for a test concerning a mean, a sample of size n = 80 is obtained. find the p-value for the following tests: a. in testing h0 : μ ≤ μ0 versus h1 : μ > μ0, the test statistic is 2.48.

Answer:

49 it all good if was 29 or 39 thank me axter

Answer:

40 and 89

Step-by-step explanation:

let x be the number then the other number is 2x + 9, then

x + 2x + 9 = 129, that is

3x + 9 = 129 ( subtract 9 from both sides )

3x = 120 ( divide both sides by 3 )

x = 40

Thus the numbers are

x = 40 and 2x + 9 = 2(40) + 9 = 80 + 9 = 89

By definition of quotient, the rational number 1/3 represents a periodic infinite decimal number. That is to say, 1/3 is equivalent to the decimal number \(0.\overline{333}\)

The quotient of a fraction is found by dividing the fraction. Results in decimal form can be finite and infinite, infinite forms can be periodic or no periodic. This fraction represents a periodic infinite decimal number.

\(\frac{1}{3} = 0.\overline{333}\)

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The expression of the fraction 1/3 as a quotient is; 0 remainder 3 or 0 r 3.

Quotient is described as the quantity produced by the division of two numbers.

Now, we want to find the quotient of 1/3. It should be noted that this quotient should not be in decimal form and so it gives us;

0 remainder 3 since 3 as a denominator is bigger than 1 as numerator.

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P(n) being true implies that P(n+1) is true.

By mathematical induction, we have shown that P(n) is true for all positive integers n.

a) Using mathematical induction, we can show that P(n) is true for all odd positive integers n.

Base case: P(1) is given to be true.

Inductive step: Assume that P(n) is true for some odd positive integer n. Then, by the given statement, P(n+2) is true. Therefore, P(n) being true implies that P(n+2) is true.

By mathematical induction, we have shown that P(n) is true for all odd positive integers n.

b) Using mathematical induction, we can show that P(n) is true for all positive integers n.

Base cases: P(1) and P(2) are given to be true.

Inductive step: Assume that P(n) and P(n+1) are true for some positive integer n. Then, by the given statement, P(n+2) is true. Therefore, P(n) and P(n+1) being true implies that P(n+2) is true.

By mathematical induction, we have shown that P(n) is true for all positive integers n.

c) Using mathematical induction, we can show that P(n) is true for all positive powers of 2.

Base case: P(1) is given to be true.

Inductive step: Assume that P(n) is true for some positive power of 2, say \(2^k.\) Then, by the given statement, \(P(2^(k+1))\) is true. Therefore, P(n) being true implies that P(2n) is true for all positive integers n less than or equal to \(2^k.\) Since any positive integer less than or equal to \(2^(k+1)\)can be written as 2n or 2n+1 for some positive integer n less than or equal to \(2^k\), it follows that P(n) is true for all positive integers n less than or equal to \(2^(k+1)\).

By mathematical induction, we have shown that P(n) is true for all positive powers of 2.

d) Using mathematical induction, we can show that P(n) is true for all positive integers n.

Base case: P(1) is given to be true.

Inductive step: Assume that P(n) is true for some positive integer n. Then, by the given statement, P(n+1) is true.

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To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer:

It is 2.

Step-by-step explanation:

The equation becomes -2y=-4x=5

But you divide by -2 to get y solo. So -4/-2=2.

Answer:

slope = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

4x - 2y = 5 ( subtract 4x from both sides )

- 2y = - 4x + 5 ( divide all terms by - 2 )

y = 2x + \(\frac{5}{2}\) ← in slope- intercept form

with slope m = 2

According the question given you jogged around the distance of 26\(\frac{2}{3}\) miles.

What is an improper fraction?

When the numerator value exceeds the denominator value, the fraction is incorrect. Incorrect fractions can also be expressed in the form of a whole number and a proper number, where the numerator is the remainder and the denominator is left unchanged.

Here, we have

Given: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week.

We have to find out how many miles did you jog.

The total jogging distance will be

= 4(6 2/3) miles

= 4 × 20/3 miles

= 80/3 miles

= 26\(\frac{2}{3}\) miles.

Hence, you jog 26\(\frac{2}{3}\) miles.

Question: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week, how many miles did you jog?

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Answer:

M=-3

Step-by-step explanation:

10=7-m

Subtract 7 from both sides

3=-m

Divide by negative

-3=m

We have to calculate the EAC for both the conveyor belt system.

