the lengths of fish in a neighborhood pond are normally distributed with a mean of 5 inches and a standard deviation of 1.2 inches. what is the probability that a sample of 10 randomly selected fish will have a mean length of of over 6 inches?

The indefinite integral ∫(2e^(-1/5x))dx can be expressed as an infinite series. The answer can be summarized as follows: The integral evaluates to a series representation involving the exponential function.

The series consists of terms that are powers of x and coefficients obtained by integrating a power series expansion of e^(-1/5x).

To explain the answer in more detail, let's consider the function f(x) = e^(-1/5x). We can rewrite the function as a power series using the Taylor series expansion for e^x: e^x = 1 + x + (x^2/2!) + (x^3/3!) + ... + (x^n/n!) + ..., where n! represents the factorial of n.

Integrating f(x) term by term, we get ∫f(x)dx = ∫(e^(-1/5x))dx = C + ∫(1 - (1/5x) + (1/(2!)(1/5x)^2 - (1/(3!)(1/5x)^3 + ... + (1/(n!)(1/5x)^n) + ..., where C is the constant of integration.

Now, we can simplify each term of the series by multiplying the constant coefficients with appropriate powers of x: C + x - (1/5)(1/5x)^2 + (1/(2!))(1/5x)^3 - (1/(3!))(1/5x)^4 + ... + (1/(n!))(1/5x)^(n+1) + ...

The resulting series is an infinite sum of terms involving powers of x and coefficients obtained from the power series expansion of e^(-1/5x). This represents the indefinite integral of 2e^(-1/5x) as an infinite series.

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Answer:

Step-by-step explanation:

The Domain is the set of X values, which is the line that is going straight.

The Range is the set of Y values, which is the line that is pointing up and straght.

So to find each value on the graph you simply look at the black dot and calculate the points. And i'm not sure if you remember but the on the Y line, when it is pointing up that means it is positive and when it is pointing down that means those values are negitvie. Same concept with the X line. On the X line, when it is points left it is negetive and when it is pointing right it is positive. Also, remember you write the points like (x,y). So now we have the basic idea of a graph now you can easliy find the points.

So, the point on the far left would be (-6,-1), why? Because it is on the left side of the X which means it will be negitvie and it is -6 blocks away from the middle point of the lines. And it goes down once with the Y line, and remeber going down equals negitive, so that if why it is -1.

Now you have that knowlegde try to figure out the rest, if stuck left me know. I hope this makes sense, sorry if not D:

Answer:

160.125

Step-by-step explanation:

Recall that the length of a curve is \(\displaystyle L=\int^b_a\sqrt{1+\biggr(\frac{dy}{dx}\biggr)^2}dx\), so we'll need to determine \(\frac{dy}{dx}\) using Fundamental Theorem of Calculus Part 1:

\(\displaystyle y=\int^x_1\sqrt{t^3-1}\,dt\\\\\frac{dy}{dx}=\frac{d}{dx}\int^x_1\sqrt{t^3-1}\,dt\\\\\frac{dy}{dx}=\sqrt{x^3-1}\)

Now that we've done so, we can plug \(\frac{dy}{dx}\) into our formula from before and get the length of the parametric curve:

\(\displaystyle L=\int^b_a\sqrt{1+\biggr(\frac{dy}{dx}\biggr)^2}\,dx\\\\L=\int^{11}_1\sqrt{1+\sqrt{x^3-1}^2}\,dx\\\\L=\int^{11}_1\sqrt{1+x^3-1}\,dx\\\\L=\int^{11}_1\sqrt{x^3}\,dx\\\\L=\int^{11}_1x^\frac{3}{2}\,dx\\\\L=\frac{2}{5}x^\frac{5}{2}\biggr|^{11}_1\\\\L=\frac{2}{5}(11)^\frac{5}{2}-\frac{2}{5}(1)^\frac{5}{2}\\\\L\approx160.125\)

Therefore, the length of the curve is about 160.125 units.

