An arc that lies between the two sides of a central angle is called _____

A. (i) The 95% confidence interval for the population mean number of years men spent in school is 6.174 to 6.826 years, meaning we can be 95% confident that the true population mean falls within this range.

A. (ii) Increasing the confidence level to 99% would result in a wider confidence interval.

A. (iii) To estimate the mean number of years in school within 0.5 year with 98% confidence, approximately 34 men would need to be included in the study.

B. Null hypothesis: The proportion of perishable food items exceeding their "best before" date is not higher than 3.5%.  Alternative hypothesis: The proportion of perishable food items exceeding their "best before" date is higher than 3.5%.

Test statistic: z = 1.647. Critical value: 1.645. P-value: approximately 0.0499. Decision: Reject the null hypothesis. Conclusion: There is evidence to suggest that the proportion of perishable food items exceeding their "best before" date is higher than 3.5% at a 5% level of significance.

(a) A random sample of 85 men revealed that they spent a mean of 6.5 years in school. The standard deviation from this sample was 1.7 years.

(i) Construct a 95% Confidence Interval for the population mean and interpret your answer.

To construct a confidence interval for the population mean, we use the following formula:

\(\[\bar{x} - z_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}} \leq \mu \leq \bar{x} + z_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}}\]\)

Given that \($\bar{x} = 6.5$\) years, s = 1.7 years, n = 85, and \($\alpha = 0.05$\) (for a 95% confidence level), we can calculate \($z_{\frac{\alpha}{2}}$\) using a standard normal distribution table or calculator. For a 95% confidence level, \($z_{\frac{\alpha}{2}}\) = 1.96 (to two decimal places).

Substituting the values into the formula, we get:

\(\[6.5 - 1.96\frac{1.7}{\sqrt{85}} \leq \mu \leq 6.5 + 1.96\frac{1.7}{\sqrt{85}}\]\)

Simplifying the expression, we find:

\(\[6.174 \leq \mu \leq 6.826\]\)

Therefore, we can be 95% confident that the population mean number of years men spend in school is between 6.174 and 6.826 years.

(ii) Suppose the question in part (i) had asked to construct a 99% confidence interval rather than a 95% confidence interval. Without doing any further calculations, how would you expect the confidence interval to change?

When the confidence level increases, the width of the confidence interval will increase. Thus, a 99% confidence interval will be wider than a 95% confidence interval.

(iii) You want to estimate the mean number of years in school to within 0.5 year with 98% confidence. How many men would you need to include in your study?

The formula for calculating the sample size required to estimate the population mean to within a specified margin of error at a given confidence level is:

\(\[n = \left(\frac{z_{\frac{\alpha}{2}}\cdot s}{E}\right)^2\]\)

In this case, s = 1.7 years, E = 0.5 year, \($\alpha = 0.02$\) (for a 98% confidence level), and \($z_{\frac{\alpha}{2}}$\) can be found using a standard normal distribution table or calculator. For a 98% confidence level, \($z_{\frac{\alpha}{2}} = 2.33$\) (to two decimal places).

Substituting the values into the formula, we get:

\(\[n = \left(\frac{2.33 \cdot 1.7}{0.5}\right)^2 = 33.53 \approx 34\]\)

Therefore, we would need to include 34 men in our study to estimate the mean number of years in school to within 0.5 year with 98% confidence.

(b) A Public Health Inspector took a random sample of 120 perishable food items from the shelves of a supermarket.

Null hypothesis: \(\(H_0:\) p = 0.035

Alternative hypothesis: \(\(H_1: p > 0.035\)\) (Note that this is a one-tailed test, since we are testing if the proportion is greater than 3.5%.)

The test statistic for a hypothesis test involving a proportion is given by:

\(\[z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\]\)

In this case,\(\(\hat{p} = \frac{x}{n} = \frac{6}{120} = 0.05\), \(p = 0.035\), \(n = 120\), and \(\alpha = 0.05\).\)

Calculating the test statistic, we find:

\(\[z = \frac{0.05 - 0.035}{\sqrt{\frac{0.035(1-0.035)}{120}}} = 1.647\]\)

The critical value for a one-tailed test with α = 0.05 is \(\(z_{0.05}\)= = 1.645 (from a standard normal distribution table or calculator).

Since the test statistic (1.647) is greater than the critical value (1.645), we reject the null hypothesis at the 5% level of significance.

Using a standard normal distribution table or calculator, we find that the area to the right of z = 1.647 is 0.0499 (to four decimal places). Thus, the p-value is approximately 0.0499.

