Mrs. Jacksy served snacks on a circular plate. How many lines of symmetry were on the plate? A. 0 B. 2 C. 4 D. Infinite number

Answers

Answer 1

Answer:

D. Infinite number

Step-by-step explanation:

A circular plate can be rotated by a part of a degree and it will look the same (as long as it does not have a design on it)

Assuming this plate does not have a design on it, we can rotate through infinite number of lines of symmetry

Answer 2

Answer:

D. infinite number

Step-by-step explanation:

Hope this helps ^_^


Related Questions

What is the product of the binomials below?

Answers

Answer:

A.

Step-by-step explanation:

When you multiply the two binomials using distributive property, you get the answer A. I could display the steps since it did not let me.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

What is the result of subtracting the second equation from the first? 8x-4y=-4 -3x+4y=5

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

(x, y) = (14/5, 87/20)

▹ Step-by-Step Explanation

8x - 4y = -4 - 3x + 4y = 5

8x - 4y = 5

-4 - 3x + 4y = 5

8x - 4y = 5

-3x + 4y = 9

5x = 14

x = 14/5

-3 * 14/5 + 4y = 9

y = 87/20

(x, y) = (14/5, 87/20)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

11x−8y=−9

Step-by-step explanation:

khan

Find X. Do not round your Answer

Answers

Answer:

83/5, 16.6, 16 3/5

Step-by-step explanation:

When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment.

6 times 18 = 5(5+x)

The total secant segment is 6+12=18

so one side = 6 times 8.

The line from the circle (but not inside) is 5.

You don't know the entire segment, but you do know that 5 is part of it. Hence 5 times (5+x).

Sorry for the trashy explanation.

Answer:

16.6

Step-by-step explanation:

Five times a number decreased by nine is equal to twice the number increased by 23. Which equation could be used to solve the problem? 5x – 9 = x + 23 5x – 9 = 2x + 23 5x + 23 + 2x = 23 5x + 23 = 2x + 23

Answers

Answer:

5x - 9 = 2x + 23

Step-by-step explanation:

5 times a number is represented by 5x, with x representing the unknown number.  

5x decreased by 9 is (5x - 9) since 9 is being subtracted by 9.  

(5x - 9) is equal to twice the number (2x), increased by 23.  

So, the equation is (2x + 23).  

Therefore, 5x - 9 = 2x + 23

The equation is 5x - 9 = 2x + 23.

The answer is option A.

Which equation could be used to solve the problem?

5 times a number is represented by 5x, with x representing the unknown number.  

5x decreased by 9 is (5x - 9) since 9 is being subtracted by 9.  

(5x - 9) is equal to twice the number (2x), increased by 23.  

So, the equation is (2x + 23).  

Therefore, 5x - 9 = 2x + 23

What is an equation example?

An equation is a mathematical announcement this is made up of expressions related to the same signal. For instance, 3x – 5 = 16 is an equation. Fixing this equation, we get the price of the variable x as x = 7.

Learn more about the equation here: https://brainly.com/question/1214333

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6x + 7y + x-8y = 7x - y
Write down three other expressions that are equal to 7x - y​

Answers

Answer:

It's pretty easy! You can manipulate the numbers to match the equation.

For example,

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

The other equivalent expressions that are equal to 7x - y​ could be; x + 8y + 6x - 9y = 7x - y, 5x + 2x - 2y + y = 7x - y and 10x + 7y - 3x - 8y = 7x - y

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; that can also be used to indicate the logical syntax's order of operations and other features.

We have been given the expression as;

6x + 7y + x-8y = 7x - y

When someone asks to solve an equation, then it usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

The other equivalent expressions that are equal to 7x - y​ could be;

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

To know more about an expression follow;

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Select all that are true.

