what is the minimum sample size required to estimate a population mean with a confidence of 95%, if the margin of error is 2 units and a standard deviation of 10 units? show formula and your calculations. round to the next whole number.

The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.

The variables for this problem are given as follows:

To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.

Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.

The table is given by the image shown at the end of the answer.

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We can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.

According to Stoke's theorem, where C = A closed curve, "the surface integral of the curl of a function across a surface limited by a closed surface is equal to the line integral of the particular vector function over that surface."

S = Any surface bordered by C.

So, by utilizing Stokes Theorem to calculate S curl F .dS.

[tex]\iint_s c u r l F \cdot d s=\int_c F d r[/tex]

Parameterize C now.

r(t) = (3 cos t, 3 - 3 sin t)

When t is in [0 2].

Now,

[tex]\begin{aligned}& \int_c F \cdot d r=\int_0^{2 \pi} F(3 \cos t, 3-3 \sin t) \cdot r^{\prime}(t) d t \\& =\int_0^{2 \pi}\left(\left(9 \cos ^2 t\right)(27)(-3 \sin t),(\sin t) \times(-27 \cos t \cdot \sin t) \cdot(-3 \sin t, 0-3 \cos t) d t\right. \\& =27 \int_0^{2 \pi} 81 \cos ^2 t \cdot t \sin ^2 t+3 \cos ^2 t . t \sin t d t \\& =27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2 t+27\left[-\cos ^3 t\right]_0^{2 \pi}\end{aligned}[/tex]

[tex]\begin{aligned}& =27 \times \frac{81}{4} \int_0^{2 \pi}\left(\frac{1-\cos 4 t}{2}\right) \\& =\frac{2187}{8}\left[t-\frac{1}{4} \sin 4 t\right]_0^{2 \pi} \\& =\frac{2187}{8}\left[2 \pi-\frac{1}{4} \sin 4(2 \pi)-0-\frac{1}{4} \sin 4(0)\right] \\& =\frac{2187 \pi}{4}\end{aligned}[/tex]

Therefore, we can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.

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 By solving 13 = 8- 5d we get the value of ‘d ’ is equal to -1.

This equation can be solved by arranging the non – algebraic equations on one side and letting the algebraic number on the other side.

13 = 8 – 5d

5d = 8-13

5d = -5

d = -5/5

d = -1.

While arranging the non - algebraic numbers on one side their signs should be changed after taking the number into another side. Similarly, while arranging the algebraic equations on one side, signs of the numbers should be changed. In an algebraic equation, the terms addition, subtraction, multiplication, division, raising to a power, and extraction of a root are applied to a set of variables to construct a statement of the equality of two expressions.

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The linear equation for the given chart is: y = -3x + 7.

From the chart given, we can use two pairs of values to find the slope (m) and the y-intercept (b), then plug in their values into the equation that is expressed in slope-intercept form as y = mx + b.

Using two points, (1, 4) and (3, -2), find the slope (m):

Slope (m) = change in y / change in x = (-2 - 4) / (3 - 1)

Slope (m) = -6/2

Slope (m) = -3

Find the y-intercept (b) by substituting m = -3 and (x, y) = (1, 4) into y = mx + b:

4 = -3(1) + b

4 = -3 + b

4 + 3 = b

7 = b

b = 7

To write the linear equation, substitute m = -3 and b = 7 into y = mx + b:

y = -3x + 7

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Answer:

(-4,4)

Midpoint= (x2 + x1 /2, y2+y1 /2)

Step-by-step explanation:

the coordinates of the midpoint between points A and B are

((xa + xb)/2, (ya + yb)/2)

in our case

((-2 + -6)/2, (0 + 8)/2) = (-8/2, 8/2) = (-4, 4)

Answer:

There is no solution

Step-by-step explanation:

x - 4y = 15

3x -12y = 12

Times the first equation by -3

-3x +12y = -45

3x - 12y = 12

0 = -33

This is untrue; 0 is not equal to -33

So, there is no solution for this system.

