4. Explain how to use division to find an
equivalent fraction for 20/16

Sides AC and DB of the rectangle ABCD are equal to 2x + 13 and 4x – 1, respectively. Angle BAC is measured by 3x + 1 and angle CAD by x + 15. Angles ABD and CDB are measured as 7x - 31 and 4x + 5, respectively. Angles BDC and ADB are measured as 7x + 1 and 9x – 7 respectively. Angles AEC and AE are measured as 5x - 15 and 3x + 3 respectively.

A rectangle is a polygon with four right angles and four sides. Two sides of the rectangle ABCD are AC and DB, with AC equal to 2x + 13 and DB to 4x - 1. Angle BAC is measured by 3x + 1 and angle CAD by x + 15. Angles ABD and CDB are measured as 7x - 31 and 4x + 5, respectively. Angles BDC and ADB are measured as 7x + 1 and 9x – 7 respectively. Angles AEC and AE are measured as 5x - 15 and 3x + 3 respectively.

You can find the missing sides and angles by looking at the rectangle's angles and sides. As an illustration, if AC = 2x + 13 and DB = 4x - 1, then DB = 72. Similar to this, if AC = x + 3 and DB = 3x - 19 then AC = 14. If AE = 3x + 3 and EC = 5x - 15, then AC = 6 is the result. If AE = 4x + 9 and DE = 6x - 7 then DB = 8 is the result.

The measures of the angles can be solved for using the supplied equations. As an illustration, if mDAC = 2x + 4 and mBAC = 3x + 1, then mBAC = 39. Similar to how mBDC = 7x + 1 if mADB = 9x - 7 and mBDC = 7x + 1 if mBDC = 7x + 1. Last but not least, mABD = 7x - 31 if mCDB = 4x + 5 and mABD = 7x - 31.

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The solution set of the inequality |x - 1 / 2| + 4 ≤ 5 / 2 is x ≥ 2 and x ≤ - 1.

In this problem we find an inequality including an absolute value, which requires some additional treatment by taking definition of absolute value into account, in order to determine the complete solution set:

For x < 1 / 2:

- x + 1 / 2 + 4 ≤ 5 / 2

- x + 9 / 2 ≤ 5 / 2

4 / 2 ≤ x

x ≥ 2

For x ≥ 1 / 2:

x - 1 / 2 + 4 ≤ 5 / 2

x + 7 / 2 ≤ 5 / 2

x ≤ - 2 / 2

x ≤ - 1

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Premise 3: 901,223 is not divisible by 6.

Valid argument form used: Modus Tollens.

Step 1: Divide 901,223 by 6.

901,223 ÷ 6 = 150,203.83333

Step 2: Round down the answer.

150,203.83333 rounded down = 150,203

Step 3: Check if the answer is divisible by 3.

150,203 ÷ 3 = 50,067.3333

Step 4: Round down the answer again.

50,067.3333 rounded down = 50,067

Step 5: Check if the answer is divisible by 3.

50,067 ÷ 3 = 16,689

Step 6: Round down the answer again.

16,689 rounded down = 16,689

Step 7: Check if the answer is divisible by 3.

16,689 ÷ 3 = 5,563

Step 8: Round down the answer again.

5,563 rounded down = 5,563

Step 9: Check if the answer is divisible by 3.

5,563 ÷ 3 = 1,854.3333

Step 10: Round down the answer again.

1,854.3333 rounded down = 1,854

Step 11: Check if the answer is divisible by 3.

1,854 ÷ 3 = 618

Step 12: Check if the answer is divisible by 3.

618 ÷ 3 = 206

Step 13: Check if the answer is divisible by 3.

206 ÷ 3 = 68.66666666

Step 14: Round down the answer again.

68.66666666 rounded down = 68

Step 15: Check if the answer is divisible by 3.

68 ÷ 3 = 22.66666666

Step 16: Round down the answer again.

22.66666666 rounded down = 22

Step 17: Check if the answer is divisible by 3.

22 ÷ 3 = 7.333333

Step 18: Round down the answer again.

7.333333 rounded down = 7

Step 19: Check if the answer is divisible by 3.

7 ÷ 3 = 2.333333

Step 20: Round down the answer again.

2.333333 rounded down = 2

Step 21: Check if the answer is divisible by 3.

2 ÷ 3 = 0.666666

Conclusion: 901,223 is not divisible by 6

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The most suitable method to obtain a random sample of four students from the statistics class would be to use a computer or random-number table to randomly select four students after numbers are assigned.

This method ensures that every student has an equal chance of being selected and that the sample is truly random. This is the only method that guarantees that the sample is random and representative of the entire class.

The other methods listed (A, C, D, and E) do not ensure randomness, as they are based on non-random criteria (such as seating arrangement, height, or time of arrival). These methods might introduce bias into the sample and lead to incorrect conclusions about the population.

