You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 361 randomly selected caterpillars observed, 53 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all caterpillars that lived to become a butterfly is betweend b. If many groups of 361 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent of these percent will not contain the true population proportion.

If the drain for a 90 percent efficient furnace and the drain for the air conditioning coil are run with a common drain, the drain should be sized large enough to accommodate the combined condensate flow from both systems.

To determine the appropriate size, you should:
1. Check the manufacturer's recommendations for both the furnace and the coil.
2. Calculate the maximum condensate flow from each system.
3. Add the two values together to find the total condensate flow.
4. Select a drain size that can handle the combined flow rate.

Learn more about furnace: https://brainly.com/question/28268048

#SPJ11

The ordered pairs (6, 3), (5, 6), (-1, 1), (6,9), (8,8) does not represent a function

From the question, we have the following parameters that can be used in our computation:

(6, 3), (5, 6), (-1, 1), (6,9), (8,8)

The general rule is that

A set of points or ordered pairs that represent a function must have unique x and y values

i.e. the x values must not point to different values

In the ordered pairs (6, 3), (5, 6), (-1, 1), (6,9), (8,8), we can see that the x value 6 points to the y values 3 and 9

This means that the the ordered pairs does not represent a function

Read more about relation and function at

https://brainly.com/question/10283950

#SPJ1

The probability that either event will occur is given as follows:

P(A or B) = 0.75.

The formula used to calculate the probability is given as follows:

P(A or B) = P(A) + P(B) - P(A and B).

The total number of events from the Venn's diagram is given as follows:

4 x 9 = 36.

Hence the probability of each outcome is given as follows:

Hence the or probability is given as follows:

P(A or B) = P(A) + P(B) - P(A and B).

P(A or B) = 0.5 + 0.5 - 0.25

P(A or B) = 0.75.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

Answer: 1

Step-by-step explanation:

Vinny's new grade in math, if the playing time reduces to 6 hours per week, would be 85.33.

If we wish to illustrate how Vinny's Math Models grade relates to the amount of time she spends playing computer games, we may employ the formula that defines an inverse proportion:

k = G x T

k = 64 x 8 = 512

For 6 hours playing:

512 = G x 6

G = 512 / 6

= 85. 33

Find out more on proportionality at https://brainly.com/question/29465808

#SPJ1

A one-tailed test has a P-value of 0.01 and a two-tailed test has a P-value of 0.053.

We must utilize the F-distribution table or calculator to address this question. The F test follows an F-distribution since it is a ratio of two variances.

a. To calculate the P-value for a one-tailed test, we must first calculate the likelihood that the F-statistic is greater than or equal to 7.46.

Using a table, we can find the area under the F-distribution curve to the right of 7.46 with 5 degrees of freedom in the numerator and 7 degrees of freedom in the denominator.

Assuming an alpha level of 0.05, we reject the null hypothesis if the P-value is less than 0.05.

For the given F-statistic of 7.46, the P-value for a one-tailed F-test with five degrees of freedom in the numerator and seven degrees of freedom in the denominator is approximately 0.01.

b. For a two-tailed test, we must calculate the likelihood of seeing an F-statistic that is 7.46 or more in either direction. This means we must calculate the area under the F-distribution curve in the distribution's two tails.

To find the p-value for a two-tailed F-test with 5 and 7 degrees of freedom and a test statistic of 7.46, we need to use an F-distribution table.

Using a table, we would look for the intersection of the row with 5 degrees of freedom and the column with 7 degrees of freedom, which gives us the critical F-value for a significance level of 0.05 (assuming equal variances in the two populations being compared). The critical F-value is 4.03.

Since the test statistic of 7.46 is greater than the critical F-value of 4.03, the p-value for the two-tailed test is less than 0.05. Specifically, the p-value is the probability of observing an F-statistic as extreme or more extreme than 7.46, which is the probability in the right tail of the F-distribution plus the probability in the left tail:

p-value = P(F > 7.46) + P(F < 1/7.46)

       = 0.052 + 0.001

       ≈ 0.053

Therefore, the p-value for the two-tailed test is approximately 0.053.