Since the p-value (0.0499) is less than the level of significance (0.05), we reject the null hypothesis and conclude that there is evidence to suggest that the proportion of perishable food items exceeding their "best before" date is higher than 3.5%.

Learn more about population mean: https://brainly.com/question/28103278

#SPJ11

There are a total of 9 women and 6 men on the council, for a total of 15 council members.

If we randomly choose 2 of them to co-chair a committee, the number of ways to choose 2 people of the same gender is:

So the total number of ways to choose 2 people of the same gender is 3+15 = 18.

The total number of ways to choose 2 people without considering their gender is 15 choose 2 = 105

So the probability of choosing 2 people of the same gender is 18/105 = 6/35

So, the probability that these chairpersons are the same gender is 6/35.

The limits of f(x) as x approaches 5 from the left and from the right are both equal to 25. However, the limit of f(x) as x approaches 5 does not exist, because the function is not defined at x = 5.

The function f(x) is piecewise defined, with two different formulas depending on whether x is less than or greater than 5. When x is less than 5, f(x) = 8x - x². When x is greater than 5, f(x) = 2x - 5.

As x approaches 5 from the left, x is less than 5, so f(x) = 8x - x². As x gets closer and closer to 5, 8x - x² gets closer and closer to 25. Therefore, the limit of f(x) as x approaches 5 from the left is equal to 25.

As x approaches 5 from the right, x is greater than 5, so f(x) = 2x - 5. As x gets closer and closer to 5, 2x - 5 gets closer and closer to 25. Therefore, the limit of f(x) as x approaches 5 from the right is equal to 25.

However, the function f(x) is not defined at x = 5. This is because the two pieces of the definition of f(x) do not match at x = 5. When x = 5, 8x - x² = 25, but 2x - 5 = 5. Therefore, the limit of f(x) as x approaches 5 does not exist.

Learn more about limits here:

brainly.com/question/7446469

#SPJ11

Answer:

32 ounces

Step-by-step explanation:

The figures show that the number of births for Florida and Michigan reduced

From the data sourced, the number of births in Florida in 2010 was 214519 while in 2011, it was 213237. For Michigan, there was decrease from 114717 to 114159.

When a person born during 2011 in the United States is chosen randomly, the person is more likely to have been born in Florida.

The probability that a randomly selected us resident in 2011 was living in Florida will be:

= 18,801,310/308,745,538

= 0.061

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Measures of variability describe diversity in a distribution.

Measures of variability describe the spread or dispersion of values in a distribution. They provide information about how spread out or clustered the data points are. Common measures of variability include the range, variance, and standard deviation.

Measures of central tendency, on the other hand, describe the center or average of a distribution. They provide information about the typical or central value around which the data points are located. Common measures of central tendency include the mean, median, and mode.

Standard deviation is a specific measure of variability that quantifies the average amount by which data points in a distribution deviate from the mean. Association refers to the relationship or connection between two or more variables in a dataset, often analyzed using correlation or regression analysis. It is not a measure of diversity in a distribution.

To know more about variability,

https://brainly.com/question/29355567

#SPJ11

Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.

An increasing exponential function is modeled by:

\(A(t) = A(0)(1+r)^t\)

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

In this problem:

Her initial balance is of $300, hence . A(0)=300

The growth rate is of 15%, hence R =0.15

Then,

\(A(t) = A(0)(1+r)^t\)

\(A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\\)

It will reach $450 after t years, for which A(t) = 450, hence:

\(A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9\)

It will take about 2.9 years for Emma's balance to reach $450

Learn more about logarithm here

https://brainly.com/question/247340

#SPJ4 .

Answer:

19/15

Step-by-step explanation: In order to solve for A add 2/3 to both sides of the equation to get A alone and 2/3 + 3/5 is equal to 10/15 + 9/15 which means the answer is 19/15.

The total surface area of the pyramid is 115 cm².

To find the area of a triangle, we use the formula:

Area = 1/2 * base * height

In this case, the height is given as 9 cm and the base is given as 5 cm.

So,

Area = 1/2 * 5 cm * 9 cm

Area = 22.5 cm²

Therefore, the area of the four triangles = 4 * 22.5 square centimeters.

area of the four triangles = 90 cm²

The area of the square = 5 cm * 5cm

The area of the square = 25 cm²

The total surface area of the pyramid = area of square + area of four triangles

The total surface area of the pyramid = 25 cm² + 90 cm²

The total surface area of the pyramid = 115 cm²

Learn more about total surface area at: https://brainly.com/question/28178861

#SPJ1

Answer:

Step-by-step explanation:

Answer:

Length of diagonal = 6

Step-by-step explanation:

Given that

Diagonal of a rectangle makes an angle of \(30^\circ\) with the longer side.

