We flip a fair coin five times. For every heads you pay me $1 and for every tails I pay you $1. Let X denote the my net winning at the end of the flips. Find the possible values and the probability mass function of X.

Answer:

λ = 1.3252 x 10⁻⁴

Step-by-step explanation:

Since we are already given the half-life, the decay expression can be simplified as:

[tex]N(t) = N_0*e^{-\lambda t}\\\frac{N(half-life)}{N_0}=0.5[/tex]

For a half-life of t =5230 years:

[tex]0.5 = e^{(-\lambda t)} \\ln(0.5) = -\lambda * 5230\\\lambda = 1.3252*10^{-4}[/tex]

The decay-rate parameter λ for C-14 is 1.3252 x 10⁻⁴

Answer: The speed that Jesse travels in still water is 6 km/hr.

Step-by-step explanation:

Let the speed that Jesse travels in still water be 'x'.

Distance = 72 km

The trip to the camp area with a 2-km/hr current takes 9 hr less time than the return trip against the current.

Speed of current = 2 km/hr

According to question, we get that

[tex]\dfrac{72}{x-2}-\dfrac{72}{x+2}=9\\\\\dfrac{x+2-(x-2)}{x^2-4}=\dfrac{9}{72}\\\\\dfrac{4}{x^2-4}=\dfrac{1}{8}\\\\32=x^2-4\\\\32+4=x^2\\\\x^2=36\\\\x=\sqrt{36}\\\\x=6[/tex]

Hence, the speed that Jesse travels in still water is 6 km/hr.

Jesse's speed in still water is determined by setting up a system of equations using the distance equals rate times time formula for both downstream and upstream travel. By accounting for the time difference and the current speed, we solve for the variable representing Jesse's speed in still water.

Jesse takes a kayak trip traveling 72 km with and against a current, and we need to find Jesse's speed in still water. Let's denote the speed in still water as v (km/hr) and the current speed as 2 km/hr. The trip downstream increases Jesse's speed to (v + 2) km/hr, and upstream decreases it to (v - 2) km/hr.

Using the distance equals rate times time formula (d = rt), we can write the following equations for the time taken downstream (td) and upstream (tu):

Given that it takes 9 hours less to travel downstream, we have tu = td + 9.

By solving these linear equations, we find the system:

Combining these gives us:

72 / (v + 2) + 9 = 72 / (v - 2)

By solving this equation, we find the value of v, Jesse's speed in still water.

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Final answer:

A linear system with three equations and five variables does not have to be consistent. The statement 'A linear system with three equations and five variables must be consistent' is false

Explanation:

A linear system with three equations and five variables does not have to be consistent. In fact, it is possible for the system to be inconsistent.

The statement that a linear system with three equations and five variables must be consistent is False. In linear algebra, the consistency of a system depends on whether there are any contradictions among the equations. For a system to be consistent, it must have at least one solution.

For example, consider the system of equations:

x + y + z = 5

2x + 3y + 4z = 10

5x + 2y + 3z = 8

Since there are more variables than equations, there will be infinitely many solutions if the system is consistent. But if the system is inconsistent, there will be no solution.

Therefore, the statement 'A linear system with three equations and five variables must be consistent' is false

Answer:

Step-by-step explanation:

a) The game tree for k = 5 has been drawn in the uploaded picture below where C stands for continuing and S stands for stopping:

b) Say we were to use backward induction we can clearly observe that stopping is optimal decision for each player in every round. Starting from last round, if player 1 stops he gets $3 otherwise zero if continues. Hence strategy S is optimal there.

Given this, player 2’s payoff to C is $3, while stopping yields $4, so second player will also chooses to stop. To which, player 1’s payoff in k = 3 from C is $1 and her payoff from S is $2, so she stops.

Given that, player 2 would stop in k = 2, which means that player 1 would stop also in k = 1.

