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The total number of samples in the sample space is 15,504.

The total number of samples in the sample space can be calculated by using the formula for combinations, which is the number of ways to select r items from n distinct objects. The formula is written as nCr and is calculated as n!/(r!(n-r)!). In this case, n is equal to 60, and r is equal to 4.

To calculate the total number of samples in the sample space, we will first calculate n!, which is 60! = 60*59*58*57*...*2*1. Then, we will calculate r! which is 4!, which is 4*3*2*1. Finally, we will calculate (n-r)!, which is (60-4)!, which is [tex]56! = 56*55*54*53*...*2*1.[/tex]

Using the formula, the total number of samples in the sample space is calculated as 60!/(4!(60-4)!) = 60!/(4!*56!) = 15,504. Therefore, the total number of samples in the sample space is 15,504.

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Answer:−2π, -6.25, 67/10, 3√5, 6 3/4

Step-by-step explanation: Search math w ay on the internet for any further math questions :)

Answer:

Step-by-step explanation:

The expression 191 divided by 3 equals 63.66666666666667 (approximately 64)

Number of bacteria that would be in a sample weighing 24 grams is,

⇒ 1.296 × 10¹⁰

Scientific notation is a way of writing a very large or very small numbers. For example; 230,000,000 can be written in scientific notation as 2.3 x 10⁸.

We have to given that;

There are 5.4 x 10⁷ bacteria are measured to be in a dirt sample that weighs 1 gram.

Hence, Number of bacteria that would be in a sample weighing 24 grams is,

⇒ 24 × 5.4 × 10⁷

⇒ 129.6 × 10⁷

⇒ 1.296 × 10¹⁰

Thus, Number of bacteria that would be in a sample weighing 24 grams is,

⇒ 1.296 × 10¹⁰

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Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Answer:

47

Step-by-step explanation:

We know, that the angle at the vertex of a rectangle is 90 degree
So, if a line drawn divides it into two angles, then one of them is complementary to the other.
Hence, ADB = 90 - EDC
= 90 - 43
= 47

Answer:

5

Step-by-step explanation:

23 x + 977 y = 2023

977 x + 23 y = 2977

add the 2 together

1000x+1000y =5000

so x+y =5

x=5-y

plug this into first equation

23(5-y) +977y =2023

solve for y =2

so x=3

x² -y² =(x+y)*(x-y) =5*1 =5

Darren's salary will be $102,724.24 in 9 years.

Annual salary can be defined as the amount of money a company pays you in exchange for the job you do during the year.

We can calculate Darren's salary in 9 years by multiplying his current salary by (1 + 5.5%) raised to the power of 9.

The formula would look like this:

Salary in 9 years = $66,648 * (1 + 0.055)^9

Plugging in the numbers and using a calculator, we get:

Salary in 9 years = $66,648 * 1.55946429

Salary in 9 years = $102,724.24

So, Darren's salary will be $102,724.24 in 9 years.

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Answer:

12.5 cm

Step-by-step explanation:

Diameter of circle = 25 cm

Radius of circle = Diameter/2 = 25/2 = 12.5 cm

Answer:

The radius of the circle would be 12.5 cm.

Step-by-step explanation:

The reason it is 12.5 cm is because r=d/2. So it would be r=25/2, and that equals 12.5 cm.

The distance between point A and point B is 214.807 km.

To find the distance between point A and point B, we can use the formula: distance = speed * time.Let's call the total distance between point A and point B "d".

For the first part of the journey, when the car was traveling at a constant speed of 78 km/hr, the distance traveled was 63% of the total distance, or 0.63d. The time taken for this part of the journey was 3.3 hours * 63% = 2.099 hours. Therefore, the distance traveled in this part of the journey was 78 km/hr * 2.099 hours = 160.862 km.

For the second part of the journey, when the car was traveling at a constant speed of 45 km/hr, the distance traveled was the remaining 37% of the total distance, or 0.37d. The time taken for this part of the journey was 3.3 hours - 2.099 hours = 1.201 hours. Therefore, the distance traveled in this part of the journey was 45 km/hr * 1.201 hours = 53.945 km.

