Two urns contain, respectively, 4 white and 2 black balls, 2 red and 3 black balls. a) Suppose that we win $3 for each Red ball selected, win $1 for each white ball selected and lose $2 for each Black ball selected. If two balls will be randomly selected from one of the urns without replacement, what is the probability that we will win the money? b) Suppose one ball was randomly selected from urn A and then transferred to urn B. After the operation, a Black ball is drawn from urn B. What is the probability that the selected Black ball is from urn A?

In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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You can do this problem in two ways.
Either the long way or the short and easy way.

Here is the easy way:

You do 180x1.06 to get you their total of $190.80

Or you can do the slightly longer way which finds you the tax amount which then you can add onto the total:

You do 180*0.06 which gets you $10.80 of tax. $10.80 is how much tax they have to pay on top of the $180, then we can do 180+10.80 to get us the grand total of $190.80.

Happy to help

A linear regression equation that represents the data set is y = -29.97x + 1048.80. Also, the number of new cases for 2026 is equal to 689 cases.

In this scenario, the Year since 2014 (x) would be plotted on the x-axis of the scatterplot while the New cases (y) would be plotted on the x-axis of the scatterplot.

On the Excel sheet, you should right click on any data point on the scatterplot, select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.

By critically observing the scatterplot (see attachment) which models the relationship given in the table, an equation for the linear regression is given by:

y = -29.97x + 1048.80

For 2026, the value of x is given by:

x = 2026 - 2014 = 12 years.

Now, we can determine the new cases for 2026:

y = -29.97(12) + 1048.80

y = -359.64 + 1048.80

y = 689.16 ≈ 689 cases.

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Answer:

x=7/6

Step-by-step explanation:

subtract the 4x from both sides of the equation

(2x+6)-4x=4x-3-4x

find common denominator

(2x+6)/5+(5(-4)x)/5=4x-3-4x

then combine fractions

(2x+6+5(-4)x)/5=4x-3-4x

then multiply the 5&4

(2x+6-20x)/5= 4x3-4x

combine terms

(-18x+6)/5= -3

then multiply everything by 5

-18x+6= -15

subtract the 6 from both sides

-18x= -21

divide -21 by -18

(-21)/(-18)=x

find greatest common multiple (3) and solve

x = 7/6

The complement of an event is the probability of the event not occurring. In this case, if the probability of an event is 4/7, then its complement would be 1 - 4/7, which simplifies to 3/7.

The complement of an event A, denoted as A', is the probability of A not occurring. In this case, if the probability of an event A is 4/7, then the probability of A' is given by:

P(A') = 1 - P(A)

Substituting the value of P(A) as 4/7:

P(A') = 1 - 4/7

To subtract fractions, we need a common denominator:

P(A') = 7/7 - 4/7

Simplifying the expression:

P(A') = 3/7

Therefore, the complement of the event with a probability of 4/7 is 3/7.

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Answer:

Hi There!! :-D

Step-by-step explanation:

5 1/2 as an improper fraction is 11/2.

We know that 5 x 2 is 10, and 10 + 1 is 11, therefore your answer is 11/2 !!!

Hope this helps you! ∩__∩

- abakugosimp

In this simulation, we are assuming that 40% of community college students never use tutoring services. We are interested in calculating the proportion of students who do not use tutoring services in random samples taken from this population.

To simulate this, we can use a random number generator to select samples from the population. For each sample, we count the number of students who do not use tutoring services and calculate the proportion.

Here are the steps to conduct this simulation:

1. Determine the sample size you want to use. Let's say you want to use a sample size of 100 students.

2. Use a random number generator to select 100 students from the population. Assign a value of 0 to those who do not use tutoring services and 1 to those who do.

3. Count the number of students with a value of 0 (who do not use tutoring services) in the sample.

4. Calculate the proportion of students who do not use tutoring services by dividing the count from step 3 by the sample size. Multiply the result by 100 to express it as a percentage.

5. Repeat steps 2-4 for a large number of samples, such as 1000 samples.

6. Finally, calculate the average proportion of students who do not use tutoring services across all the samples.

By conducting this simulation, we can estimate the proportion of students who do not use tutoring services based on the assumption that 40% of the population falls into this category.

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Answer: yes

Step-by-step explanation:

The probability of getting a difference in sample means xF − xM of at least 1 minute is 0.1160 or 11.60%.