Answers

Answer:

1

2

6

Step-by-step explanation:

1/2 +1/2 =1

length 1/2 ×4=2

wide 1/2 ×3 =1 1/2

height 1/2×3= 1 1/2

The first law of thermodynamics states that ΔE= Q− W. Is this also a statement of the principle of conservation of energy? No, the heat that is added to the system is only used to do work. No, the change in internal energy is the energy lost in the system. Yes, the heat added and the change in internal energy of the gas equal the work done by the piston. Yes, the heat that flows into the system is used to change the internal energy of the gas and becomes work done by the piston.

Answers

Answer:

yes

Step-by-step explanation:

as we see in the picture the variation of the internal energy of a system is W-Q by analogie we get the second relation in the 2nd picture wich is the first law of thermodynamics

Answer:

Yes, the heat that flows into the system is used to change the internal energy of the gas and becomes work done by the piston.

Step-by-step explanation:

I took the K12 test :)

find the midpoint of the line segment that has endpoints at (10,8) (-3,-10)

Answers

Hey there! :)

Answer:

(3.5, -1).

Step-by-step explanation:

Use the midpoint formula to solve this problem:

[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Plug in the coordinates given:

[tex](\frac{10-3}{2}, \frac{8-10}{2})[/tex]

Simplify:

[tex](\frac{7}{2}, \frac{-2}{2})[/tex]

Therefore, the coordinates of the mid-point are:

(3.5, -1).

could you plz help me with this question?​

Answers

Answer:

(a) t_n = 3n - 9

(b) t_16 = 39

Step-by-step explanation:

(a)

-3 - (-6) = -3 + 6 = 3

The common difference is 3.

t_1 = -6

t_2 = -6 + 3

t_3 = -6 + 3 + 3

t_4 = -6 + 3 + 3 + 3

t_n = -6 + 3(n - 1)

t_n = -6 + 3n - 3

t_n = -9 + 3n

t_n = 3n - 9

The formula is: t_n = 3n - 9

(b) t_16 = 3(16) - 9 = 48 - 9 = 39

Answer:

an = -6 + 3(n - 1)

a(16) = 39

Step-by-step explanation:

Explicit Formula: an = a1 + d(n - 1)

Our d (common difference) is +3

Our a1 (First term) is -6

To find a(16) (the 16th term), plug in 16 for n.

The area of circle Z is 64ft?.
What is the value of r?
r= 4 ft
r= 8 ft
D
r = 16 ft
Area
r= 32 ft
Z

Answers

Answer:

r=8

Step-by-step explanation:

Using the formula they gave us you could plug in the area (64) and divide it by pi which cancels out the pi so taking the square root of 64 gives you 8FT

Hope this helps :)

Answer:

8 ft

Step-by-step explanation:

[tex] \because \: r = \sqrt{ \frac{Area}{\pi} } \\ \\ \therefore \: r = \sqrt{ \frac{64\pi}{\pi} } \\ \\ \therefore \:r = \sqrt{64} \\ \\ \therefore r = 8 \: ft[/tex]

1. Find the sum to
(a) 8 terms of 3 + 6 + 12 + .....
(b) n terms of 27/8+9/4+3/2+....
note(u can do only that was desplayed bybthe attachment

Answers

Answer:

7 1/8

57/8

Hope this helps :)

The graph shows the function f(x) = 2*
What is the value of xwhen f(x) = 8?

Answers

Answer:

x=3

Step-by-step explanation:

f(x) = 2^x

Let f(x) =8

8 = 2^x

Rewriting 8 as 2^3

2^3 = 2^x

The bases are the same so the exponents are the same

3=x

Answer:

A. 3

Step-by-step explanation:

y = 2^x

y = 8

Plug y as 8 in the first equation.

8 = 2^x

Make the left side of the equation with a base of 2.

2^3 = 2^x

Cancel bases.