Learn more about One-Tailed Test:

https://brainly.com/question/31367829

#SPJ4

The percentage of budget that is allotted to variable expenses is 46.03%

We first have to determine the solution for what the va,riable expenses is supposed to be

$2,003 (total budget) - $1,081 (fixed expenses)

= $922

Next we will have to solve for the percentage that is the budget which is allocated to the variable expenses

This is simply written as

variable expenses / total budget * 100

($922 (variable expenses) ÷ $2,003 (total budget)) × 100 = 46.03%

Hence the percentage of budget that is allotted to variable expenses is 46.03%

Read m ore on variable expenses here:https://brainly.com/question/30191622

#SPJ1

Answer:

46.03%

Step-by-step explanation:

922 ÷ 2003 x 100 which gives you 46.03

Answer:

The slope is 5.

Step-by-step explanation:

We are given the points (-2, -5) and (0,5).

We want to find the slope between these 2 points.

The slope (m) is written with the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.

Let's label the values of the points to avoid any confusion and mistakes when calculating.

[tex]x_1=-2\\y_1=-5\\x_2=0\\y_2=5[/tex]

Now, substitute into the formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{5--5}{0--2}[/tex]

This can be simplified to:

[tex]m = \frac{5+5}{0+2}[/tex]

Add the values together.

[tex]m = \frac{10}{2}[/tex]

m = 5

The slope is 5.

The error mean square would then be given by the term of 2.71 which is option B.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally.

The three most often employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to get the mean. When all of the values are organised in ascending order, the Median is the median value of the provided data.

Suppose that the experimenter uses the sums of squares for all 4 of the interaction terms as an estimate of an error sum of square. The error mean square would then be 2.71

Learn more about Mean:

https://brainly.com/question/20118982

#SPJ4

An expression that represents the length of one side of the square is √(12x/35).

In Mathematics and Geometry, the area of a square can be calculated by using this mathematical equation (formula);

A = x²

Where:

By substituting the given parameters into the formula for the area of a square, we have the following;

-12x + 36x² = x²

36x² - x² = 12x

35x² = 12x

x = √(12x/35)

Read more on expression and square here: https://brainly.com/question/16506342

#SPJ1

Answer:

No, it is not. See justification in the diagram.

Step-by-step explanation:

You have to do polynomial long division. My math is shown in the picture below and if you have any questions, please let me know.

At the end, (x+7) does not go into 468.

First, let me explain some key terms related to the question.

- Discrete: This refers to mathematics that deals with countable or finite sets of numbers, rather than continuous sets. In other words, we're dealing with specific, separate values rather than a continuous range.
- Recurrence: This refers to a mathematical sequence where each term depends on one or more previous terms. In other words, we can use a formula to generate the next term based on previous terms.
- Relation: This refers to a mathematical expression that relates one or more variables. In this case, our recurrence relation relates the sequence An to its previous terms.

With that in mind, let's tackle the question!

We're given a recurrence relation: An = 6An-1 – 9An-2. This means that each term in the sequence An depends on the two previous terms, An-1 and An-2.

We're also given initial conditions: a0 = 2 and a1 = 3. This gives us a starting point for the sequence.

To solve the recurrence relation and find the values of An, we'll use a technique called iteration. Essentially, we'll use the recurrence relation to generate the next term in the sequence, then use that term to generate the next one, and so on.

Here's how it works:

- First, we use the initial conditions to find the first two terms of the sequence: a0 = 2 and a1 = 3.
- Next, we use the recurrence relation to generate the third term: a2 = 6a1 - 9a0 = 6(3) - 9(2) = 0.
- We continue this process, using the recurrence relation to generate each subsequent term. For example, to find a3, we use the formula An = 6An-1 – 9An-2 with n = 3: a3 = 6a2 - 9a1 = 6(0) - 9(3) = -27.
- We can keep going like this to find as many terms as we need.

Here's what the first few terms of the sequence look like:

a0 = 2
a1 = 3
a2 = 0
a3 = -27
a4 = -54
a5 = -162
a6 = -270
...
Discretehttps://brainly.com/question/31359635

#SPJ11

Call the first number "x" and the second number "y". So the first number is 3.

