A measurement of fluoride ion in tooth paste from 5 replicate measurements delivers a mean of 0.14 % and a standard deviation of 0.05 %. What is the confidence interval at 95 % for which we assume that it contains the true value?

The probability that the project will be finished in 62 weeks or less is 0.6915.

The probability that the project will be finished in 66 weeks or less is 0.9332.

The probability that the project will take longer than 65 weeks is 0.1056.

Given that:

The time to complete a construction project is normally distributed.

The mean is :

μ = 60 weeks

The standard deviation is:

σ = 4 weeks

The z-score is:

[tex]z=\frac{x-\mu }{\sigma }[/tex]

When x = 62,

[tex]z=\frac{62-60}{4}[/tex]

   [tex]=0.5[/tex]

So, P(x ≤ 62) = P(z ≤ 0.5).

From the standard table, P(z ≤ 0.5) = 0.6915

When x = 66,

[tex]z=\frac{66-60}{4}[/tex]

   [tex]=1.5[/tex]

So, P(x ≤ 66) = P(z ≤ 1.5).

From the standard table, P(z ≤ 1.5) = 0.9332

When x = 65,

[tex]z=\frac{65-60}{4}[/tex]

   [tex]=1.25[/tex]

So, P(x > 65) = P(z > 1.25).

                     = 1 - P(z ≤ 1.25).

From the standard table, P(z ≤ 1.25) = 0.8944

So, P(x > 65) = P(z > 1.25)

                     = 1 - 0.8944

                     = 0.1056

Hence, the probabilities are 0.6915, 0.9332, and 0.1056 respectively.

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The probability the project will be finished in 62 weeks or less is approximately 69.15%. The probability the project will be finished in 66 weeks or less is approximately 93.32%. The probability the project will take longer than 65 weeks is approximately 10.56%.

To find the probability that the project will be finished in 62 weeks or less, we need to calculate the z-score. The z-score formula is (x - μ) / σ where x is the value we are interested in, μ is the mean, and σ is the standard deviation. Plugging in the values, we get (62 - 60) / 4 = 0.5. Using a z-score table, we can look up the probability corresponding to a z-score of 0.5, which is approximately 0.6915 or 69.15%.

Similarly, to find the probability that the project will be finished in 66 weeks or less, we calculate the z-score: (66 - 60) / 4 = 1.5. Looking up a z-score of 1.5 in the table, we find the probability is approximately 0.9332 or 93.32%.

To find the probability that the project will take longer than 65 weeks, we can subtract the probability of it being finished in 65 weeks or less from 1. Using the z-score formula, we get (65 - 60) / 4 = 1.25. The probability of finishing in 65 weeks or less is the area to the left of this z-score, which is approximately 0.8944 or 89.44%. Subtracting from 1, we get the probability of taking longer than 65 weeks is approximately 0.1056 or 10.56%.

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Answer:

B. The data represent a sample since the data are a subset of units.

True, we have a sample and all the elements on this sample are subset for the units of the population.

Step-by-step explanation:

We need to remember that the population represent all the possible elements or individuals of interest and by the other hand the sample is a subset of the population that is used to analyze patterns in the population of interest

Let's analyze one by one the options.

A. The data represent a population since the data are all the units that are the subject of the study

False, we have a sample size n =49 not all the possible elements of the population for this case we don't have a population.

B. The data represent a sample since the data are a subset of units.

True, we have a sample and all the elements on this sample are subset for the units of the population.

C. The data represent a population since the data are a subset of units.

False, by definition the population CAN'T be a subset of the sample size, and that's not the case.

D. The data represent a sample since the data are all the units that are the subject of the study.

False, the data is a sample BUT are not all the units for the study because that only occurs when we have a population.

Answer:

236.68 feet needed for fencing

Explanation:

You are designing a rectangular enclosure with 2 rectangular sections separated by parallel walls

Let L be the length and W be the width

Perimeter of rectangle = 3(length )+ 4 (width)

[tex]P=3L+4W[/tex]

Area of the rectangle = length * width

 [tex]A=2LW[/tex]

[tex]W= \frac{A}{2L}[/tex]

[tex]W= \frac{1700}{2(60)}=14.17[/tex]

Replace the values in perimeter

[tex]P=3L+4W[/tex]

[tex]P=3(60)+4(14.17)=236.68[/tex]

So 236.68 feet needed for fencing

Answer:

(x-2)/5(x-2)

cancel x-2 from the numerator and the denominator and the answer is 1/5

Final answer:

The angle -6 radians places the terminal side in the third quadrant with a reference angle of 0.28 radians when expressed in the positive acute form and rounded to four decimal places.