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In the above condition of positive correlation, the higher a person scores on involvement, the higher they tend to score on life satisfaction. Therefore, the option B holds true.

Positive correlation can be referred to or considered as the correlation, wherein the relationship between two or more elements, that are taken into consideration, is direct. The direct relationship means that the movement of a change in one element leads to an equal movement in the other. Positive correlation also states about the measure of life satisfaction in the above condition.

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Complete question

A researcher finds a positive correlation between a measure of community involvement and a measure of life satisfaction. How should we interpret the relationship between these variables?

A) There is no relationship between involvement and life satisfaction.

B) The higher a person scores on involvement, the higher they tend to score on life satisfaction.

C) The higher a person scores on involvement, the lower they tend to score on life satisfaction.

D) Involvement and life satisfaction are probably the same variable

The given equation that should be in the standard form should be like a 4.5 x 10¹¹.

The equation in standard form:

Since

The equation is (5 x 10³) x (9 x 10⁷)

Now here we use the commutative property

So,

45 x (10³ x 10⁷)

45 x 10¹⁰

4.5 x 10¹¹

Here, we multiply the number in the 1st bracket, then add, it, and then finally in standard form.

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Answer:

Step-by-step explanation:

(5*10^3)*(9*10^7)

(5*1000)*(9*10000000)

5000*90000000

450000000000

The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The numbers are given below.

10 and 2/3

The product of the numbers 10 and 2/3 will be given as,

⇒ 10 x 2 / 3

⇒ 20 / 3

⇒ 6.67

The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.

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Yes, by definition, every NP problem can be reduced to an NP-complete problem in polynomial time.

All NP-complete problems can be reduced to each other in polynomial time since an NP-complete problem is itself an NP problem.

An NP-complete problem lies in NP, the set of all decision problems whose solutions can be verified in polynomial time. Similarly, NP can be defined as a set of decision problems that can be solved in polynomial time by a non-deterministic Turing machine. A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) to p in polynomial time.

Not sure if all NP issues can be resolved quickly. This is called the P-NP problem. However, if every NP-complete problem can be solved quickly, the definition of an NP-complete problem states that every problem in NP must be rapidly reducible to every NP-complete problem (i.e., it can be solved in polynomial time abbreviated by ). For this reason, NP-complete problems in general are often said to be harder or harder than NP problems.

A decision problem C is NP-complete if:

1. C is in NP and every problem in NP is reducible to C in polynomial time.

2. We can show that C is in NP by showing that the candidate solutions for C can be verified in polynomial time.

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The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.

The slope-intercept form is One of the most common ways to describe a line's equation. The general form of a slope-intercept form is given by

Where m is the slope and c is the y-intercept  

And the formula for Slope is given by

Here we have

Number of participants in 1st year = 26

Number of participants in 4th year = 89

Take number of years as x - coordinate

Number of participants as y - coordinate

As we know for 1 year, number of participants is 26

=>  The pair of coordinates = (1, 26)

For 4th year, number of participants is 89  

=>  The pair of coordinates = (4, 89)

Now we will find the slope-intercept form for the situation

using the coordinates (1, 26) (4, 89)

As we know slope m = (y₂ - y₁)/(x₂- x₁)  

Slope m = (89 - 26)/(4 - 1) = 63/3 = 21      

As we know slope intercept form, y = mx + c  

=> y = 21x + c --- (1)

As per the situation, Line (1) will pass through (1, 26)  

=> 26 = 21(1) + c  

=> c = 26 - 21

=> c = 5

=>  y = 21x + 5

Therefore,

The required Slope-intercept form is y = 21x + 5

To find the number of participants in the 6th year, take x = 6

=> y = 21(6) + 5

=> y = 126 + 5

=> y = 131

Therefore,

The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.

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The kind of hypothesis is being used in this study is Research hypothesis

Hypothesis

In statistics, a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon is known as hypothesis.