Hence, the correct answer is B.

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The nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

The percentage decrease theory suggests that a decrease in the price of a product or service will lead to an increase in demand for that product or service.

This theory is based on the idea that consumers are more likely to buy a product or service if its price is lower. This theory can be applied to both new and existing products or services.

For example, a retailer may decide to decrease the price of a product in order to attract more customers and increase sales. Similarly, a company may choose to reduce the cost of a service in order to make it more attractive to potential customers.

This question is using the percentage decrease theory. According to this theory,

you can calculate the percentage decrease by subtracting the current value from the original value and then dividing by the original value.

Step 1: Subtract the current number of wild tigers (3200) from the original number of wild tigers (20 years ago).

Original - Current = Change

120,000 - 3200 = 116,800

Step 2: Divide the change (116,800) by the original number of wild tigers (120,000)

Change / Original = Percentage Change

116,800 / 120,000 = 97%

Step 3: Multiply the percentage change (97%) by the original number of wild tigers (120,000)

Percentage Change x Original = Estimated Original

97% x 120,000 = 116,400

Therefore, to the nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

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Answer:4

Step-by-step explanation:

1 3/5 = 8/5
8/5 / 2/5 = 4

The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment;

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively);

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%;

Given:

Hannah makes 5 out of 8 attempted free-throws.

Now,

The average waiting time of hannah to make her first basket is 5/8

The probability of hannah making basket at her last attempt is 1/8

The probability of hannah making basket before her last attempt is 2/8

Hence, the probabilty will be 1/8 and 2/8;

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The solution of the system of equations plotted is (x,y) = (4,7).

When a system of linear equations is given, then there exist 3 cases:

Case 1: Unique single solution:

In this case, the lines of the system of equations intersect at one point. That point is the solution of both equations.

The reason we consider intersection as the solution since that the intersection point tells us that it can satisfy both of the given equations simultaneously.

Case 2: No solution:

Then there is no such point that can satisfy both equations simultaneously. Thus, there is no solution to the given system of equations.

Case 3: Infinite number of solutions:

Well, in that case, both the lines are overlapping each other. Thus, all of the points of one line lie on another line too.

And since the given lines are made up of an infinite number of points, thus we will get infinite solutions.

In your case, the lines intersect at points where x=4 and y=7, or say they intersect at coordinate (4,7). Thus, the solution of a given system of equations is x=4 and y=7.

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Answer:

102

Step-by-step explanation:

523 said they prefer chicken,

295 said they prefer pasta,

and 126 said they prefer salad.

523-295-126 =102

Converting 255 metric minutes as per the defined metric time into standard hours is equal to 2.55 hours.

Using defined metric time we have,

One day is equal to 10 hours

One hour is equal to 100 minutes

One minute is equal to 100 seconds

To convert 255 metric minutes into standard hours we have,

100 minutes = 1 hour

⇒ 1 minutes = ( 1 / 100 ) hour

⇒ 255 metric minutes = ( 255 ) ×  ( 1 / 100 ) hour

⇒ 255 metric minutes = ( 255/ 100 ) hour

⇒ 255 metric minutes = 2.55 hours

Therefore, the conversion of 255 metric minutes into standard hour using metric time is equal to 2.55 hours.

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The metadata be more appropriate than analyzing the data is a series of binary digits called bits.

The term called metadata can be defined as the data that provides information about one or more aspects of a given data and it also  provide a structured reference that helps to sort and identify all of its attributes such as Author, created Date, modified date, type of the file and the size of the file.

Here we have given that a group of students take hundreds of digital photos for a science project about weather patterns.

And also each photo file contains data representing the level of red, green, and blue for each pixel in the photo.

Where the file also contains metadata that describes the date, time, and geographic location where the photo was taken.

In this scenario, we have to analyze the metadata would be more appropriate than analyzing the data when determining the likelihood that the photo was taken or created at a particular public event.

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The recursive formula for each sequence is given as follows:

The first sequence is given as follows:

1,3,-2,5,-7,12...

The pattern is that each term is the subtraction of the second to last term by the last term, hence the formula is given as follows:

1,3,-2,5,-7,12: [tex]a_n = a_{n - 2} - a_{n - 1}[/tex]

The second sequence is given as follows:

1,2,2,4,8,32,...

The pattern is that each term is obtained by the multiplication of the two previous terms, hence the formula is given as follows:

[tex]a_n = a_{n - 1} \times a_{n - 2}, a_1 = 1, a_2 = 2[/tex]

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Amongst the given options, we can conclude that the questions 'what is the distribution of ratings for the 75 shows in this sample' and 'is there a relationship between the rating and advertising revenue of the 75 shows in this sample' can be answered using this data set. Hence, options 3 and 4 are the correct options.

