the wall thickness of 21 randomly selected glass 2-liter bottles was measured by a quality-control engineer. the wall thickness of those glass 2-liter bottles follows a normally distribution with unknown variance. the sample mean and the sample standard deviation of those 21 selected bottales was found to 4.15 millimeters and 0.09 millimeter, respectively. which of the following is the correct 90% two-sided confidence interval for the mean wall thickness?

a) The expected value for distribution A is equal to 1 and expected value for distribution B is equal to 3. b) The value of standard deviation of two distributions is same. c)  A is less than the expected value for the distribution B.

The calculation for expected value of distribution of A is given as,

E(X) = ∑[tex]^{n}[/tex][tex]_{i=1}[/tex]= [tex]X_{i}[/tex]. P (X=x)

       =0⋅ (0.50 )+1⋅(0.20)+....+4⋅0.05=1

E(X) = ∑i=1nXi.P(X=x)=0⋅(0.50)+1⋅(0.20)+....+4⋅(0.05)=1

The calculation for expected value of distribution of B is given as,

E(X)=n∑i=1 Xi.P(X=x)

      =0⋅(0.05)+1⋅(0.1)+....+4⋅(0.50)=3

E(X)=∑i=1nXi.P(X=x)=0⋅(0.05)+1⋅(0.10)+....+4⋅(0.50)

     =3

Therefore, the expected value for distribution A is equal to 1 and expected value for distribution B is equal to 3.

(b) The formula for standard deviation is given as,

σ=√E(X2)−E(X))2

The calculation for the E(X2) of distribution A is given as,

E(X2)=n∑i=1 X2i⋅P(X=x)

        =02⋅(0.50)+12⋅(0.20)2+.....+42⋅(0.05)=2.5

The calculation for the E(X2) of distribution B is given as,

E(X2)=n∑i=1 X2i⋅P(X=x)

        =02⋅ 0.05)+12⋅(0.10)+......+42⋅(0.50)

        =10.5

E(X2)=∑i=1nXi2⋅P(X=x)=02⋅(0.05)+12⋅(0.10)2+......+42⋅(0.50)

       =10.5

The value of standard deviation for the distribution A is given as,

σA=√2.5−12

   =1.225

The value of standard deviation for the distribution B is given as,

σB=√10.5−32

   = 1.225

Therefore, the value of standard deviation of two distributions is same.

(c) The expected value for distribution A is less than the expected value for the distribution B. The standard deviation is same for both distributions; the spread between both the distributions is same. Therefore, the distribution B is better than distribution A.

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well, we know that it was 195 in 1992, so "t" years later that'd be

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &195\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ t=years\dotfill &t\\ \end{cases} \\\\\\ A=195(1 + 0.012)^{t} \implies A =195(1.012)^t[/tex]

As the sample size increases the mean is 100 , if n = 1000 , the mean of the sample means will be unchanged  .

In the question ,

from the table we can observe that ,

if n = 1 , the mean is 97.656 ,

if n = 5 , the mean is 100.101 ,

if n = 10 , the mean is 100.006 ,

if n = 100 , the mean is 100.341 ,

from the table we notice that as the sample size increases from 1 to 100 , the means of the sample means are same that is 100 .

we can see that for every n , the mean is approximately equal to 100 ,

So , if n = 1000 , then the mean will also be approximately equal to  100 .

Therefore , the mean of the sample means will be unchanged .

The given question is incomplete , the complete question  is

Focus on the means. What do you notice about the means of the sample means as the sample size increases from 1 to 100? What would you expect the mean of the sample means to equal if n = 1000 ?

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Hence, he sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality is [tex](b+18.4)\geq -3.8[/tex].

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

The sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality.

Let [tex]b[/tex] be the number

As it is mentioned that the sum of [tex]x[/tex] and [tex]18.4[/tex] is at least [tex]-3.8[/tex].

Hence, the sum is greater or equal to [tex]-3.8[/tex]

i.e., [tex](b+18.4)\geq -3.8[/tex]

Hence, he sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality is [tex](b+18.4)\geq -3.8[/tex].

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The length of the 3rd side of the given triangle with 6 units and 9 units being the length of the 1st and 2nd side can be:

(B) 4 units

(C) 7 units

(F) 10 units

(E) 12 units

A triangle is a polygon with three vertices and three sides.

The angles of the triangle are formed by the connection of the three sides end to end at a point.

The triangle's three angles add up to 180 degrees in total.

So, knowing that the third side of a triangle must be longer than the sum of the first two sides and shorter than the difference between the first two sides allows us to obtain:

x > (9-6) so x > 3 and x < (9+6) so x < 15

Based on these findings, the third side length can be chosen from B. 4, C. 7, F. 10, and E. 12.