3 = x

. Mr. Wayne has a 3-year contract for his cell phone service. He pays $124.65 each month to cover everyone in his family. How much will the cell phone service cost over the 3-year period? Explain your answer​

Answers

Answer:

$4,523.40

Step-by-step explanation:

The cell phone cost is $124.65 per month. With 12 months in a year, we multiply $124.65 x 12 to get the answer $1,507.80. Since one year equals $1,507.80, we multiply this answer by 3 for 3 years to get $4,523.40. Thus three years of service with $124.65 a month would equal $4,523.40.

ε = {x: 2 x 30, x is an integer}, M = {even numbers}, P = {prime numbers}, T = {odd numbers} Find: I) MUP ii) M - T iii) P(MT) iv) P’U(MT’)

Answers

Answer:

Step-by-step explanation:

ε = {x: 2≤ x ≤30}

M = { even numbers} = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

P = { prime numbers} = {2,3,5,7,11,13,17,19,23,29}

T = {odd numbers} = {3, 5, 7, 9, 11,13,15,17,19,21,23,25,27,29}

1. M ∪ P = {2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30}

2. M - T =

n(M) - n(T)

15- 14 = 1

3. P(MT)

(MT) = M ∩ T = 0

P ∪ (M ∩ T ) = {2,3,5,7,11,13,17,19,23,29}

4. P' = not a prime number

T' = not odd number = M

P' ∪(M∩T')

P' ∪ {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

= {2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}

Towns K and L are shown on a map-
a) Work out the actual distance
between towns K and L.
b) A third town, M, is 150 km due
South of town K.
Mark M on the map with X.
c) Measure the bearing of town L
from town K.​

Answers

Answer:

a) Use a ruler for the measurement.

b) convert to centimetres then use a ruler to draw the unit on the diagram.

c) measure the angle between K and L from K

See explanations below

A complete question related to this found on brainly (ID:15577387) is stated below.

Towns K and L are shown on a map.

a) Work out the actual distance

between towns K and L.

b) A third town, M, is 150 km due

South of town K.

Mark M on the map with X.

c) Measure the bearing of town L

from town K.​

Scale: 1cm represent 50km

Step-by-step explanation:

Scale: 1cm represent 50km

a) To find the actual distance between towns K and L use a ruler to measure the distance between K and L.

Your answer would be in centimetres (cm).

The answer obtained would be multiplied by 50km because from the scale given 1cm represent 50km.

Therefore you'll get the actual distance in km.

b) Here we are told M is 150 km due

South of town K.

Since the length of the initial diagram is in centimeters, we have to find how many centimeters equals 150km.

50km = 1cm

150km = (150km × 1cm)/50km = 150cm/50

150km = 3cm

Now we can represent the distance between K and M on the diagram.

Measure 3cm from K using a ruler in the direction of south (straight line downwards). The distance of M from K would be 3cm on the south of k.

c) Draw a cross on the position of K. Also draw a cross on the position of L. Connect the distance and measure the angle from K to L. The unit would be in degrees.

From the diagram, the angle is greater than 090° but less than 180°

Find attached the diagram.

Answer:

a) 100 km

b) check the photo of my work

c) 117 degrees

Step-by-step explanation:

To get full marks take a look at the photo of my work.

Question (b) use a compass and make sure it’s 3cm aiming down {South} as u can see in the photo, then draw a line aiming {South} with a ruler. On the end of the line you put the (x) point there to get the mark.

Thank you

1
11 Kenzie monitors her investment on a technology
stock. She uses the expression 2013e2+, where t
is the time in years, to estimate the future value
of the stock. What is the meaning of 2013 in this
context?
A. beginning year
B. invested amount
C. future value
D. annual growth rate

Answers

Answer:

B

Step-by-step explanation:

The term 2013 in this context refers to the amount invested.