From the problem statement, we know:

x = y + 4 (the first number is four more than the second number)

2x = 4y + 10 (two times the first number is 10 more than four times the second number)

Now we can solve for one of the variables in terms of the other, and then substitute that expression into the other equation to solve for the other variable. Let's use the first equation to solve for x:

x = y + 4

Substitute this expression for x into the second equation:

2x = 4y + 10

2(y + 4) = 4y + 10

Distribute the 2:

2y + 8 = 4y + 10

Subtract 2y from both sides:

8 = 2y + 10

Subtract 10 from both sides:

-2 = 2y

Divide both sides by 2:

-1 = y

Now we know that the second number is -1. We can use the first equation to find the first number:

x = y + 4

x = -1 + 4

x = 3

Learn more about number visit: brainly.com/question/11418015

#SPJ4

9 5/2 in radical form is equal to 4√2 + √7.

We are able to rewrite 9 5/2 in radical form through first changing it to an improper fraction.

9 5/2 = (9 x 2 + 5) / 2 = 23/2

Now, we can express 23/2 as a mixed radical by using locating the largest perfect square that may be a aspect of 23. the largest perfect square which is much less than 23 is 16 (that's 4^2).

So, we are able to write:

23/2 = 16/2 + 7/2 = 8 + 7/2

Now, we will express 8 + 7/2 in radical form as:

8 + 7/2 = 4 x 2 + 7/2 = 4√2 + √7

Consequently, 9 5/2 in radical form is equal to 4√2 + √7.

Learn more about radical form:-

https://brainly.com/question/30347671

#SPJ4

To calculate the covariance between X and Y, we can use the formula:
Cov(X,Y) = E[XY] - E[X]E[Y]
where E[XY] is the expected value of the product of X and Y, and E[X] and E[Y] are the expected values of X and Y, respectively.

Using the given probability distributions, we can calculate the expected values as follows:
E[X] = ∑x∑y xP(X=x, Y=y)
    = (0)(0.26) + (1)(0.74)
    = 0.74
E[Y] = ∑x∑y yP(X=x, Y=y)
    = (0)(0.26) + (1)(0.36) + (2)(0.38)
    = 1.12
E[XY] = ∑x∑y xyP(X=x, Y=y)
     = (0)(0)(0.26) + (0)(1)(0.36) + (1)(0)(0.02) + (1)(1)(0.34) + (1)(2)(0.38)
     = 1.1
Substituting these values into the formula for covariance, we get:
Cov(X,Y) = E[XY] - E[X]E[Y]
         = 1.1 - (0.74)(1.12)
         = 0.0048
Therefore, the covariance between X and Y is 0.0048.

To learn more about Probability Distribution : https://brainly.com/question/24106873

#SPJ11

The spares should be kept to maintain a 90% or more probability of system success is 35

Let λ be the normal number of component disappointments per year, at that point the disappointment rate (or rate parameter) is given by λ/52 since there are 52 weeks in a year. Let's signify this by μ = λ/52.

The framework victory likelihood can be modeled utilizing the Poisson dissemination since the disappointments happen haphazardly and freely over time. Let X be the number of component disappointments in a year, at that point X takes after a Poisson conveyance with cruel λ.

To preserve a 90% or more likelihood of system victory, we got to guarantee that the number of saves is adequate to cover at the slightest 90% of the potential disappointments. This implies that the likelihood of having more than k disappointments in a year ought to be less than or break even with 0.1, where k is the number of saves.

Let Y be the number of component disappointments amid the two-week conveyance time. At that point, Y too takes after a Poisson conveyance with cruel μ/26, since there are 26 weeks in a half-year (i.e., two quarters). The likelihood of having more than k disappointments amid the conveyance time is given by:

P(Y > k) = 1 - P(Y ≤ k) = 1 - ∑_[tex]{i=0}^k (e^(-μ/26) (μ/26)^i[/tex]/ i!)

where e is the base of the common logarithm.

To preserve a 90% or more likelihood of system victory, we ought to select k such that P(Y > k) ≤ 0.1. Able to solve for k numerically, employing a spreadsheet or a computer program.

For example, utilizing Microsoft Exceed expectations or Go-ogle Sheets, ready to utilize the taking after an equation to compute P(Y > k) for distinctive values of k:

=1-POISSON(k,μ/26,TRUE)

where POISSON is the Poisson total conveyance work, with the moment contention being the cruel and the third contention being Genuine to indicate an aggregate conveyance.