Adding up the distance traveled in both parts of the journey gives us a total distance of 160.862 km + 53.945 km = 214.807 km.

So, the distance between point A and point B is 214.807 km.

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An expression for the amount of money Dominick has received from his grandfather and mother after m months is 300 + 75m + 40(m - 3).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

Dominick’s grandfather gave him $300 to start his college savings account.

There will be 300 in the expression.

Dominick’s grandfather also gives him $75 each month to add to the account.

So after m months, total amount that grandfather gave = 75m

Dominick’s mother gives him $40 each month, but has been doing so for 3 fewer months than Dominick’s grandfather.

After m months, Dominick's mother would be giving $40 for (m - 3) months

Total amount that the mother gave after m months = 40(m - 3)

Total amount in the account after m months can be expressed as,

300 + 75m + 40(m - 3)

Hence the required expression is 300 + 75m + 40(m - 3).

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It is important to remember that model selection and improvement is an iterative process and may require trying several different approaches before arriving at the best solution.

A high R^2 value of 1 on the training data and a low R^2 value of 0 on the validation data suggests that the model is overfitting. Overfitting occurs when a model is too complex and has learned the training data too well, but has poor generalization performance on new, unseen data (validation data in this case).

To address this issue, you can try the following:

Reduce the amount of features in the model or regularise it to restrict the size of the coefficients.

Increase the size of the training dataset: A bigger training dataset may provide the model a better grasp of the link between the features and the target variable.

Cross-validation: Use cross-validation techniques to better estimate the model's performance on fresh data.

Attempt a different model: A other model may be more appropriate for the problem and data.

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The system of equation  y = 4x - 1 and 12x - 3y = - 1 has no solution.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

The given system of equation is y = 4x - 1 and 12x - 3y = - 1.

Multiplying equation (i) by 3 and adding it to equation (ii) we have,

 3y =   12x - 3

- 3y = - 12x - 1

____________

  0 =     0 -  4

But 0 ≠ - 4 so, The system of the equations has no solution.

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Answer:

899

Create a divison

17÷9=12

1222

7888

909

6762

177÷12×22+22

Note that the step that is not involved in graphing a logarithmic function is: "Switch the order of the x and y values in the ordered pairs." (Option A)

With regard to the graphing problem above, note that switching the order of the x and y values in an ordered pair is not a step in graphing a logarithmic function because it is not a necessary or relevant step in the process.

To graph a logarithmic function, one typically follows the steps of creating a table of values, plotting the points, and then drawing a line of best fit to show the graph. The order of the x and y values in the ordered pair remains unchanged in this process.

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The x-axis of the graph is the upper limits of each class, while the y-axis is the cumulative frequency or cumulative relative frequency. The cumulative relative frequency for the last class is always equal to 1.

An ogive graph is a type of line graph that is used to show the cumulative frequency or cumulative relative frequency of a given set of data. To start, the data must be organized into classes with upper and lower limits. Once the data is organized, the ogive graph can be constructed. The x-axis of the graph is the upper limits of each class, while the y-axis is the cumulative frequency or cumulative relative frequency. Each plotted point on the graph will have an x-coordinate that is equal to the upper limit of the class. The cumulative relative frequency for the last class must always be 1, since all observations are less than or equal to the last class. To plot the points on the graph, start by finding the cumulative frequency or relative frequency for the first class. Then, for each subsequent class, add the cumulative frequency or relative frequency to the cumulative frequency or relative frequency of the previous class. Once all the points are plotted, draw a line connecting the points to form an ogive graph.

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If the stadium parking lot holds 20,000 cars and lisa prints 240,000 passes then 12 home games are scheduled next month.

Given that Lisa prints parking passes for the baseball stadium a month in advance the stadium parking lot holds 20,000 cars.
Lisa prints 240,00 passes,

We have to find the number of  home games are scheduled next month.

To find this we have to division of 240000 by 20000
240000/20000 = 12
Divide Two lakh forty thousand by twenty thousand we get twelve.