Answer:13.80

Step-by-step explanation:18-4.20=13.80

Answer:

Volume flow rate, Q, into the tank is 12.376 m³

Step-by-step explanation:

Here we have Bernoulli's equation presented as follows

\(\frac{P_{1}}{\rho _{1}g}+\frac{v_{1}^{2}}{2g} + z_{1} = \frac{P_{2}}{\rho _{2}g}+\frac{v_{2}^{2}}{2g} + z_{2}\)

Where:

P₁ = Pressure, of the open tank = Atmospheric pressure = 0

P₂ - Pressure at the discharge of the pipe = Atmospheric pressure = 0

ρ₁ = Density of the fluid = ρ₂

v₁ = Velocity of the fluid in the tank

v₂ = Velocity of the fluid in the pipe

d₁ = Diameter of the tank = 1.5 m

d₂ = Diameter of the pipe = 15 cm = 0.15 m

A₁ = Cross sectional area of tank = π×d₁²/4 = 1.767 m²

A₂ = Cross sectional area of pipe= π×d₂²/4 = 0.01767 m²

z₁ = Level of water in the tank = 0 m

z₂ = Level of water in the pipe = 2.5 m

Whereby the level remains constant at 2.5 m, pressure at the base, P₂ = ρ₁×g×2.5

Also

v₁×A₁ = v₂×A₂ which gives;

v₁×1.767  = v₂×0.01767

v₂ = v₁×1.767/0.01767 = 100·v₁

Hence we have;

\(\frac{0}{\rho _{1}g}+\frac{v_{1}^{2}}{2g} + z_{1} = \frac{0}{\rho _{1}g}+\frac{(100v_{1})^{2}}{2g} + z_{2}\)

\(z_{1} - z_{2} = \frac{(100v_{1})^{2}}{2g}- \frac{v_{1}^{2}}{2g}\)

\((2.5)2g = 99v_{1}^{2}}\)

v₁² = 2.5×2×9.81 = 49.05

v₁ = √49.05 = 7.0035 m/s

Therefore, since the rate of discharge = Rate of entry into the tank, we have;

Volume flow rate, Q, into the tank = v₁×A₁ = 7.0035 m/s × 1.767 m² = 12.376 m³.

Answer:

No, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.

Step-by-step explanation:

The expression is not well written. The expression is written as;

(xy^-2)/(3x²y^-4)

According to indices;

a^m ÷ a^n = a^{m-n}

Applying this to solve the question

1/3(x^{1-2})/(y^-2÷y^-4)

= 1/3(x^{-1})(y^{-2+4})

= 1/3(1/x)y²

= 1/(3x) × y²

Substituting x = 3 and y = -4

= 1/3(1/3)×(-4)²

= 1/9(16)

= 16/9

Imothy solution is incorrect.

According to Imothy solution, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.

Answer:

Step-by-step explanation:

Answer:

It would be 6

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

That small little small box above the equation indicates a 90 degree angle. Where the equation is at, I'm guessing that it has the equals 90.

7 will be the perfect answer because:

12(7) = 84

84 + 6 = 90

The equation x² y² = 4 corresponds to a hyperbola when only considering x and y as variables. When considering x, y, and z as variables, the equation corresponds to a two-sheeted hyperboloid.

a) When only x and y are the variables being considered, the equation x² y² = 4 corresponds to a circle in the xy-plane. The circle has a center at the origin (0,0) and a radius of 2.

b) If x, y, and z are the only variables being considered, the equation x² y² = 4 still represents a circle in the xy-plane, but it becomes a cylinder along the z-axis. This cylinder has a center on the z-axis and a radius of 2, extending infinitely along the z-axis.

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Answer:

1,124.12 mm

Step-by-step explanation:

Steps to answering this question :

First determine the radius of the circle from the area of the circle

Use the radius determined above to calculate the circumference

Area of a circle = nr²

where r = radius

n = pi = 3.14

100,608.7mm = nr²

to determine the radius, divide both sides of the equation by 3.14

32,040.98726mm = r²

Find the square root  of 32,040.98726mm

√32,040.98726mm

r = 179mm

Circumference of a circle = 2nr

2 x 179 x 3.14 = 1,124.12 mm

Files that are not linked to a live dataset and that you receive via email or export are examples of a(n) flat files. So, here the option(d) is correct choice for answer.