To find the probability of getting a difference in sample means xF − xM, we need to use the Central Limit Theorem.

For the female students, the sample mean running time x¯f follows a normal distribution with a mean of 8.8 minutes and a standard deviation of 3.3 minutes divided by the square root of 8 (since we are selecting 8 students). Similarly, for the male students, the sample mean running time x¯m follows a normal distribution with a mean of 7.3 minutes and a standard deviation of 2.9 minutes divided by the square root of 8.

Now, we need to find the difference in sample means xF − xM or we want to find the probability of getting a difference of at least 1 minute between the sample means of the two populations.

Using the formula for the difference in sample means, we have:

xF − xM = 8.8 - 7.3 = 1.5

The standard deviation of the difference in sample means is the square root of the sum of the variances of the two populations, which is:

sqrt[(3.3^2/8) + (2.9^2/8)] = 1.255

The z-score for a difference of 1.5 minutes is:

z = (1.5 - 0) / 1.255 = 1.195

Using a standard normal table or a calculator, we can find that the probability of getting a z-score of 1.195 or greater is approximately 0.1160.

Therefore, the probability of getting a difference in sample means xF − xM of at least 1 minute is 0.1160 or 11.60%.

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We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;

\( \purple{ \mathfrak{x \times 6 = 12 \times 5}}\)

\( \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}\)

\( \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}\)

\( \large \purple{ \mathfrak{x = 2 \times 5}}\)

\( \large \boxed{ \red{ \mathfrak{x =10}}}\)

Answer:

I believe the answer is B

The flagpole is 6 yards tall

The height of Carla from the ground, H = 15 yards

Distance between the curb and the buiding, D = 20 yards

The larger triangle is shown below:

A diagram representing the smaller triangle is shown below:

Since She lines up the top of a flagpole with the curb, the two triangles are similar and the ratio of corresponding sides will be equal

Therefore:

15/x = 20/8

20x = 15(8)

20x = 120

x = 120/20

x = 6

The flagpole is 6 yards tall

The speedometer of the car showing error and sent back to be fixed must showing speed less than 1.225 miles per minute.

As given in the question,

Distance covered by car = 10miles

Time taken by car to cover 10 miles = 8 minutes

Formula used:

Speed = ( total distance travelled ) / ( time taken )

           = 10 / 8

           = 1. 25 miles per minute

To pass the speed test ,

Range of the speedometer is 2% of the actual speed

= 2% of 1.25

= ( 2/100) × 1.25

= 0.025

Range of the speed to pass the test

= 0.025 ± 1.25

= (  1.225, 1.275)

Therefore, the speedometer of the car which was sent back to be fixed must showing the speed less than 1.225 miles per minute.

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Answer:

Step-by-step explanation:

Five fish equals two bread, and two bread equals two bananas (plus however many oranges), therefore he can get two bananas.

\(2ay + 3az = 2dx + 3dy\)

\(2ay - 3dy = 2dx - 3az\)

\(y(2a - 3d) = 2dx - 3az\)

\(y = \frac{2dx - 3az}{2a - 3d} \\ \)

a survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools The U.S. Population Census is an example of a census

Census means the procedure of counting, calculating and recording the number and information about the members of the nation's.

Generally, population census are conducted every 10 years although some nations conduct their's every 5 years.

The primary objective of population census is to know the total size of the population of a country.

Population census also enable the government to appropriate resources fairly based on the number of people in a geographical area.

In conclusion, the U.S. population census is the only example of census.

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Answer: About 20.82 liters.

Step-by-step explanation:

         To go from gallons to liters, we will multiply by 3.785. Since we are in half gallons, we will multiply 11 by 0.5 for 5.5 full gallons. Now, we will multiply;

        5.5 gallons * 3.785 = 20.8198 ≈ 20.82 liters

Answer:

I think its BD/FG=AD/EH.

Answer:

x=30

Step-by-step explanation:

4x+2x=180

6x=180

x=30

The value of x will be 30 for the given supplementary angles.

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 110° and angle 70° are supplementary angles because the sum of 110° and 70° is equal to 180°.

Given ∠EAF and ∠BAF are supplementary angles

Since sum of two supplementary angles = 180

Thus,

∠EAF + ∠BAF = 180

2x + 4x = 180

6x = 180

x = 30

therefore, the value of x will be 30 for the given supplementary angles.

