What type of variable is required to construct a confidence interval for a population​ proportion?.

The population of the small town in 2025 is 22234

The given parameters in the question are

These parameters can be represented as

a = 24597

r = 2%

The equation of the function can be represented as

P(t) = a(1 - r)^t

So, we have

P(t) = 24597 * (1 - 2%)^t

In 2025, we have

Year = 2025

This means that

t = 2025 - 2020

So, we have

t = 5

Substitute t = 5 in P(t) = 24597 * (1 - 2%)^t

P(5) = 24597 * (1 - 2%)^5

Evaluate the expression

P(5) = 22234

Hence, the population is 22234

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Answer:

20 cm²

Step-by-step explanation:

It is a right triangle.

So, using Pythagorean theorem: OS² = OR² - RS²

OR = r (radius) + 8

OS = r

RS = 16

=> r² = (r+8)² - 16²

r² = r² + 16r + 64 - 256

r² = r² + 16r - 192

16r = 192

r = 192 / 16 = 12cm²

a) 12 cm²

b) 12 + 8 = 20 cm²

The correct statement to represent the comparison between defective parts produced by machines is option d. Machine A usually, but not always, produced fewer defective parts than machine B.

As given in the question,

Number of machines in a factory = 2

Statement compares the :

Number of defective parts produced by machines during first 4 hours

for 19 days.

Observations from the given scatterplot are:

a. Machine A always produced the same number of defective parts as machine B.

False. Variation in producing number of defective parts.

b. Machine A always produced fewer defective parts than machine B.

False.

c. Machine A always produced more defective parts than machine B.

False.

d. Machine A usually, but not always, produced fewer defective parts than machine B.

True. Sometimes like when Machine A produce 7 defective parts machine B produce 5.

e. Machine A usually, but not always, produced more defective parts than machine B.

False.

Therefore, option d) Machine A usually, but not always, produced fewer defective parts than machine B is the correct answer.

The complete question is:

A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days.

Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?

a. Machine A always produced the same number of defective parts as machine B.

b. Machine A always produced fewer defective parts than machine B.

c. Machine A always produced more defective parts than machine B.

d. Machine A usually, but not always, produced fewer defective parts than machine B.

e. Machine A usually, but not always, produced more defective parts than machine B.

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Based on the graph showing the different gang-related activities reported in small and large communities, a gang-related activity which is least reported in a large community is: B. robbery.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.

Additionally, a pie chart is generally considered as the best graph to be used in graphically representing percentages and relative proportions.

According to the graph, we can logically deduce the following percentages of people that reported the different gang-related activities in small and large communities;

In conclusion, robbery is the least reported gang-related activity in a large community with a percentage of 5 percent (5%).

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When testing the differences between means, the research hypothesis suggests that population means are not equal.  (Option B)

Hypothesis refers to a concept or explanation for a trend that is based on known facts but has not yet been proved. A research hypothesis, also known as scientific hypothesis, is a statement about the expected result of a study. It is the proposed answer to the research question and generally includes an explanation (e.g., x affect y because …). It introduces a research question and proposes an expected result. It illustrates the relationship between two variables - an independent and dependent variable. Hence, when testing the difference between means, the hypothesis that suggests that population means are not equal is a research hypothesis.

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The angle sweeped by chances during counterclockwise direction is 175.15° and in radian is 3.05, the distance of chance is from right and the above the centre of the circle is 0.27 km and 0.261km respectively.

Chance is running on a circular track that has a radius 0.9 km and he goes 2.75km into the counter clockwise direction from the 3-o'clock position.

The arc length of the circle is given by,

L = 2πR(A/360)

R is the radius,

L is the length of the arc,

A is the angle made in degrees.

Putting values,

2.75 =2π(0.9)(A/360)

A = 175.15°C.

Now, converting it into radians,

A in radian is 3.05.

Distance D of chance to the right of centre of the ski trail is,

D = R(1-0.7)

D = R(0.3)

D = 0.27 Km.

The distance D' of chance above the centre of the ski trail is,

D' = R(1-0.71)

D' = R(0.29)

D' = 0.261 Km.

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The rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces will be M(a²+b²)/3.

Any item that can be rotated has the property of rotational inertia. It is a scalar value that indicates how challenging it is to alter an object's rotational velocity around a certain rotational axis. The role of mass in linear mechanics is analogous to that of rotational inertia in rotational mechanics. Because it measures moment of inertia as it is rotating, this property is also known as rotational inertia. A measurement of an object's resistance to changes in its angular velocity is called rotational inertia. Imagine turning an item with a specific torque. As the torque is being applied, measure the angular acceleration. The rotational inertia of the item increases as the resultant angular acceleration decreases.

