Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-intercept, and vertex of the function. f(x) = -(x + 1)2 + 4

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:

\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]

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Answer:

The answer to your question is the second option

Step-by-step explanation:

A Quadratic function is a polynomial of degree two. That means that the higher exponent is 2.

a) This option is incorrect because the highest power is 3 not two.

b) This option is the right answer, the highest power is 2, so, it is a quadratic function.

c) This option is incorrect, the highest power is -2.

d) This option is incorrect, the highest option is 1.

Answer:

Option 2 is the correct answer

Step-by-step explanation:

A quadratic function is a function in which the highest power to which the variable is raised is 2

1) f(x) = −8x3 − 16x2 − 4x

The given function is a cubic function because the highest power

to which the variable,x is raised is 3

2) f(x) = 3x²/4 + 2x - 5

The given function is a quadratic function because the highest power

to which the variable,x is raised is 2

3) f(x) = 4/x² - 2/x + 1

It can be rewritten as

f(x) = 4x^-2 - 2x^-1 + 1

The given function is not a quadratic function because the highest power to which the variable,x is raised is - 2

4) f(x) = 0x2 − 9x + 7

It can be rewritten as

f(x) = - 9x + 7

The given function is not a quadratic function because the highest power to which the variable,x is raised is 1

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:

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

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

The question pertains to calculating the probability of drawing exactly 3 jacks from 51 randomly drawn cards from a 52-card deck. While the probability is very high, it's not an absolute certainty. The exact calculations involve complex combinatorial mathematics.

The subject of this question pertains to probability in mathematics, specifically to calculate the likelihood of drawing 3 jacks when selecting 51 cards from a shuffled deck of 52 cards.

First off, we need to understand that in a well-shuffled 52-card deck, there are 4 Jacks. Even if you select 51 out of 52 cards, there isn't a guarantee that you will select 3 jacks because the selection is random. The scenario you provided indicates a nearly certain event (since you're pulling nearly all the cards), but it still isn't an absolute certainty.

The exact probability computation for this kind of problem are more complex as they would involve combinatorial calculations. For simplicity, let's consider a similar but simpler scenario. Let's assume you are drawing just 4 cards instead. The probability of getting exactly 3 Jacks would be a combination of the probability of picking a Jack, and the probability of picking a non-Jack card. This would be calculated as (C(4,3) * C(48,1)) / C(52,4), with C representing the combination formula. This gives us how many ways we can draw 3 Jacks and a non-Jack divided by how many ways we can draw any 4 cards.

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Final answer:

The probability of drawing 3 jacks from a standard deck of 52 cards when selecting 51 is 1 (certainty), as it is a guaranteed event given the conditions.

Explanation:

The question asks about the probability of a certain event occurring when dealing with a standard deck of 52 cards. In this case, the event is being certain to get 3 jacks when selecting 51 cards out of 52. Since there are 4 jacks in the deck, and upon drawing 51 cards you're left with only 1 card that is not drawn, it is guaranteed that you'll have the 3 jacks among the drawn cards.

Hence, the probability is 1 (certainty), as there is only one card you're not drawing and 4 chances to have drawn a jack, which means you will always end up with all 3 jacks among the chosen 51 cards.

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:

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.

The formula is used to find the diameter of circle is: [tex]d = \frac{C}{3.14}[/tex]

The diameter of circle is 5.1 cm

Solution:

Given that,

Circumference (C) of a circle is 16 cm

The formula for circumference of circle when diameter is given is:

[tex]C = \pi d\\\\\pi \text{ is a constant equal to 3.14}\\\\C = 3.14d[/tex]

Rearrange the formula to get "d"

Divide both sides by 3.14

[tex]d = \frac{C}{3.14}[/tex]

The above formula is used to find the diameter of circle

Given that, circumeference = C = 16 cm

Substituting we get,

[tex]d = \frac{16}{3.14}\\\\d = 5.095 \approx 5.1[/tex]

Thus diameter of circle is 5.1 cm

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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Answer:

True

Step-by-step explanation:

The time between customer arrivals is called inter-arrival time. According to Queueing Notation, the inter-arrival time can be model based on difference probability distribution. The probability distribution by which the inter-arrival time can be modeled include:

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:

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

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:  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:

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:

10-[6-4+(5)]×2

10-[2+5]×2

10-(7)×2

10-14= -4

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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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. 3, and 2. m x n

Step-by-step explanation:

1. for an upper triangular 2x2 matrix i.e. (a,0,c,d), three (03) unknown elements a, c, and d are needed to be specified.

2. for m x n matrix, m*n elements are needed to be specified.

Final answer:

To specify an upper triangular 2x2 matrix, 3 unknown real numbers are needed. For an m × n matrix, m × n unknown real numbers are required.

Explanation:

The question asks how many unknown real numbers are needed to specify each of the given matrices: an upper triangular 2x2 matrix, and an m × n matrix.

1. An Upper Triangular 2x2 Matrix

An upper triangular matrix has the form:

(a, b)
(0, c)

Thus, to specify an upper triangular 2x2 matrix, 3 unknown real numbers are needed: a, b, and c.

2. An m × n Matrix

An m × n matrix has m rows and n columns. To specify such a matrix, one needs m × n unknown real numbers, representing each element in the matrix.

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:

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:

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:

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:

a.

lower Quartile= 57.5

Upper Quartile=81

b.

23.5

c.

box-plot is attached in excel file

Step-by-step explanation:

The data is arranged in ascending order so, the lower quartile denoted as Q1 can be calculated as under

Q1=((n+1)/4)th score=(41/4)th score=(10.25)th score

Q1=10th score+0.25(11th-10th)score

Q1=57+0.25(59-57)=57+0.5=57.5

Q1=57.5

The data is arranged in ascending order so, the third quartile denoted as Q3 can be calculated as under

Q3=(3(n+1)/4)th score=(3*41/4)th score=(30.75)th score

Q3=30th score+0.75(31th-30th)score

Q3=81+0.75(81-81)=81+0=81

Q3=81

b)

Interquartile range=IQR=Q3-Q1=81-57.5=23.5

IQR=23.5

c)

The box-plot is made in excel and it shows no outlier. The box-plot shows the 5-number summary(minimum-Q1-median-Q3-maximum) as 25-57.5-72-81-98.

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:

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:

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: 2520 ways

Step-by-step explanation:

7!/2!

Answer:

no

Step-by-step explanation:

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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