The sub game perfect equilibrium is therefore the profile of strategies where both players always stop: (S, S, S) for player 1, and (S, S) for player 2.

c) Irrespective of whether both players would be better off if they could play the game for several rounds, neither can credibly commit to not stopping when given a chance, and so they both end up with small payoffs.

i hope this helps, cheers

Final answer:

The subgame perfect equilibrium of the envelope game for any finite integer k is that both players will choose to stop in the final round (k) and each player will keep their own money.

Explanation:

Extensive-form tree for k = 5:

Backward Induction:

To find the subgame perfect equilibrium, we start from the last round (round 5) and work our way backwards: 1. In round 5, both players have the choice to stop or continue. Since both players want to maximize their earnings, they will both choose to stop, resulting in each player keeping their own money. 2. In round 4, player 2 knows that player 1 will choose to stop in round 5. Therefore, player 2 will choose to stop in round 4, resulting in each player keeping their money. 3. In round 3, player 1 knows that player 2 will choose to stop in round 4. Therefore, player 1 will choose to stop in round 3, resulting in each player keeping their money. 4. In rounds 2 and 1, both players have the choice to stop or continue. Since both players want to maximize their earnings and they know that the other player will choose to stop in the previous rounds, they will both choose to stop, resulting in each player keeping their money.

Backward Induction Outcome for Any Finite Integer k:

Based on the backward induction analysis, the outcome of the game for any finite integer k is that both players will choose to stop in the final round (k) and each player will keep their own money. This outcome is the subgame perfect equilibrium of the game, as it represents the strategy that maximizes the earnings for both players.

Answer:

Option c) 0.80        

Step-by-step explanation:

We have to approximate the most possible correlation between spending on tobacco and spending on alcohol.

a) 0.99

This shows almost a perfect straight line relationship between spending on tobacco and spending on alcohol. Thus, this cannot be the right correlation as the relationship between spending on tobacco and spending on alcohol is not so strong.

b)-0.50

This shows a negative relation between spending on tobacco and spending on alcohol which cannot be true as they share a positive relation.

c) 0.80

This correlation shows a strong positive correlation between spending on tobacco and spending on alcohol which is correct because the relationship between spending on tobacco and spending on alcohol is positive

d)0.08

This correlation shows a very weak positive correlation between spending on tobacco and spending on alcohol which cannot be true.

Answer: [tex]Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100[/tex]

Step-by-step explanation:

The five -number summary consists of five values :

Minimum value , First quartile [tex](Q_1)[/tex] , Median , Third Quartile [tex](Q_3)[/tex]  , Maximum value.

Given : The Insurance Institute for Highway Safety publishes data on the total damage caused by compact automobiles in a series of controlled, low-speed collisions.

The following costs are for a sample of six cars:

$800, $750, $900, $950, $1100, $1050.

Arrange data in increasing order :

$750,$800, $900, $950, $1050, $1100

Minimum value =  $750

Maximum value = $1100

Median = middle most term

Since , total observation is 6 (even) , so Median = Mean of two middle most values ($900 and  $950).

i.e.  Median[tex]=\dfrac{900+950}{2}=\$925[/tex]

First quartile [tex](Q_1)[/tex] = Median of lower half ($750,$800, $900)

= $800

, Third Quartile [tex](Q_3)[/tex]  = Median of upper half ($950,  $1050, $1100)

= $1050

Hence, the five-number summary of the total damage suffered for this sample of cars will be :

[tex]Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100[/tex]

Answer: 5&3/4ths

Step-by-step explanation:

[tex]5+\frac{5}{16} +\frac{7}{16} \\\\5+\frac{5+7}{16} \\\\\5\frac{12}{16}=5\frac{3}{4}[/tex]

Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!