Explanation:

The question involves determining the quadrant of an angle measured in radians and finding its corresponding reference angle, which is a common task in Mathematics, specifically in the study of trigonometry.

To find the quadrant in which the terminal side of the angle -6 radians lies, we need to recall that one full revolution around the unit circle is 2π or approximately 6.28 radians. Since the given angle is negative, we move in the clockwise direction from the positive x-axis. Dividing -6 by 6.28, we realize that it is just shy of a full negative revolution, thereby placing the terminal side in the third quadrant.

To find the reference angle ¯θ, which is the positive acute angle the terminal side makes with the x-axis, we need to subtract the given angle from one full revolution (if necessary) and find the absolute value. Hence, ¯θ = |2×π - (-6)| = |6.28 - (-6)| = |0.28|, which is the same as 0.28 radians when rounded to four decimal places.

Answer:

The generated random variate is  X = 6.173

Explanation:

To generate an exponential random variate (with parameter λ) from a pseudo-random number U, we use the formula:

X = − ln(U)/λ

Fro the given problem, we have  U = 0.128 and λ = 3.

So, X = -In(0.128) / (1/3) = -In(0.128)/ 0.333 = 2.056/0.333 = 6.173

To generate an Exponential random variate with a given pseudo-random number, we use the formula -ln(U) / λ, where U is the pseudo-random number and λ is the rate parameter. In this case, plugging in U = 0.128 and λ = 1/3, we find that the Exponential random variate is approximately 6.147.

To generate an Exponential random variate, we use the formula:

X = -ln(U) / λ

where U is a pseudo-random number between 0 and 1, and λ is the rate parameter for the Exponential distribution.

In this case, U = 0.128 and λ = 1/3. Plugging in these values, we have:

X = -ln(0.128) / (1/3)

X ≈ -ln(0.128) / (1/3) ≈ -(-2.049) / (1/3) ≈ 2.049 / (1/3) ≈ 6.147

Therefore, the Exponential random variate is approximately 6.147.

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Answer:

48

Step-by-step explanation:

Let A and B be the two people who are able to drive. If A is driving, there are 4! ways to arrange the remaining peoplein the car seats. If B is driving, there are also 4! ways to arrange the remaining people. The number of arrangements 'n' is:

[tex]n=2*4!\\n=2*4*3*2*1\\n=48\ ways[/tex]

They can be arranged in 48 ways.

Answer:

There is only one solution, x = 5 and y = 2.

Step-by-step explanation:

To answer this question, we have to solve this system of equations.

We have that:

x - 3y = -1

4x + 3y = 26

Writing x as a function of y in the first equation, and replacing in the second, we have that:

x = 3y - 1

Replacing in the second

4x + 3y = 26

4(3y - 1) + 3y = 26

12y - 4 + 3y = 26

15y = 30

y = 2

Since we have 15y = 30, y = 2, there is only one solution.

If we had 0y = 0, there would be infinitely many solutions.

If we had 0y = a, a different of zero, there would be no solution.

Solving for x

x = 3y - 1 = 3*2 - 1 = 5

There is only one solution, x = 5 and y = 2.

Answer:it has one solution.

Step-by-step explanation:

The given system of equations is expressed as

x − 3y = −1 - - - - - - - - -1

4x + 3y = 26 - - - - - - - - 2

The first step would be to eliminate y by adding equation 1 to equation 2. It becomes

5x = 25

Dividing the left hand side and the right hand side of the equation by 5, it becomes

5x/5 = 25/5

x = 5

Substituting x = 5 into equation 1, it becomes

5 − 3y = −1

3y = 5 +1 = 6

Dividing the left hand side and the right hand side of the equation by 3, it becomes

3y/3 = 6/3

y = 2

Answer:

He stoped on 3th quarter,i.e, $C$.

Step-by-step explanation:

He ran 105 full circles ( 5280/50=105 ( rst= 30ft) ). So in the last circles he started from point S to run 30ft more.

The quarter of the circle is long 50ft/4= 12,5ft. So for 30 feets he must run 2 quarters, its 25ft. The last 5ft he ran on the 3th quarter, so he stoped on C.

This answer $C$, if $C$ is the 3th quadrant, i don't see the picture of the track.

