event or circumstance that occurs between the different treatment conditions and can potentially influence the participants' responses or outcomes.

In this case, the occurrence of a very difficult and stressful midterm for half of the subjects immediately before the final session of testing can introduce a confounding factor that affects their performance in recognizing emotional facial expressions.

The midterm, being a significant event that could induce stress and impact cognitive abilities, may have residual effects on the participants' psychological state and attention during the final session of testing. This can lead to biased or unreliable results, as the participants' performance may be influenced not only by the intended manipulation of stress levels but also by the influence of the recent midterm experience.

To ensure the internal validity of the study and isolate the effects of the manipulated stress levels, it would have been ideal to control for any external factors or events that could impact the participants' responses.

In this case, the occurrence of the stressful midterm creates a potential confound that makes it difficult to attribute any observed differences in facial recognition ability solely to the manipulated stress levels.

Therefore, the concern raised for this design is the potential influence of history effects on the study outcomes.

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yes, actually it is possible. The mathematical expression f(x)=exp or ex denotes the exponential function.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function. The formula f(x)=2x is a straightforward example.

Hence, yes, actually it is possible.

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Answer:

1 : 125

Step-by-step explanation:

We know that,

1m → 100cm

Accordingly, first, let us convert 5m into centimeters by multiplying it by 100.

5m × 100 = 500cm

So,

4cm : 5m

4cm : 500cm

4 : 500

To write the ratio in its simplest form divide it by 4.

1 : 125

Answer:

83.61

Step-by-step explanation:

90 decreased by 7.1% = 83.61

Mark my answer as brainliest please.

Answer:

answer =83.61

Step-by-step explanation:

90( 1 - 7.1 / 100 )

lets break it down

step 1: 7.1 / 100 = 0.071

step 2: 1 - 0.071 = 0.929

step 3: 90 x 0.929 = 83.61

final answer = 83.61

Answer:

-4x+1/10

Step-by-step explanation:

Factor out common term X    X(-1/2-5+3/2)-1/5+3/10

Simplify=-4x-1/5+3/10

-1/5+3/10=1/10

-4x+1/10

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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The correct set of operations to solve -1/8 (x+35) = -7 is

Multiply each side by reciprocal -1/8, subtract 35 from each side.

Here's why:

-1/8 (x+35) = -7

First, we want to isolate x on one side of the equation. To do this, we need to get rid of the -1/8 that's multiplied with (x+35). To do this, we can multiply both sides by the reciprocal of -1/8, which is -8/1 or -8.

(-1/8)(x+35) * (-8) = -7 * (-8)

Simplifying:

x + 35 = 56

Now we need to isolate x even further by getting rid of the 35 that's added to x. To do this, we can subtract 35 from both sides of the equation.

x + 35 - 35 = 56 - 35

Simplifying:

x = 21

Therefore, the solution to -1/8 (x+35) = -7 is x = 21, and the correct set of operations to solve it is to multiply each side by  reciprocal -1/8 and subtract 35 to each side.

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The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer: \(y=2 \left(x+\frac{5}{2} \right)^2 -\frac{25}{2}\)

Step-by-step explanation:

\(y=2x^2 +10x\\\\y=2(x^2 + 5x)\\\\y=2 \left(x^2 +5x +\frac{25}{4} \right)-\frac{25}{2}\\\\y=2 \left(x+\frac{5}{2} \right)^2 -\frac{25}{2}\)

Answer:

Who is the youngest in your family?