By means of division we get 12 Hence, 12 mant home games are scheduled next month

A division is a process of splitting a specific amount into equal parts.

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Each athlete receives about 0.95 liters of sports drinks.

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.

For example 4/2 = 2

To find out how much sports drink each player receives, we need to divide the total amount of sports drinks by the number of players.

20.9 liters ÷ 22 players

Apply the division operation, and we get

= 0.95 liters per player

So, each player receives approximately 0.95 liters of sports drinks. To the nearest hundredth, this is 0.95 liters.

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It will cost you to have all the dirt hauled away [tex]6.43*10^{4}[/tex]

A COST Action is an interdisciplinary research network that unites scientists and entrepreneurs to study a subject of their choice for four years. SMEs, public institutions, academic researchers, and other pertinent entities or interested parties often make up COST Actions. The cost is the total amount of money spent by a company on the creation or production of goods or services. The markup for profit is excluded. The sum of money spent to create a good or product, as seen from the seller's perspective, is the cost. The expense incurred for manufacturing a good or rendering a service that is made available by a business is often referred to as the cost. The customer's willingness to pay determines the price of a good or service.

Based on the given condition,

Formulate

[tex]20*6*30*18[/tex]

Calculate the product or quotient

[tex]120*30*18=64800[/tex]

Simplify.

[tex]6.43*10^{4}[/tex]

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The weighted average of the numbers 1 and 6 is 2 2/3

The weighted average of 1 and 6 in this instance, means the sum of the two numbers multiplied by their weights which are four-fifths and one-fourth respectively.

weighted average = (first number * weight of first number) + (second number * weight of second number)

first number = 1

weight of the first number = 2/3

second number = 6

weight of the second number = 1/3

weighted average = (1 * 2/3) + (6 * 1/3)

weighted average = 2/3 + 2

weighted average = 8/3 = 2 2/3

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The coordinates of the other endpoint include the following: C. (32.5, 47.7).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint BC = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Next, we would determine the coordinate of B with midpoint AB at (25.4, 60.1) as follows;

25.4 = (18.3 + x₂)/2

50.8 = 18.3 + x₂

x₂ = 50.8 - 18.3

x₂ = 32.5.

For the other co-ordinate of B on line segment BC, we have:

60.1 = (72.5 + y₂)/2

120.2 = 72.5 + y₂

y₂ = 120.2 - 72.5

y₂ = 47.7.

Therefore, the coordinate of B is (32.5, 47.7).

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(a) the critical value of t at P = 10% and 16 degrees of freedom is 1.337.

(b) the critical value of t at P = 10% and 11 degrees of freedom is 1.363.

(c) the critical value of t at P = 1% and 23 degrees of freedom is 2.500.

(d) the critical value of t at P = 10% and 22 degrees of freedom is 1.321.

(e) the critical value of t at P = 20% and 12 degrees of freedom is 0.8726.

(f) the critical value of t at P = 5% and 8 degrees of freedom is 1.860.

We need to find the critical t value for every one of the accompanying confidence levels and test sizes given underneath.

As we realize that in the t table there are two segments. The flat section is addressed by the image P which addresses the level of importance and the upward segment is addressed by the image '' which addresses the degrees of freedom.

(a) In this way, here the level of importance = 1 - confidence level

                                                           = 1 - 0.90 = 0.10

What's more, the degrees of freedom = n - 1

                                               = 17 - 1 = 16

Presently, in the t table, the critical value of t at P = 10% and 16 degrees of freedom is 1.337.

(b) Thus, here the level of importance = 1 - confidence level

                                                           = 1 - 0.90 = 0.10

Furthermore, the degrees of freedom = n - 1

                                               = 12 - 1 = 11

Presently, in the t table, the critical value of t at P = 10% and 11 degrees of freedom is 1.363.

(c) Thus, here the level of importance = 1 - confidence level

                                                           = 1 - 0.99 = 0.01

Furthermore, the degrees of freedom = n - 1

                                               = 24 - 1 = 23

Presently, in the t table, the critical value of t at P = 1% and 23 degrees of freedom is 2.500.