- Cutiepatutie ☺❀❤

Answer:

v = <2, 2√3>

Step-by-step explanation:

Let v be the vector of form <x,y>

Since its determinant is |4|, then:

[tex]x^2 +y^2 =4^2=16[/tex]

If it makes a π/3 angle with the positive x-axis, then the tangent relationship yields:

[tex]tan(\pi/3) = 1.732=\frac{y}{x}\\3x^2=y^2[/tex]

Replacing in the first equation:

[tex]x^2 +3x^2 =16\\x=2\\y=\sqrt{16-4}\\ y=2\sqrt 3[/tex]

Therefore, v can be represented in component form as v = <2, 2√3>.

The vector [tex]v[/tex] that lies in the first quadrant, makes an angle of [tex]\frac{\pi}{3}[/tex] with the positive x-axis, and has a magnitude of [tex]4[/tex] is:

[tex]v = 2i + 2\sqrt{3}j[/tex]

To find the vector v in component form, we start by understanding the relationships between the angle, magnitude, and components of a vector in the Cartesian coordinate system.

Given Data:

Vector Components:
In the first quadrant, the components of vector [tex]v[/tex] can be calculated using the following formulas:

Calculating Components:

For the x-component:
[tex]v_x = 4 \cdot \cos\left(\frac{\pi}{3}\right)[/tex]
The cosine of [tex]\frac{\pi}{3}[/tex] is [tex]\frac{1}{2}[/tex], so:
[tex]v_x = 4 \cdot \frac{1}{2} = 2[/tex]

For the y-component:
[tex]v_y = 4 \cdot \sin\left(\frac{\pi}{3}\right)[/tex]
The sine of [tex]\frac{\pi}{3}[/tex] is [tex]\frac{\sqrt{3}}{2}[/tex], so:
[tex]v_y = 4 \cdot \frac{\sqrt{3}}{2} = 2\sqrt{3}[/tex]

Resulting Vector:
Thus, the vector [tex]v[/tex] in component form is:
[tex]v = v_x i + v_y j = 2i + 2\sqrt{3} j[/tex]

Answer: c. 8!

Step-by-step explanation:

We know , that if we line up n things , then the total number of ways to arrange n things in a line is given by :-

[tex]n![/tex] ( in words :- n factorial)

Therefore , the number of ways 8 cars can be lined up at a toll booth would be 8! .

Hence, the correct answer is c. 8! .

Alternatively , we also use multiplicative principle,

If we line up 8 cars , first we fix one car , then the number of choices for the next place will be 7 , after that we fix second car ,then the number of choices for the next place will be 6 , and so on..

So , the total number of ways to line up 8 cars = 8 x 7 x 6 x 5 x 4 x 3 x 2 x1 = 8!

Hence, the correct answer is c. 8! .

Answer:Evaluate the function

k

(

x

)

=

−

x

2

+

6

k

(

x

)

=

-

x

2

+

6

at two different inputs and state the corresponding points.

Step-by-step explanation:

Answer:

Step-by-step explanation:

3. the diagram has 3 rectangles, 2 triangles

the surface area is the area of each shape

for the first rectangle = length x breadth = 8 x 6 = 48

for the second rectangle = length x breath = 6 x 6 = 36

for the third rectangle = length x breath = 6 x 6 = 36

for the triangles

(base x height )/2 = (8 x 4.5) /2 = 4 x 4.5 = 18

Surface Area =  48 + 18 + 36 + 36 = 138

4.  there are 4 identical rectangles and a base rectangle

4 x (5 x3 ) + ( 5 x5) = 4 x 15 + 25 = 60 + 25 = 85 ft

5. there are 2 triangles of 6 x 8 and a rectangle of 10 x 8

surface area = 2 x( (base x height)/2) + 10x8

2 x ((6 x8) /2 ) + 80 = 2 x (48/2)  + 80 = 48 + 80 = 128ft  

Answer:

a) Parameter

b) Statistic

c) Statistic

d) Parameter

e) Statistic

Step-by-step explanation:

For this case we need to remmber that a parameter describe a population of interest is fixed and not changes , and a statistic is a value that describe the sample size selected and can change between samples.

a. There are 100 senators in the 114th Congress, and 54% of them are Republicans.