Answer:

C

Step-by-step explanation:

Answer:

y=-2· e^(0.01)/ x²

Step-by-step explanation:

We calculate the given differential equation, we get

dy/dx = e^(−0.01) xy²

dy/y² = e^(−0.01) x dx

∫ y^(-2) dy= e^(−0.01) ∫ x dx

- y^(-1) = e^(−0.01) x²/2

-1/y=  e^(−0.01) x²/2

y=-2/ e^(−0.01) x²

y=-2· e^(0.01)/ x²

We use the site desmos.com, to plot graph for the solution of the the given differential equation. We get a graph.

Answer:

sinx = cosy

Step-by-step explanation:

option D is true because of the relationship between cos and sine

costheta = sine(90 - theta)

sine x = cos (90-x)

but x + y = 90

sine x = cos(x + y -x)

sineX = cos Y

Answer:

10,582

Step-by-step explanation:

We can choose 5 cards from 52 card deck in

      [tex]n = \binom{52}{5} = \frac{52!}{5!(52-5)!} = \frac{52!}{5!47!} = \frac{\cancel{47!} \cdot 48 \cdot 49 \cdot 50 \cdot 51 }{5! \cancel{47!}} = \frac{ 48 \cdot 49 \cdot 50 \cdot 51 }{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5} = 2 \; 598 \; 960[/tex]

ways.

Now, let's calculate the number of ways we can choose 5 hearts. We know that in a 52 card deck, we have 13 hearts. Therefore, the number of ways to choose 5 hearts is

       [tex]n_1 = \binom{13}{5} = \frac{13!}{5!(13-5)!} = \frac{13!}{5!8!} = \frac{8! \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13}{5!8!} = \frac{9 \cdot 10 \cdot 11 \cdot 12 \cdot 13}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5} = 1287[/tex]

Similarly, number of ways to choose 4 hearts equals [tex]\binom{13}{4}[/tex] and number of ways to choose 1 club equals [tex]\binom{13}{1}[/tex], since there are also 13 clubs in the deck.

Therefore, the number of ways of choosing 4 hearts and 1 club equals

                                   [tex]n_2 = \binom{13}{4} \cdot \binom{13}{1} = 9295[/tex]

The probability of this event is calculated as

           [tex]P(A) = \frac{\text{total number of ways to choose 5 hearts or 4 hearts and a club}}{\text{total number of ways to choose 5 cards from a deck of 52 cards}}[/tex]

Therefore

                     [tex]P(A) = \frac{n_1+n_2}{n} = \frac{1287+9295}{2598960} =0.0040716 \approx 0.0041[/tex]

Answer:

View graph

Step-by-step explanation:

The closest by default to 1100 cubic inches is taking two side and two front covers and that would give you 1080.12 cubic inches since two of the covers you must subtract 3 cm per side and side which would add 6 cm in total so outside would be 35 cm and indoor 29 cm . According the graph

29*50*3= 4350 * 2 lid = 8700 cm3

30*50*3= 4500*2 lid = 9000 cm3

So 8700+9000 = 17700 cm3 to inches 3 = 1080.12 cm3

We find the volume of the cooler by subtracting the internal volume from the external volume, and then multiplying the result by a conversion factor to change our units from cubic meters to cubic inches. The volume of the Styrofoam used in the cooler should be around 1100 cubic inches.

Firstly, to find the volume of the Styrofoam used, we need to find the volume of the outer box and then exclude the volume of the inner box (which is the cooler space).
The outer box dimensions are given in centimeters: 50.0 cm x 35.0 cm x 30.0 cm. We can convert these values into meters: 0.50 m x 0.35 m x 0.30 m and multiply them together to get the outer box volume in m³.
Secondly, the thickness of the Styrofoam is 3.00 cm, therefore the inner box dimensions are 44.0 cm x 29.0 cm x 24.0 cm. Again, we convert these values into meters: 0.44 m x 0.29 m x 0.24 m and multiply them together to get the inner box volume in m³.
To find the volume of Styrofoam used, subtract the inner box volume from the outer box volume.
Lastly, to convert this volume from m³ to cubic inches, apply the conversion factor: 1 m³ = 61023.7 cubic inches.
Then, after all calculations, we achieve the correct result of around 1100 cubic inches.

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Answer: 80cm

Step-by-step explanation:

Given:

Radius r = 16cm

Radial distance x = 5 radians

Radian is a measure of angles.

1 radian = 180°/π

To convert radial distance to linear distance

Linear distance = radial distance × radius

d = xr

d = 5 × 16cm

d = 80cm

Answer:

Option 4) The home's roof is at least 10 years or it has a security system.

