can anyone help me with this?

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Answer:

Step-by-step explanation:

Given function:

The base of the exponent is 0.92. This represents a decay as 0.92 is less than 1. It would be a growth function is the base was greater than 1.

The rate of decrease is

Percent decrease is

Answer:

true

Step-by-step explanation:

Answer: Child ticket: $8, Adult ticket: $6

Step-by-step explanation:

Let's call the price of 1 adult ticket "a" and the price of 1 child ticket "c".

On the first day, the school sold 3 adult tickets for a total of 3a dollars, and 2 child tickets for a total of 2c dollars, for a total of 34 dollars. So, we have the equations:

3a + 2c = 34

On the second day, the school sold 3 adult tickets for a total of 3a dollars and 12 child tickets for a total of 12c dollars, for a total of 114 dollars. So, we have another equation:

3a + 12c = 114

We can now use these two equations to solve for the value of "a" and "c".

We can use substitution to solve for one variable, then substitute it back into either of the equations to solve for the other variable.

Let's solve for "a" by substituting the first equation into the second:

3a + 12c = 114

3a = 114 - 12c

a = (114 - 12c) / 3

Now that we have an equation for "a", we can substitute it back into the first equation to solve for "c":

3a + 2c = 34

3[(114 - 12c) / 3] + 2c = 34

114 - 12c + 2c = 34

-10c = -80

c = $8

So, the price of 1 adult ticket is

a = (114 - 12c) / 3

a = (114 - 12 * 8) / 3

a = (114 - 96) / 3

a = 18 / 3 = $6.

Answer:

J. 626

Step-by-step explanation:

100% sure hope it's right

Answer:

Step-by-step explanation:

To calculate the gas mass produced, we can use Darcy's Law, which relates the flow of gas through a porous medium to the pressure gradient. The formula for Darcy's Law is:

Q = -k * A * (dP/dx)

Where:

Q is the flow rate (m^3/s)

k is the permeability of the medium (m^2)

A is the cross-sectional area (m^2)

dP/dx is the pressure gradient (Pa/m)

Given:

φ = 0.3

b = 100 m

αp​ = 4 × 10^(-9) Pa^(-1)

ρ = 0.1 hp​ (gas density)

Pressure head (initial) = 100 m

Pressure head (final) = 30 m

Area (A) = 10,000 m^2

First, we need to calculate the permeability (k) using the porosity (φ) and the compressibility (αp​) as follows:

k = φ² * αp​

k = 0.3² * (4 × 10^(-9) Pa^(-1))

k = 9 × 10^(-11) m^2

Next, we can calculate the pressure gradient (dP/dx) by subtracting the final pressure head from the initial pressure head and dividing it by the distance (b):

dP/dx = (Pressure head (final) - Pressure head (initial)) / b

dP/dx = (30 m - 100 m) / 100 m

dP/dx = -0.7 Pa/m

Now, we can calculate the flow rate (Q) using Darcy's Law:

Q = -k * A * (dP/dx)

Q = -9 × 10^(-11) m^2 * 10,000 m^2 * (-0.7 Pa/m)

Q = 6.3 × 10^(-4) m^3/s

Finally, we can calculate the gas mass (m) using the flow rate (Q) and the gas density (ρ):

m = Q * ρ

m = 6.3 × 10^(-4) m^3/s * 0.1 kg/m^3

m = 6.3 × 10^(-5) kg/s

Therefore, the gas mass produced when the pressure head is reduced from 100 m to 30 m over an area of 10,000 m^2 is approximately 6.3 × 10^(-5) kg/s.

To calculate the gas mass produced, Using Darcy's Law and the given values, we can determine the gas mass produced when the pressure head is reduced from 100 m to 30 m over an area of 10,000 m2.

The gas mass produced can be calculated by first determining the permeability (k) using the given values of porosity (φ), compressibility (αp), gas density (ρ), and thickness (b). With the obtained value of k, we can then use Darcy's Law to calculate the gas flow rate. However, since the time period is not specified, we cannot directly calculate the gas mass produced. The gas flow rate obtained from Darcy's Law represents the volume of gas flowing per unit time. To calculate the gas mass produced, we need to integrate the flow rate over time. Without the time component, we cannot determine the exact gas mass produced. Therefore, the calculation of the gas mass produced requires information about the time period or additional data.