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Therefore,Total patients with pneumonia or bronchitis = 25 + 30 - 10= 45Thus, there are a total of 45 patients diagnosed with pneumonia or bronchitis or both.

Among 50 patients admitted to a clinic, 25 are diagnosed with pneumonia, 30 with bronchitis, and 10 with both pneumonia and bronchitis. The number of patients with pneumonia or bronchitis (or both) can be determined as follows:Let A denote the number of patients diagnosed with pneumonia and B denote the number of patients diagnosed with bronchitis.

According to the inclusion-exclusion principle, the total number of patients with pneumonia or bronchitis is given by:Total patients with pneumonia or bronchitis = \(A + B - (A ∩ B)\)where A ∩ B represents the intersection of the sets A and B.In this case, A = 25, B = 30, and A ∩ B = 10.

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The probability for given conditions are a) p(4)=0.166, b) p(even)=0.5 and c) p(greater than 3)=0.5

A die is rolled, then the sample space for outcomes is {1,2,3,4,5,6}

Total number of outcomes =6

Thus, the probability for given conditions are a)p(4)=0.166, b)p(even)=0.5 and c)p(greater than 3)=0.5

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R, you can conclude the relationship between average weight and average life span of a dog breed. If r is close to 1, there is a strong positive correlation; if r is close to -1, there is a strong negative correlation; and if r is close to 0, there is little to no correlation between the two variables.

To calculate the correlation coefficient (r) for the given set of data, follow these steps:

List down the data points for average weight (X) and average life span (Y) of dog breeds.

Calculate the mean of X and Y.

Calculate the difference between each data point and their respective means

(Xi - X_mean and Yi - Y_mean).

Multiply the differences obtained in Step 3 for each data point and sum them up

(∑(Xi - X_mean)(Yi - Y_mean)).

Calculate the squared differences for each data point and their respective means

\((∑(Xi - X_mean)^2 and ∑(Yi - Y_mean)^2).\)

Multiply the squared differences obtained in

\((∑(Xi - X_mean)^2 × ∑(Yi - Y_mean)^2).\)

Take the square root of the product obtained in

\((sqrt(∑(Xi - X_mean)^2 × ∑(Yi - Y_mean)^2)).\)

Divide the sum obtained in Step 4 by the square root obtained in  

\((r = (∑(Xi - X_mean)(Yi - Y_mean)) / sqrt(∑(Xi - X_mean)^2 × ∑(Yi - Y_mean)^2)).\)

After calculating r, you can conclude the relationship between average weight and average life span of a dog breed. If r is close to 1, there is a strong positive correlation; if r is close to -1, there is a strong negative correlation; and if r is close to 0, there is little to no correlation between the two variables.

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The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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Answer:

Using Words: The total area of the house and deck is given by the sum: 40x20 + x(13x) .

Using Symbols: The total area of the house and deck is given by the sum: 800 + 13x^2 ft².

Step-by-step explanation:

Log (10^6x) =

6x ,

then

10^n = 10^6x

So then we obtain

n= 6x

Then answer is

OPTION A) 6x

Answer: A. 6x

Step-by-step explanation:

\(log10^{6x}=\\\\6x(log10)=\\\\6x(1)=\\\\6x\)

Answer:

56

Step-by-step explanation:

Since vertical angles are equal, we know the two angles labeled are equal.

We can then set up an equation to get

\(19x-28=9x+52.\)

Subtracting \(9x\) from both sides to isolate the variable gives us

\(10x-28=52\).

Then, adding \(28\) to both sides gives

\(10x=80,\)

and dividing both sides by 10 gives

\(x=8.\)

Now, we can find the measure of \(9x+52\) by plugging what we found for \(x\) in:

\(9(x)+52=9(8)+52=72+52=124.\)

Since the angles ? and 9x+52 make up a line, they are supplementary. Therefore, we have

\(?=180-(9x+52)=180-124=\boxed{56}.\)

Answer:

The atomic number is the number of protons (12) and the mass number is the number of neutrons and protons combined. So you'd subtract 12 from 25 (25-12=) and that'd get you 13 as your answer. If you need to find the number of electrons, it'll be the same as the number of protons unless it has a certain charge and if it does, if it's positive it has more protons (+) than electrons (-), if it is negative it has more electrons (- negatively charged) than protons (+ positively charged)

(credits to halltho)

Answer:a

Step-by-step explanation: