what factors affect the length of a confidence interval for a proportion? explain. (2pts)

The first system of equations has no solution and the second set of equations has a unique solution.

If we are having two equations as

\(a_{1} x^{2} +b_{1} x+ c_{1} =0\)

and \(a_{2} x^{2} +b_{2} x+ c_{2} =0\)

The condition at which these equations will have infinitely many solutions is

\(\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } =\frac{c_{1} }{c_{2} }\)

The condition at which these equations will have infinitely many solutions is

\(\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }\)

For, the 26th question, we have

4x +8y = -8

4x +8y +8 = 0

x +2y +2 =0 equation(1)

x =-2y +1

x +2y -1 = 0 equation(2)

On comparing these equations with the general form, we have

\(a_{1} = 1, a_{2} =1\\b_{1} = 2, b_{2} = 2\\c_{1} = 2, c_{2} = -1\)

So, \(\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }\)

Thus, this system of equations has no solution.

Now, For the 27th question, we have

2x - 3y = 6

2x -3y -6 = 0 equation(3)

\(y = \frac{2}{3}x -2 \\\\3y = 2x -6\\\\3y -2x +6 = 0\) equation (4)

On comparing these equations with the general form, we have

\(a_{1} = 2, a_{2} =3\\b_{1} = -3, b_{2} = 2\\c_{1} = -6, c_{2} = 6\)

So, \(\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }\)  

Thus, this system of equations has a unique solution.

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Answer:

8+8+8+8+8+8+8+8+8.

Step-by-step explanation:

Just add 8 nine times.

Answer:

9 + 8x

Step-by-step explanation:

it's the same but backwards

it's called a Palindrome

Hope this helped a little!

Answer:

Hope this helps...

Step-by-step explanation:

The polynomial representing the area of the is 49n² - 25

The formula for area of a square is expressed as;

Area = a²

Where a is the side length

From the image shown, we can see that the side length takes the value (7n - 5)

Substitute the value into the formula

Area = a²

Area = (7n - 5)²

Area = (7n - 5) ( 7n + 5); this is so because of the difference of two squares

Expand the bracket

Area = 49n² + 35n - 35n - 25

collect like terms

Area = 49n² - 25

Thus, the polynomial representing the area of the cube is 49n² - 25

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To determine the number of smaller boxes that would contain the same amount of cereal as a larger box, we set the expressions representing the cereal content equal to each other. Solving the equation, we find that 15 smaller boxes are required to match the cereal quantity in the larger box.

To find the number of smaller boxes that equal the same amount of cereal in a larger box, we need to equate the two expressions and solve for n.

Setting the expressions equal to each other:

10 + 6.3n = 7 + 6.5n

Simplifying the equation:

6.3n - 6.5n = 7 - 10

-0.2n = -3

Dividing both sides by -0.2:

n = -3 / -0.2

n = 15

Therefore, 15 smaller boxes would equal the same amount of cereal as the larger box.

The problem states that the expressions 10 + 6.3n and 7 + 6.5n represent the amount of cereal in the new larger box. The variable n represents the number of smaller boxes.

To find how many smaller boxes are equivalent to the larger box, we need to set the two expressions equal to each other and solve for n. This equation represents the balance between the amount of cereal in the larger box and the combined amount of cereal in the smaller boxes.

By simplifying the equation and solving for n, we find that 15 smaller boxes are needed to equal the same amount of cereal as the larger box.

This means that if the cereal manufacturer wants to package the same amount of cereal as the larger box, they would need to use 15 smaller boxes instead. This calculation helps the manufacturer determine the number of smaller boxes needed to maintain the same quantity of cereal while changing the box size.

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Answer:

3/10

Step-by-step explanation:

3/5 is equal to 6/10, and half of 6/10 is 3/10

Answer:

3/10

Step-by-step explanation:

Amount of pizza u told= 3/5

Amout u could eat of  wht u told = 1/2

Amount u could eat of pizza = 3/5 x 1/2 = 3/10

(calculation attached below)

I hope im right!!

The value of α that would generate the most stable forecast is 0.10.

Exponential smoothing is a forecasting method that uses a weighted average of past observations to predict future values. The weight of each past observation decreases exponentially as it gets older. The value of the smoothing constant, α, determines how quickly the weights decay and thus how much emphasis is placed on recent observations versus past observations. A larger value of α means more weight is given to recent observations, resulting in a forecast that is more responsive to changes in the data but also more volatile. Conversely, a smaller value of α means less weight is given to recent observations, resulting in a forecast that is more stable but less responsive to changes in the data.

Therefore, in order to generate the most stable forecast, we would want to choose a smaller value of α. Among the options given, the value of α that would generate the most stable forecast is 0.10. This would give relatively less weight to recent observations and result in a smoother, less volatile forecast. However, it is important to note that the optimal value of α depends on the specific time series being forecasted and must be chosen based on empirical evaluation of the forecast accuracy.

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H(x) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. H(x) can take any value between 0 to 12.

