if you have 200 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?

The probability of  first drawing a red card, then a jack, and then a black card is 0.0612

First we will describe the standard deck of 52 cards in terms of black, red and face cards found in a standard deck

Following is a table of distribution of colored and face card found in a standard deck:

                Type                   Number of cards

                1 - 10                                40

                Black                               26

                Red                                 26

                Face                                12

The numerical cards from digit ( 1 to 10 ) are found in all 4 suits ( Clubs, Diamonds, Spades, and Hearts ). Hence, 10 x 4 = 40

- The entire deck is split in two colors ( Red and Black ) equally. So, the number of Black and Red cards are = 52 / 2 = 26 cards.

- The face cards are of three types ( King, Queen and Jack ). These three face cards are found in each of the 4 suits. Hence, Total number of face cards are = 4 * 3 = 12

- We will now consider the probabilities associated with each type. We will define 3 events and write down their probability as expressed:

Event ( A ): First draw is a red card.

- The probability of this event can be determined with the help of the table given above. There are a total of 26 red card in a standard deck of 52 cards. Hence,

           p ( A ) = [ Number of red cards ] / [ Total cards in a deck ]

           p ( A ) = [ 26 ] / [ 52 ]

           p ( A ) = 1 / 2

- After we make the first draw of a red card. Our deck distribution is changed to Number of Red cards remaining = 25 and total deck now has 51 cards remaining.

- We will define the next event as:

Event ( B ): The second draw is a face card.

- The probability of this event can be determined with the help of the table given above. There are a total of 12 face cards in a standard deck of 52 cards which is now down to 51 cards. Hence,

           p ( B ) = [ Number of face cards ] / [ Total cards in a deck ]

           p ( B ) = [ 12 ] / [ 51 ]

           p ( B ) = 4 / 17

- After we make the first draw of a face card. Our deck distribution is changed to Number of Face cards remaining = 11 and total deck now has 50 cards remaining.

- We will define the next event as:

Event ( C ): The third draw is a black card.

- The probability of this event can be determined with the help of the table given above. There are a total of 26 black cards in the deck. The total number of cards are down to 50 cards only. Therefore,

           p ( C ) = [ Number of black cards ] / [ Total cards in a deck ]

           p ( C ) = [ 26 ] / [ 50 ]

           p ( C ) = 13 / 25

- The entire drawing process consists of 3 events which are dependent on each draw. However, for the overall event to occur i.e drawing a red card , then a face card, and then a black card. We will multiply all three outcomes as follows:

         p ( T ) = p ( A ) * p ( B ) * p ( C )

         p ( T ) = [ 1 / 2 ] * [ 4 / 17 ] * [ 13 / 25 ]

         p ( T ) =  [ 26 / 425 ] ≈ 0.0612

Hence we get the required answer.

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Alto earned $200 while Sheryl earned $300 over the summer.

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider x represent the amount of money earned by Alto and y represent the amount of money earned by Sheryl

Together they earned a total of $500.

Hence the system of equations for the situation

x + y = 500 (1)

Sheryl earned $100 more than Alto:

y = x + 100

-x + y = 100(2)

Using Substitution to solve the system.

Solving equations 1 and 2 simultaneously gives:

x = 200 , y = 300

Therefore Alto earned $200 while Sheryl earned $300 over the summer.

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The tottal number of ways to selct  15 cookies is 15504 and the ways are there to select 15 cookies if at least three is 6188.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

we have to select 15 Cookies from 6 varieties so we can think an n₁+n2+n3+n4 + N5 +N6=15 with each o≤ni ≤15

C([tex]\frac{20}{12}[/tex]) = 15504

NOW we have One category is fixed let K Chocolate chips are Selected in I way The A we have to (15-K) Cookies from the varieties

C([tex]\frac{19-k}{15-5}[/tex])

So for k=0, C1=3876

k=1, C2 =3060

k=2, C3=2380

So C =C1+C2+C3=9316.

So the number of ways 15504-9316= 6188.

Hence, The tottal number of ways to selct  15 cookies is 15504 and ways are there to select 15 cookies if at least three is 6188.

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The way that errors can be introduced are;

Giving the questionnaire to all participants when they arrive for their appointment does not follow the protocol;

The participant could fill out the questionnaire before experiencing the therapy session.

Statistical errors are defined as errors that describe the difference that exists between a value obtained from a data collection process and the 'true' value for the population. Thus, the greater the error, the less representative the data will be of the population.

