tina has a doll which she can dress with a hat, a scarf and a jacket.
she has 3 different colour hat, 4 different colour scarves and 5 different colour jackets
Tina chose a hat a scarf and a jacket for her doll
how many combinations of hat scarf and jacket can she choose ​

Answer:

  c.  x>1/2

Step-by-step explanation:

Distribute the -2 to eliminate parentheses:

  6x -2x -2 > 0

  4x -2 > 0 . . . . . . combine terms

Now, you can divide by 4:

  x -2/4 > 0

and add 1/2

  x > 1/2 . . . . . matches choice C

Answer:

[tex]x > \frac{1}{2} [/tex]

Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 1390

x = 514

p = 514/1390 = 0.37

q = 1 - 0.37 = 0.63

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.01 = 0.99

The z score corresponding to the area on the z table is 2.33. Thus, confidence level of 98% is 2.33

Therefore, the 98% confidence interval is

0.37 ± 2.33√(0.37)(0.63)/1390

Confidence interval = 0.37 ± 0.0302

Answer: = ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 65.3

Standard deviation r = 5.2

Number of samples n = 36

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

65.3 +/-1.645(5.2/√36)

65.3 +/-1.645(0.86667)

65.3+/- 1.4257

65.3+/- 1.4

= ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

Answer:

1) b1=5.831

2) b0=12.510

3) y(34)=210.764

4) y(0)=12.510

5) y=12.510+5.831x

6) R^2=0.85

Step-by-step explanation:

We have the linear regression model [tex]y=b_0+b_1 x[/tex].

We start by calculating the all the parameters needed to define the model:

- Mean of x:

[tex]\bar x=\dfrac{1}{5}\sum_{i=1}^{5}(2+3+4+5+7)=\dfrac{21}{5}=4.2[/tex]

- Uncorrected standard deviation of x:

[tex]s_x=\sqrt{\dfrac{1}{n}\sum_{i=1}^{5}(x_i-\bar x)^2}\\\\\\s_x=\sqrt{\dfrac{1}{5}\cdot [(2-4.2)^2+(3-4.2)^2+(4-4.2)^2+(5-4.2)^2+(7-4.2)^2]}\\\\\\ s_x=\sqrt{\dfrac{1}{5}\cdot [(4.84)+(1.44)+(0.04)+(0.64)+(7.84)]}\\\\\\ s_x=\sqrt{\dfrac{14.8}{5}}=\sqrt{2.96}\\\\\\s_x=1.72[/tex]

- Mean of y:

[tex]\bar y=\dfrac{1}{5}\sum_{i=1}^{5}(25+33+34+45+48)=\dfrac{185}{5}=37[/tex]

- Standard deviation of y:

[tex]s_y=\sqrt{\dfrac{1}{n}\sum_{i=1}^{5}(y_i-\bar y)^2}\\\\\\s_y=\sqrt{\dfrac{1}{5}\cdot [(25-37)^2+(33-37)^2+(34-37)^2+(45-37)^2+(48-37)^2]}\\\\\\ s_y=\sqrt{\dfrac{1}{5}\cdot [(144)+(16)+(9)+(64)+(121)]}\\\\\\ s_y=\sqrt{\dfrac{354}{5}}=\sqrt{70.8}\\\\\\s_y=8.414[/tex]

- Sample correlation coefficient

[tex]r_{xy}=\sum_{i=1}^5\dfrac{(x_i-\bar x)(y_i-\bar y)}{(n-1)s_xs_y}\\\\\\r_{xy}=\dfrac{(2-4.2)(25-37)+(3-4.2)(33-37)+...+(7-4.2)(48-37)}{4\cdot 1.72\cdot 8.414}\\\\\\r_{xy}=\dfrac{69}{57.888}=1.192[/tex]

Step 1

The slope b1 can be calculated as:

[tex]b_1=r_{xy}\dfrac{s_y}{s_x}=1.192\cdot\dfrac{8.414}{1.72}=5.831[/tex]

Step 2

The y-intercept b0 can now be calculated as:

[tex]b_o=\bar y-b_1\bar x=37-5.831\cdot 4.2=37-24.490=12.510[/tex]

Step 3

The estimated value of y when x=34 is:

[tex]y(34)=12.510+5.831\cdot(34)=12.510+198.254=210.764[/tex]

Step 4

At x=0, the estimated y takes the value of the y-intercept, by definition.