Statistics is a field of mathematics that is concerned with the collection, organization, study, understanding, and presentation of data. A data set is the collection of data aforementioned.

Here, we have been told that the data set includes the rating, market share, and advertising revenue for 75 popular tv shows. This means we will easily be able to find out the distribution of ratings for the 75 shows as well as the relationship between the rating and advertising revenue. Hence, options 3 and 4 are the correct answers.

The complete question that you have been looking for is given below -

For a study of TV shows, you obtain the rating, market share, and advertising revenue for 95 popular TV shows.

Which of these are statistical questions that could be answered from this data set? (Check all that apply.)

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The probability of getting at least two heads is there for 11/16. There are six ways to get two heads and two tales

There are 24 = 16 outcomes in all.

The phrase "at least two heads" is defined as "all outcomes" minus "at most 1 tails": tttt, or httt, thtt, ttht, ttth; that is, 5 ways; the probability of at least two heads is therefore (16-5)/16=11/16.

For instance, two heads: hhtt. How many different ways are there to arrange two h's and two t's? One may naively say 4! (4*3*2*1) However, this treats H and H, T and T as distinct when they are actually one and the same. To make up for this, we divide twice by 2: Probability is 6/16=3/8 since 24/(2*2)=6 ways.

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The question is wrong, the correct question:

A fair coin is tossed 4 times. What is the probability of getting at least 2 heads, two heads, or two tails?

Answer:

Step-by-step explanation:

The function is negative for since the leading coefficient is positive and the highest degree is odd (9) (-inf, -6).

The function is negative for since the leading coefficient is positive and the highest degree is odd (9) (-inf, -6).

It then crosses the -6 root to turn positive until it again crosses the -2 root.

(It crosses because the odd multiplicity of both roots)

The function remains negative from -2 until root 4, where it crosses into the positive, where it does not cross since there is an even multiplicity.

In light of the aforementioned, only the first option makes sense. because the leading coefficient is positive and the highest degree is odd (9) the function is negative for (-inf, -6).

Then it crosses the -6 root to become positive until it crosses again the root -2.

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42% of people are likely to see a movie today, or probability of 0.42.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. A coin flip is the most basic illustration. There are only two outcomes that can occur when you flip a coin: either heads or tails.

Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen.

The likelihood that a movie is being viewed right now is:

0.5 of 0.6(if it rains today) (if it rains today).

0.3 of 1 - 0.6 = 0.4(if it does not rain today) (if it does not rain today).

therefore adding them:

p =0.5 (0.6) +0.3(0.4)

 =0.3 +0.12 = 0.42

42% of people are likely to see a movie today, or 0.42.

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Answer: The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).

The square root function is defined for non-negative numbers, so the expression inside the square root must be non-negative.

In this case, -6x - 7 must be greater or equal to 0.

-6x - 7 ≥ 0

x ≥ (7 + 7)/6 = 14/6 = 7/3

So the domain of the function is x ≥ 7/3, or x ∈ [7/3, ∞)

In interval notation, the domain of f(x) = √-6x - 7 is x ∈ [7/3, oo)

Step-by-step explanation:

The percentage of the seats in the theater were filled by the 6th graders on the trip with expression is 56%.

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 middle school that took all of its 6th grade students on a field trip to see a symphony at a theater that has 4100 seats. The students filled 2296 of the seats in the theater.

Assume that the theater filled up [x]% of seats at the theater. Then, we can write -

[x]% = (2296/4100) x 100

[x]% = 0.56 x 100

[x]% = 56%

Therefore, the theater filled up with 56% of seats with 6th grade students.

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To shade decimal number 0.009 in a base-ten block, you would shade one 1/100th block and nine 1/1000th blocks. This can be seen in the image below.

1 tenth | 0 hundredths | 0 thousandths | 9 ten-thousandths

____   |   ____      |   ____     | ____

100th | 0

10th  | 0

1st   | 9

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Answer:

70

Step-by-step explanation:

The area for the given quadrilateral will be 5400m^2, Perimeter=300m and no. of rabbits that van fit are 270.

what are quadrilaterals?

A quadrilateral is a polygon with four sides, four vertices, and four angles.

It is formed by joining four non-collinear points. The sum of the interior angles of quadrilaterals is always equal to 360 degrees. The word quadrilateral is derived from the Latin words ‘Quadra’ which means four and ‘Latus’ means ‘sides’. Not all the four sides of a quadrilateral need to be equal in length. Hence, we can have different types of quadrilaterals based on sides and angles.

Five special quadrilaterals are shown below in the image, along with their definitions and pictures, and points for them to get proven.