Mathematically, in finance, we can express the amount to be recouped on an investment, having a particular rate of return over a couple of years using the general formula;

V = P(1+r)^t

Such as in the case of amount obtained in a compound interest formula

Where P is the present value or principal or amount invested

V is the future value

r is the rate of investment

with t being the time taken

The box plots show the average speeds, in miles per hour, for the race cars in two different races. Average Speeds of Cars in Race A 2 box plots. The number line goes from 120 to 170. For Race A, the whiskers range from 120 to 170, and the box ranges from 143 to 165. A line divides the box at 153. For Race B, the whiskers range from 125 to 165, and the box ranges from 140 to 150. A line divides the box at 145. Average Speeds of Cars in Race B

Answers

Answer:

The median speed in race A is about 153 miles per hour, and the median speed in race B is about 145 miles per hour.

Step-by-step explanation:

For comparison, we need to analyze and compare both races data which are as follows

For Race A

Maximum range = 170 miles per hour

Minimum  range = 120 miles per hour

First quartile  ≈ 142 miles per hour

Median quartile ≈ 153 miles per hour

It comes from

[tex]= \frac{142\ miles + 165\ miles}{2}[/tex]

= 153 miles

The Third quartile = 165 miles per hour

For Race B

Maximum range  = 165 miles per hour

Minimum range = 125 miles per hour

First quartile  ≈ 139 miles per hour

Median quartile = 145 miles per hour

It comes from

[tex]= \frac{139\ miles + 150\ miles}{2}[/tex]

= 145 miles

The third quartile = 150 miles per hour

Hence, the last option is correct

Which metric unit would be best to measure the volume of water in a swimming pool?​

Answers

Answer:

HEY!

your answer is

it would be best to use litres

this is because a litre is 1000 millilitres and a swimming pool is a large amount of water.

Step-by-step explanation:

hope this helps

pls put brainliest

Work out the mean for the data set below:
3, 5, 4, 3, 5, 6
Give your answer as a fraction

Answers

Answer:

13/3

Step-by-step explanation:

To find the mean of a data set, you must add all the given numbers and then divide the numbers by how many numbers there are.

3+5+4+3+5+6=26/6=4.3333...

When we convert the answer from a decimal to a fraction, we get 13/3.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .

Answers

Answer:

The amount Sam invested the first year = $2000

The amount Sally invested the last year = $1900

Complete question related to this was found at brainly (ID 4527784):

For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.

During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.

If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .

Step-by-step explanation:

First we would represent the information given with mathematical expressions.

Sam investment for 3 consecutive years:

Year 1 = x dollars

Year 2 = $2,000 less than 5/2 times the amount he invested the first year

Year 2 = (5/2)(x) - 2000

Year 3 = $1,000 more than 1/5 of the amount he invested the first year

Year 3 = (1/5)(x) + 1000

Sally investment for 3 consecutive years:

Year 1 = $1,000 less than 3/2 times the amount Sam invested the first year

Year 1 = (3/2)(x) - 1000

Year 2 = $1,500 less than 2 times the amount Sam invested the first year

Year 2 = 2x - 1500

Year 3 = $1,400 more than 1/4 of the amount Sam invested the first year.

Year 3 = (1/4)(x) + 1400

Since Sam and Sally invested the same total amount at the end of three years, we would equate their sum:

Sum of Sam investment for the 3years = x + (5/2)(x) - 2000 + (1/5)(x) + 1000

= x + 5x/2 -2000 + x/5 + 1000

= (10x+25x+2x)/10 - 1000

= 37x/10 - 1000

Sum of Sally investment for the 3years = (3/2)(x) - 1000 + 2x - 1500 + (1/4)(x) + 1400

= 3x/2 - 1000 + 2x -1500 + x/4 + 1400

= (6x+8x+x)/4 - 1100

= 15x/4 - 1100

37x/10 - 1000 = 15x/4 - 1100

37x/10 - 15x/4 = -100

(148x - 150x)/40 = -100

-2x = -4000

x = 2000

Therefore the amount Sam invested the first year = x = $2000

The amount Sally invested the last year (3rd year) = (1/4)(x) + 1400

(1/4)(2000) + 1400 = 500+1400 = 1900

The amount Sally invested the last year = $1900



Use the given information to draw a box-and-whisker plot of the data set

Minimum – 28

Maximum – 54

Lower Quartile – 32

Upper Quartile – 40

Answers

Answer:

The box-and-whisker plot of this distribution is presented in the attached image to this solution.