Step-by-step explanation:

We are given the following events in the question:

A: The home's roof is less than 10 years}

B: The home has a security system

We have to find the interpretation of event

[tex]A^c \cup B[/tex]

Now, [tex]A^c[/tex]

This represents the complement of A and consist of events other than A,

Thus,

[tex]A^c[/tex]: The home's roof is not less than 10 years or the home's roof is greater than equal to 10 years or the home's roof is at least 10 years.

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets.

[tex]A^c \cup B[/tex]

Thus, it can be interpreted as the home's roof is at least 10 years or the home has a security system.

Option 4) The home's roof is at least 10 years or it has a security system

The event A^c ∪ B represents all homes with roofs that are at least 10 years or have a security system.

When evaluating the union of the complement of event A and event B, which is denoted as Ac ∪ B, we are looking for all outcomes that are either in the complement of A or in B, or in both. The complement of event A, denoted as Ac, includes all outcomes not in A. In the context of the given events, this would mean the complement of event A (the home's roof is less than 10 years) includes homes with roofs that are at least 10 years. Event B is that the home has a security system. Therefore, Ac ∪ B represents all homes with roofs that are at least 10 years or have a security system (or both).

Answer:

716.3N

Step-by-step explanation:

Moment produced by force F = 150 N:

Mf = 150 * 30 = 4500 Ncm

The same moment is imparted at the nail.

Fn * 5 / sin (60) = 4500 Ncm

Fn = 779.423 N

Force exerted by surface on hammer pivot is:

Fx = 779.423 sin (30) - 150 = 239.7115 N

Fy = 779.423 cos (30) = 675 N

Fres = sqrt ( (Fx)^2 + (Fy)^2)

Fres = sqrt ( 675 ^2 + 239.7115^2)

Fres = 716.3 N

The force the hammer exerts on the nail is parallel to the nail. is 716.3 N

From the given information, we ned to first calculate the moment as shown:

Since Moment = Force * distance:

The same moment is imparted at the nail.

5Fn/sin (60) = 4500 Ncm

Fn = 779.42N

Next is to calculate the force exerted by the surface on the hammer pivot.

Fx = 779.423 sin (30) - 150 = 239.7115 N

Fy = 779.423 cos (30) = 675 N

[tex]F = \sqrt{ ( (Fx)^2 + (Fy)^2)}\\F = \sqrt{ ( 675 ^2 + 239.7115^2)}\\F = 716.3N[/tex]

The force the hammer exerts on the nail is parallel to the nail. is 716.3 N

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Answer:

Step-by-step explanation:

Hello!

You have two variables of interest.

X: Setup size (inches)

Y: Type the number of channels available.

Qualitative variables are those who describe characteristics of the subject of study, for example, the eye color of a person.

Quantitative variables are those that count quantities, for example, the shoe size of a person.

Continuous and discrete variables are quantitative. The difference is that the continuous variables are those who count in a determined range of valours, but between two observed values, there are infinite possible outcomes, for example, the body temperature of a cat. The normal temperature of a cat is around 38ºC, using a normal thermometer you measure the body temperature of two cats and obtain the following values 37.8 and 37.9 if you change the thermometer to one designed to take more precise measurements, it is possible that you obtain more values, for example, 37.81 and 39.94 and with a more precise tool you may become temperatures with more digits, this means that within this two temperatures there are infinite values of temperature, only limited by the equipment available.

A discrete variable is a quantitative variable but between the values, these variables take there are no other possible observations, regardless of the method of equipment used. An example of a discrete variable is the amount of money in a pocket. If you have two bills in one pocket, one is a 10 dollar bill and the other is a 20 dollar bill, there are no possible values in between, you either have ten or twenty, there is not possible, in this example, to count 15 dollars.

Then the variable "Y: Type number of channels available." is quantitative discrete, it counts the number of channels and between each channel there is nothing.

The variable "X: Setup size (inches)", the "inch" is a unit of length, and these variables are usually continuos, but in this example, your variable describes the screen width of the televisions and the type of image definition. Both are characteristics of the TVs so the variable is a qualitative one.

I hope it helps!

Answer:  b. 134

Step-by-step explanation:

Given : A minimum usual value of 135.8 and a maximum usual value of 155.9.

Let x denotes a usual value.

i.e.  135.8< x < 155.9

Therefore , the interval for the usual values is [135.8, 155.9] .

If interval for any usual value is [135.8, 155.9] , then any value should lie in this otherwise we call it unusual.

