why when i calculate the uncertainty of a group of data does my uncetinty max is not greater than the actual math

Answer:

\(f'(x)=\displaystyle -\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)\)

Step-by-step explanation:

Recall the power series \(\sin(x)=\displaystyle \sum\limits^\infty_{n=0}(-1)^n\frac{x^{2n+1}}{(2n+1)!}\).

In this case, \(x\) is replaced with \(\displaystyle \frac{1}{1+e^x}\), so our power series actually works out to be \(\displaystyle \sin\biggr(\frac{1}{1+e^x}\biggr) =\sum\limits^\infty_{n=0}(-1)^n\frac{\bigr(\frac{1}{1+e^x}\bigr)^{2n+1}}{(2n+1)!}\)! Amazing, huh?

Now, we find the derivative of the function by using the chain rule:

\(\displaystyle \frac{d}{dx}\sin\biggr(\frac{1}{1+e^x}\biggr)=\frac{d}{dx}\biggr(\frac{1}{1+e^x}\biggr)*\cos\biggr(\frac{1}{1+e^x}\biggr)=-\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)\)

You didn't specify if you just wanted the derivative of the series to be a function or a series, so I'm going to assume you want the function. Let me know if there's more to your problem.

Answer:

(-oo, -1] U [10,oo)

Step-by-step explanation:

For the function,

\(f(x) = \sqrt{x} \)

The domain is All Reals Number greater than or equal to zero, but for this function

\(f(x) = \sqrt{ {x}^{2} - 9x - 10 } \)

WE Must factor to see what values will get

\( {x}^{2} - 9x - 10 = (x - 10)(x + 1)\)

So know we Have

\( \sqrt{(x - 10)(x + 1)} \)

Set each equal to zero we have

\(x = 10\)

\(x = - 1\)

Now, we must find our interval.

If we plug in a negative number less than -1, we will get a positive interval so( -♾, -1] works. 0 doesn't work so we don't have a solution in between -1 and 10. Number greater than 10 work so We also have. [10,♾).

So our interval notation is

Answer:

(-3, 1.5)

Step-by-step explanation:

-8 +5 = -3

2 + -2 = 1.5

The amount of Protein intake is 900 kilocalorie.

We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.

Wе have to find out the amount of protein intake.

Percentage of students affected are -  \(\frac{x}{n} \times 100\)

In the question given -

Let the amount of Protein intake be y.

Then -

45 = y % of 2000

45 = \(\frac{y}{2000} \times100\)

y = \(\frac{45\times2000}{100}\)

y = 900 Kilocalorie

Hence, the amount of Protein intake is 900 kilocalorie.

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To evaluate the given integral using Green's theorem, we need to express it in the flux form.  The result of the integral is -r/6.

Green's theorem states that for a region R bounded by a simple closed curve C, the flux of the vector field F = (P, Q) across C is equal to the double integral of the curl of F over R.

In this case, we have the vector field F = (r^2xy, 1/2y^3), where r is the position vector (x, y).

The flux form of Green's theorem is:

\(∫∫R (curl F) · dA = ∫∫R (∂Q/∂x - ∂P/∂y) dA\)

Let's calculate the curl of F:

∂Q/∂x = 0

∂P/∂y = 2rxy

So, the curl of F is given by\((∂Q/∂x - ∂P/∂y) = 0 - 2rxy = -2rxy.\)

Now, let's evaluate the integral using the flux form of Green's theorem:

∫∫R (-2rxy) dA

Since the region R is a triangle with vertices (0,0), (1,0), and (0,1), we can express it as:

\(R = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}\)

Now, we can rewrite the integral:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Let's evaluate the inner integral first:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Now, evaluate the outer integral:

\(∫₀¹ -r(x-x²) dx = -r(x²/2 - x³/3) ∣₀¹ = -r(1/2 - 1/3) = -r(3/6 - 2/6) = -r(1/6) = -r/6\)

Therefore, the result of the integral is -r/6.

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Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

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Answer:

1.6 ft.

Step-by-step explanation:

Given that the conical pylons had a radius (r) of 1 foot and a height (h) of 2 foot. The volume of the conical pylons is:

Volume = πr²h/3

Therefore substituting gives:

Volume = π(1)²(2)/3 = 2π/3 ft³

Since the same amount of concrete is used to construct a spherical barrier, hence the volume of the sphere would be the same as the volume of the conical pylon.