Step-by-step explanation:

A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.

A box and whiskers plot shows 5 major information about the distribution of data. It shows:

- The maximum variable.

- The minimum variable.

- The Median.

- The first quartile.

- The third quartile.

Further info such as the range and Inter quartile range can then be obtained from this 5-number summary.

The elements of the box plot are described thus;

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.

The horizontal line inside the box is the median.

The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.

The required boxplot for this question is given in the attached image to this solution.

The median for the boxplot isn't provided, but it was assumed to be midway between the first and third quartile.

Hope this Helps!!!

The model below represents 2x+1=-X+4.

Answers

Answer:

x=1.

Step-by-step explanation:

2x + 1 = -x + 4

+x - 1 = +x - 1

3x. = 3

3/3. = x

1. = x

Solve for a 7a - 2b = 5a + b

Answers

Answer:

a=1.5b

Step-by-step explanation:

Add 2b on both sides to get 7a=5a+3b

Subtract 5a

2a=3b

divide by 2

a=1.5b

Which point is located at (4, -2)?
y
5
ТА
4
3
2+
1
2 3
Х
-5 -4 -3 -2 -11
-2
4 5
B
-4
D
b

Answers

Answer:

Point B of 4the quertant

ASAP! I do not accept nonsense answers, but BRAINLIEST will be given to the person who gets it correct with full solutions.

Answers

Answer:

A

Step-by-step explanation:

The range refers to the possible y-values.  You can assume that values on the right column are the y-values if it is not specifically expressed.  The right column is the output, or y, column.

Since you have a table, you have to state each number.  Put the numbers in numerical order.  This gives you an answer of

{46, 49, 52, 53, 58, 63, 64, 67}

How do you write r2/3 t1/3 in radical form?

Answers

I hope this helps you

Al saves pennies. He agreed to give six thirteenths of his pennies to Bev if she would give six thirteenths of what she got from Al to Carl and if Carl in turn would give six thirteenths of what he got from Bev to Dani.​ Bev, Carl, and Dani agreed and Dani received 2376 pennies. How many pennies did Al have​ initially?

Answers

Answer:

Step-by-step explanation:

Let x represent the number of pennies that Al had​ initially.

He agreed to give six thirteenths of his pennies to Bev. It means that the number of pennies that he gave to Bev is 6/13 × x = 6x/13

if she would give six thirteenths of what she got from Al to Carl, it means that the number of pennies that Carl received is 6/13 × 6x/13 = 36x/169

if Carl in turn would give six thirteenths of what he got from Bev to Dani and Dani received 2376 pennies, it means that

6/13 × 36x/169 = 2376

216x/2179 = 2376

216x = 2376 × 2179

216x = 5220072

x = 5220072/216

x = 24167

AI had 24167 pennies initially

Find the value of x
2x + 46 = 7x + 6

Answers

Answer:

7x-2x = 46-65x = 40 x = 40/5 x =8 ......

hope it helps .........

Answer:

so x=8

Step-by-step explanation:

2x+46=7x+6

subtracting 7x on both sides

2x-7x+46=7x-7x+6

-5x+46=6

subtracting 46 on both sides

-5x+46-46=6-46

-5x=-40

5x=40

x=8

i hope this will help you :)

A restaurant catered an event for 25 people. A child’s dinner cost $5 and an adult’s dinner cost $22. The party cost $431. How many children were in attendance? How many adults were in attendance?

Answers

Answer:

7 Children and 18 Adults.

Step-by-step explanation:

Sorry im late but thats the answer ^

There was 7 children attendee and 17 adult attendee.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

A restaurant catered an event for 25 people.

A child’s dinner cost $5 and an adult’s dinner cost $22.

The party cost $431.

let the number of children attendee be x and adult attendee be y.