There are two main errors in this case which are type I error and type II error.

A type I error is called false-positive and it occurs if an investigator rejects a null hypothesis that is actually true in the population.

A type II error is called false-negative and it occurs if the investigator fails to reject a null hypothesis that is actually false in the population.

Now, from the question, since the data collection protocol alls for a questionnaire to be administered to patients having knee replacement surgery after the third physical therapy appointment, then we can introduce an error by;

Giving the questionnaire to all participants when they arrive.

The participant could fill out the questionnaire before experiencing the therapy session.

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Giving a questionnaire to all par-ticipants follows the timing of theprotocol.

BReading the questionnaire to par-ticipants with poor reading skillsfollows the timing of the protocol.

CGiving the questionnaire to allparticipants when they arrive fortheir appointment does not fol-low the protocol; the participantcould fill out the questionnairebefore experiencing the therapysession.

DGiving the questionnaire to theparticipants after the appoint-ment to be completed while theyhave a snack follows the timingof the protocol.

The correct option is:

a. randomly generated from the specified probability distributions

Given,

In the question:

Values for the random variables or uncertain variable inputs to a simulation are:-

a. randomly generated from the specified probability distributions

b. equal to the most likely value

c. selected by the decision maker

d. calculated by fixed mathematical formulas

e. controlled by the decision maker

Choose the correct one.

Now, According to the question:

Let's Know:

How do you generate a random number from a probability distribution?

In general, generating a random number from a probability distribution means transforming random numbers so that the numbers fit the distribution. Perhaps the most generic way to do so is called inverse transform sampling: Generate a uniform random number in [0, 1].

The correct option is:

a. randomly generated from the specified probability distributions

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Answer:

8x^2-14xy+3y^2 (I think)

Step-by-step explanation:

You probably don't need it now but like here

With 95% of confidence interval for the time it takes salesperson to talk to a potential customer is (12.42 , 5.38).

A Random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimizing the risk of selection bias.

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ ² ,s² ,Var(X) , or V(X).

A confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level represents the long-run proportion of corresponding CIs that contain the true value of the parameter. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.

Given in the question:

n = 46

x = 8.90

σ = 6

α = 0.95

As we know that:

[tex]X[/tex] ±[tex]Z_{\alpha /2} * \frac{\beta }{\sqrt{n} }[/tex]

putting the values we get,

  8.90 ± Z (0.95/2) ×6/√46

Now, considering the positive sign, we get,

=  8.90 + 3.52

= 12.42

Now considering the negative sign,

8.90 ± Z (0.95/2) ×6/√46

= 8.90 - 3.52

= 5.38

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The graph of the solution of the inequality is shown in figure.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ x + 5 ≥ 2

Now,

Since, The inequality is,

⇒ x + 5 ≥ 2

Hence, Simplify the inequality as;

⇒ x + 5 ≥ 2

Subtract 5, we get;

⇒ x + 5 - 5 ≥ 2 - 5

⇒ x  ≥ - 3

Thus, The graph of the solution of the inequality is shown in figure.

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answer:

I believe it's D

We concluded that whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.

What is the growth factor?

The rate at which a quantity multiplies itself over time is known as its growth factor. A quantity's growth rate is the factor by which it grows (or shrinks) over time.

Here, we have

The required expression for y with respect to x is:

y = (1.7)ˣ.......(1)

Where, 1.7 = 1-unit growth factor

Now we check,

Whenever x changes by 1

x →x +1 .....(2)

Now we put Equation (2) in (1) and we get

y' = (1.7)ˣ⁺¹

y' = (1.7)ˣ (1.7).....(3)

Taking the ratio of equations 3 & 1, we get

y'/y =   (1.7)ˣ (1.7)/(1.7)ˣ

y' = 1.7y

Hence, we observe that whenever x changes by 1, the value of y  becomes 1.7 units larger than its previous value.

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Recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]     where n>1

What do you mean by recursive realtion?

A recursive sequence is one in which terms are defined by reference to one or more previously defined terms.

The recursive formula [tex]a_{n+1}=a_{n}[/tex] + d  can be used to find the (n+1)th term of an arithmetic series if you know the nth term and the common difference, d.

It is given that cost of midisze car is $50.00

Rent per day = $19.99

We need to find the sequence of costs to rent the car for 1 day, 2 days, 3 days, and so on.