Volume of sphere = 4πr³/3

4πr³/3 = 2π/3

2r³ = 1

r³ = 1/2 = 0.5

r = ∛0.5 = 0.8 ft.

Therefore the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.

Answer:

x = -3 when f(x) = -5

f(0) = 3

Step-by-step explanation:

When f(x) = -5, that means they have told you the y value. When y = -5, x = -3.

If the number is in the parentheses of the function, they are giving you the x value. When x  = 0, y = 3

Answer:

\(sin^2x\)

Step-by-step explanation:

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)

Let's apply this identity to the given expression:

\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)

Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)

Substituting this into our expression, we get:

\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)

Simplifying further:

\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)

Finally, we get the simplified expression:

\((1 - cos x)(1 + cos x) = sin^2(x)\)

To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:

Step 1: Apply the distributive property.

\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)

Step 2: Simplify the terms.

\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)

Step 3: Combine like terms.

\(\longrightarrow\sf\:1 - \cos^2 x\\\)

Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).

\(\sf\:1 - (1 - \sin^2 x)\\\)

Step 5: Simplify further.

\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)

Step 6: Final result.

\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

cost of playing x games at Adams = 7.50 + 0.45x

cost of playing x games at Jims = 1.25x

1.25x = 7.50 + 0.45x

1.25-0.45x = 7.50

0.80x =  7.50

x = 7.50/0.80 = 9.375 , but x must be an integer.

The cost is never the same. When x ≤ 9, Adams costs more. When x ≥ 10, Jims costs more.

The probability that a voter is either female or Democrat is 0.64 or 64%.

To calculate the probability, we need to determine the number of individuals who are either female or Democrat and divide it by the total number of voters.

From the table, we can see that there are 405 females and 253 Democrats. However, we need to be careful not to double-count the individuals who fall into both categories.

To find the number of individuals who are either female or Democrat, we add the number of females (405) and the number of Democrats (253), and then subtract the number of individuals who are both female and Democrat (150).

So, the number of individuals who are either female or Democrat is 405 + 253 - 150 = 508.

Now, we divide this number by the total number of voters, which is 802, to get the probability: 508 / 802 ≈ 0.64 or 64%.

Therefore, the probability that a voter is either female or Democrat is approximately 0.64 or 64%.

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The correct description for the distribution of the sample proportion of adults in the sample who don't have health insurance is X - B(120, 0.15).

B(120, 0.15) represents a binomial distribution with parameters n = 120 (the sample size) and p = 0.15 (the population proportion of adults without health insurance).

The binomial distribution is appropriate in this case because we have a fixed sample size and each individual in the sample can either have health insurance (success) or not have health insurance (failure). The sample proportion of adults without health insurance can be calculated by dividing the number of adults without health insurance by the total sample size.

Therefore, the correct description is X - B(120, 0.15).

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a. The formula for NPV is NPV = (Benefits - Costs) / (1 + Discount Rate)^n.

b. Plugging in the appropriate values, Benefits: $500 (Year 1), $4,000 (Year 2), and $7,000 (Years 3-5); Costs: $20,000 (initial payment), $1,000 (yearly maintenance from Year 2); Discount Rate: 6%.

c. The city should use a positive NPV as a criterion to decide whether to install the filtration system or not.

a. The general mathematical formula to determine the net present value (NPV) of this project is as follows:

NPV = (Benefits - Costs) / (1 + Discount Rate)^n

Where:

Benefits represent the cash inflows or benefits received from the project in each period.

Costs refer to the initial investment or cash outflows required to undertake the project.

Discount Rate is the rate used to discount future cash flows to their present value.

n represents the time period (year) when the cash flow occurs.

b. Plugging in the appropriate numbers into the formula:

Benefits: $500 in Year 1, $4,000 at the end of Year 2, and $7,000 for Years 3, 4, and 5.

Costs: Initial payment of $20,000 and yearly maintenance costs of $1,000 from Year 2 onwards.

Discount Rate: 6%.

n: 1 for Year 1, 2 for Year 2, and 3, 4, and 5 for Years 3, 4, and 5, respectively.

c. The city should use the criteria of positive net present value (NPV) to decide whether to install the filtration system or not. If the NPV is greater than zero, it indicates that the present value of the benefits exceeds the costs, suggesting that the project is financially favorable and would generate a positive return.