[tex]y(0)=12.510+5.831\cdot(0)=12.510+0=12.510[/tex]

Step 5

The linear model becomes

[tex]y=12.510+5.831x[/tex]

Step 6

The coefficient of determination can be calculated as:

[tex]R^2=1-\dfrac{SS_{res}}{SS_{tot}}=1-\dfrac{\sum(y_i-f_i)}{ns_y^2}\\\\\\\sum(y_i-f_i)=(25-24.17)^2+(33-30)^2+(34-35.83)^2+(45-41.67)^2+(48-53.33)^2\\\\\sum(y_i-f_i)=0.69+ 8.98+ 3.36+ 11.12+ 28.38=52.53\\\\\\ ns_y^2=5\cdot 8.414^2=353.98\\\\\\R^2=1-\dfrac{52.53}{353.98}=1-0.15=0.85[/tex]

Answer: (7,3)

Step-by-step explanation:

The coordinates of point B(7, 3).

The formula below gives the coordinates of the point A(x, y), which internally splits the line segment between the points P([tex]x_1[/tex],  [tex]y_1[/tex]) and Q([tex]x_2[/tex], [tex]y_2[/tex]) in the ratio [tex]m_1[/tex]: [tex]m_2[/tex],

A (x, y) = [tex]((m_1 x_2 + m_2 x_1) / ( m_1 + m_2), \;\; (m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]

Given:

Point A is (-7, 5) and point M is at (0, 4).

and, Point M is the midpoint of point A and Point B.

A (x, y) = [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]

So, x= [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]

0 = ( 1 x [tex]x_2[/tex] + 1 x (-7)) / (1 + 1)

0 = [tex]x_2[/tex] - 7

[tex]x_2[/tex] =7

and, y= [tex](m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]

4= ( 1 x [tex]y_2[/tex] + 1 x 5)/ 2

8 = [tex]y_2[/tex] + 5

[tex]y_2[/tex] = 3

Hence, the coordinates of B(7, 3).

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Answer:

Quiana has 8 text messages from Pierre.

Step-by-step explanation:

This question can be solved using a rule of three.

Quiana has 7 times more text messages from Yolanda than from Pierre.

This means that for each message that she receives from Pierre, she receives 7 from Yolanda.

She received 56 from Yolanda.

So

7 messages from Yolanda - 1 messages from Pierre

56 messages from Yolanda - x messages from Pierre

[tex]7x = 56[/tex]

[tex]x = \frac{56}{7}[/tex]

[tex]x = 8[/tex]

Quiana has 8 text messages from Pierre.

Quiana has 8 text messages from Pierre.

To find how many text messages Quiana has from Pierre, represented as p, given that Quiana has 7 times more text messages from Yolanda than from Pierre, and she received 56 text messages from Yolanda, we can set up the following equation:

p × 7 = 56

To solve for p, we divide both sides of the equation by 7:

p = 56 ÷ 7

p = 8

So, Quiana has 8 text messages from Pierre.

Answer:

4/5 and 1

Step-by-step explanation:

4/5 is greater then 3/5 and 5/5=1 whole which is greater than 3/5, 4/5 and 1 is greater than 3/5 and 1 1/5, 1 2/5 so on and so on it could go forever but 4/5, and 1 is the only ones that our after 3/5 so those are the two greatest ones in this quistion.

Hope this helps.

The  two values are 4 by 5 and 1

The following information should be considered:

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Answer:

Yessirrr you are!!!

