hirty five discrete math students are to be divided into seven discussion groups, each consisting of five students. in how many ways can this be done?

The answer of the given question based on the  the volume of the terrarium will be 70 cubic feet to  solve for x the answer is the terrarium is 7 ft long, 5 ft wide, and 2 ft tall.

A formula is mathematical expression that shows relationship between different variables or quantities. It can be used to calculate value based on given inputs or to derive  mathematical result from  set of conditions or assumptions.

To find the value of x, we can use the formula for the volume of a rectangular prism, which is:

Volume = Length x Width x Height

We are given the dimensions of the terrarium in terms of x, so we can substitute them into the formula:

Volume = (x) * (x-2) * (x-5)

We know that the volume of the terrarium is 70 cubic feet, so we can set the equation equal to 70 and solve for x:

(x) * (x-2) * (x-5) = 70

Expanding left side of equation we get:

x^3 - 7x^2 + 10x = 70

We can simplify this equation by subtracting 70 from both sides:

x^3 - 7x^2 + 10x - 70 = 0

In this case, the constant term is -70 and the leading coefficient is 1, so the possible rational roots are:

±1,±2,±5,±7,±10,±14,±35,±70

We can use synthetic division to simplify the calculation. After testing all the possible roots, we find that the only rational root is x = 7.

This means that the dimensions of the terrarium are:

Length = x = 7 feet

Width = x - 2 = 5 feet

Height = x - 5 = 2 feet

Therefore, the terrarium is 7 ft long, 5 ft wide, and 2 ft tall.

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From the given information provided, the 12th term of the geometric sequence 7, -35, 175 is -341,796,875.

To find the 12th term of the geometric sequence 7, -35, 175, we can use the formula for the nth term of a geometric sequence:

an = a₁ × r⁽ⁿ⁻¹⁾

where aₙ is the nth term, a₁ is the first term, r is the common ratio, and n is the term number we want to find.

First, we need to find the common ratio (r) between any two consecutive terms. We can do this by dividing any term by its preceding term:

r = (-35) / 7 = -5

Now, we can use the formula to find the 12th term:

a₁₂ = 7 × (-5)⁽¹²⁻¹⁾

a₁₂ = 7 × (-5)¹¹

a₁₂ = 7 × (-48828125)

a₁₂ = -341,796,875

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The mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability.

Standard deviation of the given data is 20 grams. The mean weight of the cauliflower is 400 grams. Now, for calculating the probability, we need to standardize the given mean weight of cauliflower. It will be as follows. Z-score for the mean weight of cauliflower is given as:

z = (X - μ) / σwhere X = 400 grams (mean weight of cauliflower)

μ = 400 grams (mean weight of the population)

σ = 20 grams (standard deviation)z = (400 - 400) / 20 = 0

Now, the probability of the mean weight of an individual cauliflower being between 400 and 409 grams is as follows:

P(400 < X < 409) = P(0 < Z < 0.45)

Using the standard normal distribution table, the probability is 0.1745.

The mean weight of a random sample of 36 of the cauliflowers is between 400 and 409 grams. The mean weight of a random sample of 36 of the cauliflowers is given by:

(X-μ)/ (σ/√n)where μ = 400 grams (mean weight of cauliflower)

σ = 20 grams (standard deviation)

n = 36 (number of samples)

Now, we need to standardize the sample mean. It will be as follows:

z = (X - μ) / (σ/√n)z = (400 - 400) / (20 / √36)

z = 0

As the z-score is zero, the probability will be equal to 0.5. Hence, the mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability than the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams.

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Answer:

linear equations produce straight lines when graphed, and their rate of change remains constant

Nonlinear equations do not produce straight lines when graphed.

To determine whether its linear or nonlinear, you can graph it and see if it produces a straight line, or check if it can be written in the form y= Mx+b

Step-by-step explanation:

The probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test is of:

0%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 48, \sigma = 15, n = 20, s = \frac{15}{\sqrt{20}} = 3.354[/tex]

The probability is one subtracted by the p-value of Z when X = 60, considering the standard error calculated with the Central Limit Theorem, hence:

Z = (60 - 48)/3.354

Z = 3.58

Z = 3.58 has a p-value of 1.

