Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning.

Given: Ballet dancers like classical music.

If you like classical music, then you enjoy the opera.

Answer:

d

Step-by-step explanation:

t+2>3

t>1 (subtraction POE)

all solutions given are answers:

7>1

4>1

8>1

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE

As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.

So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.

Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.

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The complete question is given below:

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:

"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."

Answer:

D: Infinitely many solution

Step-by-step explanation:

The lines overlap so they will share all the same solutions

Answer:

y=-2/3x+8

Step-by-step explanation:

first, find the y intercept, or b.

write your equation so far: y = -2/3x + b

Now substitute in your given point (6,4)

so now we got: 4 = -2/3(6) + b

which gives you: 4 = -4 + b

Now, we find b.

4 = -4 + b  

+4    +4      < isolating b...

8 = b

now put it back in..

y=-2/3x+b

hope this helped luv <3

The number of students in each classroom will be best modeled by a discrete relationship.

What is discrete relationship?

Discrete relationships are those relationships that contain finite or countable elements which means that the elements of such a relationship are distinct.

We are given four choices, from which we need to find the one which can be best modeled by this.

The weight of dog over time, the temperature inside a car and the cost of bananas cannot be modeled by discrete relationship because these are continuous variables.

Hence, the number of students in each classroom will be best modeled by a discrete relationship.

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Answer:

x = 13

Step-by-step explanation:

3x + 12 + 5x + 16 + 4x + 18 = 202

combine like terms

12x + 12 + 16 + 18 = 202

12x + 46 = 202

       -46     -46

12x = 156

divide by 12

x = 13

Hope this helped! Have a nice rest of ur day! Plz mark as brainliest!!!

-Lil G

Add all the sides together (don´t forget parenthesis) Put the x´s with the x´s and the same with the other numbers. The subtract additional numbers from the total. The divide what left from the number in front of the x.

(3x + 12) + (5x + 16) + (4x + 18) = 202

8x + 28 + (4x + 18) = 202

12x + 46 = 202

      - 46     -46

12x = 156

/12      /12

x = 13

To summarize, a perfectly egalitarian society has a Gini index of 0, and a perfectly totalitarian society has a Gini index of 1.

The Gini index (G) measures how much the income distribution differs from absolute equality.

On the other hand, a perfectly totalitarian society (where a single person receives all the income) will have a Gini index of 1. This means that there is a huge inequality between individuals, with the single person receiving all of the income.

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K-means clustering is an iterative algorithm that partitions a data set into k clusters, where k is predefined.

It works by first randomly selecting k points as cluster centers, also known as centroids. All points are then assigned to the nearest cluster center based on a distance metric, such as Euclidean distance. This process is repeated until the centroids no longer move, which is when the clusters have stabilized. The formula for calculating the distance between two points is d = sqrt((x1-x2)^2 + (y1-y2)^2).

Hierarchical clustering is a type of clustering algorithm that builds a hierarchy of clusters. It starts by assigning each point to its own cluster, then combines the two closest clusters and repeats the process. The calculation used to determine the distance between two clusters is the distance between their two closest points, also known as the single linkage method. The formula for calculating the distance between two clusters is d = min(d1, d2, ..., dn), where d1, d2, ..., dn are the distances between the two closest points in the two clusters.

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61 matchsticks need to make 20 squares.

Given,

From the figure,

Matchsticks are used to make the pattern.

To make these 4 squares, you need 13 matchsticks.

To find the how many matchsticks do you need to make 20 squares?

Now, According to the question:

Let the need matchsticks be 'n'

The number of the squares to make 1 square , you need 4 matchsticks,

and when you need to add one square, you need three more matchsticks .

So , we have to make  n no. of squares you need

4 + 3(n - 1) matchsticks     (n \(\geq\) )

= 4 + 3n - 3

= 1 + 3n

When, n = 20

1 + 3 x 20

= 61

Hence, 61 matchsticks need to make 20 squares.