Beginning with k = 26 (i.e., one save per week), able to increment k until we discover the littlest esteem that fulfills P(Y > k) ≤ 0.1. In this case, we discover that k = 35 saves are required to preserve a 90% or more likelihood of framework victory. 

To know more about probability refer to this :

https://brainly.com/question/24756209

#SPJ4

The answer is (b) x+y=C.

The given equation is [tex]xdy + ydx = 0.[/tex]

We can rewrite this equation as:

dy/dx = -y/x

This is a first-order linear differential equation that can be solved using separation of variables.

We can write it as:

dy/y = -dx/x

Integrating both sides, we get:

ln|y| = -ln|x| + ln|C|

where C is the constant of integration.

Simplifying this expression, we get:

ln|y| = ln|C/x|

Taking the exponential of both sides, we get:

|y| = |C/x|

Since |C| is a constant, we can replace it with another constant, say k, giving:

|y| = k/|x|

where k is a non-zero constant.

Now, we can rewrite this expression as:

y = ± k/x

where the ± sign depends on the sign of y.

Therefore, the solution to the differential equation xdy + ydx = 0 is y = ± k/x.

We can rewrite this solution in different forms:

a) y = Cx, where C = ± k

b) x + y = C, where C = k/2

c) xy = C, where C = ± k^2

d) x = Cy, where C = ± k

Therefore, the answer is (b) x+y=C.

To learn more about constant visit:

https://brainly.com/question/1597456

#SPJ11

For a piece of string art created by 16 evenly spaced nails around the circumference of a circle. The measure of angle BXC is equals to the 90°.

We have a piece of string art is made by placing 16 evenly spaced nails around the circumference of a circle. See the above figure. We have to determine the measure of angle BXC. Now, using the inscribed angle theorem , the measure of angle BXC, [tex] m\angle BXC = \frac{ 1}{2} ( m \hat {AD} + m \hat {BC}) [/tex]

Measure of AD = [tex] 2(\frac{ 1}{16})360°[/tex] = 45°

The measure of BC = [tex] 6(\frac{ 1}{16} )360°[/tex]

= 135°

Now, Using the above formula the measure of angle BXC [tex] = \frac{ 1}{2} ( m \hat {AD} + m \hat {BC})[/tex]

[tex]= \frac{ 1}{2} ( 45° + 135°)[/tex]

= 90°

Hence, required value is 90°.

For more information about angle, visit :

https://brainly.com/question/1309590

#SPJ4

Complete question:

The above figure complete the question.

28. A piece of string art is made by placing 16 evenly spaced nails around the circumference

of a circle. A piece of string is wound from A to B to C to D. What is measure of angle BXC.

The standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

To find the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students, we need to use the binomial distribution.

Given that 71.6% of all first-time, full-time freshmen believe that same-sex couples should have the right to legal marital status, the probability (p) that a randomly selected student from this population believes this is:

p = 0.716

Since we are interested in the number of students in a sample of nine who believe this, we can model this using the binomial distribution with parameters n = 9 and p = 0.716.

The formula for the standard deviation of a binomial distribution is:

σ = sqrt(n * p * (1 - p))

Substituting in the values of n and p, we get:

σ = sqrt(9 * 0.716 * (1 - 0.716))

σ = 1.168

Therefore, the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

To learn more about deviation visit:

https://brainly.com/question/2554578

#SPJ11

Answer:

Solving for y

exact form for y = 4/3

Demical form for y = 1/3

Mixed number for y = 1 1/3

( BTW all of these answers all right it juts depends on what exactly there asking for, for example if there asking for the exact form for y it would be 4/3 )

Answer:

If not choose all that apply, technological process will shift the PPC right (outwards)

Step-by-step explanation:

The production possibilities curve represents the maximum amount of goods and services that a country can produce with its limited resources. It is a graphical representation of the trade-offs a country must make between producing one good or service over another. Any factor that can increase production will shift the curve outward, indicating an increase in the maximum amount of goods and services that can be produced.