Kindly refer to the attached diagram of the rectangle ABCD such that diagonal BD makes angles of \(30^\circ\) with the longer side CD and BA.

\(\angle CDB =\angle DBA =30^\circ\)

Side AD = BC = 3 units

To find:

Length of diagonal BD = ?

Solution:

We can use the trigonometric ratio to find the diagonal in the \(\triangle BCD\) because \(\angle C =90^\circ\)

Using the sine :

\(sin\theta = \dfrac{Perpendicular }{Hypotenuse }\)

\(sin\angle CDB = \dfrac{BC}{BD}\\\Rightarrow sin30^\circ = \dfrac{3}{BD}\\\Rightarrow \dfrac{1}2 = \dfrac{3}{BD}\\\Rightarrow BD =2 \times 3 \\\Rightarrow BD = \bold{6 }\)

So, the answer is:

Length of diagonal = 6

Answer:

22

Step-by-step explanation:

1 week = 7 days

2 weeks= 14 days

14+8=22

The simplified form of the expression\(5x(3x^2 + 6) is 15x^3 + 30x.\)This means option D\(, 15x^3 + 30x,\) is the correct answer.

To simplify the expression 5x(3x^2 + 6), we can apply the distributive property, which states that when a number is multiplied by a sum, we can distribute the multiplication to each term within the sum. Let's simplify the expression step by step:

5x(3x^2 + 6)

Using the distributive property, we multiply 5x by each term inside the parentheses:

= 5x * 3x^2 + 5x * 6

= 15x^3 + 30x

Therefore, the simplified form of the expression\(5x(3x^2 + 6) is 15x^3 +\)30x. This means option D, 15x^3 + 30x, is the correct answer.

It's important to remember to distribute the multiplication to each term within the parentheses when simplifying expressions involving the distributive property. In this case, each term inside the parentheses, 3x^2 and 6, is multiplied by 5x, resulting in 15x^3 and 30x, respectively. These terms cannot be combined further, so the simplified form is 15x^3 + 30x.

for more such question on simplified visit

https://brainly.com/question/723406

#SPJ8

Answer: you know now that i think about it not really

Step-by-step explanation:

Answer:

I think that is complete bs anyone can wear any mask and look thinner but the most important part is wearing a mask and having the mask fit comfortably around your face.

Step-by-step explanation:

Please wear a mask in public!!

Answer:

It is not possible to determine the probability that a person with an iron deficiency is 20 years or older without additional information.

The probability would depend on various factors such as the prevalence of iron deficiency in different age groups and the age distribution of the population. Without knowing these factors, we cannot calculate the probability.

Responder:

$ 555,911.5

Explicación paso a paso:

Dado

Principal = $ 545,680

Interés = 2,25%

Tiempo = 10 meses = 10/12 años

Debemos buscar la cantidad después de 10 meses.

Monto = Principal + Intereses

Interés = PRT / 100

Interés = 545,680 * 2,25 * 10/1200

Intereses = 12,277,800 / 1200

Interés = 10.231,5

Cantidad = 545,680 + 10,231.5

Cantidad = 555,911.5

por lo tanto, la cantidad después de 10 meses es $ 555,911.5

Answer:

I'm not the best nor I am the worst at these Type of problems but

Step-by-step explanation:

6.85 - 4.83= 2.2

I hope this helps or is right

Answer:

27.9

Step-by-step explanation:

62 percent *45 =

(62:100)*45 =

(62*45):100 =

2790:100 = 27.9

Answer: 140.00%

Step-by-step explanation: Cuz The first step is to divide 63 by 45 to get the answer in decimal form:

63 / 45 = 1.4000

Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:

1.4000 * 100 = 140.00%

We can prove that the answer is correct by taking 140.00 percent of 45 to get 63:

(45 x 140.00)/100 = 63

Note that our calculator rounds the answers up to two decimals if necessary. Once again, the answer is as follows:

140.00%

And PLZPLZPLZPLZPLZPLZPLZPLZPLZMAKE MAKE ME THE BrainliestAND I DID THE TEST TODAY

Answer: d . 0.14

Step-by-step explanation: i got it correct on edge

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

For more such question on speed. visit :

https://brainly.com/question/26046491

#SPJ8

Answer:

Step-by-step explanation:

Pls check

The missing code that can replace to assign the total of all values in purchase List to sum, is: REPEAT UNTIL (n > purchaseList.length)

The syntax for a REPEAT UNTIL loop in most programming languages is as follows:

REPEAT {

// code to be executed

} UNTIL (condition)

or

DO {

// code to be executed

} UNTIL (condition)

Looping is a programming construct that allows a certain block of code to be executed repeatedly. The two main types of loops are for loops and while loops.