Conversely, if the NPV is negative, it implies that the costs outweigh the present value of the benefits, indicating a potential financial loss. Therefore, a positive NPV would indicate that the city should proceed with installing the filtration system, while a negative NPV would suggest not undertaking the project.

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Note this question belongs to the subject Business.

The first-order autocorrelation (ρ₁) is ρ₁ = Cov(X₂, X-₁) / √(V(X₂) * V(X-₁)).

The given AR(1) model is represented by the equation X₂ = a + 0₁ X-₁ + ε₂, where X₂ represents the value of the variable at time period 2, a is a constant term, 0₁ is the autoregressive coefficient, X-₁ represents the value of the variable at time period 1, and ε₂ is the error term.

To calculate the expected value (E(X₂)), we take the expectation of the AR(1) model:

E(X₂) = E(a + 0₁ X-₁ + ε₂)

Since E(a) = a and E(ε₂) = 0 (assuming the error term is mean-zero), we have:

E(X₂) = a + 0₁ E(X-₁) + E(ε₂) = a + 0₁ E(X-₁) = a + 0₁ X-₁

Therefore, the expected value of X₂ is a + 0₁ X-₁.

To calculate the variance (V(X₂)), we need to consider the variance of the error term:

V(X₂) = V(a + 0₁ X-₁ + ε₂) = V(ε₂) = σ²

Where σ² represents the variance of the error term.

The first-order autocorrelation (ρ₁) can be calculated as the covariance between X₂ and X-₁ divided by the square root of the product of their variances:

ρ₁ = Cov(X₂, X-₁) / √(V(X₂) * V(X-₁))

The second-order autocorrelation (ρ₂) can be calculated in a similar manner, considering the covariance between X₂ and X-₂.

In summary, for the given AR(1) model, the expected value of X₂ is a + 0₁ X-₁, the variance of X₂ is σ², and the first and second-order autocorrelations depend on the covariance between X₂ and X-₁, and X₂ and X-₂, respectively, divided by the appropriate variances.

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Answer:

Answer = 25

Step-by-step explanation:

125 = 5f

125/5 = f

25 = f

The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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Solution:

From the given table;

Where, the November values is used as 100 percent;

To find the missing percentages of Elm leaves

For the month of May

To find the missing percentages of Hazel leaves

What is the independent and dependent variable?

An independent variable is a variable that does not depend on any other variable.

For example,

x is an independent variable because for every value of x, there is a different value of y

A dependent variable is a variable whose value depends upon an independent variable.

For example;

From the expression above, the value of y depends on the value of x

Using Euler integration, the next values of x and y can be determined as follows:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Euler integration is a numerical method used to approximate solutions to differential equations. It is based on the concept of dividing the interval into small steps and using the derivative at each step to calculate the next value. In this case, we are given the current values of x=2, y=8, and y'=9, with a step size of delta_X=5.

To determine the next values of x and y, we use the following formulas:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Substituting the given values into the formulas, we have:

x_next = 2 + 5 = 7

y_next = 8 + 5 * 9 = 53

Therefore, the updated values of x and y using Euler integration are x=7 and y=53.

It's important to note that Euler integration provides an approximate solution and the accuracy depends on the chosen step size. Smaller step sizes generally lead to more accurate results. Other numerical methods, such as Runge-Kutta methods, may provide more accurate approximations.

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The value of the variable T is 60

These are described as expressions that are composed of coefficients, factors, constants, variables and terms.

These algebraic expressions are also identified by mathematical or arithmetic operations, such as;

We have;

T= 3db

Substitute the values

T = 3(4)(5)

expand

T = 60

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The total energy of a harmonic oscillator can be expressed in terms of the amplitude (A) and phase angle (ϕ) as well as the angular frequency (ω). It is given by the equation E = 1/2 mω²A², where m represents the mass of the oscillator.

To express the total energy in terms of A and ϕ, we can use the given expression for the position of the harmonic oscillator: x(t) = Acos(ωt - ϕ).

The total energy (E) can be obtained by substituting x(t) into the expression for energy (E = 1/2 mω²x²).