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Answer:

6 packages

Step-by-step explanation:

30/5 is 6

Answer:

the answer is 6

Step-by-step explanation:

30 divided by 5

to get the equation of any straight line, we simply need two points off of it, so hmmm let's use say (-1 , -1.25) and (8 , -3.5)

\((\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1.25})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3.5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3.5}-\stackrel{y1}{(-1.25)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-1)}}}\implies \cfrac{-3.5+1.25}{8+1}\implies \cfrac{-2.25}{9}\implies -\cfrac{~~ \frac{225}{100}~~}{\frac{9}{1}} \\\\\\ -\cfrac{225}{100}\cdot \cfrac{1}{9}\implies -\cfrac{9}{4}\cdot \cfrac{1}{9}\implies -\cfrac{1}{4}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1.25)}=\stackrel{m}{-\cfrac{1}{4}}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+1.25=-\cfrac{1}{4}(x+1)\implies y+\cfrac{5}{4}=-\cfrac{1}{4}x-\cfrac{1}{4} \\\\\\ y=-\cfrac{1}{4}x-\cfrac{1}{4}-\cfrac{5}{4}\implies y=-\cfrac{1}{4}x-\cfrac{6}{4}\implies y=-\cfrac{1}{4}x-\cfrac{3}{2}\)

The most appropriate choice for percentage and fraction will be given by-

The process of conversion of fraction to percentage has been explained.

What is fraction and percentage?

Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

If a number is taken as fraction of 100 then the fraction is known as percentage.

To convert a fraction into percentage, we have to simply multiply the fraction with 100.

For example.

Suppose we have a fraction \(\frac{1}{4}\), we need to convert  \(\frac{1}{4}\) to percentage.

So on multiplying \(\frac{1}{4}\) by 100, we obtain = \(\frac{1}{4} \times 100\) = 25%

So, \(\frac{1}{4}\) is equivalent to 25%

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a) The probability of selecting 8 yellow jelly beans can be calculated using the hypergeometric distribution. The formula for this is (number of ways to choose 8 yellow jelly beans) divided by (number of ways to choose 14 jelly beans). The number of ways to choose 8 yellow jelly beans from 17 is calculated as "17 choose 8" and the number of ways to choose 14 jelly beans from the total of 90 (17+35+38) is calculated as "90 choose 14". Dividing these two values will give the probability of selecting 8 yellow jelly beans.

b) The probability of selecting B yellow and 5 green jelly beans can be calculated using a similar approach as in part a), where B is the number of yellow jelly beans selected. We can vary B from 0 to 8 and calculate the probability for each value. Then, we can sum up these individual probabilities to obtain the overall probability.

c) The probability of selecting at least one yellow jelly bean can be found by calculating the complement of selecting no yellow jelly beans. The complement probability is equal to 1 minus the probability of selecting no yellow jelly beans. The probability of selecting no yellow jelly beans can be calculated as the ratio of the number of ways to choose 14 jelly beans from the total of 73 (35+38) (since we exclude the yellow jelly beans) divided by the number of ways to choose 14 jelly beans from the total of 90 (including all jelly beans).

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The solution is :

B. The domain of F(x) is all real numbers.

E. It is increasing.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

Given the function

f(x) = 2 • 5x

y intercept occurs at x = 0

f(0) = 2  • 5(0)

f(0) = 2 • 0

f(0)= 0

Hence the y intercept (0,0)

The domain are the input values x that makes the function exists. According to the function, the function f(x) will exist for al values of x hence the domain of F(x) is all real numbers.

If x = 0, f(x) = 0. This shows that the range of the values is y >0

The value of function f(x) also increases for increasing value of x, hence it is increasing.

Hence, The solution is :

B. The domain of F(x) is all real numbers.

E. It is increasing.

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Answer:

f(2) = 3(2) + 1

f(2) = 6 + 1

f(2) = 7

Answer:

f(2) = 7

Step-by-step explanation:

To evaluate f(2) substitute x = 2 into f(x) , that is

f(2) = 3(2) + 1 = 6 + 1 = 7

Answer:

x = 6

Step-by-step explanation:

35 - 2x = 23

35 - 23 - 2x = 0

35 - 23 = 2x

12 = 2x

x = 6

35- 2x = 23

Subtract 35 from both sides.

Subtract 35 from 23 to get −12.

Divide both sides by −2.

Divide −12 by −2 to get 6.

Answer:

  y = -5/7x -1/7

Step-by-step explanation:

You want the equation -5x -7y = 1 written in slope-intercept form.

The slope-intercept form of the equation for a line is ...

  y = mx +b

We can put the given equation into this form by solving for y.