Given,

Here we know that a researcher states that he expects that there will be a significant difference between 20- and 30-year- old's after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance.

And we need to find the kind of hypothesis is being used in this study.

While we looking into the given question we know that a researcher contacts the research on 20- and 30-year- old's after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance.

And her record the result accordingly.

Basically this one refers his research hypothesis.

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[tex](-2-i)^{2}[/tex] can be simplified by multiplying the integer by itself.

Multiply the integer by itself.

[tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]

[tex](-2-i)^{2} =((-2)^{2}+(-i)^{2})[/tex]

Simplify

[tex](-2)^{2} +2.(-2).(-i)+(-i)^{2}[/tex]

[tex]=4+4i-1[/tex]

Make use of the property [tex]i^{2} =-1[/tex] to decrease the imaginary units.

[tex]4+2i+21i+1(-1)[/tex]

Simplify and use the a+bi formula in standard form.

[tex]3+4i[/tex]

A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.

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The true statement is;

There is a greater percentage of Los Angeles residents who own a car than New York City residents who do

Given,

Following is the presentation of the values:

The number of residents in Los Angeles own a car = 3251

The number of residents in New York City  own a car = 1478

Total residents who own a car = 4729

Los Angeles  residents who do not own a car = 869

New York City residents who do not own a car = 6182

Total residents who do not own a car = 7051

Total Los Angeles residents sampled = 4120

Total New York City residents sampled = 7660

Total residents of both cities sampled = 11780

Here,

Percentage of Los Angeles residents who own a car = (3251/4120)×100 = 78.9%

Percentage of New York City residents who own a car = (1478/7660)×100 = 19.3%

Then,

The total number of people in the poll who own a car = 4729

Therefore,

The correct option is that there is a greater percentage of Los Angeles residents who own a car than New York City residents who do.

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Answer: B

Step-by-step explanation:

The value of 2 divided by 3 is 0.67

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

2 divided by 3

To start with, we need to represent the expression properly as a quotient

So, we have the following representation

2 divided by 3 = 2/3

Evaluate the quotient expression using a calculator

This gives

2 divided by 3 = 0.67

Hence, the solution to 2 divided by 3 is 0.67

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Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.

In the given question, Elizabeth's family went to NYC for their vacation.

At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.

We have to find the price of each item.

Let the price of one t-shirt = $x

Let the price of one Key chain = $y

According to question

Price of three t-shirts and four key chains = $134

So the equation is

3x + 4y = $134……………….(1)

Also,

Price of four-shirts and five Key chains = $175

So the equation is

4x+5y = $175……………………..(2)

Now solving the equation using the elimination method.

Multiply Equation (1) by 5 and Equation (2) by 4, we get

15x+20y = 670....................(3)

16x+20y = 700......................(4)

Subtract equation 4 and 3, we get

x = 30

Now put the value of x in equation 1,

3*30 + 4y = $134

90+4y=$134

Subtract 90 on both side, we get;

4y = 44

Divide by 4 on both side, we get;

y = 11

Hence, the price of one t-shirt is $30 and one key-chain is $11.

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p < 0.10, there is sufficient evidence to conclude that the machines' maker should perform a recalibration.

In this question we have,

The population mean μ = 1.00

The sample size n = 49

The sample mean X = 1.06

The standard deviation σ = 0.22cm

The significance level α = 0.10

So, the hypothesis is:

The null hypothesis: H0: μ = 1

The alternative hypothesis: Ha: μ ≠ 1

Thus, the test statistic value is,

z = (X - μ)/(σ/√n)

= (1.06 - 1)/(0.22/√49)

= 0.06 / 0.03142

= 1.91

So, for z = 1.91, the p-value is 0.028067.

The provided significance level of 0.10 is not met by the p-value of (0.028067).

Therefore, there is enough evidence to support the claim that the machines' manufacturer needs to recalibrate them.