Solutions :

Equivalent Annual Cost or (EAC) for the SYSTEM-A

\($\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times $\)tax rate )

                                \($=-855,000(1-0.23)+\left[\left(\frac{280,000}{4}\right)\times 0.23\right]$\)

                               \($= (-85,000 \times 0.77 ) + (70,000 \times 0.23)$\)

                               = $ 49,350

Year      Annual Cost flow     Present value factor    Present Value of Annual

                                                     at 10%                              cash flow

1                    -49,350                  0.909091                          -44,863.64

2                  -49,350                   0.826446                          -40,785.12

3                   -49,350                  0.751315                            -37,077.39

4                   -49,350                 0.683013                         -33,706.71  

     Total                                    $ 3.169865                       $ -156,432.86  

Therefore, Net Present value = present value of the annual cash flow - initial investment.

           = 156,432.86 - 280,000

          = $ 436,432.86 (negative)

Now the EAC or the Equivalent Annual Cost for System A :

\($\text{EAC}= \text{Net present value / (PVIFA 10 percent, 4 years)}$\)

        \($=\frac{436,432.86}{3.169865}$\)

        \($= 137,681.86 $\) dollar (negative)

\($\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times $\)tax rate)

\($=79,000(1-0.23)+\left[\left(\frac{360,000}{6}\right) \times 0.23\right]$\)

\($=(-78,000 \times 0.77)+(60,000 \times 0.23)$\)

= -$ 47,030

Year      Annual Cost flow     Present value factor    Present Value of Annual

                                                     at 10%                              cash flow

1                    -47,030                  0.909091                          -42,754.55

2                  -47,030                   0.826446                          -38,867.77

3                   -47,030                  0.751315                           -35,334.34

4                   -47,030                 0.683013                            -32,122.12

5                  -47,030                  0.620921                            -29,201.93

6                  -47,030                 0.564474                            -26,547.21  

    Total                                     $ 4.355261                       $  -204,827.91

Net Present Value = Present Value of annual cash inflows – Initial Investment

\($= 204,827.91 - 360,000$\)

= -$ 564,827.91 (negative)

EAC for system B:

Equivalent Annual Cost for system B \($=\frac{\text{net present value}}{\text{PVIFA 10 \text percent, 6 years}}$\)

\($=\frac{-564,827.91}{4.355261}$\)

= -$129,688.66 (negative)

Answer: 185.7 miles

Step-by-step explanation:

To find the total distance, add the smaller distances together.

47.8 + 72 + 65.9 = 185.7

Answer: Exact Form: 28/5

Step-by-step explanation:

Answer:

y = 28/5

Step-by-step explanation:

Let's solve the problem,

→ 4/5 = y/7

→ y = 7 × (4/5)

→ [ y = 28/5 ]

Hence, the value is 28/5.

Answer: did anyone find the answer???

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

perpendicular lines have reciprocol slopes,the given line has a gradient of _1/3 nd its reciprocal is 3

Answer:

This line is aray because it has a beginning and it has no end

The general solution is \($$\begin{pmatrix}x \\ y\end{pmatrix} = c_1e^{(7+\sqrt{3})t}\begin{pmatrix}5 \\ 1+\sqrt{3}\end{pmatrix} + c_2e^{(7-\sqrt{3})t}\begin{pmatrix}5 \\ 1-\sqrt{3}\end{pmatrix}$$\)

We can write the system of differential equations in matrix form as:

\(\frac{d}{dt}\begin{pmatrix}x \\ y\end{pmatrix} = \begin{pmatrix}6 & -5 \\ -2 & 8\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}\)

To find the general solution, we first need to find the eigenvalues and eigenvectors of the coefficient matrix:

\($$\begin{pmatrix}6-\lambda & -5 \\ -2 & 8-\lambda\end{pmatrix} = 0$$\)

Solving the determinant, we get:

\($$(6-\lambda)(8-\lambda) - (-2)(-5) = 0$$\)

Simplifying, we get \($\lambda^2 - 14\lambda + 46 = 0$\). Using the quadratic formula, we get:

\($$\lambda = \frac{14 \pm \sqrt{(-14)^2 - 4(1)(46)}}{2} = 7 \pm \sqrt{3}$$\)

Thus, the eigenvalues are \(\lambda_1 = 7 + \sqrt{3}$ and $\lambda_2 = 7 - \sqrt{3}\)

To find the eigenvectors, we solve the system of equations\($(A - \lambda I)\mathbf{v} = \mathbf{0}$\) for each eigenvalue. For\($\lambda_1 = 7 + \sqrt{3}$\), we have:

\($$\begin{pmatrix}-1-\sqrt{3} & -5 \\ -2 & 1-\sqrt{3}\end{pmatrix}\begin{pmatrix}v_1 \\ v_2\end{pmatrix} = \begin{pmatrix}0 \\ 0\end{pmatrix}$$\)

Solving this system, we get the eigenvector \($\mathbf{v}_1 = \begin{pmatrix}5 \\ 1+\sqrt{3}\end{pmatrix}$\).