Let's check all options

a. 137  ,

since  135.8< 137 < 155.9

So , it is usual.

b. 134

since 134<135.8 (Minimum value)

So , it is unusual.

c. 146  

since  135.8< 146 < 155.9

So , it is usual.

d. 155  

since 135.8< 1155 < 155.9

So , it is usual.

Hence, the correct answer is b. 134 .

You can use the fact that unusual points are those points which lie far away from the normal area of points.

The value which would be considered unusual is given by

Option b: 134

Usually, we use interquartile range along with two quartiles [tex]Q_1[/tex] and [tex]Q_3[/tex]  to get the anomalies.

Those values who lie below  [tex]Q_1 - 1.5 \times IQR[/tex] or above [tex]Q_3 + 1.5 \times IQR[/tex] are called anomalies.

But since in the case when these things are not obtainable, we check manually which point is lying away from mean or outside of usual range etc.

Suppose  that minimum usual value is given to be 'a' and the maximum usual value be 'b', then it is written as interval [a,b]

If some value is lying outside this range of values (the spread from a to b), then it means it is either smaller than minimum which is < a, or bigger than maximum of that range which is > b.

Since the given usual minimum value is 135.8

and the given usual maximum value is 155.9

thus, the range of usual value is [135.8, 155.9] which shows that usually, values should lie inside that interval which is > 135.8 and < 155.9

All options except the second options lie in the interval.

For second option, we have 134 < 135.8

thus, this value being smaller than usual minimum value, thus, it will be considered unusual.

Thus,

The value which would be considered unusual is given by

Option b: 134

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Answer:

void distance(int x1, int x2, int y1, int y2){

pointsDistance = sqrt((x2-x1)^(2) + (y2-y1)^(2));

}

Step-by-step explanation:

Suppose we have two points:

[tex]A = (x_{1}, y_{1})[/tex]

[tex]B = (x_{2}, y_{2}[/tex]

The distance between these points is:

[tex]D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]

So, for points (1.0, 2.0) and (1.0, 5.0)

[tex]D = \sqrt{(1 - 1)^{2} + (5 - 2)^{2}} = \sqrt{9} = 3[/tex]

I suppose this questions asks me to write a code, since i have to attribute the result to pointsDistance. I am going to write a C code for this, and you have to include the math.h library.

void distance(int x1, int x2, int y1, int y2){

pointsDistance = sqrt((x2-x1)^(2) + (y2-y1)^(2));

}

Answer:

pointsDistance = sqrt (pow(x2 - x1,2.0) + pow(y2 - y1,2.0));

Step-by-step explanation:

No, it is not advisable to predict the stopping time for your large SUV using model trained for compact cars.

Prediction means generating the values of the dependent variable using some specific models in machine learning.

Given that, the model is trained on 20 compact cars and the model is developed such that it predicts the stopping time for a vehicle by using its weight.

Here the dependent variable is stopping time which is required to be predicted. As the model is trained on compact cars that is medium size cars and if we expect the same model to predict stopping time for large SUV, then model is going to predict false stopping time as the weights for large SUV is quiet higher than the compact cars. So, model may consider it as an outlies and will lead to incorrect prediction.

Therefore, it is not advisable to use the same model for predicting the stopping time for your large SUV.

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Final answer:

Using a stopping time model developed from compact car data to predict the stopping time for a large SUV is not advisable due to differences in vehicle dynamics, which may lead to inaccurate results.

Explanation:

When a consumer group develops a model to predict the stopping time of a vehicle based on its weight, the model must be used within the context of the data from which it was derived. Using the model, which was built on data from 20 compact cars, to predict the stopping time of a larger SUV is not advisable due to differences in vehicle dynamics, size, weight distribution, and potentially different braking systems. Models are designed to be predictive within the range of data they are based on, and extrapolating them beyond that range can lead to inaccurate predictions. Specifically, the heavier mass of an SUV compared to compact cars means that it would likely have a longer stopping distance due to greater momentum, and this may not be represented in a model calibrated to lighter vehicles.

Answer:

1) a.) Your confidence interval estimate is narrower

2) c.) The width of a confidence interval estimate for a proportion will be narrower for 90% confidence level than for a 95% confidence level

Step-by-step explanation:

Confidence Interval can be stated as  M±ME where

Margin of Error determines the range of the confidence interval around the mean.

Margin of error (ME) of the mean can be calculated using the formula

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

From the formula we can reach the following conclusions:

Since your sample size (49) is bigger than your friend's (36), your confidence interval is narrower, because margin of error is narrower.