Here,

The major calculations are attached in image.

Moment of Inertia of plate passing through O is I = Ma²/12

and, ly = Mb²/12

by perpendicular axis theorem I2 = Ma²/12+Mb²/12

The distance of edge and the center is d = √(a²+b²)/4

So by parallel axis theorem, IA = Ma²/12+ Mb²/12 + Md² = M(a²+b²)/3

M(a²+b²)/3 is the rotational inertia of the block about a rotating axis passing through one of its corners and perpendicular to its large faces.

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V=Vw-ce^-kt is the velocity V as a function of time t when wind is blowing 20 knots and after 1 half hour the boat moves at 10 knots

Acceleration is a vector quantity that is defined as the rate at which an object's velocity varies. When an object's velocity changes, it is said to be accelerating.

On occasion, sports broadcasters will suggest that a person is accelerating if they are traveling quickly. But speed has nothing to do with acceleration. Even while traveling very quickly, a person may not be accelerating. Changing the speed at which an item is travelling is what acceleration is all about. A substance is not accelerating if its velocity is not changing. The information on the right depicts an object that is speeding as it moves northward. Throughout time, the velocity is shifting. Every second, the velocity is changing by a fixed amount of 10 m/s.

How to solve?

Based on the information from the exercise, we have the equation:

dt/dv=k(Vw−V)

where V is velocity of the boat in knots/hour, tt is time in hours, Vw is velocity of wind.

This equation can be written:

dv/dt = k(Vw -V)

dv/Vw-V =kdt

Now, the variables are separated, tt appears only on the right side, and v only on the left. Integrate the left side in relation to v, and the right side in relation to t:

dv/Vw-V =kdt

∫dv/Vw-V =∫kdt

let Vw -V = u

-dv=du

dv= -du

∫-du/u =k∫dt

-ln|u| =kt +C

-ln|Vw-V| = kt + C

V=Vw-ce^-kt

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Answer:

-2.8y-7.52

Step-by-step explanation:

multiply 0.4 by each of the numbers in the parentheses then simplify

Answer: -2.8y-7.52

Step-by-step explanation:

The increase in the price of the bananas = 8%

We know that the formula for percent change:

percent change = [(new value - old value)/ old value ] * 100

Here, the price for bananas was 75 cents per pound over last month. today, we see that it's been marked up to 81 cents per pound.

old value = 75 cents per pound

new value = 81 cents per pound

So, the percent increase in the price of bananas would be,

percent increase in price = [(81 - 75)/ 75 ] * 100

percent change = (6/75) * 100

percent change = 8%

Therefore, the increase is 8%

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A right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.

The right circular cylinder is a cylinder with circular bases that are parallel to one another.

Three dimensions make up its form.

The two bases of the cylinder are joined at their centers by the cylinder's axis.

Sphere:

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.

The radius of the right circular cylinder will be:

The formula for the volume of a sphere: V = 4/3πr²

Now, substitute r = 12 as shown:

V = 4/3πr²

V = 4/3π12²

V = 4/3π144

V = 7238.22947

Rounding off: 7238 units³

Nw, the formula for the volume of a right circular cylinder:

V = πr²h

Substitute V = 7238 and calculate for r as follows:

V = πr²h

7238 = πr²h

r² = 7238/πh

r = √7238/πh

Therefore, a right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.

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The integration of the given function is as follows.

What is anti derivative?

In calculus, an antiderivative, inverse derivative, primitive perform, primitive integral or integral of a perform f could be a differentiable perform F whose spinoff is adequate to the initial perform f. this could be explicit symbolically as F' = f

Main body:

f (x) = x/8 +1/8x + (1/8)^x

to find the anti derivative , we need to integrate the function;

apply sum rule:

[tex]\int\ f{(x)} + g (x)\, dx[/tex] = [tex]\int\ f {(x)} \, dx + \int\ g {(x)} \, dx[/tex]

[tex]\int\ {(x/8)} \, dx[/tex] = x² /16

[tex]\int\ f {(1/8x)} \, dx[/tex] = 1/8 ln|x|

[tex]\int\ f {(1/8^x)} \, dx[/tex] = [tex]-\frac{1}{3\ln \left(2\right)\cdot \:8^x}[/tex]

hence

[tex]\int \frac{x}{8}+\frac{1}{8x}+\frac{1}{8^x}dx[/tex]= [tex]\frac{x^2}{16}+\frac{1}{8}\ln \left|x\right|-\frac{1}{3\ln \left(2\right)\cdot \:8^x}+C[/tex]

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The number of ways to divide the shares into 10 equal segments is 120

from the question, we have the following parameters that can be used in our computation:

Total number of segments, n = 10

Numbers to people, r = 3

The number of ways of dividing the segment is then calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation, so, we have the following representation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have the following representation

Total = 10!/7!3!