1 - 1 = 0.

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Answer:

Step-by-step explanation:

E

Answer:

Trina is 56 years old

Explanation:

If Duane is 6 years older than his brother, who just turned 14, we are adding 14+6, which is 20.

If trina is 4 years less than TRIPLE Duanes' age, then we first find triple of Duanes' age 20 x 3, which is 60. Then we find 4 less than 60, which is 56.

A system loses 640 J of potential energy. In the process, it does 660 J of work on the environment and the thermal energy increases by 120 J .  Change in kinetic energy is -1420 J.

Solution:

To find the change in kinetic energy, we can use the conservation of energy principle. In this case, the loss of potential energy is converted into work done on the environment and an increase in thermal energy, as well as the change in kinetic energy.

The equation for this would be:

Loss of Potential Energy = Work Done + Increase in Thermal Energy + Change in Kinetic Energy

Let's plug in the values:
-640 J (loss of potential energy) = 660 J (work done) + 120 J (increase in thermal energy) + Change in Kinetic Energy

Now, solve for the change in kinetic energy:
-640 J = 660 J + 120 J + Change in Kinetic Energy
-640 J = 780 J + Change in Kinetic Energy

Change in Kinetic Energy = -640 J - 780 J
Change in Kinetic Energy = -1420 J

So, the change in kinetic energy is -1420 J.

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Step-by-step explanation:

Total surface area is 2πr²+2πrh

2× 22/7 × 5/4× 5/4 + 2 × 22/7 × 5/4 × 11/4

continue like this to get your right answer

There are a few different reasons why certain categorical variables may not be allowed in a linear regression model:

Some software packages require categorical variables to be converted to numerical variables before they can be included in a linear regression model. This is typically done using one-hot encoding, where each category is represented by a binary variable indicating whether or not it is present.

If the number of categories for a given variable is very large, this can create a very large number of new variables, which may exceed the capacity of the software or the memory available on the computer running the analysis.

Some software packages may not allow categorical variables with a very large number of categories, again because of the potential computational demands of encoding these variables as binary variables.

If a categorical variable has a large number of categories relative to the sample size, it may not be possible to estimate the coefficients for each category with enough precision to be useful. Some software packages may not allow categorical variables with missing values, unless those missing values are explicitly coded as a category.

Overall, the decision to include or exclude categorical variables from a linear regression model will depend on a variety of factors, including the number of categories, the software being used, the size of the dataset, and the research question being addressed.

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Let (x1, y1) = (9,7) and (x2, y2) = (6,3)

By distance formula,

d = (x2 - x1)² + (y2 - y1)²

d = (6 - 9)² + (3 - 7)²

d = (-3)² + (-4)²

d = 9 + 16

d = 25 units

the length of the flower's stem after it was cut is 2/3 of a foot long.

Laura's flower has a stem that is 11/12 of a foot long. If she cuts 3/12 of a foot off the stem, we need to subtract 3/12 from 11/12 to find the length of the remaining stem. To subtract fractions with the same denominator, we simply subtract their numerators and keep the denominator the same. Therefore, we have:

11/12 - 3/12 = 8/12

We can simplify the fraction 8/12 by dividing both the numerator and the denominator by their greatest common factor, which is 4. Therefore, we have:

8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3

the fraction to show the length of the flower's stem after it was cut

To subtract fractions with the same denominator, we simply subtract their numerators and keep the denominator the same. Therefore, we have:

11/12 - 3/12 = 8/12

Therefore, the length of the flower's stem after it was cut is 2/3 of a foot long.

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The average total lung capacity (TLC) of an average man is around 6 liters. However, the average total lung capacity of a man like Tom Sietas cannot be determined precisely as it depends on factors like height, weight, age, and physical condition.

