you have an opaque urn with three blue balls and two white balls. one by one, you draw (remove) a ball from the urn, note its color, and put it aside (do not return it to the urn). 1) what is the probability that your first draw is a white ball? 2) what is the probability that your first two draws are blue balls? 3) what is the probability that your first three draws are blue balls? 4) what is the probability that you pull blue, white, blue, white, blue in that order? 5) suppose you return the ball you draw to the urn after each draw. what is the probability that your first three draws are blue balls?

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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Answer:

No, some of them are, but not all of them

Step-by-step explanation:

I hope this helped you out!

Answer:

Step-by-step explanation:

No; all multiples are not multiples of 6, for example 3×3 = 9 is not a multiple of 6.

However as 6 = 2×3 all multiples of 6 are also multiples of 3.

Multiples of 3:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60.

The multiples of 6 Answer:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 1

Answer:

0.14 per ounce

Step-by-step explanation:

1.26 ÷ 9= 0.14

Hope this helps! :)

The unit price of peach would be $0.14.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a 9-ounce can of peaches sells for $1.26.

9-ounce can of peaches sells for $1.26.

Then -

1 ounce of peach will cost = (1.26/9) = $0.14

Therefore, the unit price of peach would be $0.14.

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Answer:

I got for the retail price $367. 50 and for the retail plus tax I got $396.90.

Step-by-step explanation:

To find the retail you have to figure out what 210% of 175 is. To do this you divide 175 by 100. after yiu get that number you multiply it by 210. after you multiply it you should get 367.50 . then to find the retail value plus tax you divide 367.50 by 100 and get 3.675. multiply 3.675 by 8 and then you get 29.40 . add 367.50 and 29.40 and you get $396.90

n the case of errors-in-variables bias, the OLS estimator is consistent but no longer unbiased in small samples. This is the correct statement.

In statistics, the errors-in-variables bias is a form of statistical bias that occurs when an independent variable (IV) is measured with error. The presence of the errors-in-variables (EIV) bias means that the OLS estimator will be consistent but no longer unbiased. This means that the OLS estimator can still give reliable estimates, but the estimates are no longer accurate.

The errors-in-variables (EIV) bias can be corrected by using methods such as instrumental variables or two-stage least squares (2SLS) regression. In small samples, the EIV bias can have a more significant impact on the accuracy of the OLS estimator.

In such cases, other estimation methods such as maximum likelihood estimation or the generalized method of moments (GMM) may be used to improve the accuracy of the estimates

Therefore, option C: the OLS estimator is consistent but no longer unbiased in small samples, is the correct .

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Neil is growing sugar crystals for his science fair experiment. He wants to find out if the amount of sugar affects the size of the crystal. Neil adds 18 tablespoons of sugar to his first bowl of water. He plans to add less sugar to the second bowl.

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Answer:

Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer: Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer:

b is 100

Step-by-step explanation:

Answer:

Average is 100

Median is 87.5

Step-by-step explanation:

For average you add up all numbers and divide by how many there are, in this case all numbers added together equals 600, then you divide by 6.

For median, you put the valuse from least to greatest and find the number in the middle, for these numbers, there are 2, 75 and 100, so you add those together and divide them by 2.

The population mean u and standard deviation σ are known and the sample size n is large, then the mean of the sample mean will be equal to the population mean and the standard deviation of the sample mean will be equal to the population standard deviation divided by the square root of the sample size. This is called the Central Limit Theorem.

The distribution of the sample mean, X, is approximately a normal distribution with a mean of μ and a standard deviation of σ/√n.b)

 The sample size is 36; therefore, we need to calculate the z score and find the area under the standard normal curve.

z = (X - μ) / (σ / √n)z

= (77.8 - 74) / (12 / √36)z

= 1.5P(X > 77.8) is equal to the area to the right of 77.8 under the standard normal curve.

Using the same formula above, we can calculate the z score and find the area to the left of 69.7 under the standard normal curve.

z = (X - μ) / (σ / √n)z

= (69.7 - 74) / (12 / √36)z

= -1.75P(X < 69.7) is equal to the area to the left of 69.7 under the standard normal curve.

Using the standard normal table or calculator,

P(Z < -1.75) = 0.0401.d)

We can also use the same formula above to calculate the z score and find the area to the right of 72.5 under the standard normal curve.

z = (X - μ) / (σ / √n)z = (72.5 - 74) / (12 / √36)z = -0.75P(X ≥ 72.5) is equal to the area to the right of 72.5 under the standard normal curve.

Using the standard normal table or calculator, P(Z ≥ -0.75) = 0.7734.

Sampling distribution of x is approximately a normal distribution with a mean of 74 and a standard deviation of 2.

Therefore, μ = 74 and σ = 2, X is normally distributed with

μ = 74 and σ = 2 / √36 = 1/3.

(b) P(X > 77.8) = 0.0668(c) P(X < 69.7) = 0.0401

(d) P(X ≥ 72.5)

= 0.7734.