According to the question:

Cost become = 50.00 + 19.99n where n represents the number of days

Recursive formula become:

[tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]      where n>1

Therefore, recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]     where n>1

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Answer: 2

Step-by-step explanation:

solve in parentesis than divide by 0.5 or 1/2 then 2^3= 4 so

that minus 4 equals 2

Answer:

Where is the equation? It's ok but still.

Step-by-step explanation:

[tex]z = \frac{0.08 - 0.083}{\sqrt{0.083 * 0.917/100} }[/tex]

  = 0.108

pₐ = P( z < -0.108 ) = 0.4562

So the p-value obtained was a very high value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%)

Data given and notation

n = 100 represent the random sample taken

X=8 represent the people with depression or a depressive illness

p = 8/100 = 0.08 estimated proportion of people with depression or a depressive illness

p₀ = 0.083  is the value that we want to test

α = 0.05 represent the significance level  assumed

Confidence = 83% or 0.83  assumed

z  would represent the statistic (variable of interest)

pₐ represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportions of people with depression or a depressive illness is lower than the general adult population value of 8.3% or 0.083:  

Null hypothesis:  

p ≥ 0.083

Alternative hypothesis:  

p < 0.083

When we conduct a proportion test we need to use the z statistic, and the is given by:

[tex]z = \frac{p- p_{0} }{\sqrt{p_{0} ( 1 - p_{0} )/ n } }[/tex]                       ---------------------  (1)  

The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value .

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z = \frac{0.08- 0.083 }{\sqrt{0.083 ( 1 - 0.083 )/ 100 } }[/tex]

 =  - 0.083 / √ 0.0076

 = -0.083 / 0.028

 = -0.108

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed is α = 0.05 . The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

     pₐ = P( z < -0.108 ) = 0.4562

So the p value obtained was a very high value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%).

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Answer: 14 Adult tickets

Step-by-step explanation:

The equation for the total number of tickets would be

x+y=18

5x+3y=82

y=18-x

5x+3(18-x)=82

2x=28

x=14

x= Number of adult tickets

Answer: (-84, 272)

x = -84

y = 272

Hope this helps!

Answer:

Below

Step-by-step explanation:

-6x - 2y = - 40       <====multiply this entire equation by -1 to get:

6x + 2y = 40      <=====   then add it to the second equation

-7x -2y = -44         to get:

-x = -4    

          so x = 4     use this value in one of the equations to compute y

-6(4) - 2y = -40

-2y = -16

y = 8                    (4,8)

The number of ft that Luke climbed, given the elevation he started from, and the summit, is 5, 050 ft

The number of feet that Luke climbed, can be found by the formula:

Number of feet climbed = Summit of K2 - Luke's starting elevation

Summit of K 2 = 28, 251 ft

Luke's starting elevations = 23, 201 ft

Elevation climbed by Luke was therefore:

= 28, 251 - 23, 201

= 5, 050 ft

In conclusion, the total elevation that Luke climbed from his starting point to the summit of K2 is 5, 050 ft.

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The largest area is found to be 8702.5 [tex]ft^{2}[/tex].

We know that area of rectangle

A = xy ........ (1)

Perimeter of rectangle (given) = 590 ft

Using x and y as two variables ;

5x + 2y = 590

solve yb in term of x

y = -5/2 x + 295......(2)

Now we will get area only in one variable from (1) and (2)

A = x ((-5/2)x + 295)

A = -5/2 [tex]x^{2}[/tex] + 295x

differentiate it with respect gto x

A' = -5x + 295........ (3)

find the critical point to get your minima and maxima value.

Put A' = 0,  x = 295/5 = 59

x = 59

then , from (2)

y= (-5/2 × 59) + 295 = 147.5

y = 147.5

again differentiate (3)

A'' = -5 < 0. i.e critical point x = 59 is point of maxima.

So, maximum area = 59 × 147.5

Largest area = 8702.5 [tex]ft^{2}[/tex]

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Answer:

A Acute angle (Give me pointssss)

Step-by-step explanation:

Its right bc im smart

Answer: -9/2

Let's solve this equation step-by-step.

−8+2(3+8)=−4(g+1)

Step 1: Simplify both sides of the equation.

−8+2(3+8)=−4(g+1)

−8+2(3+8)=(−4)(g)+(−4)(1) (Distribute)

−8+22=−4g+−4

(−8+22)=−4g−4 (Combine Like Terms)

14=−4g−4

Step 2: Flip the equation.