The 54% here is a parameter since represent the proportion for all the population of interest on this case.

b. In a 2011 Gallup poll of 1008 adults living in the United States, 11% said they are satisfied with the condition of the national economy.

The 11% here is a statistic since we have a random sample and from this sample we calculate the proportion of interest for this case.

c. A survey of hospital records in 120 hospitals throughout the world shows the mean height of 180 cm for adult males.

The mean height of 180 cm is a statistic since we have a survey not all the population of interest

d. The 59 players on the roster of a championship football team have a mean weight of 248.6 pounds with a standard deviation of 44.6 pounds.

The 44.6 pounds is a parameter since we are interested on all the possible players and we have the info for all of them

e. In a random sample of households in the United States, it is found that 51% of the sampled households have at least one high‑definition television.

The 51% here is a statistic since we have a result from a sample not from the population

Answer:

P = 100 lbs in tension

F = 125 lbs in shear force downward direction

Moments are: 50 lb-ft and 125 lb-ft both in counter clockwise direction

Step-by-step explanation:

Forces

If we consider the entire structure as a system with two external forces P and F acting on it.

Translating these forces at point E,

Hence point E experiences the following forces:

P = 100 lbs in tension

F = 125 lbs in shear force

Moments

The bending moments are caused by the forces acting at respective offsets from point E

P = 100 lbs causes a bending moment of Mp = 100 lbs * (6/12) ft = 50 lb-ft

F = 125 lbs causes a bending moment of Mf = 125 lbs*(12/12)ft = 125 lb-ft

Moments are: 50 lb-ft and 125 lb-ft

Answer: 1. Route ABC is a right triangle.

2. Route CDE ia not a right triangle.

3. Distance HJ= 23.32miles

4. Distance GE = 17

5. Missing length= 35

6. The sides 16, 60, 62 do NOT belong to a right triangle.

Step-by-step explanation:

Going by Pythagoras theorem, for triangle to be proven to be a right triangle, the condition below must be satisfied.

Hypotenuse² = Opposite² + Adjacent²

For question 1,

Hyp =13, opp = 5, Adj is 12

Going by Pythagoras rule.

Since 13²= 5² + 12²

Then triangle ABC is a right triangle.

For question 2,

Using the same Pythagoras theorem to prove,

In triangle CDE,

Hyp= 22, opp= 18, Adj = 14

Since 22² is not = 18² + 14²

then CDE is not a right triangle.

For question 3,

For triangle HIJ, since it is confirmed to be a right triangle, then we use the Pythagoras theorem to calculate the missing side.

Longest side if the triangle= IJ = hypotenuse = 25

HI = 9.

IJ² = HI² + HJ²

HJ²= IJ² - HI²

HJ² = 25² - 9²

HJ² = 625 - 81

HJ= √544

HJ = 23.32miles

For question 4,

FGE is also shown to be a right triangle and the missing side GE is the longest side which is also the hypotenuse.

FG= 8, FE =15

Using the Pythagoras theorem,

Hyp² = FG² + FE²

GE² = 8² + 15²

GE² = 289

GE = √289

GE = 17.

For question 5,

The hypotenuse is given as 37, one side is given as 12, let's call the missing side x

Going by Pythagoras theorem,

37² = 12²+ x²

x²= 37² - 12²

x²= 1225

x=√1225

x=35.

The missing side is 35inches.

For number 6,

The numbers given are 16, 60, 62

To know if three sides belong to a right angle, we simply put them to test using Pythagoras theorem.

It is worthy of note that the longest side is the hypotenuse.

This brings us to the equation to check below that since:

62² Is not = 60² + 16²

Then the side lengths 16, 60, 62 do not belong to a right angle.

Answer:

813 seats

Step-by-step explanation:

Given that,

In the auditorium, the number of seats in the 1st row = 21

In the auditorium, the number of seats in the 2nd row = 29

Therefore, the increasing number of seats in each of the row = 8.