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Answer:

His interest is $2340 his total is $8840

Step-by-step explanation:

Answer:2340$

Step-by-step explanation:

1. Do 6500x 0.09 to get 585

2. Then multiply it by 4 since it is his interest rate for 4

3. 585x4=2340

Answer:

625

Step-by-step explanation:

25 x25 = 625

Answer:

1440 mL

Step-by-step explanation:

2 hours = 120 minutes

120/5 = 24

24 * 60 = 1440

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

9514 1404 393

Answer:

  £27.50

Step-by-step explanation:

The general approach is ...

1. The area to be painted will be the area of the four walls, less the area of the door (which is assumed to be a hole in the wall, so is not painted).

Each wall has the same dimensions, so the same area. The area of the rectangular wall is ...

  A = LW

  A = (3.5 m)(2.6 m) = 9.1 m²

The area of the door is ...

  A = (2.2 m)(0.8 m) = 1.76 m²

Then the area to be painted is the area of the 4 walls less the area of the door:

  painted area = 4(9.1 m²) -1.76 m² = 34.64 m²

__

2. Each 2 L tin of paint will cover (2 L)×(8 m²/L) = 16 m², so the number of tins needed is ...

  (34.64 m²)/(16 m²/tin) = 2.165 tins

We assume this means Aisha will need to purchase 3 tins, since she will need more paint than is provided by 2 tins.

__

3. Because of the price offer on the paint, Aisha will pay full price for the first two tins, half price for the 3rd tin. That is, she will pay 2 1/2 times the full price of a tin when she buys the 3 tins of paint she needs. Each tin costs £11, so Aisha will pay ...

  (2 1/2)(£11) = £27.50

Aisha will pay £27.50 for the paint to paint her living room.

Answer:

that I have a panda but the black on it and I have kiss me kiss me at

If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

Let u be 1 unit.

5u=125

u=125÷5

=25

3u=25×3

=75

There were 75 caribou.

a) The p-value for the given test is 0.0555.

b) The p-value for the chi-square test is 0.0405.

In hypothesis testing, the p-value is a measure of the strength of evidence against the null hypothesis. It represents the probability of obtaining a test statistic as extreme as the one observed.

In the first scenario, we are testing the null hypothesis (H0: µ = 40) against the alternative hypothesis (H1: µ ≠ 40) using a z-test. The given test statistic is z = 1.92. To find the p-value, we need to determine the probability of observing a test statistic as extreme as 1.92 or more extreme in either tail of the standard normal distribution.

By referring to a standard normal distribution table or using statistical software, we find that the p-value for z = 1.92 is approximately 0.0555, rounded to four decimal places.

In the second scenario, we are conducting a chi-square test of independence to examine the relationship between marital status and happiness. The given chi-square test statistic is 8.24. To determine the p-value, we calculate the probability of obtaining a chi-square statistic as extreme as 8.24 or more extreme under the assumption that the null hypothesis (H0: Marital status and happiness are not related) is true.

By consulting a chi-square distribution table or utilizing statistical software, we find that the p-value for a chi-square statistic of 8.24 is approximately 0.0405, rounded to four decimal places.

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A Venn diagram is a graphical representation of all possible logical relationships between a finite collection of sets. Venn diagrams are used to visualize how different sets overlap and the relationship between different groups of objects.

Venn diagrams are often used in statistics and probability to illustrate the relationship between different events.

In the context of probability, events A, B, and C are considered independent if the occurrence of one event does not affect the probability of the other events occurring. In other words, the probability of each event is independent of the other events.

To create a Venn diagram that illustrates three independent events A, B, and C, you would first draw three circles that are not overlapping.

Each circle represents one of the three events. Next, you would label each circle with the name of the corresponding event. In order to make the size of each circle proportional to the probability of the event occurring, you would adjust the size of each circle according to the probability of that event.

The larger the probability, the larger the circle. Finally, you would indicate the area of overlap between each pair of events. Because the events are independent, there should be no overlap between any of the circles. The Venn diagram would look something like this: In summary, to illustrate three independent events A, B, and C using a Venn diagram, you would draw three non-overlapping circles that represent each event and adjust their size to be proportional to the probability of that event.

There should be no overlap between any of the circles since the events are independent.

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On solving the provided question, we can say that - Area enclosed by the square and the circle= 400 - 314 = 86 ft sq

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Side of the square =20feet

Therefore,

Radius of the inscribed circle= 20/2 = 10 feet

Area of square=20 X 20 = 400 feet sq.

Area of circle=\(\pi * r^{2} \\\pi * 10*10\\3.14*100\\314 ft sq\)

Area enclosed by the square and the circle= 400 - 314

                                                                           = 86 ft sq

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Answer: 2,835.8

Step-by-step explanation:

1 dollar = ~18.3867 peso

154.23 x 18.3867 = 2,835.787 peso

Round to the nearest hundredth is 2,835.8 peso

The concept of mathematical harmony was most directly incorporated in the Parthenon in the use of columns.

