7/8 + 3 5/6= Put your answer in the comments

The 90% CI for the mean tension μ of all the screens produced on this day = (292.32, 320.32).

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence. It is calculated from a sample of data, and provides a measure of the precision and uncertainty of the estimate.

a. Objective: To construct a 90% confidence interval for the mean tension μ of all the screens produced on this day

STATE: State the parameter you want to estimate and the confidence level.

Parameter: In the given problem we are asked to estimate the mean tension μ of all the screens produced on this day, by listing a range of plausible values. Hence, the parameter of interest is the true mean tension of the population (μ).

Confidence level: As mentioned in the problem, we need to estimate the range of plausible values that the true mean tension (μ) can take with 90% confidence. Hence,

Confidence level = 90%

PLAN: Identify the appropriate inference method and check conditions.

Name of procedure: Statistical inference by Confidence interval approach - Since the population standard deviation is unknown, the underlying distribution would be assumed to follow a t distribution with n - 1 degrees of freedom.

Check conditions:

- The data is normally distributed; although the sample size is small.

From the summary statistics and dot plot, the data does appear to be symmetric and approximately normally distributed.

- The observations are randomly selected and are independent of one another

This is ensured the data collection

The population variance is unknown

Since the conditions are met, we may construct the 90% CI as folllows:

General Formula:

Sample Mean ±  Margin of Error

= Sample Mean ± \(t_{n-1}\)SE

Specific Formula:

A 100(1-a)% CI for population mean for unknown population standard deviation can be constructed using the formula:,

\(\bar x \± t_{a,n-1}\frac{s}{\sqrt{n} }\)

where \(\bar x\), s, n  denote the mean, standard deviation and size of the sample and the t denotes the critical value for n - 1 degrees of freedom at a % level of significance.

Work:

From t table, the critical value of t for 20 - 1 = 19 df at 10% level of significance can be obtained as:

Table is mentioned below

Substituting the descriptive and the critical value in the CI formula:

306.32 ± (1.729) \((\frac{36.209}{\sqrt{20} } )\)

306.32 ±  (1.729)(8.097)

≈ 306.32 ±  14

≈ (292.32,320.32)

The 90% CI for the mean tension μ of all the screens produced on this day = (292.32, 320.32)

CONCLUDE:

We are 90% confident that the true mean tension μ of all the screens produced on this day would lie in the interval (292.32, 320.32).

b. Given:

The manufacturer’s goal is to produce screens with an average tension of 300 mV. Here, we need to test:

\(H_{0}\) : μ= 300   Vs     \(H_{a}\) :  μ ≠ 300

Using the Confidence Interval approach for testing the hypothesis,

Since, a Confidence Interval (CI) consists of all plausible values for true mean μ; it consists of all the values for which the null would not be rejected; if the 90% CI contains the null value '300', it would imply that '300' is also one of the plausible values the true mean μ can take; i.e. there would be a pretty good chance that μ is indeed equal to '300'; hence, we would fail to reject H0 based on such a CI.

Here, we find that the 90% CI for μ (292.32, 320.32) does contain the null value '300'. And hence, we fail to reject Họ: = H=300  at 10% level of significance. Hence, based on the interval, we may state that there is not enough convincing evidence that the screens produced this day don’t meet the manufacturer’s goal.

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The complete question is:

The amount of mg required per kg for the patient is 2,438.1mg/kg

Proportions are ratios of two integers.

Given the medication with a strength 125mg/5ml which has been ordered at 25 mg/kg.

For a patient that weighs 215lb, the weight in kg will be 97.5224kg

Since 25mg = 1 kg

x = 97.5224kg
x = 25 * 97.5224
x = 2,438.06

Hence the amount of mg required per kg for the patient is 2,438.06mg/kg

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Answer:

The given function f(x) = (x - 6)^2 is a transformation of the parent function f(x) = x^2. Specifically, it is a vertical translation of the parent function, where the vertex (minimum point) is shifted 6 units to the right.

STEP BY STEP DESCRIPTION

The transformation can be described as follows:

1. The function remains a parabola opening upwards, as in the parent function.

2. The minimum point moves 6 units to the right of the origin, as indicated by the sign of the x term inside the function.