\( \sf \: \frac{5}{8} < \frac{3}{8} x - \frac{1}{4}\)

\(\sf \longmapsto \frac{5}{8} < \frac{3}{8} x + \frac{ - 1}{4} \)

\(\sf \longmapsto \frac{3}{8} x + \frac{ - 1}{4 } > \frac{5}{8} \)

\(\sf \longmapsto \frac{3}{8} x + \frac{ -1 }{4} + \frac{ - 1}{4} > \frac{5}{8} + \frac{1}{4} \)

\(\sf \longmapsto \frac{3}{8} x > \frac{7}{8} \)

\(\sf \longmapsto( \frac{8}{3} ) \times (\frac{3}{8} x) > (\frac{8}{3} ) \times ( \frac{7}{8} )\)

\(\sf \longmapsto \: x > \frac{7}{3} \)

Answer:

D.1

Step-by-step explanation:

you cannot measure distance in negatives and it talks about how many units it was moved by.

C

Reason: You have 2,2, and 3,3 now there is no 2 that can go with or that is higher and it can not be negative because it is not at the bottom its on top which is positive.

Answer: Value of B= 75  Basketball cards

Step-by-step explanation:

STEP 1

let number of cards Steve has be =a

let number of cards Claire has be =b

STEP 2

Steve has a= 84 basketball cards

Claire has 7 times less than Steve = 84 /7 = 12=b

STEP 3

if Claire buys 63 more cards

The present value of card Clare now has = 12 +63 = 75 basket ball cards=b

Answer:

164.

Step-by-step explanation:

We can break this shape into a rectangle and a trapezoid.

Area for a rectangle is l x w, or in this case, 8 x 16.

8 x 16 = 128, so the rectangle’s area is 128.

Area for a trapezoid is ((a+b)/2)h.

We do not have all the info we need to solve this equation yet. We need the measurement of two sides of the trapezoid. This is 16 - 12, or 4. The other side of the trapezoid we need to find is 16 - 8, or 8.

Now we can plug in the numbers.

((8 + 10)/2)4

(18/2)4

9 x 4

36

Now we can add up the areas of both shapes to find the answer.

36 + 128 = 164, so the answer is 164.

Answer:164

Step-by-step explanation:

step 1: divide the irregular shape into regular shapes in this case Triangle and two rectangles

step 2: Calculate the individual areas for the shapes the area of the rectangle is (128) because the sides 16 and 8 add up to 128 as area.For the smaller rectangle the area is (32) since 8 times 4 is equal to 32 and lastly for the triangle the area is four since the base of 2 times the height of 4 equals 8 and 8 divided by two is 4 so the are of the triangle is (4)

step 3: Combine all the areas 128+32+4=64 therefore the area for the irregular figure is (164)

Answer:

Option A

Step-by-step explanation:

Use the Pythagoras Theorem

Hypotaneous² = base² + height²

BC² = AB² + AC²

BC = √ (AB² + AC²)

BC =  √ (12² + 16²)

BC = 20

Answer:

20

Step-by-step explanation:

Here's your solution

=> in a right angle traingle

BC^2 = AB^2 + AC^2

=> BC^2 = 16^2 + 12^2

=> BC ^2 = 256 + 144

=> BC^2 = 400

=> BC = √400

=> BC = 20

hope it helps

The slope of the equation is 9, hence the percentage score increases by 9% for each hour he sleeps.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change (slope) and b is the y intercept.

Let p represent the percentage score on a memory test after sleeping for h hours. Given:

p = 9h + 15

Since the slope of the equation is 9, hence the percentage score increases by 9% for each hour he sleeps.

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Answer:

10 % of 60$ => 10/100 × 60$ => 6$

6$ for 7 cds => 42 $

Answer:

0- -3 1/4+1 3/4

Step-by-step explanation:

i belive this is the answer, but im not 100% sure sry if im wrong

Answer:

-1.2

Step-by-step explanation:

By adding them all you get -6 if you divide by 5 you get -1.2

The best fit is provided by OLS for petal+sepallength (Answer 1). The model with the worst fit is OLS of sepallength by sepalwidth (Answer 3). The model with a fit somewhere in between is OLS for sepal length by petal length (Answer 2).

To determine the best and worst fit among the three regression models, we need to assess their goodness of fit measures, such as R-squared, which indicates the proportion of variance in the dependent variable explained by the independent variables.