What is lung capacity? Lung capacity refers to the total amount of air that your lungs can hold. Lung capacity is measured by a spirometer, a machine that measures the amount of air that you can breathe in and out. The total lung capacity (TLC) is the sum of four different volumes that include the tidal volume, inspiratory reserve volume, expiratory reserve volume, and residual volume.What is Tom Sietas’ total lung capacity?Tom Sietas is a German freediver who set a world record for holding his breath for 22 minutes and 22 seconds underwater in 2012. He is known for his exceptional lung capacity and has been reported to have a total lung capacity of 14 liters, which is more than double the average TLC of an average man. However, this figure may vary depending on several factors like height, weight, age, and physical condition.

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The value of x in this equation is -¼ so, the approximate solution to the equation "-1+3=12x+5" is (x = -¼).

As equation given is -1+3=12x+5

Thus, 2 = 12x+5

12x = -3

x = -3/12

x = -¼

Hence the value of x in this equation is -¼.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. A linear equation with two variables, however, has two solutions.

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In order to calculate the expected revenue of a toll bridge during a particular daytime period, we need to know how many passenger cars and other vehicles are expected to pass through the bridge, as well as the toll charges for each type of vehicle.Let's say that X is the number of passenger cars and Y is the number of other vehicles. Then, we can use the following formula to calculate the expected revenue of the toll bridge:h[tex](X, Y) = 1.00X + 2.50Y[/tex]This formula takes into account the toll charges for each type of vehicle and multiplies them by the number of vehicles that are expected to pass through the toll bridge during the daytime period.

For example, if we expect 100 passenger cars and 50 other vehicles to pass through the toll bridge during the daytime period, then the expected revenue of the toll bridge would be[tex]:h(100, 50) = 1.00(100) + 2.50(50) = 100 + 125 = $225[/tex]

Therefore, the expected revenue of the toll bridge during the particular daytime period would be $225.

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The upper and lower 3-sigma control chart limits for this DNA sample data are UCL = 18.53 and LCL = 0

When we are given data on the DNA samples taken over the past 10 days, we can calculate the upper and lower 3-sigma control chart limits. The sample size is 100, and the defective number of DNA samples is given for each of the ten days.

The 3-sigma control limits for a process control chart can be calculated using the following formula: Upper control limit (UCL) = Mean + (3 × Standard Deviation) and Lower control limit (LCL) = Mean - (3 × Standard Deviation),where the mean is the average value of the data, and the standard deviation is the spread of the data around the mean.

Here, we need to calculate the mean and standard deviation of the defective samples for the past 10 days. The average number of defectives per day (mean) is (7+9+9+11+7+8+0+11+13+2) / 10 = 77 / 10 = 7.7

To calculate the standard deviation, firstly, calculate the variance: variance = sum of the squared differences from the mean divided by the number of samples = [tex][(7-7.7)^2 + (9-7.7)^2 + ... + (2-7.7)^2] / 10[/tex]  ≈ 13.01 2.. Now, take the square root of the variance which gives standard deviation. So, standard deviation = [tex]\sqrt{13.01\\}[/tex] ≈ 3.61

Using the 3-sigma rule UCL = Mean + (3 * Standard Deviation) = 7.7 + (3 * 3.61) ≈ 18.53    and   LCL = Mean - (3 * Standard Deviation) = 7.7 - (3 * 3.61) ≈ -3.13. However, since the LCL cannot be negative, we set it to 0 in this context. So, the upper and lower 3-sigma control chart limits are: UCL = 18.53 LCL = 0

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The expressions 10x-7 and 7-10x represent the statement "seven less than ten times a number".

The verbal expression "seven less than ten times a number" can be written mathematically in different ways, depending on the intended meaning. One possible expression is:

10x - 7

In this expression, "10x" represents ten times a number, and "-7" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting 7 from the product of 10 and the number x.

Another possible expression is 7 - 10x

In this expression, "10x" represents ten times a number, and "7 - 10x" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting the product of 10 and the number x from 7.