3. The shape and orientation of the parabola remain unchanged from the parent function.

To verify the transformation, we can graph the function using a graphing calculator. Here is a graph of f(x) = (x - 6)^2:

[Graph of f(x) = (x - 6)^2]

As we can see from the graph, the transformation shifts the minimum point of the parabola from the origin to the point (6, 0).

Answer:

-6/5

Step-by-step explanation:

3/2x - 5/4y = 15

-5/4y = -3/2x + 15

multiply each side by (-4/5)

(-4/5)(-5/4y) = (-4/5)(-3/2x + 15)

y = -6/5x - 12

rate of change: -6/5

If the plant produces 53 seeds, the model predicts that approximately 57.5% of the seeds will sprout.

To predict the percent of seeds that sprout if the plant produces 53 seeds, we can try to establish a relationship between the number of seeds produced and the sprout percentage based on the given data points.

We can create a scatter plot of the given data points to visualize the relationship.

Seeds Produced: 65, 55, 56, 70, 44, 63, 51

Sprout Percent: 51, 54, 67.6, 49, 70.4, 49.8, 72.6

Based on the scatter plot, we can see if there is a clear pattern or trend. Let's assume that there is a linear relationship between the number of seeds produced and the sprout percentage.

Using the data points provided, we can perform linear regression to estimate the relationship and predict the sprout percentage for 53 seeds produced.

After performing linear regression on the given data points, the estimated equation for the relationship between the number of seeds produced (x) and the sprout percentage (y) is:

y = -0.3933x + 79.2133

Using this equation, we can plug in x = 53 to predict the sprout percentage for 53 seeds produced:

y = -0.3933 * 53 + 79.2133

Calculating this expression, we find:

y = 57.5

Therefore, if the plant produces 53 seeds, the model predicts that approximately 57.5% of the seeds will sprout.

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Answer:

5/6

Step-by-step explanation:

Rise over run.

10 over 12 = 10/12

10/12 simplified is 5/6

The slope is 5/6

Answer:

5/6

Step-by-step explanation:

Rise over run.

10 over 12 = 10/12

10/12 simplified is 5/6

The slope is 5/6

Answer:

1/12

Step-by-step explanation:

3/36=1/12

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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Answer:

C) -1/3

Step-by-step explanation:

Slope=rise/run

Slope=-1/3

The proportion of 1040r tax forms completed in less than 77 minutes = 0.06301

How to find the proportion of the tax forms?

The time required to complete a 1040r tax form = normally distributed

Mean = \(\mu\) = 100 minutes

Standard deviation  = \(\sigma\) = 15 minutes

The proportion of 1040r tax forms completed in less than 77 minutes is given by ,

P( X< 77 ) = P ( Z < \(\frac{77-100}{15}\)  )

                = P( Z < - 1.53 )

                =0.06301

Cumulative probability in the normal distribution =0.06301 or 6.301%

What is normal distribution?

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The number of dominoes are in each row for the artist is 42 dominoes.

From the information, the domino artist has 6 sets of 28 Domino’s. The total Domino will be:

= Number of set × Amount in each set

= 6 × 28

= 168

Since she arranges all the dominoes into four equal rows. This will be:

= Total number / Rows

= 168 / 4

= 42

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Answer:

$64,000

Step-by-step explanation:

Number of shares times the profit per share equals total profit.

2000 * 32 = 64,000

Answer:

-1020

Step-by-step explanation:

-17 x - 5 x - 12 =

- 17 x 60 =

- 1020

Answer:

a: the second choice, and pounds=10

b. the second choice, and points=90.

Step-by-step explanation:

for a , you just divide the pounds by the price and you get 5 for each.

for b, you just divide the points by the tickets and you get 9 each.

Answer:

2000

Step-by-step explanation:

(4x5) x 100

Answer:

2000

Step-by-step explanation:

40 x 50 can be easily done by multiplying 4 and 5 which is 20 and adding the remaining 0's which is 2000

3 21divde by 6, use 3 which is 18. now 21 subtracted by18 is 3

A)

Start by graphing the function on the different intervals.

For this, we graph as if they were independent functions and then join them on the same graph.

for x<4

for x>=4

then, for g(x)

B)

To find the x-intercepts:

equal g(x) to 0.

for x<4

for x>=4

then, for g(x)

For g(x) the x-intercepts are -4, 0 and 19

C)

finally, using the graph we can see that the function is positive in the intervals [-4,0)∪[4,19) because in these intervals g(x) is above the x-axis.