Since the confidence level 90% has smaller statistic than the confidence level 95%, its confidence interval is narrower.

That is, we can estimate narrower confidence intervals with less confidence.

Answer:the company bought 12 computers and 4 printers.

Step-by-step explanation:

Let x represent the number of computers that the company bought.

Let y represent the number of printers that the company bought.

The company buys a total of 16 machines. It means that

x + y = 16

Each computer costs $550 and each printer costs $390. If the company spends $8160 for all the computers and printers that was bought, it means that

550x + 390y = 8160 - - - - - - - - - - 1

Substituting x = 16 - y into equation 1, it becomes

550(16 - y) + 390y = 8160

8800 - 550y + 390y = 8160

- 550y + 390y = 8160 - 8800

- 160y = - 640

y = - 640/ - 160

y = 4

Substituting y = 4 into x = 16 - y, it becomes

x = 16 - 4

x = 12

The company bought 12 computers and 4 printers.

To solve this problem, we can set up a system of equations. Let x represent the number of computers and y represent the number of printers. We have two equations: x + y = 16 and 550x + 390y = 8160. We can solve this system by substitution or elimination. Let's use elimination.

Multiply the first equation by 390: 390x + 390y = 6240. Subtract this equation from the second equation: (550x + 390y) - (390x + 390y) = 8160 - 6240. Simplify: 160x = 1920. Divide both sides by 160: x = 12.

Substitute this value into the first equation: 12 + y = 16. Solve for y: y = 4. Therefore, the company bought 12 computers and 4 printers.

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The probability that the first resistor is 100Ω is 1/3. The probability that the second resistor is 100Ω, given that the first resistor is 50Ω, is 2/7. The probability that the second resistor is 100Ω, given that the first resistor is 100Ω, is also 2/7.

(a) Probability that the first resistor is 100Ω:

The total number of resistors is 15, with 5 of them labeled 100Ω.

So, the probability is 5/15 or 1/3.

(b) Probability that the second resistor is 100Ω, given that the first resistor is 50Ω:

If the first resistor is 50Ω, there are still 4 resistors labeled 100Ω out of the remaining 14 resistors.

So, the probability is  4/14 or 2/7.

(c) Probability that the second resistor is 100Ω, given that the first resistor is 100Ω:

If the first resistor is 100Ω, there are still 4 resistors labeled 100Ω out of the remaining 14 resistors.

So, the probability is  4/14 or 2/7.

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Answer: 0.4667

Step-by-step explanation:

According to 68–95–99.7 rule , About  99.7% of all data values lies with in 3 standard deviations from population mean ([tex]\mu[/tex]).

Here , margin of error = 3s , where s is standard deviation.

As per given , we have want our sample mean [tex]\overline{x}[/tex] to estimate μ μ with an error of no more than 1.4 point in either direction.

If 99.7% of all samples give an [tex]\overline{x}[/tex] within 1.4 , it means that

[tex]3s=1.4[/tex]

Divide boths ides by 3 , we get

[tex]s=0.466666666667\approx0.4667[/tex]

Hence, So [tex]\overline{x}[/tex] must have 0.4667 as standard deviation so that 99.7 % 99.7% of all samples give an [tex]\overline{x}[/tex] within 1.4 point of μ .

To estimate the mean score of an MCAT with an error of no more than 1.4 points, one needs to calculate the standard deviation for the sample mean that allows 99.7% of samples to fall within this range. After determining this standard deviation, apply the Central Limit Theorem to increase sample size and approach the population mean.

To estimate the mean score μ of those who took the Medical College Admission Test on your campus with an error of no more than 1.4 points in either direction, you are seeking a standard deviation for the sample mean ¯x that will allow for 99.7% of samples to fall within this range. This relates to the 68 – 95 – 99.7 rule, which in this context will be interpreted as within three standard deviations of the mean, hence, you need ¯x to have a standard deviation of 1.4/3.

Using the formula for ¯x standard deviation which is σ/√n (where σ is population standard deviation and n is the sample size), you can rewrite the formula as 1.4/3 = 6.2/√n and solve for n to get the desired sample size.

This use of the empirical rule and standard deviations is part of a bigger concept known as the Central Limit Theorem, which states that as sample size increases, the sample mean gets nearer to the population mean.

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Answer:

Relative Extrema: \left(\frac{2}{\sqrt{e}},-\frac{6}{e}\right)

Step-by-step explanation:

There is only one extreme minimum point that is \left(\frac{2}{\sqrt{e}},-\frac{6}{e}\right) and there is no any point of reflection for this function.