−4g−4=14

Step 3: Add 4 to both sides.

−4g−4+4=14+4

−4g=18

Step 4: Divide both sides by -4.

−4g/−4 = 18/−4

g = −9/2

a) The area to the left of 25 is 0.63056

b) The area to the left of 16 is 0.12167

c) The area to the right of 22 is 0.56618

d) The area to the right of 28 is  0.20233

e) The area between 16 and 30 is  0.75666

Given,

The mean of the distribution = 23

Standard deviation  = 6

We have to find the following areas

(a) Entering the values

(b) Entering the values

(c) Entering the values

(d) Entering the value

(e) Entering the values

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14t-5t is another way to write the expression ​t⋅(14−5)

A number system is defined as a system of writing to express numbers.

The given expression is t(14-5)

An expression is combination of variables, numbers and operators.

t times of fourteen minus five

Here t is the variable

We need to find other way to write this expression

t(14-5)

Apply distributive property

14t-5t

9t

Hence, 14t-5t is another way to write the expression ​t⋅(14−5)

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40/3 feet /second fast the top of the ladder sliding down the wall.

What is ladder?

A ladder is a piece of gear used for climbing up or down objects that consists of repeated bars or steps (rungs) between two upright lengths of metal, wood, or rope.

Typically, these ladders work best for outdoor tasks like roof access or exterior painting. A straight ladder's reach is typically two feet higher than its height.

Given:

A 10 foot ladder is leaning against a wall when the base begins to slide away from the wall. when the base is 8 feet from the wall, the base is moving at the rate of 4 feet per second.

We have dx/dt = 4 feet per second

We want to find dy/dt.

From given information,

x^2 + y^2 = 10^2         ..(1)

When x = 8

⇒ y = √(10^2 - 8^2)

y = √(100 - 64)

y = √36

y = 6 feet

Now differentiate equation (1) with respect to t

[tex]2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\ x\frac{dx}{dt} + y\frac{dy}{dt} = 0\\ \frac{dy}{dt} = -\frac{x}{y} \frac{dx}{dt}[/tex]

Plug x = 8, y = 6 and dx/dt = 10

⇒

[tex]\frac{dy}{dt} = -\frac{8}{6}(10)\\ \frac{dy}{dt} = -\frac{40}{3}[/tex]

Hence, 40/3 feet /second fast the top of the ladder sliding down the wall.

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Answer:

y = 100 - 10x

Step-by-step explanation:

Let y₀ be the original water level before any marbles were removed

Let y = water level after x marbles are removed.

Let d be the water level drop for every marble removed

Then we have the general equation:

y = y₀ - x.d  

We have to find d and y₀

So we get one equation for the water level after removal of 2 marbles

80 = y₀ - 2d     [1]

After 4 more marbles were removed, the water level drops to 40ml. That means for 4 marbles removed, the water level drops from 80 to 40. So drop in water level for 4 marbles = 80-40 = 40ml

For each marble then, water level drop = 40/4 = 10ml. This is the value of d

Plug this value of d into [1] to get the original water level y₀

80 = y₀ - 2( 10)

80 = y₀ - 20

100 = y₀

or,

y₀ = 100

So original water level is 100ml and the equation for water level after x marbles are removed is

y = 100 - 10x

Answer:

58

Step-by-step explanation:

72 + 1 - 5 x 3

= 72 + 1 - 15

= 73 - 15

= 58

Answer: Brian payed $24.00

How u do it:

Discount= original price x discount%/100

Discount = 40 × 40%/100

Discount = 40 x 0.4 

You save = $16.00

Final Price = Original Price - Discount

Final Price = 40 - 16

Final Price = $24.00

Answer:

5/2 or 2.5

Step-by-step explanation:

Slope is rise/run. We take the difference of the y-coordinates and divide it by the difference of the x-coordinates.

From this, we get [tex](7--3)/(5-1)[/tex], or [tex]10/4[/tex], which can be simplified to 5/2, or 2.5.

Based on this output of multiple regression analysis, critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance is Approximately F = 2.50.

A single dependent variable and a number of independent variables can be analyzed using multiple regression, a statistical approach. Using independent variables whose values are known, multiple regression analysis aims to predict the value of the single dependent value.

When doing multiple regression, each independent variable's value is taken into account in order to predict the value of the single dependent variable. Example: A researcher chooses to examine student performance at a certain school over time.

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