Evaluate the quotient

Total = 120

Hence, the number of ways is 120

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The degrees of freedom for goodness-of-fit chi-square tests are calculated with the formula: df=bins(or categories)−1−number of parameters of the distribution and the degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) .

In the given question we have to calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity.

When a categorical variable has more than two levels, a chi-square goodness-of-fit test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.

The degrees of freedom in this case are calculated with the formula:

df=bins(or categories)−1−number of parameters of the distribution.

The degrees of freedom for the chi-square are calculated using the following formula:

df = (r-1)(c-1)

where r is the number of rows and c is the number of columns.

The null hypothesis can be rejected if the observed chi-square test statistic is higher than the crucial value.

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Answer:

C = 50.27

Step-by-step explanation:

Hope this helps!

Answer:

C = 16 pi

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi * r

C = 2 * pi * 8

C = 16 pi

The expected value of the mean, variance and standard deviation are-

For the given data in the question-

The formula for the mean;

μ = n×n /N

Put the values,

μ = 5×5/7

μ = 3.57

μ ≈ 4 (mean)

The formula for the variance is;

σ = nμ/N × (N - μ)(N - n)/N(N - 1)   ....eq 1

σ = 5×4/7 × (7 - 4)(7 - 5)/7(7 - 1)  

σ = 0.61 (variance)

For the calculation of the standard deviation-

δ = √σ   ...eq 2

δ = √0.61

δ = 0.78 (standard deviation).

Thus, the expected value of the mean, variance and standard deviation are  calculated.

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Answer: 29 inches.

Step-by-step explanation:

The formula to find the hypotenuse is a^2 + b^2 = c^2.

20^2= 400, and 21^2=441. Together, it was 841. Square root that, and your answer is 29.

-

a^2 + b^2 = c^2

20^2 + 21^2 = c^2

400 + 441= c^2

881 = c^2

29=29

I believe the answer you seek would be that the area of the shaded region would be [tex]64.43 cm^2[/tex].

Hope this helps!

If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .

An assumption is said to as a hypothesis when it is supported by evidence. Any investigation that turns the research questions into predictions must start here. Variables, the population, and the relationships between the variables are among its constituent parts. A hypothesis used to examine the link between two or more variables is known as a research hypothesis.

One dependent variable and one independent variable are shown to be related. For instance, eating more vegetables will help you lose weight more quickly. In this scenario, increasing your vegetable intake is an independent variable, while weight loss is the dependent variable.

It makes a claim that conflicts with the premise. There is no connection between the independent and dependent variables, which is a negative assertion. The emblem stands for.

Hence, If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .

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Answer:

(2x - 1) (4x + 3)

Step-by-step explanation:

The correct option D)c = –3, d = –2; for which the expression becomes real number.

For the given question,

The expression is-

= i(2 + 3i)(c + di)

Simplifying,

= i(2c + 2di + 3ci + 3d²)

= 2ci + 2di² + 3ci² + 3di³

= 2ci - 2d -3c - 3di

= (2c - 3di)i - 2d - 3c

Now, again for expression to produce a real number, the coefficient of must be zero.

Let's evaluate each choice.

A: 2c - 3d = 2x2 -3x3 = -5

B: 2x(-2) - 3x3 = -13

C: 2x3 - 3x(-2) = -12

D: 2x(-3) - 3x(-2) = 0

As option D only has the positive number, thus define the expression.

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The complete question is-

What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di)

choices: A)c = 2, d = 3 B)c = –2, d = 3 C)c = 3, d = –2 D)c = –3, d = –2

Answer: D) c = –3, d = –2

Step-by-step explanation:

Correct on Edge

Using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².

A shape's area can be calculated by contrasting it with squares of a known size.

The square meter (abbreviated as m2), which is the area of a square whose sides are one meter long, is the common unit of area in the International System of Units (SI).

Three such squares would be the same size as a form with a three-square-meter area.

The area of any other shape or surface is a dimensionless real number, and the unit square is defined in mathematics to have area one.

So, the area of the square:

A = b²

Where B is the square's long side.

A = 450in²

A = b²

b² = 450

b = √450

b = 15√2 in

Therefore, using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².