\(O(x) = (12Cx)(0.2)^x(0.8)^{(12-x)]\). O(x) is a probability distribution of the random variable x. The expected value of x is 2.4. The standard deviation of x is 1.385.

Explanation: Given, the number of applicants (n) = 12.

The probability of a lie detector test suggesting a truthful person as deceptive = 0.2.

The probability of a lie detector test suggesting a truthful person as truthful = 0.8.

Let x be the number of people who the lie detector says are being deceptive.

a) The distribution of x (the number of people who the lie detector says are being deceptive) is binomial because the following conditions are satisfied: There are n independent trials, where n = 12.

Each trial has only two possible outcomes – either the lie detector test suggests that the applicant is deceptive or the lie detector test suggests that the applicant is truthful. The probability of the lie detector test suggesting that a truthful person is deceptive (p) remains the same in each trial, where p = 0.2. The outcomes of each trial are independent of each other. Therefore, the distribution of x is given by:

\(O(x) = (12Cx)(0.2)^x(0.8)^{(12-x)]\)

Where C is the symbol of combination. It can be calculated as follows:

\(C = (12Cx) = 12! / [x! \times (12 - x)!]\)

b) The expected value of x is given by:

E(x) = np

E(x) = 12 × 0.2

= 2.4

The standard deviation of x is given by:

\(\sigma(x) = \sqrt{np(1-p)}\)

\(\sigma(x) = \sqrt{12 \times 0.2 \times 0.8}\)

σ(x) = √(1.92)

σ(x) = 1.385

Hence, H(x) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Here, H(x)  can take any value between 0 to 12.

\(O(x) = (12Cx)(0.2)^x(0.8)^{(12-x)]\)

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Step-by-step explanation:

hindi mai questions do please

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

To solve the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0, we need to simplify and rearrange the equation to its standard form and then solve for p.

Combining like terms, the equation becomes:

3p^2 - 10p + 5 = 0

Now, we can use the quadratic formula to solve for p. The quadratic formula states:

p = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -10, and c = 5. Substituting these values into the quadratic formula, we have:

p = (-(-10) ± √((-10)^2 - 4 * 3 * 5)) / (2 * 3)

Simplifying further:

p = (10 ± √(100 - 60)) / 6

p = (10 ± √40) / 6

p = (10 ± 2√10) / 6

Now, we can simplify and find the two possible values of p:

p₁ = (10 + 2√10) / 6

p₂ = (10 - 2√10) / 6

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

In simplified form, the solutions are:

p₁ = (5 + √10) / 3

p₂ = (5 - √10) / 3

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Answer:

w=-2

Step-by-step explanation:

9(w-4)-7w=5(3w-2)

9w-36-7w=15w-10

9w-7w-15w=-10+36

-13w=26

w=-2

The inter-quartile range of the given data set is 13

The interquartile range (IQR) measures the spread of the middle half of your data. It is the range for the middle 50% of your sample. Use the IQR to assess the variability where most of your values lie. Larger values indicate that the central portion of your data spread out further.

Given data is : 3, 16, 18, 25, 26, 29, 31, 50

The median of the given data is 25.5

Now, we have to find the median for data 3,16,18 and 25 which is 17.

Lastly we have to find the median for the data 26, 29, 31, and 50 which is 30.

Hence, the inter quartile range is

= Q3 -Q1

= 30-17

=13

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Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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Answer:

$3.06

Step-by-step explanation:

Based on the question that was given, we can see that for every *one* pound,  the cost of the bananas is $0.68.

Since we are looking for how much 4 1/2 pounds is worth, we can convert this to 4.5 and simply multiply $0.68 by 4.5, giving us a grand total of $3.06

Answer:

4 1/2 pounds of bananas will cost $3.06.

Step-by-step explanation:

4 1/2=9/2

0.68*9/2

0.68*4.5

3.06

The null hypothesis will be same as the claim value which is 75%.

What is null hypothesis?

The null hypothesis is a statistical claim that no statistical significance can be found in a set of given observations. To determine the validity of a theory, hypothesis testing is carried out using sample data. Its symbol is H₀, and it is occasionally referred to as simply "the null".

We are given that the claim is that the proportion is less than 75%.

So, the statement of the null hypothesis states that the population value is the same as the claim value.

So,

H₀ : p = 75% = 0.75

If this null hypothesis is correct, then 75% of all students at the researcher's school finished their homework assignments last night.

Hence, this will mean that the null hypothesis is true.

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Question: No homework? Refer to Exercise 1. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265.

Explain what it would mean for the null hypothesis to be true in this setting.

we have

1) -1/10

step 1

Between the number 0 and number 1 there are 10 spaces

so

each space is

(1-0)/10=1/10

so

-1/10 is 1 space at left of zero

answer part 1 is C

part 2) we have

1/5

Remember that

1/5 is equivalent to 2/10

so

2 spaces at right of zero

answer part 2 is D

Part 3) we have

9/10

correspond to 9 spaces at right of zero

answer part 3 is F

Part 4) we have

-0.5

-0.5=-1/2=-5/10

5 spaces at left of zero

answer part 4 is B

Part 5) we have

0.6

0.6=6/10

6 spaces at right of zero

answer part 5 is E

Part 6) we have

-4/5

-4/5=-8/10

8 spaces at left of zero

answer part 6 is A

The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

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Answer:

Well you got 1/4 + 1/12

So we have to have the same denominator in order to solve this

So by finding a common multiple, you would be able to solve this

So in this case is the common multiple.

we already have a 12 so we leave that be.