Step-by-step explanation:

The correct student is Dean.

To determine which student is correct, let's analyze the information given in the box plots for both classes:

For Mr. Yan's class, the box plot shows:

- Minimum value (lower whisker): 1

- Maximum value (upper whisker): 9

- Lower quartile (Q1): 2

- Median (Q2): 4

- Upper quartile (Q3): 7

- Interquartile range (IQR): Q3 - Q1 = 7 - 2 = 5

For Mrs. Gonzalez's class, the box plot shows:

- Minimum value (lower whisker): 1

- Maximum value (upper whisker): 9

- Lower quartile (Q1): 4

- Median (Q2): 5.5

- Upper quartile (Q3): 7

- Interquartile range (IQR): Q3 - Q1 = 7 - 4 = 3

Now let's evaluate each student's statement:

- Nadine: The medians are the same because both sets of data have the same minimum and maximum values. This statement is incorrect because the medians are different. Mr. Yan's class has a median of 4, while Mrs. Gonzalez's class has a median of 5.5.

- Kendrick: Mr. Yana's class has a greater median because the box in that box plot is larger. This statement is incorrect because the size of the box does not determine the median. The median is the value that divides the data into two equal halves, and it is indicated by the line inside the box.

- Tahara: Mrs. Gonzalez's class has a greater median because the line inside that box is located at a greater value. This statement is correct. The median for Mrs. Gonzalez's class is 5.5, which is greater than the median for Mr. Yan's class, which is 4.

- Dean: The medians are both 7 because the upper quartile for the sets of data is 7. This statement is incorrect because the median is not determined by the upper quartile but by the value that separates the higher half from the lower half of a data sample.

Therefore, the only correct statement is made by Tahara, who correctly identifies that Mrs. Gonzalez's class has a greater median because the line inside the box is located at a greater value (5.5) compared to Mr. Yan's class (4).

The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

On a coordinate plane, a graph has a number of hours on the x-axis and a number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).

We know that the equation of the line passing through the two-point is given as

[tex]\rm (y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Then we have

[tex]\rm y-1 = \dfrac{2-1}{4-2} \times (x-2)\\\\y = \dfrac{1}{2}\ x - 1+1 \\\\y = \dfrac{1}{2}\ x[/tex]

The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.

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Answer:

first one is 1/2 second one is y = 1/2 x

Hope it helps!!!

Answer:

The sample consisting of 64 data values would give a greater precision.

Step-by-step explanation:

The width of a (1 - α)% confidence interval for population mean μ is:

[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]

So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).

That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.

Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.

The two sample sizes are:

n₁ = 25

n₂ = 64

The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.

Width for n = 25:

[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]        

Width for n = 64:

[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]

Thus, the sample consisting of 64 data values would give a greater precision

Answer:

Confidence Interval with sample size 25 = Broader, less precision; Confidence Interval with sample size 64 = Narrower, more precision

Step-by-step explanation:

Confidence Interval is the range around sample statistic, which contains the actual population parameter. Confidence level is the percentage probability, with which the population parameter is expected to be in confidence interval.

When sample size increases : the margin of error, ie sampling error between population parameter & sample statistic decreases. The reduced margin of error increases the level of confidence & precision in confidence interval range. So, the confidence interval range becomes narrower.  

Hence, confidence interval becomes narrower & has more precision, when sample size increases from sample number = 25 to sample number = 64.

Answer:

0.00205%

Step-by-step explanation:

Use binomial probability:

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

n = 30, r = 24, p = 0.42, and q = 0.58.

P = ₃₀C₂₄ (0.42)²⁴ (0.58)³⁰⁻²⁴

P ≈ 0.00205%

Answer:

33 yd

Step-by-step explanation:

To find the area of a triangle, you can follow the formula:

(base x height) / 2

By putting this formula into context, you can substitute the values of the terms with the information provided in the problem:

(base x height) / 2

(11 yd x 6 yd) / 2

66 yd / 2

33 yd

Answer:

Neither

Step-by-step explanation:

In direct variation, as one number increases, the other number also increases and as one number decreases, the other number also decreases. In inverse variation, as one number increases, the other number decreases and as as one number decreases, the other number increases.