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Correct question:
Which represents a side length of a square that has an area of 450 square inches?

a. 15 start root 2 end root inches in.

b. 16 start root 3 end root inches in.

c. 112. 5 in.

d. 115. 5 in.

answer:

1.92 pounds or 23/12 lb

step-by-step explanation:

first convert 3/4 and 1/3 to fractions that have the same denominator such as 9/12 and 4/12. then add the two numbers together and subtract it by 3 to get the answer. hope that helps!

Answer:

B. 21

Step-by-step explanation:

Composite numbers have more than two factors.

Answer: 21

Step-by-step explanation:

The Area of annulus - the region between the two circle is 50.26cm²

According to the question,

The length of chord of the large circle which is tangent to the small circle : AB = 8cm

Le the radius of large circle "R" and radius of smaller circle "r"

AB is a tangent to the smaller circle

AM = 8/2

=> AM = 4cm

In ΔOAM,

Using Pythagoras theorem ,

OA² = OM² + AM²

=> R² = r² + (4)²

=> R² - r² = 16

So, the area of annulus = π(R² - r²)

=> 16π (putting π = 3.14)

=> 50.26cm² is required area

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Simplified form of fourth root of 2401x¹²y¹⁶  is  7x³y⁴

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Given,

⁴√2401 x¹² y¹⁶=⁴√7*7*7*7 (x³)⁴(y⁴)⁴

                       =⁴√(7)⁴ (x³)⁴(y⁴)⁴

                       =⁴√(7 x³y⁴)⁴

                       =  7 x³y⁴

Therefore, Simplified form  fourth root of 2401x¹²y¹⁶  is  7x³y⁴.

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We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

The correct interpretation of a 99% confidence interval is that we are 99% confident that the true population mean falls in it.

The probability that it contains the true population mean is 99%.

Given  99% confidence interval : 4.1 < μ < 5.6

Then, the correct interpretation is we are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

Hence the answer is We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

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She owe $167.25 of the credit card company at the end of 3 months.

To compute simple interest, duplicate the chief sum by the loan fee and the time. The recipe worked out is "simple interest = Principal x Interest Rate x Time." This condition is the easiest approach to ascertaining interest.

We ave,

interest = 10%, loaned amount = $250, monthly payment = $50

Then,

interest of first month = $250×1×0.1 = $25

She makes a payment of $50

Then $250 - $50 + $25 = $225

Second month:

interest = $225 ×0.1 = $22.5

Payment of $50

remain loan = $225 - $50 + 22.5 = $197.5

And third month

interest = $197.5×0.1 = $19.75

payment of $50 Then

Net payable loan = $197.5 - $50 + $19.75 = $167.25

Thus, remaining loan amount is $167.25.

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The equation of the hyperbola is

[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 3650 = 0[/tex]

What is a hyperbola?

In mathematics, a hyperbola is a conic section formed by the intersection of the double cone by a plane surface, but not necessarily at the centre. It is a type of smooth curve lying in a plane and has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The standard form of writing an equation of the hyperbola is,

[tex]\frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]

Where (h, k) is the centre; a is the distance from the centre to vertices; b is the distance from co-vertices to the centre.

Given,

Foci of the hyperbola are (13, -1); (-13, -1)

Co-vertices are (0,11); (0,-13)

As we know that the centre of the hyperbola is the midpoint of the foci, then it will be (h,k) = (0,-1)

Distance from centre to foci is, c = 13 [2c = 26; c = 26 / 2 = 13]

Distance from co vertices to foci is, b = 12 [ 2b = 24; c = 24 / 2 = 12]

let us assume a is the distance from the centre to the vertices.

we know that,

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

then,

[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]

[tex]a = \sqrt{ {13}^{2} - {12}^{2} } [/tex]

[tex]a = \sqrt{169 - 144} [/tex]

[tex]a = \sqrt{25} [/tex]

[tex]a = 5[/tex]

Now, the equation of the hyperbola is,

[tex] \frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]

[tex] \frac{ {(x - 0)}^{2} }{ {5}^{2} } - \frac{ {(y + 1})^{2} }{ {12}^{2} } = 1[/tex]

[tex] \frac{ {x}^{2} }{25} - \frac{ {y}^{2} + 2y + 1 }{144} = 1[/tex]

[tex] \frac{144 {x}^{2} - 25 {y}^{2} - 50y - 50 }{25 \times 144} = 1[/tex]

[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 50 = 25 \times 144[/tex]

Hence the required equation is,

[tex]144 {x}^{2} - 25 {y}^{2} - 3650 = 0[/tex]

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