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The inverse of a function is f^-1(x) = 3(x + 17)/2 and f^-1(x) = x + 10

What is function ?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.

Functions can be roughly categorized into four sorts. based on the element Numerous to one function, onto function, one to one and onto function, into function.

1.f(x) = 2x/3 - 17

Finding the inverse

y = f(x)

  = 2x / 3 - 17

Exchange the variables, x for y and y for x

x = 2y / 3 - 17

Isolate the variable y

Adds 17 both sides

x + 17 = 2y / 3

Multiply by 3 both sides

3(x+17) = 2y

Divide by 2 both sides

y = 3(x + 17)/2

let f^-1(x) = y

f^-1(x) = 3(x + 17)/2

2. f(x) = x - 10

Finding the inverse

y = f(x)

  = x - 10

Exchange the variables, x for y and y for x

x = y - 10

Isolate the variable y

Adds 10 both sides

y = x + 10

Multiply by 3 both sides

3(x+17) = 2y

let f^-1(x) = y

f^-1(x) = x + 10

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There are 20 numbers in the set.

Given,

Set of numbers is 120

one number is increased by 300

and, mean increases to 135.

To find the how many numbers are in the set?

Now, According to the question:

Let the number of numbers be 'n'

Then, (sum of numbers)/n = 120

or, old sum = 120n

if one number is increased by 300, the new sum = (old sum + 300)

Then, (new sum)/ n= 135

or new sum = 135n = old sum + 300 = 120n + 300

The equation will  be:

135n = 120n + 300

15n = 300

n = 20

Hence, There are 20 numbers in the set.

In the question:

The mean of a set of numbers is 120. if one number is increased by 300, the mean increases to 135.

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Answer:

distance between two cities will be 9 000 000 km

Answer:

Step-by-step explanation:Scale of a map is 1:3000000 i.e, 1cm on map =30km so distance of towns on map =3.5cm Actual distance = 3.5×30=105km

We are 67% confident that the proportion of students who are tell me that they did their homework over the weekend.0.087 with a margin of error of 0.0175

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

87/1000 = 0.087

We have a 67% confidence level that the percentage of left-handed students is 0.087, with a 0.0175 margin of error.

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The system of equations which is used to find out the cost of each item (i.e cotton candy and funnel cake) bought by two families McCartney and Lennon Family is

3c + 2f = $24

2c + 4f = $32

We have given that

McCartney family bought

total number of bags of cotton = 3

total number of funnel cakes = 2

total cost of 3 bags and 2 funnel cakes is $24.

Lennon Family bought

total number of bags = 2

total number of funnel cake = 4

total cost of 2 bags and 4 funnel= $32

we have to find out the system of equations which used to find the cost of each item.

let the cost of each funnel cake be f and cotten candy be c .

then, using the above data we get

3c + 2f = $24 ---(1)

2c + 4f = $32 --(2)

Hence, equation (1) and (2) make a system of linear equations which is used to determine the cost of each item.

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Complete question:

HEME At the circus, the McCartney family bought 3 bags of cotton candy and 2 funnel cakes for $24. The Lennon Family bought 2 bags of cotton candy and 4 funnel cakes for $32. Which system of equations could be used to find the cost of each item? Let f represent funnel cake and c represent cotton candy

The value of x is [tex]\frac{37 - b}{a}[/tex] by taking a and b as non-zero constant . It is solved by using simple arithmetic calculations .

What are arithmetic calculations?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.,

Addition : (+)

The addition is the process of taking two or more numbers and adding them together. In other words, it is the total sum of all the numbers.

Subtraction : (-)

Subtraction is the process in which we remove objects from the original group.

Multiplication : (×)

Multiplication is adding the same number to itself a certain number of times.

Division : (÷)

The division is breaking a large object or group into smaller parts or groups.

Here ,

given equation: ax + b = 37

To calculate value of x :

ax  = 37 - b

As, it is given that a is non-zero constant then,

x = (37 - b)/a

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The inequality that represents the greatest number of boxes he can move in one trip is 255 + 50b ≤ 4000.