Therefore, the length of the 3rd side of the given triangle with 6 units and 9 units being the length of the 1st and 2nd side can be:

(B) 4 units

(C) 7 units

(F) 10 units

(E) 12 units

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Complete question:
A triangle has two sides of lengths 6 and 9. What value could the length of the third side be? Check all that apply

A.15

B.4

C.7

D.2

E.12

F.10

Answer:

Part A: The LSRL is y^ = 7.76 + 0.6x.

Part B: y^ = 7.76 + 0.6(19.5) = 19.46

y^ = 19.46%

Part C: 22.7 - 19.46 = 3.24. The residual is 3.24. This means that the value was underpredicted. 

Step-by-step explanation:

The room is 10 ft by 12 ft

The area of the room = 120 sq ft

1 yard= 3 feet

1 square yard=9 sq feet

The area of the room = 120 sq ft or 120/9=13.33 sq yards

Answer: 13.33 sq yards

"The scatter plot shows a linear association."  

What is scatter plot ?

Several dots are plotted on horizontal and vertical axes to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences (called variables).

But how?  Well, linear means: "arranged in or extending along a straight or nearly straight line." Which if you didn't notice.. All the points on the graph, make up a generally straight line.

"No association" means there is no line or association with any of the points.  So, you'd pick that if the points were all over the graph in no order, line or combination; which isn't the case.  

"Negative association" is when the top of the points come from the left of the graph lowering into the right. While Positive association would be from right to left.  So, it couldn't be choice "Negative Association" since it's coming from right to the left of the graph.

"The point  (2, 14) is an outlier."  If you didn't know, an outlier is one dot out of a whole group.  Think of it as if EVERYONE was wearing pink except one; who wore black.  It's just the out of placed kind of dot; but it's supposed to be there.  When you look at the graph, there is no dot or outlier at point (2,14) so, that's automatically out as well.

Ending with the last choice "The scatter plot shows a linear association." which is not just true but is the only one that'd make since.

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The average commute for 95% of the students is between 19.0 and 4.2 miles.

The average distance is 19 miles.

Therefore, the standard deviation is 4.2 miles.

A) 2.7 = 19 - a(4.2)

where;

a deviates from the mean by a certain number of standard deviations. Thus;

a = (19 - 2.7) ÷ 4.2

a = 3

In a normal distribution, 3 standard deviations from the mean indicate that 95% of the data falls within that range.

B) The data are 2 standard deviations apart from the mean at the 95% confidence level. Thus;

CI = 19 ± 2(4.2)

CI = (18 - 10.2) OR (18 + 10.2)

CI = (7.8, 28.2)

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Answer:

Point on the line: (0, 15)

Slope: 3

Step-by-step explanation:

Step 1: Put the equation in slope-intercept form

    The slope-intercept form is written like this: y = mx + b

    m = slope

    b = y-intercept

    1. y = 3 + 3(x + 4) → y = 3x + 15

Step 2: Retrieve the values from the equation

    y-intercept = 15

    slope = 3

Probability - The answer to the problem is P(Y = 4) = 3/32

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

Mean = 120

Standard Deviation = 5

Z = (X - Mean)/Standard Deviation

Z = 1/2

(i) P(Y = 4) = 6/4 * (1/2)^2 * (1-1/2)^6-4

P(Y = 4) = 3/2 * 1/4 * 1/4

P(Y = 4) = 3/32

(ii)P(X > 500) = 1 - P(X ≤ 500)
= 1 - Φ(500; 480, 10)
= 1 - 0.9772
= 0.0228

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a. test statistic =  1.35

p-value =  0.198439

b. Support the null hypothesis.

So you have the hypothesis:

H₀:μ=4

H₁:μ≠4

with the sample information you calculate the statistic using the t-distribution with 14 (n-1) degrees of freedom:

t=x[bar] - μ ⇒ t=  4.8 - 4    =  0.8   = 1.347≅ 1.35

   s/√n               2.3/√15     0.59

The p-value is defined as the probability corresponding to the calculated statistic (or of obtaining a value as extreme as the value of the statistic) if possible under the null hypothesis.

p-value: 0.198439

b.

Since the calculated p-value is greater than the significance level, you don't reject the null hypothesis.

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The exponential equation that models the population of the bacteria is:

y = 5*(7)^x

The general exponential equation is of the form:

y = A*(b)^x

Where A is the initial value, b is the base, and x is the variable.

Initially, Zach counted 5 bacteria, then:

A = 5

And we know that after one hour, Zach saw 35 bacteria, then we can write the equation:

35 = 5*(b)^1

35 = 5*b

35/5  =b

7 = b

Then the exponential equation is:

y = 5*(7)^x

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Answer:

-5/6=-1/4-7/10 x /×60

60×(-5/6)=60×(-1/4)+60(-7/10 x)

-50=-15-42 x

-50+15=-42 x

-35=-42 x

35=42 x

x=35/42

x=5/6

Angles 1 and 2 are neighboring, hence the fourth choice is accurate. Angles 1 and 2 are adjacent.