Squaring x(t) and simplifying, we get x²(t) = A²cos²(ωt - ϕ). Taking the average of this expression over a period (which is 2π/ω), we find the average of cos²(ωt - ϕ) is 1/2. Therefore, the time-averaged energy is given by E = 1/2 mω²A².

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Answer:

Step-by-step explanation:ideas are just as important as getting the correct answer. Technology: Many ... accuracy requested; and be prepared to explain your method to your classmates. If don't know how ... How many steps would you take to finish a journey of 1000 miles? ... (a) Graph the solutions to the inequality 6h + 75 ≥ 345 on a number line.

The magnification n can be found by using the formula n = -s'/s, where s' is the image distance and s is the object distance. The value of s' obtained from this new equation can be found by rearranging the formula to s' = -ns.

To find the magnification n, we can use the formula n = -s'/s, where s' is the image distance and s is the object distance. In this case, the object is placed 45.0 centimeters from the mirror, so s = 45.0 cm. The magnification can be found by calculating the ratio of the image distance to the object distance. By rearranging the formula, we get n = -s'/s.

To find the value of s' obtained from this new equation, we can rearrange the formula n = -s'/s to solve for s'. This gives us s' = -ns. By substituting the value of n calculated earlier, we can find the value of s'. The negative sign indicates that the image is inverted.

Using the given values, we can now calculate the magnification and the value of s'. Plugging in s = 45.0 cm, we find that s' = -ns = -(2/3)(45.0 cm) = -30.0 cm. This means that the image is located 30.0 centimeters from the mirror and is inverted compared to the object.

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Step-by-step explanation:

in this graph we r going to see the relation of tge angles so

For angle 1

For angle 2

For angle 3

For angle 4

The same is true for the rest of angles.

In the given figure:

step 1 has 2 blocks

step 2 has 6 blocks

step 3 has 12 blocks

1)

2) n( n + 1 )

n( n + 1 ) is valid

3)

Since the expression can also write as:

Thus, n^2 +n is also valid

4)

n + n + 1 is not valid

Answer :

b) n( n + 1 )

c) n^2 + n

Answer: On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 8 pi.

Step-by-step explanation:

The function is y = sin(0.5*x)

We know that sin(0) = 0, so this graph must pass trough the point (0,0)

We know that the maximum of the sin(x) is 1, when x = pi/2. and the minimum is -1 when x = (3/2)*pi

but in our case the function is valuated in 0.5*x

then the maximum is when:

0.5*x = pi/2

x = pi/(2*0.5) = pi

and the minimum is when

0.5*x = (3/2)*pi

x = 3*pi

Now, knowing that sin(2*pi) = 0

The other 0 of the sin is when we have 0.5*x = 2*pi

x = 2*pi/0.5 = 4*pi

this means that in 4*pi we have one cycle, then in 8*pi we have tow cycles.

Then the correct option is:

"On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 8 pi."

Answer:

d

Step-by-step explanation:

Answer:

a. What is the slope of the line?

\(y = -3x-3\)

b. What is the x-intercept of the line? (Where does the line cross the x-axis?)

\((-1,0)\)

c. What is the y-intercept of the line? (Where does the line cross the y-axis?)

\((0, -3)\)

Step-by-step explanation:

Calculate slope:

\(m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{-3-0}{0-(-1)} \\m = \frac{-3}{1}\\m = -3\)

Calculate y-intercept:

(Pick any point that lies on the line)

\((-1,0)\)

\(b = y - (mx)\\b = 0 - (-3 * -1)\\b = 0 - (3)\\b = -3\)

Create function:

\(y = -3x-3\)

Get x-intercept:

Set y = 0:

\(0 = -3x-3\\3 = -3x\\-1 =x\)

\((-1,0)\)

Get y-intercept:

Set x = 0:

\(y = -3x-3\\y = -3 * 0 -3\\y = 0 - 3\\y = -3\)

\((0, -3)\)

There are 8 green markers and 36 markers in total.

The probability of picking a single green marker is 8/36 or 2/9.

Since the marker was replaced, you still have an 2/9 chance of drawing a green marker on the second draw.

P(both green) = 2/9 • 2/9 = 4/81

Answer:

232 in^2

Step-by-step explanation:

80 + 80 + 20 + 20 + 16 + 16 = 232

Check previous answer for better explanation!