We need to convert 1/4 to x/12

To Do that we multiplying it by 3

so 3/12 + 1/12

Now add normally and keep the denominator

4/12

or 1/3

Answer:

\(\sf \cfrac{1}{4}+\cfrac{1}{12}\)

First find the Least Common Denominator (LCM) of 4, 12.

Join the denominators.

\(2^{-3}\) is the same as \(\frac{1}{2^3}\) because of the rule \(x^{-k} = \frac{1}{x^k}\)

The negative exponent says to take the reciprocal of the base to make the exponent positive. The original base is 2, of which the reciprocal is 1/2.

Answer:

18/28

Step-by-step explanation:

To best emphasize that the number of defects has remained relatively consistent throughout the year, the production manager should use a line graph. A line graph is ideal for showing the trend or pattern of data over a continuous period, making it a suitable choice for representing monthly defect rates over the course of a year.

By plotting the months on the x-axis and the number of defects on the y-axis, the production manager can connect the data points with a line to illustrate the overall trend. This will allow the board of directors to visually observe any fluctuations or consistency in the defect rates.

In this case, the line graph will show a relatively stable pattern with slight variations in the number of defects over the months. It will demonstrate how the defect rate has remained consistent over time, with occasional fluctuations but no significant upward or downward trends.

By using a line graph, the production manager can effectively present the information and highlight the key message that the number of defects has remained relatively consistent throughout the year.

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The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.

In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:

Each term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.

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The full question is:

How many terms are in the following expression 6 + 2 x - 4 y + 5 z

Answer:

no this can't become a number that can be graphed

214 boxes of chocolate, 321 bags of caramel corn item was sold.

Boxes of chocolate sell for $6 each and bags of caramel corn sell for

$5 each. A total of 535 items were sold and $2889 was

raised.

set of  of chocolate was sold x boxes,

because  a total of 535 items more sold .

so the caramel corn was sold (535 -x) bags,

and boxes of  chocolate sell for $6 each , bags of caramel corn for each and  $2889 was raised.

so 6 x+ 5.(535-x) = $2889.

6 x+ 5.535-x = $2889.

6 x+ 2675 - 5x = $2889.

6x - 5x =2889-265

x =214

so the caramel corn was sold 535-x =535-214 = 321

214 boxes of chocolate, 321 bags of caramel corn was sold.

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Caramel corn bags cost $5 apiece, while chocolate boxes cost $6 each. 535 products in total were sold, bringing in a total of $2889 then there exists 214 boxes of chocolate, 321 bags of caramel corn was sold.

Any one of the forms, including addition, subtraction, multiplication, and division, should be used for the algebraic expression. Bring the variable to the left side and the other values to the right side in order to find the value of x. To find the answer, simplify the values.

Let set of  of chocolate was sold x boxes,

because  a total of 535 items more sold .

so the caramel corn was sold (535 - x) bags, and boxes of  chocolate sell for $6 each , bags of caramel corn for each and  $2889 was raised.

From the given information, we get

6x + 5(535 - x) = $2889

simplifying the above equation, we get

6x + 5 × 535 - 5x = $2889

6x + 2675 - 5x = $2889

6x - 5x = 2889 - 265

x = 214

So the caramel corn was sold = 535 - x

Substitute the value of x in the above equation, we get

= 535 - 214

= 321

There exists 214 boxes of chocolate, 321 bags of caramel corn was sold.

Therefore, the correct answer is option b) 214 boxes of chocolate, 321 bags of caramel corn.

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Step-by-step explanation:

Hi there!

The word Question of this equation (1/4x-2=5) is:

The difference of one fourth of number and 2 is 5.

Reason:

The one fourth of number is unknown number. So, let the number be "x". The number is 1/4 X .

Then the difference of it and 2 is 5.

Which brings an algebraic expression: 1/4x-2=5.

Hope it helps!

Answer:To evaluate the exponential expression 6(4+2)² - 32, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, we simplify the expression inside the parentheses:

4 + 2 = 6

Next, we square the result:

6² = 36

Now, we substitute the squared result back into the expression:

6(36) - 32

Next, we perform the multiplication:

6 * 36 = 216

Finally, we subtract 32:

216 - 32 = 184

Therefore, the value of the given exponential expression 6(4+2)² - 32 is 184.

Answer:

Step-by-step explanation:

A is the answer

Answer:

Option A. f(x) = 4(3)x

is the answer.

Step-by-step explanation:

Answer:

21/5

Step-by-step explanation:

21/5

4x5=20

20+1=21