g you would like to obtain a 90% confidence interval with margin of error 0.02, what is the minimum sample size you need?

area=147 cm squared

7 x 7 = 49

49 x 3 = 147

The given argument is valid. The conclusion ~(A.U) follows from the premises using Rules of inference and Replacement.

To construct a formal proof of validity for the given argument using only Rules of inference and Replacement, we need to show that if all the premises are true, then the conclusion must also be true. The argument we need to prove is as follows:

To prove this argument, we'll use a proof by contradiction. We'll assume the negation of the conclusion, ~(A.U), and show that it leads to a contradiction. Here's the formal proof:

Contradiction (Contradiction, 13, 4)

Since we have reached a contradiction from the assumption of ~(A.U), we can conclude that ~(A.U) must be false. Therefore, the argument is valid, and the conclusion ~ (A.U) follows from the premises.

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The inverse transform of a signal H(z) can be found by solving for h(n). The inverse Z-transform can be obtained by;h(n) = [(-1/2) ^ (n-1) sin(n)] u(n - 1)

The inverse transform of a signal H(z) can be found by solving for h(n).

Here’s how to find the inverse transform of

H(z) = (z^2 - z) / (z^2 + 1)

1: Factorize the denominator to reveal the rootsz^2 + 1 = 0⇒ z = i or z = -iSo, the partial fraction expansion of H(z) is given by;H(z) = [A/(z-i)] + [B/(z+i)] where A and B are constants

2: Solve for A and B by equating the partial fraction expansion of H(z) to the original expression H(z) = [A/(z-i)] + [B/(z+i)] = (z^2 - z) / (z^2 + 1)

Multiplying both sides by (z^2 + 1)z^2 - z = A(z+i) + B(z-i)z^2 - z = Az + Ai + Bz - BiLet z = i in the above equation z^2 - z = Ai + Bii^2 - i = -1 + Ai + Bi2i = Ai + Bi

Hence A - Bi = 0⇒ A = Bi. Similarly, let z = -i in the above equation, thenz^2 - z = A(-i) - Bi + B(i)B + Ai - Bi = 0B = Ai

Similarly,A = Bi = -i/2

3: Perform partial fraction expansionH(z) = -i/2 [1/(z-i)] + i/2 [1/(z+i)]Using the time-domain expression of inverse Z-transform;h(n) = (1/2πj) ∫R [H(z) z^n-1 dz]

Where R is a counter-clockwise closed contour enclosing all poles of H(z) within.

The inverse Z-transform can be obtained by;h(n) = [(-1/2) ^ (n-1) sin(n)] u(n - 1)

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Answer:11

Step-by-step explanation:

Answer: its 12 and 8 10 12 14 16 either of those

Step-by-step explanation:

The impedance of the circuit element is (4 + 5i) ohms

Impedance is a measure of the opposition to electrical flow in an alternating current circuit. The unit of impedance is ohms. It is given by:

Impedance (Z) = Voltage (V) / Current (I)

Given that V = 35 + 13i, I = 5 - 3i, hence:

Z = (35 + 13i) / 5 - 3i

Z = (4 + 5i) ohms

The impedance of the circuit element is (4 + 5i) ohms

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                                             Question 16

Given that two golfers completed one round of golf.

It is stated that the first golfer had a score of +6 and the second golfer had a score of -3.

It is clear that the first golfer is 6 over par, while the second golfer is under 3.

Thus, the equation becomes:

\(-3 + x = 6\)

adding -3 to both sides

\(-3+3+x = 6+3\)

simplify

\(x = 9\)

Thus, the second golfer has taken 9 more shorts.

                                             Question 17

When we talk about credit, it means:

Credit = +

When we talk about debt, it means:

Debit = -

Thus,

Credit = +84

Debt = -29

Balance = 84 + (-29)

              = 84 - 29

               = 55

Thus, the balance is: 55

Answer: A, B, C, E

Step-by-step explanation:

Answer:

The cost of one bottle of water is $1.25

The cost of one apple is $0.75

Step-by-step explanation:

Answer:

I know that the bank account one is b I am not sure on the other one I'm sorry

Answer:

6. B 7. C 8. A 9. D 10. C

Step-by-step explanation:

The solution of the expression is x = (-1 ± i√3)/2 and the domain of the expression is all values of x l x ≥ 0 (option c).