If the focus is on finding the result of subtracting 7 from ten times a number, the first expression is more appropriate. If the focus is on finding the result of subtracting the product of 10 and a number from 7, the second expression is more appropriate.

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Therefore, the probability of getting a total of 7 is 6/36, which reduces to 1/6. The probability of getting a total of 8 is 5/36.

In mathematics, probability is a measure of the likelihood that an event will occur. It is usually expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. The probability of an event A is denoted by P(A), and it is defined as the ratio of the number of outcomes favorable to A, to the total number of possible outcomes in the sample space.

Here,

a) The sample space for tossing two fair dice can be represented as a table, where each row represents the outcome of one die, and each column represents the outcome of the other die. The sample space for this experiment would consist of all possible combinations of the two dice outcomes. Here's how the sample space table would look like:

       1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

b) To find the probability of getting a total of 7 or 8, we need to count the number of possible outcomes that result in these totals, and then divide by the total number of possible outcomes in the sample space.

For a total of 7, there are 6 possible outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).

=6/36

For a total of 8, there are 5 possible outcomes (2+6, 3+5, 4+4, 5+3, 6+2).

=5/36

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Complete question:

Two fair dice are tossed together once, what is:

a. draw the sample space for the following outcome

b. find the probability of getting a total of 7 and 8 ​

Using expressions,

4a. x= 0 is not possible.

4b. x= 1 is not possible.

5a. (9x-5)(9x+5)

5b. (x-3)(2x+1)

6. 1/(3x-7)

7a. x = (-5,∞)

7b. x = (∞,2]

7c. x = (-3,7]

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Let's examine the writing of expressions.

The other number is x, and a number is 6 greater than half of it.

As a mathematical expression, this proposition is denoted by the expression x/2 + 6.

Here the values of x has to be such that the denominator is not equal to zero.

So, x cannot be zero and x cannot be 1 as these two values in the respective questions will make the denominator zero.

a. 81x²-25

= 81x² + 45x-45x-25

=9x(9x+5)-5(9x+5)

= (9x-5)(9x+5)

b. 2x²-5x-3

= 2x² + x - 6x -3

= x(2x+1)-3(2x+1)

=(x-3)(2x+1)

Next, the intervals for x are as follows:

x = (-5,∞)

x = (∞,2]

x = (-3,7]

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Answer:

43 seashells

Step-by-step explanation:

x = 26

x + 31 - 14

(26) + 31 - 14

57 - 14

= 43

Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

The slope is the rate at which the pool is being filled.

A slope of 2 means a filling rate of 2 inches per minute.

Answer: The height of the water increases 2 inches per minute.

to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

To find 7/8 of 3.5, we can simply multiply 7/8 and 3.5 together.

7/8 x 3.5 = (7/8) x (7/2) = 49/16

So, the answer is 49/16. However, we need to write the answer as a mixed number in the simplest form.

To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. In this case, 49 divided by 16 is 3 with a remainder of 1.

So, the mixed number is 3 1/16.

To simplify the mixed number, we need to check if we can reduce the fraction part (1/16) further. 1 is not divisible by any number other than 1 itself, so it is already in its simplest form.

Therefore, the final answer is 3 1/16.

In summary, to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

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we can say that the entries in the matrix are highly constrained, with only one unique value per row or column. The matrix is usually denoted as a scalar multiple of the identity matrix or a vector of constants, depending on whether it is row-wise or column-wise identical.

In the row-wise identical matrix, all entries in each row are the same, but the entries in different rows can be different.

In the column-wise identical matrix, all entries in each column are the same, but the entries in different columns can be different.

Thus, we can say that the entries in the matrix are highly constrained, with only one unique value per row or column. The matrix is usually denoted as a scalar multiple of the identity matrix or a vector of constants, depending on whether it is row-wise or column-wise identical.

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The process of trying out the resulting equation on a second sample to see if it still fits well is called “cross-validation”.