The term "Angle" refers to the separation between line segments or rays that converge at a single point.

The following may be said about angles 1 & 2:

In a line that proceeds from left to right, there is a ray in the middle that forms a right angle, a second ray between the two right angles, and one light that labels both the left angle and the right angle.

We can draw just as in the image.

Angles 1 and 2 are neighboring because they share a vertex, as seen in the image.

Angle 2 equals 90 degrees

Angle 1 equals 45 degrees

Angles 1 and 2 are adjacent, so option 4 is correct because it describes the relationship between them.

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According to the empirical law of statistics, 99.7% of the males are between 54.5" and 81.5" tall.

The 68-95-99.7 rule, also known as the empirical rule, indicates where most of the values in a normal distribution are distributed: The majority of values—about 68%—fall within the range of the mean. The average value is within two standard deviations for about 95% of the data. Almost all values, 99.7% of them, fall within a 3 standard deviation range.

Here,

mean=68 inch

standard deviation=4.5 inch

The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.

68−4.5=63.5

68+4.5=72.5

The range of numbers is 63.5 to 72.5

The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.

68−2⋅4.5=59

68+2⋅4.5=77

The range of numbers is 59 to 77

Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.

68−3⋅4.5=54.5

68+3⋅4.5=81.5

The range of numbers is 54.5 to 81.5

99.7% of the boys are between 54. 5 and 81. 5 inches tall using the empirical rule of statistics.

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The probability that headway is within 1 standard deviation of the mean value is 0.890.

What is mean value?

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

The mean of a discrete probability distribution of a random variable X is equal to the sum over all possible values weighted by the likelihood of each value. To calculate the mean, one must multiply each potential value of X by its probability P(x), then add all of these products.

Given mean value is P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995).

The cdf for the distribution is

[tex]F(x)=\left \{ {{1 -\frac{1}{x^6} ,x > 1} \atop {0,x\le 1}} \right.[/tex]

Now calculate the value of F(1.445) and F(0.995).

F(1.445) = 1 - (1/(1.445)⁶)

F(0.995) = 0

Now putting the value of F(1.445) and F(0.995) in  P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995):

P( 0.995 ≤ x ≤ 1.445)

=1 - (1/(1.445)⁶)  - 0

=0.890

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the limit of f (x) g(x) exists as x!0 is exist.

what is function existance ?

The EXISTS function returns a Boolean value to indicate whether a list contains at least one element.

let,

f(x)  =  1    at x=Q

also, f(x)  = -1  at x=Q'

now, g(x)  = -1  at x = Q

also, g(x) = 1 at x = Q'

Here,

[tex]\lim_{n \to \infty} f(x)[/tex]      and [tex]\lim_{n \to \infty} g(x)[/tex]   does not exist.

but,    f(x) + g(x)  =  (f+g)(x) = 0 at x = Q and also at x = Q'

⇒  (f+g)(x) = 0 ∀ x∈IR

⇒   [tex]\lim_{n \to \infty} (f+g)(x)[/tex]  = 0 exist.

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The revised values of the mean and standard deviation are respectively; 154 cm and 5 cm

Let us assume that the number of Patients is denoted as P. We are given;

Mean = 156 cm

We know that mean here is gotten from the formula;

Mean = Total height/number of patients

Thus;

Total Height = 156P  cm

We are told that each height was measured 2 cm more. Thus;

Total height reduction = 2P cm

Thus;

Actual Total Height = 156P - 2P = 154P cm

Mean = 154P/P  = 154  cm

Therefore, as each reading and mean both have shifted by 2 then Standard deviation will remain same as 5cm

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The pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

It is given that:

In a mixture of raisins and dates, the ratio by weight of raisins to dates is 7 to 3

Let the common factor be x:

7x = raising

3x = dates

7x + 3x = 7

10x = 7

x = 7/10

7x = 7(7/10)

Raisin =  49/10 pounds

Thus, the pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.

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Answer:

-2, -6

-1, -3

0,0

1,3

2,6

Step-by-step explanation:

nsd fbvdvjben ebtv

Step-by-step explanation:

when x is -2 y is y=3x

y=3×-2

y=-6 do that for all

The likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.

Here,

If the first die is red and the second one is green, then the sample space S is the following:

S=

(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), (5, 1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)

Hence n(S)=36.

Let's list the losing combinations:

E={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 1),

(2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6,5)}

n(E)=15

There are 36 total possiblities.

Out of which, winning probability is 21.

=21/36

=7/12

Given that the winning combination is 21 and the total combination is 36, the chance of rolling a winning combination is 7/12.