So, x+ y = 25..............(1)

and, 5x + 22y = 431.......(2)

Solving the Equation (1) and (2) we get

5(25 - y) + 22y= 431

125 - 5y + 22y= 431

17y = 431-125

17y = 306

y = 18

and, x= 25-18 = 7

Hence, there was 7 children attendee and 17 adult attendee.

Learn more about Equation here:

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Large samples of women and men are​ obtained, and the hemoglobin level is measured in each subject. Here is the​ 95% confidence interval for the difference between the two population​ means, where the measures from women correspond to population 1 and the measures from men correspond to population​ 2: negative 1.76 g divided by dL less than mu 1 minus mu 2 less than minus 1.62 g divided by dL. Complete parts​ (a) through​ (c) below.
a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men? Because the confidence interval does not include includes nothing​, it appears that there is is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men. ​(Type an integer or a decimal. Do not​ round.)
b. Write a brief statement that interprets that confidence interval.
A. There is​ 95% confidence that the interval from minus 1.76 g divided by dL to minus 1.62 g divided by dL actually contains the value of the difference between the two population means left parenthesis mu 1 minus mu 2 right parenthesis .
B. There is​ 95% confidence that the difference between the two population means left parenthesis mu 1 minus mu 2 right parenthesis is either minus 1.76 g divided by dL or minus 1.62 g divided by dL .
C. There is​ 95% confidence that the difference between the two population means is not 0.
D. There is​ 95% confidence that the interval from minus 1.76 g divided by dL to minus 1.62 g divided by dL does not contain the value of the difference between the two population means left parenthesis mu 1 minus mu 2 right parenthesis .
c. Express the confidence interval with measures from men being population
1. and measures from women being population
2. Choose the correct answer below.
A. negative 1.62 g divided by dL less than mu 1 minus mu 2 less than 1.76 g divided by dL
B. negative 1.76 g divided by dL less than mu 1 minus mu 2 less than minus 1.62 g divided by dL
C. 1.62 g divided by dL less than mu 1 minus mu 2 less than 1.76 g divided by dL
D. negative 1.76 g divided by dL less than mu 1 minus mu 2 less than 1.62 g divided by dL.

Answers

Answer:

(a) Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

(b) The correct option is (A).

(c) The correct option is (C).

Step-by-step explanation:

The 95% confidence interval for the difference between the two population​ mean hemoglobin level is:

CI = (-1.76 < μ₁ - μ₂ < -1.62)

(a)

The hypothesis to test the equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men is:

H₀: The two population means are equal, i.e. μ₁ = μ.

Hₐ: The two population means are not equal, i.e. μ₁ ≠ μ.

The (1 - α)% confidence interval can be used to draw conclusion about the hypothesis test.

Decision rule:

If the (1 - α)% confidence interval does not consist of the null value then the null hypothesis will be rejected and vice-versa.

The 95% confidence interval for the difference between the two population​ means is:

CI = (-1.76, -1.62)

The 95% confidence interval does not consist of the null value, i.e. 0.

Thus, the null hypothesis will be rejected.

"Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men."

(b)

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

So, the 95% confidence interval (-1.76, -1.62) implies that there is a 95% confidence that the above interval actually contains the value of the difference between the two population means, (μ₁ - μ₂).

The correct option is (A).

(c)

Now it is provided that the measures from men is denoted as population  1 and measures from women is denoted as population  2.

The confidence interval for the difference between two mean is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm MOE[/tex]

According to the information:

[tex]\bar x_{1}=\bar x_{2}\\\\\bar x_{2}=\bar x_{1}[/tex]

So, the new confidence interval will be:

[tex]CI=-(\bar x_{2}-\bar x_{1})\pm MOE[/tex]

Then the confidence interval with measures from men being population

1 and measures from women being population  2 is:

[tex]CI=(1.62<\mu_{1}-\mu_{2}<1.76)[/tex]

The correct option is (C).

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