A single table of data is contained by flat file. It allows users to specify data attributes, such as columns and data types, on a table-by-table basis and stores these attributes separately from the application. This type of file is often used to import data into data warehouse projects.

In a flat file database, each line of a plain text file contains a single record. Records are separated by using tabs and commas. The one of advantage of a flat file database is that it is easy to understand and can help us sort results easily. A data set that is not directly connected to a data source. These are usually exported as csv or excel files that you manage yourself or email to you.

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Answer:

I THINK ITS B. THE DORSAL FIN

Step-by-step explanation:

Because all fish and different Marine animals

have it in different spots of he/she's body

Hope I helped SORRY if you get it wrong

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

m = 50

Step-by-step explanation:

∠ D and ∠ A are vertically opposite angles and are congruent , then

m - 130 = 20 - 2m ( add 2m to both sides )

3m - 130 = 20 ( add 130 to both sides )

3m = 150 ( divide both sides by 3 )

m = 50

Answer:

Jamal makes:

60 bricks

Step-by-step explanation:

9 bricks ⇒ 12 bricks

45 bricks ⇒ x bricks

x = 12 * 45 / 9

x = 60

by process:

√×=n√an×x

hope itz helpful

Answer:

m = 3/13

Step-by-step explanation:

The Slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 3 and the x increase by 13, so the slope is

m = 3/13

Answer:

Step-by-step explanation:

To find the slope of the line that passes through the points (-4,5) and (9,8), we can use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

= (8 - 5) / (9 - (-4))

= 3 / 13

= 0.231

Therefore, the slope of the line that passes through the points (-4,5) and (9,8) is 0.231.

We estimate that the average number of roommates per semester for all students at the local college is 0.7.

The best point estimate for the average number of roommates per semester for all students at the local college would be the sample mean, which is calculated as the sum of the number of roommates for all students in the sample divided by the number of students in the sample.

Using the information given in the problem, we have:

Sample size (n) = 133

Sample mean (\(\bar X\)) = 0.7

Therefore, the best point estimate for the population mean (μ) is the sample mean:

μ ≈ \(\bar X\) = 0.7

So, we estimate that the average number of roommates per semester for all students at the local college is 0.7.

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The length of the missing side (hypothenuse) is equal to 5

"Information available from the question"

Opposite side of the triangle(y) = 3

Adjacent side of the triangle (z)= 4

Hypothenuse side of the triangle = x

Pythagorean Theorem

This formula is used to find the missing side of a right angle triangle if two sides are given.

\(x^{2} =y^2+z^2\)

Let's substitute the values into the formula and solve for the hypothenuse

\(x^{2} =3^2+4^2\)

\(x^{2}\) = 9 + 16

\(x^{2}\) = 25

\(x=\sqrt{25}\)

x = 5

The length of the missing side (hypothenuse) is equal to 5.

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2. When it begins descending, the airplane's altitude (height) is 33,000 feet. Then, the starting value for its altitude would be 33,000

3. y = mx + b

where m is the slope,b the y-intercept, x represents time (in minutes), and y represents altitude (in feet).

In the context of this problem, the starting value for the airplane's altitude is the y-intercept.

The slope is found finding the ratio between altitude lost and time. Given that after 8 minutes, the airplane lost 33,000 - 17,000 = 16,000 feet, the slope is:

16,000/8 = 2,000 ft/min. Then the equation is:

y = 2000x + 33000

4. The information "After traveling for 4 hours and 1800 miles, an airplane begins a steady descent" is not relevant

step 1

so so s ososoosososososososososososososoosososososzosoosossoosososo

Step-by-step explanation:

The most important thing to remember is: SOH CAH TOA

sin(x) = opposite/hypotenuse

cos(x) = adjacent/hypotenuse

tan(x) = opposite/adjacent

So in #1:

We have the angle and hypotenuse and need to solve for the side opposite of the angle. This smells like a sine question.

sin(42)=x/25

this means that x=25sin(42). Plug that into the calculator and get: 16.73.