The value of the variable x for the triangle base length is derived as 5.

Using the proportionality theorem for evaluating x as follows:

JD/DK = PJ/PK

3x/(4x + 1) = 20/28

3x × 28 = 20(4x + 1) {cross multiplication}

84x = 80x + 20

84x - 80x = 20 {collect like terms}

4x = 20

x = 20/4 {divide through by 4}

x = 5

Therefore, the value of the variable x for the triangle base length is derived as 5.

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Answer:

the answer is 6.63

Step-by-step explanation:

The given box plot represented by the data sets in option A and B.

From the given box plot, we have

Minimum value = 3

Maximum value = 18

First quartile (Q1) = 7

Third quartile (Q3) = 13

Median = 10

Option A:

3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18

Median = 12

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option B:

3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Option C:

3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option D:

2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Therefore, the correct options are B and D.

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mugi lado Puti is answre

Answer:

Step-by-step explanation:

To find the equation for the nth term in the sequence, we need to determine the pattern or rule that generates the sequence.

From the given information, we can see that the sequence is not arithmetic because the differences between consecutive terms are not constant. Instead, the sequence appears to be quadratic because the second difference between consecutive terms is constant.

Using the given values of a₁, a₃, and a₅, we can find the first few differences:

a₃ - a₁ = 4 - (-6) = 10

a₅ - a₃ = 14 - 4 = 10

So, the first difference is 10, which indicates a linear term in the equation for an. We can now use the given value of a₁ and the first difference to find the constant term in the quadratic equation. Let d be the common difference, then we have:

a₂ = a₁ + d = -6 + 10 = 4

a₄ = a₃ + d = 4 + 10 = 14

a₆ = a₅ + d = 14 + 10 = 24 - 1

a₇ = a₆ + d = 24 - 1 + 10 = 33

Now, we can find the second difference between consecutive terms:

a₄ - 2a₃ + a₂ = 14 - 2(4) + (-6) = 0

a₆ - 2a₅ + a₄ = 19 - 2(14) + 4 = -5

a₇ - 2a₆ + a₅ = 33 - 2(19) + 14 = 9

Since the second difference is constant (-5), this confirms that the sequence has a quadratic term in its equation. Let's assume the equation for the nth term is:

an = an² + bn + c

Substituting the values we know, we get three equations:

a₁ = a₁² + b₁ + c --> -6 = c

a₃ = a₃² + b₃ + c --> 4 = 9a + b + c

a₅ = a₅² + b₅ + c --> 14 = 25a + 5b + c

Solving this system of equations, we get:

a = 1/2, b = 19/2, and c = -6

Therefore, the equation for the nth term in the sequence is:

an = (1/2)n² + (19/2)n - 6.

The quadratic function to represent the given situation is                         y=-(1/312)x²+x+3

A quadratic function is of the form y=g(x) where g(x) is a polynomial in x with degree 2.

The baseball is hit at a initial height of 3 feet. The baseball follows a path of a parabola.

Maximum height=81 feet

Distance from home plate =156 feet

So, (156,81) is the vertex of the parabolic path.

We know that when vertex is at (h,k) then the vertex form of the parabola is  y=a(x-h)²+k

So the quadratic equation is of the form

y=a(x-156)²+81

Now the initial height is given as 3 feet.

So at x=0, y=3

Putting the values in the equation we get:

3=a(0-156)²+81

or, -78=a×156²

or, a=-(78÷156²)

or, a=-(1/312)

So the quadratic equation can be written as

y=-(1/312)(x-156)²+81

Simplifying we get : y=-(1/312)x²+x+3

The quadratic function to represent the path of the baseball is given by y=-(1/312)x²+x+3

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Answer: 29

Step-by-step explanation:

29 ÷ 8 = 3 remainder: 5

I solved using long division.

Answer:

29

Step-by-step explanation:

30

24

5

8x3=24

24+5= 29

Beacuase it had to be smaller than 30

Answer:

The answer would be greater since its being multiply the answer will always be greater than what you're multiplying.

Step-by-step explanation:

The product WILL be greater than the other two factors. When multiplying by a fraction the product is GREATER than the lesser factor.

Answer:

The function h(x) is decreasing on the interval (3, ∞).

Step-by-step explanation:

Please take a look at the attached image.

You will see a graph of the given function h(x) = -2\(\sqrt{x-3}\). The function is decreasing.

The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).