An increase in the production of investment goods will shift the curve outward because it will increase the amount of capital goods that can be used to produce other goods and services. Investment goods are items like machinery, equipment, and infrastructure that are used to produce other goods and services. By increasing the production of investment goods, a country can increase its productive capacity, allowing it to produce more goods and services in the future.

An increase in the production of consumer goods will not shift the curve outward because it does not increase the country's productive capacity. Consumer goods are items that are consumed immediately, like food, clothing, and electronics. While an increase in the production of consumer goods can lead to short-term economic growth, it will not increase the country's long-term productive capacity.

Technological progress, on the other hand, will shift the production possibilities curve outward. Technological progress refers to advancements in technology that increase productivity, reduce costs, and improve efficiency. By adopting new technologies, a country can produce more goods and services with its existing resources, allowing it to shift its production possibilities curve outward.

In conclusion, an increase in the production of investment goods and technological progress will shift the production possibilities curve outward, while an increase in the production of consumer goods will not.

More question on increase : https://brainly.com/question/11360390

#SPJ11

Answer:

search-icon-header

Search for questions & chapters

search-icon-image

Question

Bookmark

If x=2 and x=3 are roots of the equation 3x

2

−2kx+2m=0 then (k,m)=

Medium

Solution

verified

Verified by Toppr

Correct option is A)

Since x=2 and x=3 are roots of the equation 3x

2

−2kx+2m=0

⇒12−4k+2m=0⇒2k−m=6 ...(i)

and ⇒27−6k+2m=0⇒6k−2m=27 ...(ii)

On multiplying (i) by 3 and subtracting (ii) from it, we get

6k−3m=18

−

6

k

+

−

2m=

−

2

7

−m=−9

∴m=9

On putting m=9 in (i), we get

2k=15⇒k=

2

15

∴(k,m)=(

2

15

,9)

Hence, Option A is correct.

Answer:

A. 2x+3 and B. 3y² - 2y + 4 and E. x²/2 - 3x + 7 are polynomial expressions.

The domain and range for the relation are

for the graph: domain is [-3 3] and range is [-1 3]

domain is [-2 4] and range is [-3 0]

The mathematics domain and range refer, respectively, to a function's input values as well as its output.

The set of possible input values that can be used for the function is called the domain or independant variable(s), while also comprising all necessary values for the calculation of appropriate results.

Conversely, the range or dependent variable(s) represents every conceivable result obtainable from specific sets of inputs within the domain. It essentially displays the function's abilities to produce an output value based on any given input it receives.

Learn more about domain and range at

https://brainly.com/question/2264373

#SPJ1

Answer:

3.29 cm.

Step-by-step explanation:

The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

376.8 = (1/3)π(6^2)h

Simplifying:

376.8 = 36πh

h = 376.8 / (36π)

h ≈ 3.29 cm

Therefore, the height of the orange cone is approximately 3.29 cm.

Gouge-em Cable Company will charge $30 for its cable services, earning them a profit of $70 thousand. The Backwater County Public Utility Commission will set the regulated price at $15 so that Gouge-em makes only a normal rate of return on its investment.

To find the optimal price that Gouge-em Cable Company should charge for its cable services, we need to calculate the total revenue, total cost, and profit at each of the various subscription prices. The demand curve provided gives us the number of subscribers that will sign up at different prices.

Price Quantity Demanded Total Revenue Total Cost Profit

$10 100 $1,000 $640,200 -$639,200

$20 80 $1,600 $640,160 $959,840

$30 60 $1,800 $640,120 $1,159,880

$40 40 $1,600 $640,080 $959,920

$50 20 $1,000 $640,040 $359,960

To maximize profit, Gouge-em Cable Company should charge the price where marginal revenue equals marginal cost. Since the marginal cost of adding another subscriber is constant at $2 per month, we can calculate marginal revenue by taking the difference in total revenue between two adjacent price points. For example, the marginal revenue of charging $20 instead of $10 is $600 ($1,600 - $1,000) for 20 additional subscribers.

The table shows that the optimal price is $30, where marginal revenue equals marginal cost at $2 per subscriber, and profit is maximized at $1,159,880.