According to the question,

The number of seats in a row continues to increase by 8 seats with each additional row. For example, 29, 37, 45 etc.

To find the number of seats in the 100th row, we have to use statistical formula.

As 21 is the total seats in the 1st row, and there is an increase of 8 seats, the formula should be = 21 + (n - 1) × 8

we have to deduct 1 so that we get 99th rows seat numbers as we have to add 21 with that to find the 100th number row.

As the question is to determine the number of seats in the 100th row, therefore, n = 100.

The number of seats in the 100th row = 21 + (100 - 1) × 8 = 21 + 99 × 8

= 21 + 792 = 813 seats.

Answer:

C makes most sence

Step-by-step explanation:

Answer:  [tex]\dfrac{1}{12}[/tex] or 8.33%

Step-by-step explanation:

The conversion rate is given by :-

Conversion rate =(number of conversions ) ÷( total number of visitors)

As per given , we have

600 people visited your landing page, but only 50 visitors submitted the form..

i.e . Total number of visitors= 600

Number of conversions = 50

Then , the conversion rate  would be:-

Conversion rate = (50) ÷ 600 [tex]=\dfrac{50}{600}=\dfrac{1}{12}[/tex]

Hence, the conversion rate of your form = [tex]\dfrac{1}{12}[/tex]

In percentage , the conversion rate= [tex]\dfrac{1}{12}\times100=8.33\%[/tex]

The conversion rate is calculated by dividing the number of form submissions by the total number of visitors to the page and multiplying by 100. In this case, the conversion rate is 8.33%.

The conversion rate is central to tracking the effectiveness of your landing page. It's calculated by dividing the number of conversions (in this case, form submissions) by the total number of visitors to the page, then multiplying by 100 to get a percentage. In this case, the formula would look like this: (Number of forms submitted / Total visitors) x 100.

Plugging in your numbers, we get: (50 / 600) x 100 = 8.33%. So, the conversion rate of your form was 8.33%.

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The dot plot shows the distribution of order weights. There were no orders between 196 and 197 pounds. The most common order weight was 187.5 pounds, and the average weight was closer to 196 pounds.

1. To find the number of orders between 196 and 197 pounds, we need to look at the dot plot. From the given data, there are no orders between 196 and 197 pounds.

2. The most common order weight from the dot plot is 187.5 pounds.

3. To determine if the average weight is closer to 196 or 197 pounds, we need to calculate the mean of the data. The mean weight is calculated as the sum of the weights divided by the total number of weights. In this case, the mean weight is closer to 196 pounds.

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Answer:

Option (E) 648

Step-by-step explanation:

the 3 digit number can be represented by the blanks as " _ _ _  "

Now,

we have 10 choices ( i.e 0,1,2,3,4,5,6,7,8,9) available for each place in the blank if no condition is applied.

For the hundreds digit, using the conditions given in the question, we have 8 choices left

as 1 and 0 cannot be included in the hundreds place.

for the tens place

we will have 9 choices left out of 10 ( as 1 choice is less because we cannot have same number as on the hundred place )

similarly, for the ones place we have 9 choices left out of 10 ( as 1 choice is less because we cannot have same number as on the tens place )

Therefore,

Total possibilities = 8 × 9 × 9 = 648

Hence,

Option (E) 648

Answer:

0.140625

Step-by-step explanation:

Given that multiple-choice questions each have four possible answers (a comma b comma c comma d )​, one of which is correct. Assume that you guess the answers to three such questions.

Each question is independent of the other with constant probability

p = Prob for correct guess = 1/4 = 0.25

q = prob for wrong guess = 1-p = 0.75

Hence

[tex]P(CWW)\\= P(C)*P(W)*P(W)[/tex], since each question is independent of the other

=[tex]0.25*0.75*0.75\\= 0.140625[/tex]

Answer:

The required probability is [tex]\dfrac{5}{12}[/tex].

Step-by-step explanation:

If a fair dice is rolled then total outcomes are

{(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)}

We need to find the probability that the second die lands on a higher value than the first.