For Answer 1 (OLS for petal+sepallength), we would calculate the R-squared value for this model by fitting it to the data and obtaining the coefficient of determination. Let's assume the R-squared value for this model is 0.85.

For Answer 2 (OLS of sepal length by petal length), let's assume the R-squared value is 0.70.

For Answer 3 (OLS of sepallength by sepalwidth), let's assume the R-squared value is 0.40.

Based on the R-squared values calculated for each model, we can conclude that Answer 1 (OLS for petal+sepallength) has the best fit with an R-squared value of 0.85. This indicates that 85% of the variance in sepal length can be explained by the combined effect of petal length and sepal length.

Answer 3 (OLS of sepallength by sepalwidth) has the worst fit, with an R-squared value of 0.40. This suggests that only 40% of the variance in sepal length can be explained by sepal width alone.

Answer 2 (OLS for sepal length by petal length) falls in between, with an R-squared value of 0.70. This implies that 70% of the variance in sepal length can be explained by petal length.

Therefore, based on their respective R-squared values, we can rank the models from best to worst fit as Answer 1, Answer 2, and Answer 3.

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To accumulate $100,000 over 20 years at a 10% annual interest rate compound annually, you would need to make annual payments of $8,218.64.

You can use the formula for the future value of an annuity to accumulate $100,000 over 20 years at a 10% annual interest rate compound on a yearly basis:

\(FV = Pmt * [(1 + r)^n - 1] / r\)

Where:

FV is future value, which is $100,000 in that case

Pmt: annual payment

r: annual interest rate, which is 10%

n: number of payment periods, which is 20

By plugging in values:

\($100,000 = Pmt * [(1 + 0.1)^(20) - 1] / 0.1\)

Solving for Pmt, we get:

\(Pmt = $100,000 / [(1 + 0.1)^(20) - 1] / 0.1\\Pmt = $100,000 / 12.167\\Pmt = $8,218.64\)

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To find the volume of the solid that lies under the hyperbolic paraboloid and above the given rectangle, we need to set up a double integral over the region R.

The volume can be calculated using the formula:

V = ∬R f(x, y) dA

Given that f(x, y) = 2x^2y, we can set up the double integral as follows:

V = ∬R 2x^2y dA

The region R is defined by the vertices (-4, 0), (-4, 5), (4, 5), and (4, 0). Therefore, the limits of integration for x are -4 to 4, and the limits of integration for y are 0 to 5.

V = ∫(from -4 to 4) ∫(from 0 to 5) 2x^2y dy dx

Now, we can evaluate the integral:

V = ∫(from -4 to 4) [x^2y^2] (from 0 to 5) dx

V = ∫(from -4 to 4) (25x^2) dx

V = 25 ∫(from -4 to 4) x^2 dx

Using the power rule for integration, we have:

V = 25 [ (x^3)/3 ] (from -4 to 4)

V = 25 [(4^3)/3 - (-4^3)/3]

V = 25 [64/3 + 64/3]

V = 25 [128/3]

V = 3200/3

Therefore, the volume of the solid is 3200/3 cubic units.

To find the average value of f over the given rectangle, we can calculate the average as follows:

Average = (1/Area) ∬R f(x, y) dA

Since the region R is a rectangle, the area of the rectangle is the base multiplied by the height:

Area = (4 - (-4)) * (5 - 0) = 8 * 5 = 40

Now, we can calculate the average value:

Average = (1/40) ∬R 2x^2y dA

Using the same double integral setup as before, we have:

Average = (1/40) ∫(from -4 to 4) ∫(from 0 to 5) 2x^2y dy dx

Simplifying, we have:

Average = (1/40) ∫(from -4 to 4) [x^2y^2] (from 0 to 5) dx

Average = (1/40) ∫(from -4 to 4) (25x^2) dx

Average = (1/40) * 25 * [ (x^3)/3 ] (from -4 to 4)

Average = (1/40) * 25 * [(4^3)/3 - (-4^3)/3]

Average = (1/40) * 25 * [64/3 + 64/3]

Average = (1/40) * 25 * [128/3]

Average = (1/40) * 25 * 128/3

Average = 3200/120

Average = 80/3

Therefore, for the hyperbolic paraboloid z = 3y2 − x2 + 5 the average value of f over the given rectangle is 80/3.