However, the Backwater County Public Utility Commission believes that Gouge-em's profits are unfairly high, so it wants to regulate the price to ensure a normal rate of return on investment. A normal rate of return is typically around 10% of total investment. Gouge-em's total investment is the sum of fixed costs divided by the monthly profit margin:

Total investment = Fixed costs / Monthly profit margin

= $640,000 / ($1,159,880 / 5)

= $27,627,724.51

A 10% return on investment is $2,762,772.45 per year, or $230,231.04 per month. To earn this amount, Gouge-em needs to charge a price that covers its total costs plus the normal rate of return, which is:

Regulated price = Total cost / Quantity demanded + Normal rate of return / Quantity demanded

= $640,000 / 60 + $230,231.04 / 60

= $10.17

Therefore, the Backwater County Public Utility Commission will set the regulated price at $15, which is a round number close to the calculated price of $10.17. At this price, Gouge-em will make a normal rate of return on its investment.

To learn more about Public Utility here:

brainly.com/question/30748959#

#SPJ11

The the approximate value of √8  is option B: between 2.8 and 2.9

An approximate number is a value derived close to the exact figure, yet a slight variance remains present. It is used to show that exact figures are precise and require no estimation.

However, these numbers are seen as estimates since their exact representation cannot be achieved through a finite number of digits. A close but lower value than a number is known as its approximate value by defect, with a desired level of accuracy.

Therefore, the radical expression for the square root of 8 is √8, but it can also be written as 2√2. Additionally, it can be expressed as a fraction, which is approximately equal to 2.828. Hence option B is correct.

Learn more about approximate  value from

https://brainly.com/question/201331

#SPJ1

The correct expression is the one in option A; [tex]-3^{15}[/tex]

Here you need to remember two rules for exponents, these are:

[tex]x^n*x^m = x^{n +m}\\\\[/tex]

And:

[tex](x^n)^m = x^{n*m}[/tex]

Now our expression is:

[tex]-(3^2*3^3)^3[/tex]

Using the first rule we will get:

[tex]-(3^2*3^3)^3 = -(3^{2 + 3})^3 = -(3^5)^3[/tex]

Using the second rule:

[tex]-(3^5)^3 = -3^{3*5} = -3^{15}[/tex]

The correct option is a

Learn more about exponents at:

https://brainly.com/question/847241

#SPJ1

The probability that a random point on AK will be on CH is 1/2

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and it is equal to 100% in percentage.

probability = sample space /total outcome

The total outcome is the range of AK.

range = highest - lowest

= 10-(-10) = 10+10 = 20

sample space of CH = 4-(-6)

= 4+6 = 10

Therefore probability that a random point on AK will be on CH is 10/20

= 1/2

learn more about probability from

https://brainly.com/question/24756209

#SPJ1

The probability of getting exactly 1 blue marble is 9/22 or approximately 0.409.

The probability of getting exactly 1 blue marble can be calculated in two steps:

Step 1: The probability of drawing a blue marble on the first draw is:

P(Blue on first draw) = 3/12

After drawing a blue marble, there will be 2 blue, 4 red, and 5 green marbles left in the bag.

The probability of drawing a non-blue marble on the second draw is:

P(Non-blue on second draw) = 9/11

Alternatively, if a non-blue marble is drawn first, there will be 3 blue, 4 red, and 4 green marbles left in the bag. The probability of then drawing a blue marble on the second draw is:

P(Blue on a second draw after non-blue on the first draw) = 3/11

So the probability of getting one blue and one non-blue marble on the first and second draws in any order is:

P(One blue and one non-blue) = P(Blue on first draw) × P(Non-blue on second draw) + P(Non-blue on first draw) × P(Blue on second draw after non-blue on first draw)

P(One blue and one non-blue) = (3/12) × (9/11) + (9/12) × (3/11) = 27/132

Step 2: There are two possible orders in which we can get exactly 1 blue marble is:

blue on the first draw and non-blue on the second draw, or non-blue on the first draw and blue on the second draw.

The probability of getting exactly 1 blue marble is:

P(Exactly 1 blue) = P(One blue and one non-blue) + P(One non-blue and one blue)

P(Exactly 1 blue) = 27/132 + 27/132 = 54/132

Simplifying, we get:

P(Exactly 1 blue) = 9/22

Therefore, the probability of getting exactly 1 blue marble is 9/22 or approximately 0.409.

To learn more about probability visit:

brainly.com/question/30648498