So, total favorable outcomes are

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

Formula for probability:

[tex]Probability=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]Probability=\dfrac{15}{36}[/tex]

[tex]Probability=\dfrac{5}{12}[/tex]

Therefore, the required probability is [tex]\dfrac{5}{12}[/tex].

Answer:

c. Asking people leaving a local election to take part in an exit poll

Step-by-step explanation:

Asking people leaving a local election to take part in an exit poll best represents the highest potential for nonresponse bias in a sampling strategy because of the importance of the local election compared to the exit polls.

It is worthy of note that nonresponse bias occurs when some respondents included in the sample do not respond to the survey. The major difference here is that the error comes from an absence of respondents not the collection of erroneous data. ...

Oftentimes, this form of bias is created by refusals to participate for one reason or another or the inability to reach some respondents.

Answer:

116.45 is the minimum score needed to be stronger than all but 5% of the population.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 10

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.05

P(X > x)  

[tex]P( X > x) = P( z > \displaystyle\frac{x - 100}{10})=0.05[/tex]  

[tex]= 1 -P( z \leq \displaystyle\frac{x - 100}{10})=0.05[/tex]  

[tex]=P( z \leq \displaystyle\frac{x - 100}{10})=0.95 [/tex]  

Calculation the value from standard normal z table, we have,  

[tex]P(z<1.645) = 0.95[/tex]

[tex]\displaystyle\frac{x - 100}{10} = 1.645\\x =116.45[/tex]  

Hence, 116.45 is the minimum score needed to be stronger than all but 5% of the population.

Answer:

option C. (x + 4) and (x − 8)

Step-by-step explanation:

A factor is one of the linear expressions of a single-variable of the polynomial.

Given: y = (1/4)(x + 4)(x - 8)

When y = 0

∴ (1/4)(x + 4)(x - 8) = 0 ⇒ multiply both sides by 4

∴ (x + 4)(x - 8) = 0

So, the factors of the function are (x+4) and (x-8)

The answer is option C. (x + 4) and (x − 8)

$4.95

Step-by-step explanation:

Initial price of gas was $5.00 a month ago

Today price of a gas is $5.50 per gallon

Increase in price= $5.50-$5.00=$0.50

%increase= 0.50/5.00 *100 =10%

Current price= $5.50

decrease current price by 10% is by multiplying the current price by 90%

90/100 * 5.50 = $4.95

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Answer:

[tex] l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)[/tex]

And then the maximum occurs when [tex] l'(\theta) = 0[/tex], and that is only satisfied if and only if:

[tex] \hat \theta = \bar X[/tex]

Step-by-step explanation:

For this case we have a random sample [tex] X_1 ,X_2,...,X_n[/tex] where [tex]X_i \sim N(\mu=\theta, \sigma)[/tex] where [tex]\sigma[/tex] is fixed. And we want to show that the maximum likehood estimator for [tex]\theta = \bar X[/tex].

The first step is obtain the probability distribution function for the random variable X. For this case each [tex]X_i , i=1,...n[/tex] have the following density function:

[tex] f(x_i | \theta,\sigma^2) = \frac{1}{\sqrt{2\pi}\sigma} exp^{-\frac{(x-\theta)^2}{2\sigma^2}} , -\infty \leq x \leq \infty[/tex]

The likehood function is given by:

[tex] L(\theta) = \prod_{i=1}^n f(x_i)[/tex]

Assuming independence between the random sample, and replacing the density function we have this:

[tex] L(\theta) = (\frac{1}{\sqrt{2\pi \sigma^2}})^n exp (-\frac{1}{2\sigma^2} \sum_{i=1}^n (X_i-\theta)^2)[/tex]

Taking the natural log on btoh sides we got:

[tex] l(\theta) = -\frac{n}{2} ln(\sqrt{2\pi\sigma^2}) - \frac{1}{2\sigma^2} \sum_{i=1}^n (X_i -\theta)^2[/tex]

Now if we take the derivate respect [tex]\theta[/tex] we will see this:

[tex] l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)[/tex]

And then the maximum occurs when [tex] l'(\theta) = 0[/tex], and that is only satisfied if and only if:

[tex] \hat \theta = \bar X[/tex]

Answer:

We can conclude that the value of 1732 is a statistic who represent the sample selected. And the value of 1622 represent the population mean from all the customers with the previous data.