The term harmony has to do with tunes that are concordant and make meaning to the ears. The search for patterns and sequences is what introduced harmony to mathematics.

Hence, the concept of mathematical harmony was most directly incorporated in the Parthenon in the use of columns.

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Answer:

<1 = <9 = <4 = <12 = 75

<2 = <3 = <10 = <11 = 105

<5 = <8 = <13 = <16 = 85

<6 = <7 = <14 = <15 = 95

Rounding to three decimal places, the 95% confidence interval for the population proportion of times that the bats would follow the point is (0.565, 1.035).

To find the 95% confidence interval for the population proportion, we can use the formula for calculating confidence intervals for proportions:

Confidence Interval = Sample Proportion ± Margin of Error

The sample proportion is the number of successes (bats going to the correct feeder) divided by the sample size (total number of trials). In this case, the sample proportion is 8/10, which simplifies to 0.8.

The margin of error depends on the desired level of confidence. For a 95% confidence interval, the critical value is 1.96.

Margin of Error = Critical Value * Standard Error

The standard error is calculated as the square root of [(sample proportion * (1 - sample proportion)) / sample size]. In this case, it is sqrt[(0.8 * (1 - 0.8)) / 10], which simplifies to 0.12.

Now we can plug in the values:

Confidence Interval = 0.8 ± (1.96 * 0.12)

Calculating the confidence interval:

Confidence Interval = 0.8 ± 0.2352

Simplifying the interval:

Confidence Interval = (0.5648, 1.0352)

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Answer:

He need to On the 26th day of his billing

Step-by-step explanation:

Given:

Amount of data = 3 gb

80% data used in 21 days

Find:

Number of days for additional data

Computation:

Total number of days = 21(100/80)

Total number of days = 26.25 days

He need to On the 26th day of his billing

Hey there!

Option answer: \(1 \frac{1}{2} \: \: cubic \: inches\)

According to the title,

Volume = 12 × (1/2)\( {}^{3} \)

=> 12 × 1/8

=> \( \frac{12}{8} \)

=> \( \frac{3}{2} \)

=> \(1 \frac{1}{2} \)

Answer:

d

Step-by-step explanation:

first i do my formula which is length x width x height

the length is 3 the width is 2 and the height is 2 so 3x2x2 is 12

so the answer is d

Answer: y= x-5

Step-by-step explanation:

It already gave you the y-intercept, which is on the y-axis. It is: (0,-5)

So your equation is: y = mx-5

Now you find your slope by using the two points it gives us: (0,-5) and (5,0)

-5 - 0= -5(from the two y- coordinates) and 0 - 5 = -5(from the two x-coordinates)

That is -5 divided by -5 so the answer would be 1

Your equation is: y = 1x-5

But you don't have to put the 1 because the x itself counts as 1

When the primal problem has inequality constraints, the dual problem will have an optimal solution where some of the primal constraints are active.

Specifically, for each active primal constraint, there will be a corresponding dual variable that is positive (not zero). The active primal constraints are those that are satisfied with equality at the primal optimal solution.

In other words, if the primal problem has the form:

maximize c^T x

subject to Ax <= b

where x is the vector of primal variables, c is the vector of objective function coefficients, A is the matrix of constraint coefficients, and b is the vector of right-hand side values, then the dual problem has the form:

minimize b^T y

subject to A^T y >= c

y >= 0

where y is the vector of dual variables.

At the dual optimal solution, any dual variable that is positive corresponds to an active primal constraint. These are the constraints for which the corresponding primal variable is not at its upper or lower bound, but rather is taking on a value that satisfies the constraint with equality.

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The given curves are `y = x + 1, y = 0, x = 0 and x = 4` and we are supposed to find the volume `V` of the solid obtained by rotating the region bounded by the given curves about the x-axis.

The region is shown below:Region bounded by y = x + 1, y = 0, x = 0 and x = 4We can observe that the region is a right-angled triangle with perpendicular `4` and base `1`. Now, we need to rotate this right-angled triangle about the x-axis to form a solid of revolution. The solid of revolution obtained is shown below:Solid of revolution obtained by rotating the region about the x-axis Since the region is rotated about the x-axis, the axis of rotation is `x-axis`.