(d) In this way, here the level of importance = 1 - confidence level

                                                           = 1 - 0.90 = 0.10

Furthermore, the degrees of freedom = n - 1

                                               = 23 - 1 = 22

Presently, in the t table, the critical value of t at P = 10% and 22 degrees of freedom is 1.321.

(e) Thus, here the level of importance = 1 - confidence level

                                                           = 1 - 0.80 = 0.20

Furthermore, the degrees of freedom = n - 1

                                               = 13 - 1 = 12

Presently, in the t table, the critical value of t at P = 20% and 12 degrees of freedom is 0.8726.

(f) In this way, here the level of importance = 1 - confidence level

                                                           = 1 - 0.95 = 0.05

Furthermore, the degrees of freedom = n - 1

                                               = 9 - 1 = 8

Presently, in the t table, the critical value of t at P = 5% and 8 degrees of freedom is 1.860.

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The complete question is:

What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.)

(a) 90% confidence, n = 17

(b) 90% confidence, n = 12

(c) 99% confidence, n = 24

(d) 90% confidence, n = 23

(e) 80% confidence, n = 13

(f) 95% confidence, n = 9

In the expression "3(x+2)," there is only one variable, "x." There are two factors in this expression: "3" and "(x + 2)." The "3" is performing multiplication , so it is multiplying the expression "(x + 2)" by 3, the answer is product.

In mathematics, a variable is a symbol that represents a value that can change or vary. Variables are often used in mathematical equations and formulas to represent unknown or unspecified values.

A factor is an element in a mathematical expression that is being multiplied by another element In general, a mathematical expression can have multiple factors. The factors of a polynomial are the terms that are being multiplied together to form the polynomial.

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Answer:

0.238

Step-by-step explanation:

Make any multiplication or division from left to right:

[tex]\frac{2}{7} - \frac{1}{21}[/tex]

0.286 - [tex]\frac{1}{21}[/tex]

0.286 - 0.048

Calculate:

0.286 - 0.048 =

0.238

Hope it helps

Subtraction is what difference means.

Therefore, the fractional difference between 2/7 and 1/21 is 5/21

0.238 in decimal form.

21 is the least common multiple between 7 and 72. (LCM). Divide the numerator and denominator of each fraction by the number that will bring the denominator of each fraction to the LCM:

2/7-1/21 = 2*3/7*3 - 1/21

Subtract the numerators such that the fractions have like denominators now:

6/21 - 1/21 = 6 - 1/21 = 5/21

Consequently, the outcome is

2/7 - 1/21 = 5/21

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Answer:

Multiply each term in the first expression by each term in the second expression and combine like terms. x³-3x² - 4x + 12

Step-by-step explanation:

The value of the equation is A = 56x + 21

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( -7 ) ( -8x - 3 )   be equation (1)

On simplifying the equation , we get

A = ( -7 ) ( -8x ) - ( 7 ) ( -3 )

On further simplification , we get

A = 56x + 21

Hence , the equation is A = 56x + 21

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An equation of the line that passes through the point (-8, -4) and (0, 5) in slope-intercept form is y = 9x/8 + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following data points on the line:

Points on the x-axis = (-8, 0).

Points on the y-axis = (-4, 5).

Therefore, a linear equation in slope-intercept form of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 5 = (5 + 4)/(0 + 8)(x - 0)

y - 5 = 9x/8

y = 9x/8 + 5

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The type of measurement scale is interval. A quantitative measuring scale with order, meaningful and equal differences between the two variables, and arbitrary zero presence is known as an interval scale.

In mathematics, an interval is quantified in terms of numbers. Every number between two specific integers is considered to be an interval. Between those two values, this range encompasses all real numbers. Real numbers can be of any type you can imagine. A fourth is a musical interval that spans four staff positions in Western music notation, and a perfect fourth is one that spans five semitones. The interval can be calculated by counting both the lines or spaces that the two notes are on as well as all the lines or spaces in between. A third of a second separates B from D. A sixth space separates A from F.

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