  -5x -7y = 1

  -7y = 5x +1 . . . . . add 5x to get the y-term by itself

  y = -5/7x -1/7 . . . . divide by -7

The probability of a student spending time reading given that the student spends time watching TV is  \(P(Reading|Watching\:\:TV)=0.12\)

If any two occurrences in sample space S, A and B, are specified, then the conditional probability of event A given B is:

\(P(A|B)=\frac{P(A\:and\:B)}{P(B)}\)

Probability theory is an important branch of mathematics that is used to model and analyze uncertain events in various fields, including science, engineering, finance, and social sciences. The concept of probability is based on the idea of random experiments, where the outcomes are uncertain and can vary each time the experiment is performed.

The probability of an event can be determined by analyzing the possible outcomes of the experiment and assigning a probability to each outcome based on the assumptions of the model. The theory of probability has several applications in real life, such as predicting the outcomes of games of chance, evaluating risks in insurance and finance, and making decisions in scientific research.

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Answer:

28.26

Step-by-step explanation:

3×3=9

9×3.14=28.26

Answer:

The answer is 28.26

Step-by-step explanation:

Why? Ok so here it is:

The formula is (pi)(r)squared

In this case, you will replace pi with 3.14 and replace r with 3 because that's the radius.

So it would be (3.14)(3)

You would get 9.42

Now you just need to square it

When squared, you'll get 28.26 inches squared

Answer:

\(3\frac{1}{3}\) or \(\frac{10}{3}\)

Step-by-step explanation:

We could use the combined rate equation to find the combined rate of work.

Combined rate of work formula: \(\frac{1}{t_{b}} = \frac{1}{t_{1} } + \frac{1}{t_{2} }\), where \(t_{1}\) is the individual time for object A, \(t_{2}\) the individual time for object B and \(t_{b}\) is the time for A and B together.

The time it takes Irina to paint the room alone, \(t_{1}\) = 5 hours

The time it takes Paulo to paint the room, \(t_{2}\) = 10 hours

1) Substitute object A (Irina) and B (Paulo) into the formula given above, and change \(t_{b}\) into an \(x\).

\(\frac{1}{{x}} = \frac{1}{5 } + \frac{1}{10 }\)

2) Add the fractions.

\(\frac{1}{x} = \frac{3}{10}\)

3) Solve for the \(x\).

\(x(3) = 1(10)\\3x = 10\\x = \frac{10}{3} \\\)

4) Change them into a mixed fraction.

\(3\frac{1}{3}\)

Note: \(\frac{10}{3}\) or \(3\frac{1}{3}\) are both correct. Write the answer according to the question. In this case, there is no specific rule, so I choose \(3\frac{1}{3}\).

Since the value of y can be known from equation 1, we can use the substitution method to solve the system of equations. By entering the value of y in equation 2, we can quickly get the value of x. So the option B is correct.

The system of equation are:

y = 1/2x...................(1)

2x + 3y = 28...................(2)

To solve the system of equation we use substitution method because the value of y is know from the equation 1. We can find easily the value of x by putting the value of y in equation 2.

Now putting the value of y in equation 2.

2x + 3(1/2x) = 28

2x + 3/2 x = 28

7/2 x = 28

Multiply by 2 on both side, we get

7x = 56

Divide by 7 on both side, we get

x = 8

Now putting the value of x in equation 1

y = 8/2 = 4

The solution of the system of equation is (8, 4).

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To calculate the debt-equity ratio, we need to divide the total debt by the owners' equity.

The equation for the debt-equity ratio is:

Debt-equity ratio = Total debt / Owners' equity

Given the balance sheet information for 2013 and 2014:

2013:

Total debt = Long-term debt = $271,700

Owners' equity = Common stock and paid-in surplus + Accumulated retained earnings = $200,000 + $132,481 = $332,481

Debt-equity ratio (2013) = $271,700 / $332,481

2014:

Total debt = Long-term debt = $285,300

Owners' equity = Common stock and paid-in surplus + Accumulated retained earnings = $200,000 + $171,358 = $371,358

Debt-equity ratio (2014) = $285,300 / $371,358

Equity Multiplier:

The equity multiplier is a measure of how much of a company's assets are financed through debt. It is calculated by dividing total assets by owners' equity. The equation for the equity multiplier is:

Equity multiplier = Total assets / Owners' equity

2013:

Total assets = $917,617

Owners' equity = $332,481

Equity multiplier (2013) = $917,617 / $332,481

2014:

Total assets = $983,646

Owners' equity = $371,358

Equity multiplier (2014) = $983,646 / $371,358

Total Debt Ratio:

The total debt ratio is a measure of the proportion of a company's assets that are financed through debt. It is calculated by dividing total debt by total assets. The equation for the total debt ratio is:

