A random sample of 100 preschool children in Camperdown revealed that only 60 had been vaccinated. Provide an approximate 95% confidence interval for the proportion vaccinated in that suburb.
a) We have 95% confidence that the interval, .5842 ≤ μ ≤ .7903 will contain the population proportion of children who have been vaccinated.
b) We have 95% confidence that the interval, .5504 ≤ μ ≤ .6560 will contain the population proportion of children who have been vaccinated.
c) We have 95% confidence that the interval, .5199 ≤ μ ≤ .6800 will contain the population proportion of children who have been vaccinated.
d) We have 95% confidence that the interval, .5040 ≤ μ ≤ .6960 will contain the population proportion of children who have been vaccinated.

Answer:

6(4+x)

Step-by-step explanation:

Answer:

6(x+4)

Step-by-step explanation:

We want to write an algebraic expression for "six times the sum of four and a number"

Let's break this down.

The sum of four and a number:

The words "sum" indicates addition. We can call " a number" x, since it is unknown.

So, the sum of four and a number is: (x+4).

Six times:

The word "times indicates multiplication. We are multiplying six and the sum of four and a number.

So, we have: 6(x+4)

The algebra expression for "six times the sum of four and a number" is 6(x+4)

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

9514 1404 393

Answer:

  -2 5/9

Step-by-step explanation:

w +(-x) -2/3 = w -x -2/3 = -5/9 -4/3 -2/3

  = -(5/9 +4/3 +2/3) = -(5/9 +(4+2)/3) = -(5/9 +2)

  = -2 5/9

Answer:

48/125.

Step-by-step explanation:

a. The distribution needed to solve this problem is the binomial distribution. The binomial distribution is a probability distribution that describes the number of successes in a sequence of independent experiments each of which yields success with probability p. In this case, each experiment is the student guessing the answer to one of the three questions, and success is the student guessing the answer correctly. The probability of success is

p= 1/5, since there are five possible answers to each question and the student is guessing randomly.

b. The probability that the student got only one question correct is given by the binomial distribution with n=3, p= 1/5, and k=1:

P(X=1)= (3/1) * (1/5) * (4/5)^2

Therefore, the probability that the student got only one question correct is  48/125.

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Answer:

He rolled a 6, 16 times

He rolled not a 6, 4 times

Brian did not roll 6 in the dice 14 times.

Subtraction is mathematic operation. Which is used to remove terms or objects in expression.

Given, Brian is playing a game of dice. He gets 10 points for each 6 he rolls. He loses 4 points every time he does not roll a 6.

After 20 tries his score is 144 points.

If he rolled 6 each time,

his score would be 200.

Subtracting the number 144 to 200.

200 - 144

= 56

And 56/4

= 14

That means he did not roll 6, 14 times.

Therefore, 14 times he did not roll 6.

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Answer:

a^2 + b^2 + c^2 +2ab + 2ac + 2bc

The area of circle C, which passes though points W and Z is 324π square meters.

The center of the outer circle, Point D, is where we want to calculate the area of the circle has a WZ diameter and WC and CZ radii.

That YZ = YD = 10 cm is known.

Let DC = x and CY = 10 - x

The outer circle's radius can be expressed as 8 + 8 + x or 10 + 10 - x, which we can equate to determine its value of x

8 + 8 + x = 10 + 10 - x

Simplify

16 + x = 20 - x

Subtract 16 on both side, we get

x = 4 - x

Add x on both side, we get

2x = 4

Divide by 2 on both side, we get

x = 2

As a result, the circle's radius is

= 8 + 8 + x

= 16 + x

= 16 + 2

= 18 cm

The area of circle = πr²

The area of circle = π(18)²

The area of circle = 324π

Thus, the circle's area is 324π square meters.

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The complete question is:

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ.

What is the area of circle C, which passes though points W and Z?

A. 81

B. 164

C. 324

D. 1296

The test statistic for this sample and the p-value for this sample is  t = 0.467.

Given:

sample of size n=305

M=83.6

SD=14.9.

Significance level of α = 0.001 . H o : μ = 82.4 H a : μ ≠ 82.4

To find the Test statistic

\(test=\frac{\bar x-\mu}{\frac{s.t}{\sqrt{n} } }\)

    \(=\frac{82.4.6-83.6}{\frac{14.9}{\sqrt{305} } }\)

     \(0.467\)

P-value:

With t = 0.467.

p-value = (1 - 0.467)

0.533 > 0.001

So, fail to reject H₀

Therefore, the failing to reject the Null Hypothesis.