For direct variation, [tex]y=kx[/tex] and for indirect variation, [tex]y=\frac{k}{x}[/tex] where k is a constant.

x  2    5   20  40

y  40  20  5     2

Here,

[tex]\frac{2}{40}=\frac{1}{20}\\ \frac{5}{20}=\frac{1}{4}\\ \frac{20}{5}=4 \\\frac{40}{2} =20[/tex]

So, this is neither a direct variation nor an indirect variation.

Answer

The circumference of a circle is the length of its side, the area is the amount of space within it.

Step-by-step explanation:

The circumference of a circle represents the distance around the circle's boundary, while the area represents the surface area enclosed by the circle.

The difference between the circumference and area of a circle lies in their respective measurements and what they represent.

Circumference: The circumference of a circle is the measurement of the distance around the outer boundary of the circle. It is essentially the perimeter of the circle. The circumference is calculated using the formula:

Circumference = 2πr or πd

Where r represents the radius of the circle and d represents the diameter. It is a linear measurement and is typically expressed in units such as centimeters, inches, or meters.

Area: The area of a circle is the measurement of the region enclosed by the circle's boundary. It represents the total surface area within the circle. The area of a circle is calculated using the formula:

Area = πr²

Where r represents the radius of the circle. The area is a two-dimensional measurement and is typically expressed in square units such as square centimeters, square inches, or square meters.

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Answer:

y = -1/4x +4

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

-2x-8y = -32

Add 2x to each side

-2x+2x-8y =2x -32

-8y = 2x-32

Divide each side by -8

-8y/-8 = 2x/-8 -32/-8

y = -1/4x +4

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W  

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W    

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Let [tex]\mu[/tex] = mean power consumption of microwave ovens.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W  

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W    

Here, null hypothesis states that the mean power consumption of microwave ovens is no more than 250 W.

On the other hand, alternate hypothesis sates that the mean power consumption of microwave ovens is more than 250 W.

The test statistics that would be used here is One-sample z test statistics as we know about the population standard deviation;

                       T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.

Answer:

Step-by-step explanation:

Let x represent the quantity (in liters) of the higher percentage solution, the 0.23% solution. Then 1-x will be the quantity of 0.03% solution. The amount of salt in the mix is ...

  0.23%·x +0.03%·(1 -x) = 0.18%·1

Multiply by 100% and subtract 3:

  20x = 15

  x = 15/20 = 0.75 . . . . liters of 0.23% solution

  1-x = 1-0.75 = 0.25 . . liters of 0.03% solution

The lab tech needs 750 mL of 0.23% solution and 250 mL of 0.03% solution.

Answer:

Here, we have BC // ST, by applying Thales theorem:

UB/US = UC/UT

=>UB = UC x US/UT =6 x 12/(6 + 18) = 3

=> x = US - UB = 12 - 3 = 9

=> Option C is correct.

Hope this helps!

:)

Answer:

D.) 108 in.2

Step-by-step explanation:

Use the equations you know to help you figure this out. It may not be easy, but for you to understand, you need to learn how to do it. If you want work, try it out.. Not to be rude...

Answer:

D) 108 inches squared.

Step-by-step explanation:

When you have the height of a pyramid, you must find the area of the base. Then multiply the base and height. When you find the product, divide this by three. There's your answer.

Answer:

0.5

Step-by-step explanation:

The sample space of a fair six-sided die and a fair four-sided die rolled simultaneously is given below:

[tex](1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\[/tex]

where in each pair (x,y), x represents the four-sided die and y represents the six sided die.