The given equation is -x² = √x. To solve this equation, we need to isolate x on one side of the equation. We begin by squaring both sides of the equation to eliminate the radical:

(-x²)² = (√x)²

x⁴ = x

Now we have a quartic equation, which we can solve by factoring:

x(x³ - 1) = 0

We can further simplify this equation by factoring the cubic term using the difference of cubes formula:

x(x - 1)(x² + x + 1) = 0

From this factorization, we can see that the solutions are x = 0, x = 1, and the solutions of the quadratic factor x² + x + 1 = 0. To find the solutions of the quadratic, we can use the quadratic formula:

x = (-1 ± √1 - 4(1)(1))/2(1)

x = (-1 ± i√3)/2

Therefore, the solutions to the equation -x² = √x are x = 0, x = 1, and x = (-1 ± i√3)/2.

Now let's consider the domain of the solutions, which is determined by the inequality x ≥ 0. This inequality means that the solutions must be greater than or equal to 0. We can see that x = 0 and x = 1 satisfy this inequality.

For the solution x = (-1 ± i√3)/2, we can see that it does not satisfy the inequality x ≥ 0 because it is negative. Therefore, the solutions to the equation -x² = √x in the domain x ≥ 0 are x = 0 and x = 1.

Finally, let's consider the inequality x ≤ 0. This inequality means that the solutions must be less than or equal to 0. We can see that x = 0 satisfies this inequality. However, x = 1 and x = (-1 ± i√3)/2 do not satisfy this inequality. Therefore, the solutions to the equation -x² = √x in the domain x ≤ 0 are x = 0.

Hence the correct option is (c).

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Complete Question:

Solve the expression -x² = √x . And identify the domain of the expression,

A. all values of x

B. all values of x l x ≥ 1

C. all values of x l x ≥ 0

D. all values of x l x ≤ 0

Answer:

√21 is irrational

Step-by-step explanation:

√21 = 4.58257569495584 which is a non-terminating decimal.

Therefore √21 is irrational.

Answer: No, it cannot be a rational number.

Step-by-step explanation:

A rational number is defined to be a whole number (ex. 1, 2, 3) or can be decimals that continuously repeat the digits after the point. In the case of a square root, they can be rational--but this only applies to perfect squares: √100, √64, √16, etc, which would give an outcome of a whole number. Therefore, √21 is not a rational number, as the decimal value is 4.57257, and is not continuous (ex. 3.666666).

Answer:

5 times

Step-by-step explanation:

Jenna wil most likely pull a yellow marble 1/3 of the time, because the total number of marbles is 6, and there are 2 yellow marbles, 2/6 which is 1/3. 1/3 times 15 is 5. So Jenna will most likely pull a yellow marble 5 times.

Answer:

YOUR ANSWER ISSS 4.

Step-by-step explanation:

B. 4

\(90+4x=4\)

Answer:

Option C.

Step-by-step explanation:

For a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

\(M = \frac{x_1 + x_2 + ... + x_n}{N}\)

And the variance is given by:

\(v = \frac{(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2}{N}\)

Then for our set:

{70, 80 ,75, 75, 80}

We have 5 elements, then N = 5

The first thing we need to find is the mean.

\(M = \frac{70 + 80 + 75 + 75 + 80}{5} = 76\)

Then the variance will be:

\(v = \frac{(70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2}{5} = 14\)

The correct option is C, 14.

The answer for the derivative of m(x) is:

m'(x) = -10x(x^2 – 9)^(3/2) - 15x^3(x^2 – 9)^(1/2)

This is the final result after applying the product rule and the chain rule.

We can use the product rule and the chain rule to find the derivative of the function

First, let's break down the function as follows:

\(= -5x^2 · (x^2 – 9)^3/2\)

Using the product rule, we have:

Taking the derivative of the first term:

Taking the derivative of the second term using the chain rule:

\(= 3x(x^2 – 9)^(1/2)\)

Putting it all together:

\(= -10x(x^2 – 9)^(3/2) - 15x^3(x^2 – 9)^(1/2)\)

To compute the derivative of a function, we need to apply the rules of differentiation, which include the product rule and the chain rule. In this case, we have a product of two functions, \(-5x^2\) and \(V(x^2 – 9)^3\), where V represents the square root. We apply the product rule to differentiate the two functions.

The product rule states that if we have two functions, u(x) and v(x), then the derivative of their product, u(x) · v(x), is given by u'(x) · v(x) + u(x) · v'(x). We use this rule to differentiate the two terms in the product.For the first term, \(-5x^2\), the derivative is straightforward and is simply -10x.

For the second term, \(V(x^2 – 9)^3\), we need to use the chain rule because the function inside the square root is not a simple polynomial. The chain rule states that if we have a function g(u(x)), where u(x) is a function of x, then the derivative of g(u(x)) is given by g'(u(x)) · u'(x). In this case, we have \(g(u(x)) = V(u(x))^3\), where \(u(x) = x^2 – 9\). We need to apply the chain rule with \(g(u) = V(u)^3\) and \(u(x) = x^2 – 9\).