Total debt ratio = Total debt / Total assets

2013:

Total debt = Long-term debt = $271,700

Total assets = $917,617

Total debt ratio (2013) = $271,700 / $917,617

2014:

Total debt = Long-term debt = $285,300

Total assets = $983,646

Total debt ratio (2014) = $285,300 / $983,646

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Answer:

(x, y) = (1, 4)

Step-by-step explanation:

Given:  x+y=5 and 2x-y=-2

Solve for y and x

x+y=5; solve for y

y = 5 - x; substitute into other equation

2x-y= -2

2x - (5 - x) = -2

2x - 5 + x = -2; combine x's

3x - 5 = -2; add 5 to both sides

3x =3; divide by 3

x = 1; use this to solve for y

x+y=5

1 + y = 5; subtract 1 from both sides

y = 4

(x, y) = (1, 4)

Surface area of a rectangular prism formula

where w is width, l is length, and h is height.

Substituting with w = 4 ft, l = 6 ft, and h = 10 ft, we get:

On solving the provided question we can say that Therefore, the radius of the circle is 9.

The radius of a circle is a line segment that joins the center of the circle to any point on its circumference. It is essentially half of the diameter of the circle. The radius is denoted by the letter 'r' and is used to calculate many other properties of the circle, such as its area, circumference, and diameter.

The length of the radius is an important characteristic of a circle, as it determines the size and shape of the circle. If two circles have the same radius, they will have the same size and shape. The radius is also used in many real-world applications, such as calculating the distance between two points on a map or the distance between the center of the earth and a satellite in orbit.

The equation \((x+8)^{2} +(y-2)^{2} =81\)  represents a circle with center (-8, 2) and radius 9.

\((x-h)^{2} +(y-k)^{2} =r^{2}\)

Comparing this to the given equation, we see that \(h = -8, k = 2\), and \(r^2 = 81, so r = 9.\)

Therefore, the radius of the circle is 9.

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Student A has the highest shares for both Day 3 and Day 10. Student B has the lowest shares for both Day 3 and Day 10. This is because the growth rate of the function of student A is the highest (1.4 > 1.3 > 1.2)

4. The functions for each student to predict how many shares each student's post will be received on Day 3 and then on Day 10 are: For Student A: f(x) = 100(1.4)^x

On Day 3, the function for student A can be written as f(3) = 100(1.4)^3 = 274 shares. On Day 10, the function for student A can be written as f(10) = 100(1.4)^10 = 2,745 shares.

On Day 3, the function for student B can be written as f(3) = 100(1.2)^3 = 172 shares. On Day 10, the function for student B can be written as f(10) = 100(1.2)^10 = 619 shares.

The function for student C is:f(x) = 200(1.3)^xOn Day 3, the function for student C can be written as f(3) = 200(1.3)^3 = 878 shares. On Day 10, the function for student C can be written as f(10) = 200(1.3)^10 = 19,202 shares.

Student A has the highest shares for both Day 3 and Day 10. Student B has the lowest shares for both Day 3 and Day 10. This is because the growth rate of the function of student A is the highest (1.4 > 1.3 > 1.2), while the growth rate of the function of student B is the lowest.5. The new function representing Amber's photo shares is:f(x) = 3(4)x + 45

This function represents the photo shares of Amber after she decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility. The new function is an upward shift of the original function by 45 units.

The new function representing Amber's photo shares has a y-intercept of 45, which means that Amber's photo will be shared by 45 people even if she does not share her photo with anyone.6. The student whose post travels the fastest is student A.

This is because the growth rate of student A's function is the highest, which means that the rate at which shares increase is the fastest. The function for student A is f(x) = 100(1.4)x

The growth rate of the function for student A is 1.4, which is greater than the growth rate of the functions for students B and C.7. If I had to choose, I would prefer a post with fewer friends initially but more shares, like Amber. This is because the value of the function f(x) = 3(4)x + 45 is greater than the value of the function for students B and C.

Although student A has the highest shares, the initial number of friends is lower compared to Amber.

On Day 3, the function representing Amber's photo shares can be written as f(3) = 3(4)3 + 45 = 57 shares. On Day 10, the function representing Amber's photo shares can be written as f(10) = 3(4)10 + 45 = 333 shares.

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Answer: 44800000

Step-by-step explanation:56000 x 800=44800000

44800000÷56000=800

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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