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Answer:

The solution is (\(\frac{7}{12}\) , \(\frac{67}{6}\))

Step-by-step explanation:

∵ y = 14x + 3 ⇒ (1)

∵ y = 2x + 10 ⇒ (2)

→ Equate equations (1) and (2) to find x

∵ 14x + 3 = 2x + 10

→ Subtract 2x from both sides

∴ 14x - 2x + 3 = 2x - 2x + 10

∴ 12x + 3 = 10

→ Subtract 3 from both sides

∴ 12x + 3 - 3 = 10 - 3

∴ 12x = 7

→ Divide both sides by 12 to find x

∵ \(\frac{12x}{12}\) \(\frac{7}{12}\)

∴ x = \(\frac{7}{12}\)

→ Substitute the value of x in equation (1) or (2) to find y

∵ y = 2(\(\frac{7}{12}\)) + 10

∴ y = \(\frac{7}{6}\) + 10

∴ y = \(\frac{67}{6}\)

∴ The solution is (\(\frac{7}{12}\) , \(\frac{67}{6}\))

The probability that both candies are of same color is 0.22

Probability:

                Probability means possibility.The value is expressed from zero to one.In other words probability is simply how likely something is to happen.

The distribution of colors of candies in a bag is as follows.

    Brown      0.1

    Red         0.3

   Yellow      0.2

   Green      0.2

   Orange    0.2

The probability for both candies are Orange.

                = 0.2 x 0.2

                = 0.04

The probability for both candies are Brown.

               =  0.1 x  0.1

               = 0.01

The probability for both candies are Yellow.

               = 0.2 x 0.2

               = 0.04

The probability for both candies are Green.

              = 0.2 x 0.2

              = 0.04

The probability for both candies are Red.

             = 0.3 x 0.3

             = 0.09

Now,

       The total probability  that they are the same color

                    = 0.04 + 0.01 + 0.04 + 0.04 + 0.09

                    = 0.22

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Answer:

not 35

Step-by-step explanation:

it 18

Answer:

n^2+3n-18

Step-by-step explanation:

Hope this helps :)

The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Given information:Position of a particle moving along the x-axis varies in time according to the expression x = 3t², where x is in meters and t is in seconds.

To determine the position at the following times. a. t = 3.30 s, b. t = 3.30 s + Δt xf and c. Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 3.30 s. a. To find the position when t = 3.30 s, substitute t = 3.30 s in x = 3t².x = 3t² = 3(3.30)² = 32.67 metersTherefore, the position at t = 3.30 s is 32.67 meters.

b. To find the position when t = 3.30 s + Δt, substitute t = 3.30 s + Δt in x = 3t².x = 3t² = 3(3.30 s + Δt)² = 3(10.89 + 6.6Δt + Δt²) = 32.67 + 19.8Δt + 3Δt²Therefore, the position when t = 3.30 s + Δt is 32.67 + 19.8Δt + 3Δt².c. Velocity is given by Δx/Δt.Δx/Δt = [x(t + Δt) - x(t)]/ΔtBy substituting the given values, we have;Δx/Δt = [x(3.30 + Δt) - x(3.30)]/Δt= [3(3.30 + Δt)² - 3(3.30)²]/Δt= 19.8 + 6ΔtTaking the limit of Δx/Δt as Δt → 0, we have;Δx/Δt = 19.8 + 6(0)Δt = 19.8Therefore, the velocity at t = 3.30 s is 19.8 m/s.

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The one-way ANOVA model for the response variable is y ij = μ + τ i + ε ij

The one-way ANOVA model for the response variable in the context of an experiment assessing the effect of multiple treatments is as follows:

y ij = μ + τ i + ε ij

where:

y ij represents the jth value of the response variable for the ith treatment.

μ is the overall mean of the response variable.

τ i is the effect of the ith treatment.

ε ij is the random error term representing the variability in the response variable that is not explained by the treatments.

In this model, the treatment effect (τ_i) represents the differences in the response variable among the different treatments. The error term (ε_ij) accounts for the random variability and any other factors that may influence the response variable but are not included in the model.

The goal of performing the ANOVA is to assess whether there are significant differences in the means of the response variable across the treatments. This is done by analyzing the variation between the treatment means (sums of squares) and comparing it to the variation within each treatment group (residual sums of squares). The F-test is commonly used for this purpose.

By analyzing the model, we can estimate the treatment means, test for the significance of the treatment effects, and make inferences about the differences between the treatment means. The model provides a framework for understanding the relationship between the treatments and the response variable in the context of the experiment.

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In computer programming, variables are used to store and manipulate data. In this case, an int variable named strawsoncamel has been declared and assigned a value.

To increase the value of strawsoncamel by 1, you can use the increment operator (++). This operator adds 1 to the current value of the variable and assigns the result back to the variable.

For example, if strawsoncamel has a value of 5, the statement strawsoncamel++; would increase its value to 6. This can be useful in many scenarios, such as counting or iterating through a loop. It's important to note that the increment operator can also be used in other ways, such as ++strawsoncamel, which increments the value of the variable before it is used in an expression.

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To increase the value of the variable strawsoncamel by 1, you can use the increment operator "++". So the statement would be:
strawsoncamel++;

This will increment the value of strawsoncamel by 1. The increment operator is an example of an operator in programming, which performs a specific operation on a variable. In this case, it increases the value of the variable by 1, which is also known as an increment.
To increase the value of the integer variable `strawsoncamel` by 1 using the increment operator, follow this step:
Write the statement: `strawsoncamel++;`
This line of code will use the increment operator (`++`) to increase the value of the variable `strawsoncamel` by 1.