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Answer:

x = -5

Step-by-step explanation:

Please write this as y = x^2 + 10x + 25.  Here the coefficients are {1, 10, 25}.

The equation of the axis of symmetry is x = -b/[2a], which here is

x = -10 / [2*1] = -5

Answer:

Step-by-step explanation:

\(\frac{150km}{2hr}\) divided by two is \(\frac{75km}{1hr}\).

Answer:

Yes

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 4)

y = 8x - 4

Step 2: Find

yes.

you just have to check like this: 1 is x and 4 is y.

4 = 8(1) - 4

4 = 8 - 4

4 = 4

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.

Answer:

The coordinates of the point is (5.5, -2)

Step-by-step explanation:

Okay, what we want to do here is to get the point that divides the line that joins the points (3,3) to (7,-5) in the ratio 5 to 3

Generally, given the ratio a:b and we want to divide the line joining the points (x1,y1) and (x2,y2) in that ratio, we use the condensed formula below;

Let’s call the point dividing the line in the given ratio z.

The coordinates of Z is;

{(bx1 + ax2)/(a+b), (by1 + ay2)/(a+b)}

In this question (x1,y1) = (3,3)

While (x2,y2) = (7,-5)

while a:b = 5:3

Substituting these values into the coordinate equation for point z, we have ;

{((3(3) + 5(7))/(5+3), ((3)(3) + 5(-5))/(5+3)}

= {44/8 , -16/8} = {5.5, -2}

Answer:

20%

Step-by-step explanation:

20/25 = blue

This means 5/25 of the balls in the bag are NOT blue

(25-20 = 5)

We need to convert 5/25 to a percentage

\(\dfrac{5}{25} = \dfrac{5\times4}{25\times4}=\dfrac{20}{100}\)

% = per cent

"per" means "out of"

"cent" means "one hundred"

so

20/100 = 20%

Answer:

320 Students

Step-by-step explanation:

Hope this helps :)

Step-by-step explanation:

To design a track that meets the given requirements, we need to determine the outer diameter of the track based on the specified track width.

1. Track width: 12.5 meters

2. Inner diameter: 113 - 186 meters

To calculate the outer diameter, we add twice the track width to the inner diameter:

Outer diameter = Inner diameter + 2 * Track width

Using the minimum inner diameter (113 meters), the outer diameter would be:

Outer diameter = 113 + 2 * 12.5 = 138 meters

Using the maximum inner diameter (186 meters), the outer diameter would be:

Outer diameter = 186 + 2 * 12.5 = 211 meters

Therefore, the dimensions of the track would be a circle with an inner diameter of 113 - 186 meters and an outer diameter of 138 - 211 meters.

To calculate the area of the track, we use the formula for the area of a circular ring:

Area of track = π * (Outer radius^2 - Inner radius^2)

We can calculate the outer and inner radii as follows:

Outer radius = Outer diameter / 2

Inner radius = Inner diameter / 2

Using the minimum and maximum values:

Minimum outer radius = 138 / 2 = 69 meters

Maximum outer radius = 211 / 2 = 105.5 meters

Minimum inner radius = 113 / 2 = 56.5 meters

Maximum inner radius = 186 / 2 = 93 meters

Now we can calculate the area of the track:

Minimum area of track = π * (105.5^2 - 56.5^2)

Maximum area of track = π * (93^2 - 69^2)

To determine the amount of astroturf and pavement needed, we subtract the area of the track from the total area of the outer circle (based on the maximum outer radius):

Total area of outer circle = π * (105.5^2)

Minimum astroturf area = Total area of outer circle - Minimum area of track

Maximum astroturf area = Total area of outer circle - Maximum area of track

The pavement area would be equal to the minimum and maximum area of the track.

Please note that the above calculations assume a perfectly circular track. In practice, adjustments might be required based on the specific terrain and engineering considerations.

Answer:

It is 1/45

Step-by-step explanation:

The probability of drawing two yellow marbles=4/45.

It is given that Total number of marbles=10 ,number of yellow marble is 2, number of pink marble is 3 and number of blue marble is 5.

To find the probability of drawing two yellow marbles if the first one is not placed back into the bag before the second draw.

The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

The probability of drawing first yellow marble=2/10=1/5

When first yellow marble is not placed back into the bag before the second draw.

Then, number of remaining  yellow marble=1

Total number of marbles=9

The probability of drawing second yellow marble =4/9

Now, the probability of drawing two yellow marbles =1/5*4/9=4/45

Hence, the probability of drawing two yellow marbles=4/45

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Answer:

5

Step-by-step explanation:

Answer: x = (10 - 6.75) ÷ 0.75

Step-by-step explanation:

x stands for the maximum number of toppings you can afford.

10 stands for the amount of money you have (10$).

6.75 is the amount of money spent on the Burger alone.

0.75 is the money spent on each topping with your remaining money.

Answer:

1000

Step-by-step explanation:

From a purely financial perspective, receiving $1 now is generally more advantageous due to the time value of money.