Total Number of Possible Outcomes =24

Event A is the event that the six-sided die is an even number.

n(A)=12

Therefore, the probability that the six-sided die is an even number:

P(A)=12/24=0.5

Answer:

Step-by-step explanation: (2x-4)-(6x+6)

= 2x -4 - 6x - 6        [ opening brackets]

= 2x-6x -4-6                   [ bringing the same variables and numbers together]

= -4x-10

=2(2x-5)

Answer:

-4x-10

The 6x + 6 becomes negative due to the negative sign before the parenthesis. You then subtract 6x and 6 from 2x and -4 to get -4x-10

Answer:

- 1. 15

Step-by-step explanation:

Z score is used in statistic to calculate deviation of an observed value from mean value of sample of observation.

Mathematically it is given by

[tex]z = observed \ value - mean\ value/ standard\ deviation[/tex]

using the above formula and substituting the value of of

mean = $42,800

standard deviation = $8,365

observed value =$30,000

Z = (8,365 - 42,800) / $30,000

   =  - 34,435/ 30,000 =  - 1. 14783

  = - 1. 15 ( to the nearest hundredth)

- 1. 15  Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000

Answer:180

Step-by-step explanation:

100 - 10 is 90

90 x 2 is 180

I did a reverse calculation you can also check this is correct by knowing that half of 180 is 90 and 100 dollars is 10 more than 90 dollars.

Answer:

The value of test statistics is 25.

Step-by-step explanation:

We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;

380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560

Let [tex]\sigma[/tex] = population standard of the reading and writing section SAT score of the students in this school

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \leq[/tex] 100     {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma[/tex] > 100     {means that the reading and writing section SAT score of the students in this school is higher than 100}

The test statistics that would be used here is One-sample Chi-square test statistics;

                        T.S. =  [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2} __n_-_1[/tex]

where, [tex]s^{2}[/tex] = sample variance =  [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]  = 13135.8

            n = sample of 11th-grade students = 20

So, the test statistics  =  [tex]\frac{(20-1)\times 13135.8^{2} }{100^{2} }[/tex]

                                     =  24.96 ≈ 25

Hence, the value of test statistics is 25.

Answer: (-2,3)

Step-by-step explanation:

Answer:

25.1

Step-by-step explanation:

area = pi x r x r

r x r = 50.3 / pi = 16.0109

r = 4.00137

circumference = pi x 2 x r = pi x 2 x 4.00137 = 25.141

Answer:

Null hypothesis: H0 = 0.50

Alternative hypothesis: Ha > 0.50

z = 3.16

P value = P(Z>3.16) = 0.0008

Decision: we reject the null hypothesis and accept the alternative hypothesis. That is, the clerk used a method favoring Party A.

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 95% confidence interval) ---- reject Null hypothesis

Z score < Z(at 95% confidence interval) ------ accept Null hypothesis

Step-by-step explanation:

Given;

n = 40 represent the number of samples taken

Null hypothesis: H0 = 0.50

Alternative hypothesis: Ha > 0.50

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 40

po = Null hypothesized value = 0.50

p^ = Observed proportion = 30/40 = 0.75

Substituting the values we have

z = (0.75-0.50)/√(0.50(1-0.50)/40)

z = 3.16227766

z = 3.16

To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.

P value = P(Z>3.16) = 0.0008

Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 3.16) which doesn't falls with the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0008 which is lower than 0.05. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.

The length of the 'top' vector is sqrt(3^2 + 3^2) = 3sqrt2

The length of the 'bottom' vector is sqrt(4^2 + 1^2) = sqrt17

Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean. A 95% confidence interval does not mean 95% probability. It is used to express how confident we are that the true population parameter lies within the confidence interval.

With a lower limit of 10.6 and an upper limit of 29.1, and confidence interval of 95%, the correct option is

With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.

Final answer:

The 95% confidence interval represents the range within which the true mean of all widgets is likely to fall, not the individual sample mean.

Explanation:

A 95% confidence interval for widget width of 10.6 < μ < 29.1 means:

With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.

There is not a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.

Therefore, the correct interpretations are A and F.