Step-by-step explanation:

Previous concepts

A statistic or sample statistic "is any quantity computed from values in a sample", for example the sample mean, sample proportion and standard deviation

A parameter is "any numerical quantity that characterizes a given population or some aspect of it".

Solution to the problem

For this case the analyst knows that from previous records that the mean for all the customers (that represent the population of interest) is [tex] \mu = 1622[/tex]

He have a random sample of n =500 customers from the previous month and he knows that 1732 represent the sample mean for the selected customers calculated from the following formula:

[tex] \bar X = \frac{\sum_{i=1}^{500} X_i}{500}= 1732[/tex]

So on this case we can conclude that the value of 1732 is a statistic who represent the sample selected. And the value of 1622 represent the population mean from all the customers with the previous data.

Final answer:

The number 1732 represents the sample mean of monthly credit card purchases for a sample of 500 customers, distinct from the population mean of $1622.

Explanation:

The number 1732 in the scenario given refers to the sample mean, which is the average amount of money spent on purchases last month by the 500 customers in the sample. This contrasts with the population mean, which the analyst knows to be $1622 for all customers holding the credit card. The difference between the sample mean and the population mean can be a subject of further statistical analysis to understand customer behavior and spending patterns better.

Answer:

The correct answer is B=0.0262

Step-by-step explanation:

91÷3525 = 0.0262

The attached picture below gives a step by step explanation of how I arrived at my answer.

Please let's endeavor to always upload complete questions to avoid wrong answers.

Answer:

[tex]\frac{\sqrt[3]{90 x^2 y z^2} }{6 y z}[/tex]

Step-by-step explanation:

step 1;-

Given [tex]\frac{\sqrt[3]{5 x^2} }{\sqrt[3]{12 y^2 z} }[/tex]

now you have rationalizing  denominator  (i.e monomial) with

[tex]\frac{\sqrt[3]{5 x^2} }{\sqrt[3]{12 y^2 z} } X \frac{\sqrt[3]{(12 y^2 z)^{2} } }{\sqrt[3]{(12 y^2 z)^2} }[/tex]

By using algebraic formula is

now simplification , we get denominator function

again you have to simplify numerator term

now simplify

        cancelling y and 2 values

we get Final answer

[tex]\frac{\sqrt[3]{90 x^2 y z^2} }{6 y z}[/tex]

Answer:

a) [tex]Q(t) = 112.8*(0.766)^{t}[/tex]

b) When t = 10, Q = 7.845.

Step-by-step explanation:

The value of a quantity after t years is given by the following formula:

[tex]Q(t) = Q_{0}(1 + r)^{t}[/tex]

In which [tex]Q_{0}[/tex] is the initial quantity and r is the rate that it changes. If it increases, r is positive. If it decreases, r is negative.

a) Write a formula for Q as a function of t.

The initial value of a quantity Q (at year t = 0) is 112.8.

This means that [tex]Q_{0} = 112.8[/tex].

The quantity is decreasing by 23.4% per year.

This means that [tex]r = -0.234[/tex]

So

[tex]Q(t) = 112.8*(1 - 0.234)^{t}[/tex]

[tex]Q(t) = 112.8*(0.766)^{t}[/tex]

b) What is the value of Q when t = 10?

This is Q(10).

[tex]Q(t) = 112.8*(0.766)^{t}[/tex]

[tex]Q(t) = 112.8*(0.766)^{10} = 7.845[/tex]

When t = 10, Q = 7.845.