A for loop is used to execute a block of code a specified number of times. It typically starts with a variable initialization, then a condition is checked, and if the condition is true, the code block inside the loop is executed, and then the variable is updated.

The missing code that can replace the empty parentheses in the REPEAT UNTIL statement to assign the total of all values in purchase List to sum, is:

REPEAT UNTIL (n > purchaseList.length)

This means that the loop will continue to execute until the value of n is greater than the length of the purchaseList. In each iteration, the value of purchaseList[n] is added to the sum, and then n is incremented by 1. So, this loop will iterate through all the elements in the purchaseList, adding each one to the sum, until it reaches the end of the list. This will give the total sum of all purchases made in the last month.

To know more about programming code visit:

https://brainly.com/question/28848004

#SPJ4

Answer:

x = -2

Step-by-step explanation:

5x - 5 = 9x + 3

- 5 = 4x + 3

- 8 = 4x

- 8/4 = 4x/4

x = -2

Answer:

Step-by-step explanation:

When your desired form is expanded, it becomes ...

  a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2

This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.

a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2

b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2

c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2

d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2

_____

Additional comment

If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.

False. A rectangle is conventionally used in a process flowchart to represent a storage area or queue. Triangles are typically used in flowcharts to represent decision points, where a choice must be made between two or more alternatives.

Rectangles are used to represent activities or operations, while arrows connecting the shapes indicate the flow or direction of the process. The use of standardized shapes in flowcharts helps to make them easily understandable and accessible to a wide range of individuals, regardless of their background or experience with the specific process being depicted.

To learn more about rectangle : brainly.com/question/15019502

#SPJ11

Frank has $54 left with him from the initial $65.

Now, Frank had $65 with him initially.

It is given that he spent $2 per day for 7 days (a week), implying that he spent $2 x 7 = $14 total.

Now, it is also given that he had to divide $9 between him and his brothers equally, i.e., 9/3 = $3.

Each brother (including Frank) gets $3 after the equal division.

Now, we have an expression in our hand:

65 - 2x7 + 9/3

Where, 2x7 implies the $14 he spent in the week

9/3 implies the division of money between him and his two brothers.

Solving the expression,

65 - 14 + 3 = $54

Thus, Frank has $54 left with him from the initial $65.

To learn more about expressions, visit the link:

brainly.com/question/14083225

#SPJ4

Frank has $54 left with him from the initial $65.

Now, Frank had $65 with him initially.

It is given that he spent $2 per day for 7 days (a week), implying that he spent $2 x 7 = $14 total.

Now, it is also given that he had to divide $9 between him and his brothers equally, i.e., 9/3 = $3.

Each brother (including Frank) gets $3 after the equal division.

Now, we have an expression in our hand:

65 - 2x7 + 9/3

Where 2x7 implies the $14 he spent in the week

9/3 implies the division of money between him and his two brothers.

Solving the expression,

65 - 14 + 3 = $54

Thus, Frank has $54 left with him from the initial $65.

To learn more about expressions, visit the link:

brainly.com/question/14083225

#SPJ4

The ratio of cleaning product to water for the condition is 1/5

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.

Given it is recommended that 4 ounces of the product are diluted using 20 ounces of water.

to find the ratio of cleaning products to water

ratio = cleaning product/water

cleaning product = 4 ounce

water = 20 ounces

ratio = 4/20

4/20 is equivalent to 1/5

ratio = 1/5

Hence option A is correct.

Learn more about ratios;

https://brainly.com/question/13419413

#SPJ1

Answer:

  1056

Step-by-step explanation:

You want the product of the LCM and the GCF of 22 and 48.

One way to find the LCM of two numbers is to start with their product, then divide out the extra factor:

  LCM(A, B) = (A×B)/GCF(A, B)

Since we want the product of the LCM and the GCF, we can start with this and multiply by the GCF:

  LCM(A, B) · GCF(A, B) = ((A×B)/GCF(A, B)) · GCF(A, B)

  LCM(A, B) · GCF(A, B) = A×B

Using this for the given numbers, we get ...

  LCM(22, 48)·GCF(22, 48) = 22·48 = 1056

__

Additional comment

If you want to go to the trouble of finding the LCM and GCF, you get ...

  22 = 2·11

  48 = 2·24

  LCM(22, 48) = 2·11·24 = 528

  GCF(22, 48) = 2

  LCM·GCF = 2·528 = 1056

Answer:

subtracting a negititive is the same as adding so -66.1+55.6

Hope This Helps!!!