(Make sure you are in degrees mode)

For #2:

We are given the angle, the opposite side, and have to solve for the adjacent side. Looks like we need the tangent.

tan(75)=12/x

This means that x=12/tan(75). Calculator says: 3.22

For #3:

We have the angle, adjacent, and have to solve for the hypotenuse. This would be a cosine.

cos(36)=19/x

Solve for x: x=19/cos(36). Calculator says: 23.49

For #4:

We have the angle, adjacent side, and need the opposite side. This is another tangent problem.

tan(53)= x/7

Solving for x: x=7tan(53). Calculator says: 9.29

Answer:

22.608 units

Step-by-step explanation:

Basically, the circumference of a circle is the distance around a circle, sort of like the perimeter of a figure. It has a unique formula which is \(C=2\pi r\) where \(r\) is the radius, which is the distance between the circle and its center. Using our given information, we can find the circumference:

\(C=2\pi r\\C=2(3.14)(3.6)\\C=22.608\)

Therefore, the circumference of a circle with a radius of 3.6 units is 22.608 units.

Answer:

Circumference is...

Step-by-step explanation:

Multiply the radius by 2 to get the diameter.

Multiply the result by π, or 3.14 for an estimation.

That's it; you found the circumference of the circle.

dont worry I already took this lesson.

Answer:

d

Step-by-step explanation:

the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.0564 rounded to three decimal places. The final answer is 0.056.

The problem given can be solved by using the central limit theorem.

According to the central limit theorem, if the sample size is sufficiently large, then the sample mean will follow a normal distribution with a mean of μ and a standard deviation of σ/√n, where n is the sample size.Using this formula, we can find the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years. The formula is:

P(Z < (X-μ)/(σ/√n))

where Z is the standard normal distribution, X is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X = 21.8, μ = 22, σ = 2, and n = 100. Plugging these values into the formula, we get:

P(Z < (21.8-22)/(2/√100)) = P(Z < -1.58)

Using Excel or a standard normal distribution table, we can find that the probability of Z being less than -1.58 is 0.0564.

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Answer:

ur welcoem

Step-by-step explanation:

area: 40p² + 24p

wide: 8p

(40p² + 24p)/ 8p

5p + 3

so, length: 5p + 3 -> (a)

perimeter = wide x 2 + length x 2

16p + (10p + 6)

26p + 6 -> (b)

Answer:

336.

Step-by-step explanation:

8P3 = 8! / (8 - 3)!

       = 8*7*6*5*4*3*2*1 / 5*4*3*2*1

       = 8*7*6

       = 336

Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles.

Scalene-Triangle-1

In the figure, all three symbols that are given on each side are different, which denotes that all three sides are unequal.

One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.

The sum of all three angles of an equilateral triangle is equal to 180 degrees.  60° + 60° + 60° = 180°

the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on

Examples of right angles are all around us. We can see right angles in the corners of a room, book, cube, windows, and at several other places.

Examples of obtuse angles include 166°, 121°, 110°, 117°, and 91°.

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The figure above shows two circles, one inside the other. The equation x^2 + y^2 = 2 represents the smaller circle, while the larger circle is not explicitly defined in the question.

However, we can see from the graph that the center of both circles is at the origin (0,0) and that the larger circle has a radius twice as big as the smaller circle.

Therefore, the radius of the larger circle is 2 times the radius of the smaller circle, which is the square root of 2. So the answer is (a) √2.
The given equation of the circle is x^2 + y^2 = 2. To find the radius of this circle, we can rewrite the equation in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

In this case, the equation is already in the standard form with h = 0, k = 0, and r^2 = 2. Therefore, the radius of the larger circle is r = √2. So, the correct answer is a) √2.

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Answer:

Huda found the product of –3 and 9 as positive.

Step-by-step explanation:

Given the expression and result below :

Huda evaluated the expression below. Negative 3 (8 minus 5) squared minus (negative 7) = negative 3 (3) squared minus (negative 7) = negative 3 (9) minus (negative 7) = 27 minus (negative 7) = 34

-3(8 - 5)² - (-7) =

Step 1:

- 3(3)² - (-7)

Step 2:

-3(9) - (-7)

Step 3:

27 - (-7) = 34 (error in the third step)

-3(9) = - 27

Hence,

-27 - (-7) = - 27 + 7 = - 20

Answer:

its B on edge

Step-by-step explanation:

I just took the test