You can find it in attached pictures of graphs.

Answer:

\int \limits_{-2}^{4} f(x) \, dx

Step-by-step explanation:

The objective is to write

                       [tex]\int \limits_{-3}^{1} f(x) \, dx + \int \limits_{1}^{4} f(x) \, dx - \int \limits_{-3}^{-2} f(x) \, dx[/tex]

as a single integral in the form

                                       [tex]\int \limits_{a}^{b} f(x)\, dx[/tex].

We consider the segments [tex][-3, 1], [1, 4][/tex] and [tex][-3,-2][/tex].  If we combine the first and the second  segment, we obtain

                                 [tex][-3,1] \cup [1,4] = [-3,4][/tex]

Therefore, adding the first two integrals gives

                       [tex]\int \limits_{-3}^{1} f(x) \, dx + \int \limits_{1}^{4} f(x) \, dx = \int \limits_{-3}^{4} f(x) \, dx[/tex]

Now,we have

                                  [tex]\int \limits_{-3}^{4} f(x) \, dx - \int \limits_{-3}^{-2} f(x) \, dx[/tex]

To subtract them, we need to find the difference of the segments [tex][-3,4][/tex] and [tex][-3,-2][/tex].

                                [tex][-3,4] \; \backslash \; [-3,-2] = [-2,4][/tex]

Therefore,

                          [tex]\int \limits_{-3}^{4} f(x) \, dx - \int \limits_{-3}^{-2} f(x) \, dx = \int \limits_{-2}^{4} f(x) \, dx[/tex]

Thus, the single integration of all the definite integral is mentioned below:

[tex]\int_{-2}^{4} f(x) dx[/tex]

Given the integral is,

[tex]\int_{-3}^{1} f(x) dx + \int_{1}^{4} f(x) dx - \int_{-3}^{-2} f(x)dx[/tex]

We need to change the whole definite integral into a single integral.

Now, we have the limits of integrations are [ - 3, 1 ], [ 1, 4 ], and [ - 3, -2 ].

Now, the first limit and second limit of integration are in addition, therefore combining forms of the integration are the union of these units.

Thus,

[ - 3, 1 ] U [ 1, 4 ] = [ -3 , 4 ]

Now, the second limit and third limit of integration are in subtraction, therefore combining forms of the integration are the intersection of these units.

Thus,

[ 1, 4 ] intersection [ - 3, -2 ] = [ null set]

Now, the combination of [ -3 , 4 ] and [ -null set] is [  - 2, 4].

Thus, the single integration of all the definite integral is mentioned below:

[tex]\int_{-2}^{4} f(x) dx[/tex]

To know more about the integrals, please refer to the link:

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Final answer:

To find the percent of households having more cars than a two-car garage can hold, sum the probabilities for 3, 4, 5, and 6 cars, which results in 19%.

Explanation:

The student is interested in finding out what percent of American households have more cars than a two-car garage can hold, with the given probability distribution for the number of cars owned. To calculate this, we would sum the probabilities of households owning more than two cars.

The probabilities of owning 3, 4, 5, and 6 cars are 0.12, 0.04, 0.02, and 0.01 respectively. Adding these probabilities together gives us the percent of households with more cars than the garage can hold:

0.12 + 0.04 + 0.02 + 0.01 = 0.19

Therefore, 19% of American households own more cars than a two-car garage can hold.

Answer:

D. ​Inferential, because the statistics are used to make an inference about the population

Correct, the objective of this study is obtain information from the population with a sample and then use any method to estimate the population mean, the parameter of interest.

Step-by-step explanation:

An inferential study consists in take information about a population by a sample and use this information to see what would be the possible values for the population of interest

By the other hand a descriptive study is obtained from observing and measuring some variables of interest but without manipulate the data.

For this case we have sample averages for the viewing time per month.

Let's analyze one by one the possible options:

A. ​Inferential, because the statistics are used to describe the sample

False the study is inferential but the idea is not just obtain information about the sample, we want to see the population parameters not the statistics

B. ​Descriptive, because the statistics are used to describe the sample

False for this case we have averages calculated from the sample mean and is not possible to consider this study as descriptive.

C. ​Descriptive, because the statistics are used to make an inference about the population

False, the statistics are used to make an inference about the population, this statement is correct, but the problem is that this study is not descriptive.

D. ​Inferential, because the statistics are used to make an inference about the population

Correct, the objective of this study is obtain information from the population with a sample and then use any method to estimate the population mean, the parameter of interest.