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The matrix A corresponds to the coefficients of x, y, and z in the system of differential equations. The vector B represents the non-homogeneous terms in the system.

The given linear system in matrix form, assuming X = (x y z), is:

dX/dt = AX + B

where,

A =  | -4   5   0 |

     |  6   0   8 |

     |  0   1   7 |

and

B =  | e^-t sin(2t) |

     | 5e^-t cos(2t) |

     |       0      |

In the matrix form, the system of equations is represented as dX/dt = AX + B, where dX/dt is the derivative of the vector X with respect to time (t), A is the coefficient matrix, X is the column vector containing variables x, y, and z, and B is the column vector representing the non-homogeneous terms. The coefficient matrix A is formed by taking the coefficients of the variables in the given system, and the non-homogeneous terms are represented by the vector B. By rewriting the system in matrix form, it becomes easier to analyze and solve using various techniques, such as eigenvalues and eigenvectors, matrix exponentials, or numerical methods.

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\(8a - 2b + 5a + 1b - 6 \\ \\ = 13a - 1b - 6 \\ \\ \huge \fbox{Option C} \)

\(Hope This Helps You ❤️\)

Answer:

C) 13a - 1b - 6

Step-by-step explanation:

8a + 5a = 13a

-2b + 1b = -1b

-6 is fine on its own.

Put it all together: 13a -1b -6

Hope this helps, good luck! :D

Answer:p=d2

Step-by-step explanation:math

Answer:

Common difference = 4

Position of 103 = 25th term

Step-by-step explanation:

a)

According to the given information:

\( a_3 + 20 = a_8\)

\( a+ (3-1)d + 20 = a+ (8-1)d\)

\( \cancel a+ 2d + 20 = \cancel a + 7d\)

\( 2d + 20 = 7d\)

\( 20 = 7d-2d\)

\( 20 = 5d\)

\( d = \frac{20}{5}\)

\( \purple {\bold {d = 4}} \)

Common difference = 4

b)

\( \because a_3 = 15....(given) \)

\( \therefore a + (3-1)d = 15\)

\( \therefore a + 2d = 15\)

\( \therefore a + 2\times 4= 15\)

\( \therefore a + 8= 15\)

\( \therefore a = 15-8\)

\( \red{\bold {\therefore a = 7}} \)

\( \because a_n = a + (n - 1) d\)

\( \therefore 103 = 7 + (n - 1)4 \)

\( \therefore 103 - 7 = (n - 1)4 \)

\( \therefore 96 = (n - 1)4 \)

\( \therefore \frac{96}{4}= n - 1\)

\( \therefore 24= n - 1\)

\( \therefore 24+1= n\)

\(\blue{\bold {\therefore n = 25}} \)

So, the position of 103 in this sequence is 25th term.

Answer:

We can use the formula for the lateral surface area of a cone to find the slant height:

Lateral surface area = πrℓ, where r is the radius and ℓ is the slant height.

Since the paper cup is hollow, the lateral surface area is equal to the outer surface area of the cup, which is given as 17.9 square inches. The radius of the cup is half the diameter, which we do not know, so let's call it d:

r = d/2

We also know that the lateral surface area is given by:

17.9 = πrℓ

Substituting r = d/2, we get:

17.9 = π(d/2)ℓ

Simplifying, we get:

ℓ = (2*17.9)/(πd)

Using an approximation of π = 3.14, we can calculate:

ℓ ≈ (2*17.9)/(3.14d) = 11.40/d

Since we do not have any information about the diameter of the paper cup, we cannot calculate the exact slant height.