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Answer:

Step-by-step explanation:

false true true false

Answer:

false true true and false

Step-by-step explanation:

Answer:

(-3.4,2.7)

Step-by-step explanation:

The reason it's asking for an estimate, is because the intersection point is not on exact integer coordinates.

Start with the x-value of the intersection point. All options contain either -3.4 or -3.7. The x-value of the intersection point is closer to -3 than -4, so -3.4 is a better estimate.

Do the same with the y-value. Since the intersection point is closer to 3 than 2, 2.7 is the best estimate here.

Answer:

Last choice:  (-3.4, 2.7)

Step-by-step explanation:

Well, you could actually solve the two line equations and arrive at the answer but that is not the intent of the question.

The solution of the two line equations is the point at which the two lines intersect

At this point the x value is closer to -3 than to -4. So the x value from the choices would be -3.4 rather than -3.7

We can eliminate 1st and 3rd choices

The y value is closer to 3 than it is to 2 so the y-value estimate would be 2.7

Correct choice: (-3.4, 2.7)

I have marked the solution point with an X in the attached image

The expected value and the standard deviation of the points per game for the player is -6.5 and 65.43 respectively.

Given:

In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played.

From the given table:

E ( X ) = 9.5 * 5 points

= 47.5

E ( Y ) = 5.4 * - 10

= -54

E ( X + Y ) = 47.5 + ( -54 )

= 47.5 - 54

= -6.5

SD ( X ) = 12.5 * 5

= 64.5

SD ( Y ) = - 11

SD ( X + Y ) = [tex]\sqrt{64.5^2 + (-11)^2}[/tex]

= 65.43

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Full question:

Is in the image uploaded.

In the scale drawing of the 2 pentagons the value of x is 3

To find the value of x in the pentagon, the scale factor is first determined

The scale factor is solved for as follows

AB * r = PQ

in the figure AB = 5 and PQ =2.5

5r = 2.5

r = 2.5 / 5

r = 0.5

Using the scale factor r = 0.5

6 * r = x

6 * 0.5 = x

3 = x

x = 3

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26% of 78

= 26*(1/100)*78

=(26/100)*78

=0.26*78 = 20.28

so, the required answer is 20.28.

what is percentage?

answer: The quantity of something represented as if it were a portion of a sum total of 100; a portion or share of a whole.

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The percent markup price is equivalent to 42.86%.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a department store buys 200 shirts at a cost of ​$1400 and sells them at a selling price of ​$10 each

Cost price of 200 shirts = C.P. = $1400

Selling price of 200 shirts = S.P = $(10 x 200) = $2000

Percentage markup = [(2000 - 1400)/1400] x 100 = (600/1400) x 100 = 600/14 = 42.86%.

Therefore, the percent markup price is equivalent to 42.86%.

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Answer: the answer would round up to 43

Step-by-step explanation:

The equation to determine the number of players is (x-y)/z and there are 11 players in total.

Given: Lacrosse players raised $1581.75 to attend a tournament. They allocated $968.50 for the bus rental and $55.75 for each player's meals.

Let,

x = amount raised to attend a tournament.

y = amount allocated for bus rental

z = amount for each player's meals

Number of players = (x-y)/z

                               = (1581.75-968.50)/55.75

                               = 613.25/55.75

                               = 11

Therefore, the equation to determine the number of players is (x-y)/z and there are 11 players in total.

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Variable, x, represents the independent variable and the dependent variable is the distance, because the distance depends on the time. A function relating these variables is R(x) = 60x. So R(3) = 180 miles, meaning after 3, a distance of 180 miles was covered.

The dependent variable is the outcome or result that is being measured or observed, while the independent variable is the factor that is manipulated or changed to see its effect on the dependent variable.

Therefore, we can say that: the independent variable, x, represents the time and the dependent variable is the distance, because the distance depends on the time.

A function relating these variables is R(x) = 60x, representing the distance covered as a function of time at a constant speed of 60 miles per hour.

So, R(3) = 60 * 3 = 180 miles, meaning after 3 hours of driving, Hannah will have covered a distance of 180 miles.

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The independent variable x represents time in hours and the dependent variable R(x) represents distance in miles. The relationship between these variables is expressed by the function R(x) = 60x, signifying the distance (in miles) Hannah would have driven after x hours. For instance, R(3) equals 180, implying that after 3 hours, Hannah would have driven 180 miles.

In this context, the independent variable, x, represents the time in hours and the dependent variable, R(x), is the distance in miles, because the distance depends on the time. A function relating these variables is R(x) = 60x. This is because Hannah's speed is 60 miles per hour, so the formula for distance (Rate x Time) becomes 60 times the number of hours (x). So R(3) equals 180, meaning after 3 hours, Hannah would have driven 180 miles.

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