The study is descriptive. It uses statistics to provide summaries about the average TV viewing times per month among citizens, without making any inferences about a larger population. Therefore, the correct option is B.

The study in question is descriptive. Descriptive statistics are used to describe the main features of a collection of data in quantitative terms. They provide simple summaries about the sample and the measures. The data mentioned here are providing a summary of the average TV viewing times per month for the citizens. They describe various elements of interest within a particular set and there isn't any interpretation or inference being made about the larger population from which the sample was drawn. Therefore, the correct option is B. Descriptive, because the statistics are used to describe the sample.

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Answer:

Step-by-step explanation:

Given that a claim was made as

"People who often attend cultural activities, such as movies, sports events and concerts, are more likely than their less cultured cousins to survive the next eight to nine years, even when education and income are taken into account, according to a survey by the University of Umea in Sweden" (American Health, April 1997, p. 20).

a) Yes, this can be tested by conducting a randomized experiment.  Selecing two groups of persons i who attend and other who do not attend and compare their life

This can be done from the data source already existing about persons who died recently under homogeneous conditions of environemnt

b) Yes, we can conclude provided random sample are taken and homogeneous conditions were followed

c) Yes, 100% true, though cannot say precisely how these helps as there is no scientific measurement, but it is a fact it improves health.

d) Other factors, are family history, bad habits, disease already present in the persons, etc.

Randomized experiments for this claim may not be feasible. The study only finds a correlation, not causation, between cultural activity attendance and longevity. The suggested benefits of such activities need more research for validation. Other factors like lifestyle habits and medical history should also have been considered.

(a) Testing this claim through a randomized experiment might not be practically or ethically feasible. A randomized experiment involves randomly assigning individuals to different conditions or treatments and looking at the outcomes. In this case, it would involve controlling individuals' cultural activity habits over a span of eight to nine years, which is unlikely to be feasible or ethical due to potential intrusion on personal liberties.

(b) The study conducted, being an observational study, can report correlations but does not establish causation. In other words, although the study found that people who often engage in cultural activities are more likely to survive the following eight to nine years, it did not prove attendance at cultural events causes people to live longer. There might be other unnoticed factors or variables at play.

(c) The statement in the article is speculative. While there could potentially be a link between these activities and enhanced immunity or coping skills, the evidence provided does not confirm this hypothesis. Further experimental studies would be needed to validate this claim.

(d) In addition to education and income, other factors such as lifestyle habits (like diet, exercise, smoking, alcohol use) and medical history (pre-existing conditions, genetic factors) could have been taken into account. These factors could significantly influence one's lifespan and should ideally be controlled for in a study like this.

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Answer:

a)g: 3x + 4y = 10   b) a:x+y = 5           c) c: 3x + 4y = 10

h: 6x + 8y = 5         b:2x + 3y = 8         d: 6x + 8y = 5

Step-by-step explanation:

a) Has no solution

g: 3x + 4y = 10

h: 6x + 8y = 5

Above Equations  gives  you  parallel lines refer attachment

b) has exactly one solution

a:x+y = 5

b:2x + 3y = 8

Above Equations  gives  you  intersecting lines refer attachment

c) has infinitely many solutions

c: 3x + 4y = 10

d: 6x + 8y = 5

Above Equations  gives  you  collinear lines refer attachment

i) if we add   x + 2y = 1 to equation x + y = 5 to make an inconsistent system.

ii) if we add   x + 2y = 3 to equation x + y = 5 to create infinitely system.

iii) if we add  x + 4y = 1 to equation x + y = 5 to create infinitely system.

iv) if we add to x + y =5 equation x + y = 5  to change the unique solution you had  to a different unique solution

The 3 systems of linear equations are:

a)

y = 4x + 3

y = 3x + 1

(no solution).

b)

y = 4x + 3

y = 3x + 1

(one solution)

c)

y = 4x + 3

y = 4x + 3

(infinite solutions)

Such that the graphs can be seen below, where the solutions are the intersections between the lines.

a) A system of linear equations has no solution when both lines are parallel. And parallel lines have the same slope and different y-intercept, so this system can be:

y = 4x + 3

y = 4x + 6

This system has no solutions.

b) We get only one solution if the slopes are different:

y = 4x + 3

y = 3x + 1

Has only one solution.

c) We have infinite solution if both lines are the same line, so in the system:

y = 4x + 3

y = 4x + 3

We have infinite solutions.

The graphs of the 3 systems can be seen, in order, below:

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