The time value of money refers to the idea that money has a greater value in the present than in the future. This is because money can be invested or used to generate additional income over time.

Therefore, from a purely financial standpoint, receiving $1 now is more beneficial because it allows for immediate access to the funds, enabling the possibility of utilizing or investing it right away.

Choosing to receive $1 a month from now may involve an opportunity cost. By waiting, you are forgoing the potential benefits or opportunities that could arise from having the money now. For example, you could invest the $1 and earn interest or use it to cover immediate expenses.

However, personal circumstances and preferences can influence the decision. If there are no pressing financial needs and the individual prefers delayed gratification or has a specific plan for the money in the future, opting to receive $1 a month from now might be a more suitable choice.

In conclusion, from a financial perspective, receiving $1 now is generally advantageous due to the time value of money. However, personal preferences, immediate financial needs, and specific plans can also factor into the decision-making process.

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The value of x for the given figure will be equal to √212.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Apply the Pythagorean theorem for the first triangle,

H² = x² - 6²

Apply the Pythagorean theorem for the second triangle,

B² = 27² - x²

Apply the Pythagorean theorem to the third triangle,

H² = 27² - x² - 21²

H² = -x² + 288

x² - 6² = -x² + 288

2x² = 424

x² = 212

x=√212

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Hi!  This looks like homework...

so I can help!

What you would need to do first is find the height of the triangle, you know, the dashed line.  15 is the hypotenuse side length.  Now we need to solve for a^2 + b^2 = c^2 (hypotenuse formula)  a^2 = 10^2, and c^2 = 15^2.   So now..

if a^2 + b^2 = c^2, then c^2 - a^2 = b^2.  Just moving stuff around. :D

That would be 15^2 - 10^2 = b^2, which is 225 - 100 = b^2.  The result is 125 = b^2.  

ehaggghh it's a decimal

b^2 is 125... and b is 11.1803398875.  So I can see a snippet of your paper that says round to the nearest tenth.  Yay.

that would be 11.2.  :>

The height is 11.2!! So now... oh noes you have to do it again.

Except this time, you're solving for a^2!

Switch the formula like this: c^2 - b^2 = a^2

13^2 - 11.2^2 = a^2 (base)

43.56 = a^2

6.6 = a

So now, the base is 6.6 + 10, which is 16.6 in total.  13 and 15 are the two side lengths.  But you don't need those.  You only need the height, 11.2.  So multiply 16.6 x 11.2, and you get 185.92, or 185.9.  Then divide that by two, since it's a triangle, not a square.  That's 92.96.  Yay you have the area!  

Hypotenuse formula: a^2 + b^2 = c^2
Use this if you don't have the given height, so you can solve for it.  The dashed line separated the triangle into two parts, so you could find the needed sides of both triangles.  Later, when you get into triangle proofs, you could use the "by construction" postulate to be able to find the similarity or congruence done here.

Have a good day!

Based on the given scenario, the following measurements are accurate:

1. The distance from the man's feet to the base of the monument is 185√3 feet.

2. The distance from the man's feet to the top of the monument is 1,110 feet.

The first accurate measurement states that the distance from the man's feet to the base of the monument is 185√3 feet. This measurement indicates the length of one of the sides of the triangle formed by the man, the base of the monument, and the top of the monument.

The second accurate measurement states that the distance from the man's feet to the top of the monument is 1,110 feet. This measurement represents the height of the monument from the man's position.

The other options provided in the scenario are not accurate based on the given information. The statement that the distance from the man's feet to the top of the monument is 370√3 feet contradicts the previous accurate measurement, which states it as 1,110 feet. Similarly, the statement that the distance from the man's feet to the base of the monument is 277.5 feet conflicts with the previous accurate measurement of 185√3 feet.

Regarding the last statement, it is not possible to determine from the given information whether the segment representing the monument's height is the longest segment in the triangle. The lengths of the other sides of the triangle are not provided, so we cannot make a comparison to determine the longest segment.

To summarize, the accurate measurements based on the scenario are the distance from the man's feet to the base of the monument (185√3 feet) and the distance from the man's feet to the top of the monument (1,110 feet).

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Answer:

B

Step-by-step explanation:

In fact in this case there is only a value of y when x is equal to 0

Answer:

2

because ans = 4. and input =half so,4/2 .=2

Answer:

(2xinput)-4=Output

Step-by-step explanation:

i think this is what ur looking for and have a good day :)

Given that the are of the great circle is 227 km^2.

The hemisphere is the half of a sphere, the surfsce area wiill be:

SA= (1/2)surface area of the sphere+ base area

the curve surface area will be:

and we know that the base area is:

substituting:

The surface area is: 680.96 square kilometers.

Answer:

So there is an exact form and decimal form,

Step-by-step explanation:

Exact form

x=2 root 3-3, -2 root 3-3

or

\(x=2\sqrt{3} -3, -2 \sqrt{3} -3\)

decimal form

x= 0.46410161