To apply the chain rule, we first take the derivative of the function \(g(u) = V(u)^3\) with respect to u. The derivative of \(V(u) = u^(1/2\)) is \(1/(2u^(1/2))\).

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The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer:

25

Step-by-step explanation:

5x(4+1)=

4+1=5

5x5=25

A.  The simplified sum is 241x^2.

B. The sum simplifies to:

∑N=−∞^∞ X(M)⋅Y(N) = X(M)⋅Y(0)

The simplified sum is X(M)⋅Y(0).

(A) ∑N=0^241 x^2:

To simplify this sum, we need to evaluate the expression x^2 for each value of N from 0 to 241 and sum up the results.

∑N=0^241 x^2 = x^2 + x^2 + x^2 + ... + x^2 (241 terms)

Since x^2 is constant for each term, we can simply multiply x^2 by the number of terms, which in this case is 241:

∑N=0^241 x^2 = 241 * x^2

Therefore, the simplified sum is 241x^2.

(B) ∑N=−∞^∞ X(M)⋅Y(N):

This sum represents an infinite series where X(M) and Y(N) are the terms being multiplied.

Since the range of N is from negative infinity to positive infinity, we can observe that for every term X(M)⋅Y(N) with a positive N, there will be a corresponding term with a negative N that cancels it out due to the multiplication.

Therefore, the sum simplifies to:

∑N=−∞^∞ X(M)⋅Y(N) = X(M)⋅Y(0)

The simplified sum is X(M)⋅Y(0).

Note that this simplification assumes that X(M) and Y(N) are well-defined functions that do not depend on the specific value of N.

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To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

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Answer:

Step-by-step explanation:

Unfortunately other people have promised to give Brainliest before and they never did. However, I'll answer the third question and tell you that it's 8 sides.

The prompt provides the position of a child on a circular staircase as she descends from the top of a tower. The child's position in feet and time in minutes are given by a mathematical expression.

The task is to determine the height of the tower.The problem describes the position of a child on a circular staircase, as she descends from the top of a tower. The child's position in feet and time in minutes can be described using a mathematical expression. To determine the height of the tower, we need to use this expression and solve for the unknown variable.

One possible mathematical expression for the child's position is given by:

x(t) = h - r cos(t/2)

where h is the height of the tower, r is the radius of the circular staircase, t is the time in minutes, and x(t) is the child's position in feet from the origin at the base of the tower.

To solve for the height of the tower, we need to find the value of h that satisfies the given expression for all values of t. This can be done by using the initial condition given in the problem: at t=0, the child is at the top of the tower, so x(0) = h.

Thus, we have:

x(0) = h - r cos(0/2) = h - r = 0

Solving for h, we get:

h = r

Therefore, the height of the tower is equal to the radius of the circular staircase.

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The answer to the coefficient of correlation a. is the square root of the coefficient of determination

The coefficient of correlation (also known as "r") is the square root of the coefficient of determination (also known as "r-square" or "R²"). So the answer is (b) is the square root of the coefficient of determination.

Step-by-step explanation:

1. The coefficient of correlation (r) measures the strength and direction of a linear relationship between two variables.
2. The coefficient of determination (R²) measures the proportion of the variance in the dependent variable that is predictable from the independent variable.
3. To find the coefficient of correlation (r) from the coefficient of determination (R²), you simply take the square root of the R² value.

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Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

If the coach buys the packs of Gummi Bears at $0.60 and resales them at $1 , then the percent markup for the candy is (d) 67% .

The price for which the Coach buys Gummi Bears is = $0.60 ;

the price at which the Coach resales them is = $1 ;

So , the Markup is the difference in the price of purchase and price of resale of the candy ,

that means ; the \(Markup = \$1 - \$0.60\) ;

= $0.4

So , the Percent Markup is = \(\frac{0.4}{0.6} \times 100\)

= 66.66666...

≈ 67% .

Therefore , the percent Markup for the Candy is 67% .

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x = 2 is the solution to the equation 5x - 2 = 8.

What is the logarithm?

A logarithm is a power to which a number must be raised in order to get some other number. For example, the base ten logarithms of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 102 = 100.

The change of base formula for logarithms allows us to change the base of a logarithm without changing the value of the logarithm.

The formula is: logb(x) = (logc(x)) / (logc(b))

To solve 5x - 2 = 8 using the change of base formula, we will first bring the equation to one side and get 2 = 5x - 8.

Then we will add 8 to both sides of the equation to get 2 + 8 = 5x, which gives us 10 = 5x.

Finally, we will divide both sides of the equation by 5 to get x = 2.

x = 2

Therefore, x = 2 is the solution to the equation 5x - 2 = 8.

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