The solution of the inequality is 74.

The number of trips he would make to deliver 310 boxes is 5.

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is ≤

The form of the inequality is:

Weight of the worker + weight of the cart + (weight of the boxes x number of boxes) ≤ 4000

160 + 95 + (50 x b) ≤  4000

255 + 50b ≤ 4000

In order to determine the value of b, take the following steps:

Combine similar terms:

50b ≤ 4000 - 255

50b ≤ 3745

b ≤ 3745 / 50

b ≤ 74.9

The number of boxes he can carry is 74

Number of trips = total number of boxes / number of boxes he can carry in one trip

= 310 / 74

= 4.1

= 5 trips

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The rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.

Given that,

In the same time it took to row 25 miles against the current, a rowing team was able to row 50 miles while travelling with it. 2 miles per hour was the current's speed.

We have to calculate the rowing team's speed in still water.

We know that,

Let rowing rate in still water = r

And current rate = c = 2 mph

Rowing with the current means the overall speed is r + c = r + 2

Rowing against the current means the overall speed is r - c = r - 2

Distance = Rate × Time

50 = (r+2) × t  ----->equation(1)  

25 = (r-2) × t  ----->equation(2)

By solving

Divide equation(1) by equation(2)

50/25 = (r+2) × t / (r-2) × t

2=r+2/r-2

2(r-2)=r+2

2r-4=r+2

2r-r=2+4

r=6mph

Substitute in equation(1)

50 = (r+2) × t

50=(6+2)×t

50=8t

t=50/8

t=6.25 hrs

t= 6 hours 15 minutes

Therefore, the rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.

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the sample mean is the point estimator of μ

Sample Mean:

The Sample Mean is the average mathematical value of a sample’s values. It is a statistical indicator used to analyze various variables over time. Statisticians and researchers obtain it by dividing the total sum of values of all data fragments and then dividing it by the total number of data sets.

Point Estimate:

p=x/

p is the point estimate for the population proportion, x is the number of

successes, n is the sample size

p= + /2

for the population proportion

x= + /2

for the population mean

= − /2

  is the margin of error

the sample mean is the point estimator of μ

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The average rate of change to the function is (d) 3/2

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

g(x) = 3/2x + 1

Also, we have the interval to be

-2 < x < 8

This interval can be expressed as

a = -2 and b = 8

So, we start by calculating g(-2) and g(8)

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

g(-2) = 3/2 * (-2) + 1

g(-2) = -2

Also, we have

g(8) = 3/2 * (8) + 1

g(8) = 13

The average rate of change to the function is then calculated as

Rate = [g(8) - g(-2)]/[8 + 2]

So, we have

Rate = (13 + 2)/(8 + 2)

Evaluate

Rate = 3/2

Hence, the average rate is 3/2

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The domain for the given graph is obtained as {1, 2, 3, 4}.

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

From the graph of the given exponential function,

The set of ordered pairs can be written as follows,

{(1, 10), (2, 20), (3, 40), (4, 80)}

Since the domain is the set of first elements for a given pair of ordered set.

The domain is given as {1, 2, 3, 4}.

Hence, the domain obtained from the given graph is {1, 2, 3, 4}.

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The graph missing in the question is attached here.

The coordinates of points A and B are (-4, 5) and (2, 6) respectively. Point B is close to the origin by 0.1 unit

The positions or coordinates of points A and B are (-4, 5) and (2, 6) respectively

In order to use the Pythagorean Theorem to find the straight-line distance from each point to the origin (Consider the attached image):

Distance for point A

d = √((-4)²+5²)

d = √41 = 6.40 units

Distance for point A

d = √(2²+6²)

d = √40 = 6.32 units

To find which point is close to the origin and by how much:

The distance of B is less, so point B is close to the origin

Difference of distance =   6.40 - 6.32  = 0.08 ≈ 0.1 unit

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