Similarly, for \($\lambda_2 = 7 - \sqrt{3}$\), we have:

\($$\begin{pmatrix}-1+\sqrt{3} & -5 \\ -2 & 1+\sqrt{3}\end{pmatrix}\begin{pmatrix}v_1 \\ v_2\end{pmatrix} = \begin{pmatrix}0 \\ 0\end{pmatrix}$$\)

Solving this system, we get the eigenvector\($\mathbf{v}_2 = \begin{pmatrix}5 \\ 1-\sqrt{3}\end{pmatrix}$.\)

Therefore, the general solution is:

\($$\begin{pmatrix}x \\ y\end{pmatrix} = c_1e^{(7+\sqrt{3})t}\begin{pmatrix}5 \\ 1+\sqrt{3}\end{pmatrix} + c_2e^{(7-\sqrt{3})t}\begin{pmatrix}5 \\ 1-\sqrt{3}\end{pmatrix}$$\)

where \($c_1$\) and \($c_2$\) are constants determined by the initial conditions.

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Answer:

For the first one:

A' (-8,6)

B' (-9,10)

C' (-3,9)

D' (-2,5)

Step-by-step explanation:

Answer:

Step-by-step explanation: A

Answer:

B

Step-by-step explanation:

10 to 4

4 divided by 2 = 2, 2 x 5 = 10

15 to 6

6 divided by 2 = 3, 3 x 5 = 15

35 to 14

14 divided by 2 = 7, 7 x 5 = 35

Given the following trinomial:

Since the given trinomial is quadratic, there are two factors in this equation.

Step 1: Determine the factors of the first term, 2x².

There are no other possible factors of 2x² but 2x and x.

Therefore, we can now generate the initial factors.

Let A and B represent the unknown constants of the factors to be able to get the product of 2x² + 7x + 4.

Step 2: Let's determine A and B.

Let's think of possible constants of A and B that have a product of 4 and a sum of 7x when adding A multiplied by x and B multiplied by 2x.

Let's list down possible pairs.

TABLE

Sum of 4 (A and B) Sum of 7x

1 and 4 1(x) + 4(2x) = x + 8x = 9x

2 and 2 (2)(x) + 2(2x) = 2x + 4x = 6x

4 and 1 4(x) + 1(2x) = 4x + 2x = 6x

-1 and -4 -1(x) - 4(2x) = -x - 8x = -9x

-4 and -1 -4(x) - 1(2x) = -4x - 2x = -6x

None of the possible factors are possible to complete the equation, therefore, we can say that the given trinomial is not a perfect square and is not factorable.

If we are tasked to factor the trinomial by completing the square, we get:

The constant must be 3 and not 4 for it to be factorable and will

give you (2x + 1)(x + 3) = -1.

Answer:

a & c are the correct answer

Step-by-step explanation:

Answer:

Just think of which number, when you multiply it with 20 will give you -8

and then you multiply that number with -4 to get y. Hope it helps!

Answer:

C. 1170 miles per 18 hours

D. 455 miles per 7 hours

Step-by-step explanation:

1170/18=65

455/7=65

an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is t minimize the time it takes to travel from $a$ to $b$?

The relationship will be a solid line .

How to find the relationship between the given amounts?

Given:

The amount of one lunch =$4

The amount of the school lunch card=$100

Let, the amount remaining on the card= b

Let the number of lunches to buy  = a

The equation is given by,

b = 100 - 4a

When 1 lunch is bought ,a= 1 ;

b= 100 - 4(1) = 96

When 2 lunches are bought ,a= 2;

b= 100 - 4 (2)= 92

When 3 lunches are bought ,a= 3;

b= 100 - 4 (3)= 88

When 4 lunches are bought ,a= 4;

b= 100 - 4 (4)= 84

Since ,the decrease is gradual and same, the relationship will be a solid line.

The complete question is:

What is the relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card. Is the relationship a solid line or a set on unconnected points?

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Answer:

41

Step-by-step explanation:

Hey There!

So to solve this problem the first thing that we want to do is solve for x

angle P and angle S are supplementary angles meaning that they will add up to equal 180

so 180=8x+3+2x+7

step 1 combine like terms

8x+2x=10x

3+7=10

now we have

180=10x+10

step 2 subtract each side by 10

180-10=170

10-10 cancels out

now we have

170=10x

step 3 divide each side by 10

10/10 cancels out

170/10=17

so x=17

So remember in parallelograms opposite angles are congruent so angle Q is congruent with angle S

so we just plug in 17 into 2x+7 and we will get the value of angle Q

17x2=34

34+7=41

so angle Q = 41