Cross-validation is a technique used to evaluate the performance of a statistical model on a new independent dataset, which was not used in training the model. This process helps to assess the generalization capability of the model and helps to determine whether the model is overfitting or underfitting the data. By testing the model on a new independent dataset, we can get a better idea of how well the model is likely to perform on new data in the future. Cross-validation can also help in selecting the best model from a set of competing models.

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The balance after 6 years when the interest is compounded monthly is $7289.60

To find the balance after 6 years when the interest is compounded monthly, we can use the formula:

A = P(1 + r/n)^(nt)

where:

In this case, P = $5000, r = 6.3% = 0.063 (annual interest rate as a decimal), n = 12 (since interest is compounded monthly), and t = 6.

Plugging in these values, we get:

A = $5000(1 + 0.063/12)^(12*6)

Evaluate

A = $7289.60

Therefore, the balance after 6 years when the interest is compounded monthly is $7289.60

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Answer:

$25.96

Step-by-step explanation:

Since the tip is 18% of the fare, he pays 118% of the fare.

118% of $22 =

= 1.18 × $22

= $25.96

The ratio of the surface area to the volume of the cylinder is 2/r + 1/9.

Mathematically, the surface area (SA) of a cylinder can be calculated by using this formula:

SA = 2πrh + 2πr²

Where:

By substituting the given parameters into the formula for the surface area of a cylinder, we have;

Surface area (SA) of cylinder = (2 × π × r × 18) + 2πr²

Surface area (SA) of cylinder = 36πr + 2πr²

For the volume, we have:

Volume of cylinder = πr²h

Volume of cylinder = πr²(18)

Volume of cylinder = 18πr²

Now, we can determine the ratio;

Ratio = (36πr + 2πr²)/18πr²

Ratio = 2/r + 1/9

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The variance of 2X + 3Y is 35.52.

The solution to the problem is as follows:

First, find the mean and variance of X and Y:

E(X) = 3/5

Var(X) = 3/25

E(Y) = 1

Var(Y) = 1/25

Then, use the properties of variance to find the variance of 2X + 3Y:

Var(2X + 3Y)

= 4Var(X) + 9Var(Y) + 12Cov(X,Y)Cov(X,Y)

= E[(2X - 6/5)(3Y - 1)]

= 6E(XY) - 6E(X) - 3E(Y) + 2

= 6 * (integral from 0 to infinity integral from 0 to infinity of xyf(x,y)dxdy) - 6 * 3/5 - 3 * 1 + 2 = 6 * (integral from 0 to infinity 15xye^-3xdydx) - 8

= 54/5

Therefore,

Var(2X + 3Y) = 4(3/25) + 9(1/25) + 12(54/5)

                     = 888/25

                     = 35.52.

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Using L'Hopital's rule, verified that Lim_x→0 (4^(2 x) - 1)/(7 x) = (2 log(4))/7

To solve the limit, we can use L'Hopital's rule. First, let's rewrite the limit as

lim_x→0 [(4^(2x) - 1)/x]/(7/2)

Now, we can apply L'Hopital's rule to the numerator

lim_x→0 [(4^(2x) - 1)/x] = lim_x→0 [8x*4^(2x-1)] = 0

So we get:

lim_x→0 [(4^(2x) - 1)/x]/(7/2) = (0)/(7/2) = 0

Therefore, the limit is 0.

Now let's verify the given answer using logarithmic properties

(4^(2x) - 1)/(7x) = (2 log(4))/7

Multiplying both sides by 7x

4^(2x) - 1 = 2x log(4)

Using the identity a^2 - b^2 = (a+b)(a-b), we can rewrite the left-hand side as:

(4^x + 1)(4^x - 1) = 2x log(4)

Dividing both sides by (4^x - 1)

4^x + 1 = (2x log(4))/(4^x - 1)

Now, taking the limit as x approaches 0, we get:

lim_x→0 [(2x log(4))/(4^x - 1)] = lim_x→0 [(2 log(4))/(ln(4) × 4^x)] = (2 log(4))/7

Therefore, the given answer is verified.

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