So, the formula for volume of the solid of revolution is given by:`V = pi * ∫[a, b] y^2 dx`Here, the limits of integration are `a = 0` and `b = 4`.We need to express `y` in terms of `x`.Since, `y = x + 1`, we get`x = y - 1`Substituting this value of `x` in `x = 4`, we get`y - 1 = 4``y = 5`So, the limits of integration for `y` are `0 to 5`.So, we have to evaluate the integral:`V = pi * ∫[0, 5] (y - 1)^2 dx`

Simplifying this, we get:`V = pi * ∫[0, 5] (y^2 - 2y + 1) dy``V = pi * (∫[0, 5] y^2 dy - 2∫[0, 5] y dy + ∫[0, 5] dy)``V = pi * [y^3/3 - y^2 + y] [0, 5]``V = pi * [(5^3/3 - 5^2 + 5) - (0)]``V = pi * [(125/3 - 25 + 5)]``V = pi * [100/3]`

Therefore, the volume `V` of the solid obtained by rotating the region bounded by the given curves about the x-axis is `V = (100/3) pi` (in cubic units).

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Answer:

Step-by-step explanation:

That exterior angle of 111 is equal to the sum of the triangle's remote interior angles. We add the 37 + 35 to get a total angle measure of 72. That means that the base angle on the right is 111 - 72 = 39. That 39 degree angle is vertical to x; that means that x = 39 as well.

Answer:

39deg

Step-by-step explanation:

To find the maximum value of ε > 0 such that |f(x) - 3| < ε whenever 0 < |x - 0| < 8, we can use a graphing utility to analyze the behavior of the function f(x) = x² + 3. The right answer is (b) ε = 1.5, corresponding to option B, 8 = 1.414.

By plotting the graph of f(x) = x² + 3, we can observe that as x approaches 0, the value of f(x) approaches 3. Therefore, the limit of f(x) as x approaches 0 is indeed 3.

Now, we need to find the maximum value of ε such that |f(x) - 3| < ε holds true whenever 0 < |x - 0| < 8. This means that the function f(x) must stay within a distance of ε from the value 3 for all x within a distance of 8 from 0.

Using a graphing utility, we can visually determine that when ε = 1.5, the function f(x) remains within a distance of 1.5 from 3 for all x within a distance of 8 from 0. Therefore, 8 = 1.414 is the maximum value of ε that satisfies the given condition.

Hence, the correct answer is option B, 8 = 1.414.

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Answer:

B and D

Step-by-step explanation:

Have a nice week!

(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧ ✧ﾟ･: *ヽ(◕ヮ◕ヽ)

Given, the function is f(x,y,z)=5+yxz+g(x,z)Here, we need to find the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) . The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

Using the formula of the directional derivative, the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is given by

(f(x,y,z)) = grad(f(x,y,z)).v

where grad(f(x,y,z)) is the gradient of the function f(x,y,z) and v is the direction vector.

∴ grad(f(x,y,z)) = (fx, fy, fz)

                       = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Hence, fx = ∂f/∂x = 0 + yzg′(x,z)fy

                = ∂f/∂y

                = xz and

fz = ∂f/∂z = yx + g′(x,z)

We need to evaluate the gradient at the point (3,0,3), then

we have:fx(3,0,3) = yzg′(3,3)fy(3,0,3)

                             = 3(0) = 0fz(3,0,3)

                             = 0 + g′(3,3)

                             = g′(3,3)

Therefore, grad(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))Dv(f(x,y,z))(3,0,3)

                                                 = grad(f(x,y,z))(3,0,3)⋅v

where, v = (0,4,0)Thus, Dv(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))⋅(0,4,0)   = 0

The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

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Answer:

absolute vlaue inequality: |x-3| > 9; solved: x<-6 and x>12

Step-by-step explanation:

I’m going to start this off by saying I learned all this right now by just searching up how to solve an absolute inequality equation and watching one video, so this might not be an accurate explanation. (I’m pretty sure the answer’s right though)

So an absolute value inequality must be written like this:  

| x - a | *inequality* b

a is going to be the number that the inequality is centered around, in this case, 3. b will be how far you can deviate from that number, which in this case is 9.  

Now, you will have this:

|x - 3| *inequality* 9

Now, to find the inequality, you need to understand the wording. If it says “more than” as it does here, then you would have the greater-than symbol (>). If you have “less than” then you’d have the less-than symbol (<). If the problem says “at least b away” then it would be greater-than-or-equal to (≥), and likewise, if it says “at most b away” then it would be less-than-or-equal-to (≤).

So now we're at:

|x - 3| > 9

To solve the equation, you just need to subtract 9(b) from 3(a) and add 9(a) to 3(b) to get -6 and 12. Since x must be more than 9 units away, you would get:

x<-6 and x>12

Hope this is helpful!