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Answer:

e^4 d^2

-------------------------

b^3

Step-by-step explanation:

b^-3 c^0 d^2

-------------------------

e^-4

Negative exponents flip positions

e^4 c^0 d^2

-------------------------

b^3

c to the zero power is 1

e^4 d^2

-------------------------

b^3

Answer:

d^2 e^4

--------------

    b^3

Step-by-step explanation:

Answer:

Factoring the polynomials and then simplifying:

\( \frac{ {x}^{2} - 20x + 91}{ {x}^{2} - 35x + 196} \times \frac{ {x}^{2} - 74x + 1288}{ {x}^{2} - 92x + 2116 } \)

\( \frac{(x - 7)(x - 13)}{(x - 7)(x - 28)} \times \frac{(x - 28)(x - 46)}{(x - 46)(x - 46)} \)

\( \frac{x - 13}{x - 46} \)

Answer:

x−46

x−13

Step-by-step explanation:

Explanation in picture :)

the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

The minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is as follows:

95% confidence, within 5 percentage points, and a previous estimate of 0.25.

The formula to calculate the sample size required for the study to determine the proportion is given by:

`n = Z²pq / E²`

Where n = sample size

Z = z-value (1.96 at 95% confidence interval)

E = margin of error

p = estimated proportion of the population

q = 1 - pp

q = estimated proportion of population without the condition (1 - 0.25 = 0.75)

Given,

Z = 1.96E = 0.05p = 0.25q = 0.75

Substituting these values in the above formula, we get;

`n = (1.96)²(0.25)(0.75) / (0.05)²``n = 384.16`

Therefore, the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.

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The most important thing to notice about a table of q-sort correlates is d. general patterns that emerge.

Q-sorting is a method of ranking items in order of preference or importance, and Q-sort correlates are used to identify relationships between the ranked items. The correlations in the table represent how strongly the items are associated with each other based on their rankings.

While the exact value of the correlations is important for statistical analysis, the most valuable information in a table of q-sort correlates is the general patterns that emerge. These patterns can help to identify groups of items that are closely related to each other, as well as those that are more distantly related.

Understanding the wording of specific items may also be important, as it can impact how the items are ranked and how they relate to each other. However, the primary focus of a table of q-sort correlates is on the relationships between the items, rather than the items themselves.

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Answer:

8.8412 x 5 = 44.206

11.0515 x 4 = 44.206

Step-by-step explanation:

division

To find two more multiplications with an answer of 44.206, let's use the following equation:

1) \(2.1 x 21.05 = 44.2055\)In this calculation, if we multiply

2.1 by 21.05, we get an answer of 44.2055, which is very close to 44.206. 2) \(4.020 x 11.001 = 44.22602\)By multiplying 4.020 by 11.001, we obtain a product of 44.22602, which is also close to the desired answer of 44.206. In conclusion,

we have provided two additional multiplications that have answers very close to 44.206. The first multiplication of\(2.1 x 21.05\)  yields 44.2055, while the second multiplication of esults in 44.22602. Although the exact solution of 44.206 was not achieved, both calculations provide results within a very small margin of deviation.

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The expression is expanded and simplified to 7y - 4

Note that algebraic expressions are described as mathematical expressions that are composed of coefficients, factors, constants, variables and terms.

They are also made up of some mathematical operations. These operations are;

From the information given, we have that;

5(y - 2) + 2(y - 3)

expand the bracket, we have;

5y - 10 + 2y - 6

collect the like terms

5y + 2y - 10 + 6

add the values

7y - 4

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Answer:

alright, lets say danetta's dinner bill is 20 dollars, and she ordered 4 things, so the equation would be x times 5=20, and edwards would be 25 dollars, so that equation would be x times 5=25

Step-by-step explanation:

The polynomial function in Standard form is f(x) = \(x^{3} -7x^{2} +36\)

The given zeroes of the polynomial are -2,3,6

The zeroes of the polynomial can also be written as:

x = -2,3,6

Now, expressing the zeroes as an equation, we get

x = -2, x = 3, x = 6

Equating the above zeroes to 0, we get

x + 2 = 0 , x - 3 = 0, x - 6 = 0

Multiplying the above equations:

(x + 2) × (x - 3) × (x - 6) = 0×0×0

(x + 2) × (x - 3) × (x - 6) = 0

(\(x^{2} -x-6\)) × (x - 6) = 0

\(x^{3} -6x^{2} -x^{2} +6x-6x+36\) = 0

\(x^{3} -7x^{2} +36\) = 0

Expressing the above polynomial in the form of function, we get

f(x) = \(x^{3} -7x^{2} +36\)

Hence, The function in Standard form is f(x) = \(x^{3} -7x^{2} +36\)

Complete Question: Write a polynomial function $f$ of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. write the function in standard form. -2, 3, 6

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Answer:

1. UT = MN

2. m<QWR = 30

3. SB = MN

4. y = 51

5. JL (with the line segment symbol above)