Now

as given quadrilateral is rectangular in shape because opposite sides are equal and parallel.

and Length = 90m and breadth=60m

Therefore,

Area=L*B =90*60=5400m^2

Perimeter=2(L+B)=2*150=300m

one rabbit takes 20m^2 of area

No. of rabbits that can fit in 5400m^2 of area=5400/20=270

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The estimate of the integral by parts ∫₀³f(x)g'(x) = 62.1

Integration is the process of reverse differentiation. It is the process of finding the anti-derivative of a function.

Since we have the integral  [tex]\int\limits^3_0 {f(x)g'(x)} \, dx[/tex] and f(x) = x³. To evaluate the integral within the limits, we use integration by parts.

So, for any integral by parts

 [tex]\int\limits^a_b {u(x)v'(x)} \, dx = [u(x)v(x)]^{a} _{b} - \int\limits^a_b {v(x)u'(x)} \, dx[/tex]

So, for the given integral   [tex]\int\limits^3_0 {f(x)g'(x)} \, dx[/tex], we have that

 [tex]\int\limits^3_0 {f(x)g'(x)} \, dx = [f(x)g(x)]^{3} _{0} - \int\limits^3_0 {g(x)f'(x)} \, dx[/tex]

So, we have that

 [tex]\int\limits^3_0 {f(x)g'(x)} \, dx = [f(x)g(x)]^{3} _{0} - \int\limits^3_0 {g(x)f'(x)} \, dx\\= [f(x)g(x) - f(0)g(0)] - [{g(3)f'(3) - g(0)f'(0)}][/tex]

Now, we have that f(x) = x³. So,f'(x) = 3x².

So,

Also, form the table

Substituting these into the equation, we have that  

[tex]\int\limits^3_0 {f(x)g'(x)} \, dx = [f(3)g(3) - f(0)g(0)] - [{g(3)f'(3) - g(0)f'(0)}]\\= [27 \times 4.9 - 0 \times 2.3] - [{4.9 \times 27 - 2.3\times 27}]\\= (132.3 - 0) - (132.3 - 62.1)\\= 132.3 - 132.3 + 62.1\\= 0 + 62.1\\= 62.1[/tex]

So, integral [tex]\int\limits^3_0 {f(x)g'(x)} \, dx = 62.1[/tex]

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Answer:

536

Step-by-step explanation:

Answer: 536

Step-by-step explanation:

Step 1: As we know, a whole of something is equal to 100%. In this case, we want to find what 67% of 800 is. We know that 100% of 800 is, well, just 800.Step 2: If 100% of 800 is 800, then we can get 1% of 800 by dividing it by 100. Let's do 800 / 100. This is equal to 8.0. Now we know that 1% is 8.0.Step 3: Now that we know what 1% of 800 is, we just need to multiply it by 67 to get our solution! 8.0 times 67 = 536. That's all there is to it!

Donald's work seems to be inaccurate. He substitutes u = x3 in the first step, however he does not correctly adjust the bounds of integration. He divides by x in the subsequent phase, which results in a division by zero at x = 0.

Additionally, it appears like Donald made a mistake while integrating sin(u)du in the final step. It should have been -cos(u) + C rather than x*cos(u) + C. One could try an alternative approach or use a calculator or computer to assess the integral to verify the work. Another option would be to look up the right answer in a book or internet resources.

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Answer: I'm sorry but this equation is not valid, and it does not make any sense to me. There is no variable q and the equation is not a mathematical equation so I cannot give you a value of q. Also, the statement p = 13.6 is not related to the equation provided. Therefore, I cannot answer this question. Can you please provide more context or clarify what you are trying to ask?

Answer:

Step-by-step explanation:

P = 2l+b)

P = 2(20 + 15)

P = 2(35)

P = 70 feet

Answer:

70 feet

Step-by-step explanation:

      length = 20 feet

        width = 15 feet

[tex]\sf \boxed{\text{Perimeter of rectangle = 2* ( length * width)}}[/tex]

                             [tex]\sf = 2* (20 + 15)\\\\ = 2 * 35\\\\= 70 \ feet[/tex]

Answer:

Step 1

Step-by-step explanation:

I believe is correct pls report if wrong idc it is my fault

The dating web site Oollama.com requires its users to create pro les based on a survey in which they rate their interest (on a scale from 0 to 3) in positive categories: physical fitness, music, spirituality, education, and alcohol consumption.

A new Oollama customer, Erin O'Shaughnessy, has reviewed the pro les of 40 prospective dates and classi ed whether she is interested in learning more about them. Based on Erin's classi cation of these 40 pro les, Oollama has applied a logistic regression to predict Erin's interest in other pro les that she has not yet viewed. The resulting logistic regression model is as follows:

Log odds of Interested = −0.920 + 0.325 × Fitness − 3.611 × Music

+5.535 × Education − 2.927 × Alcohol

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Answer: 141.78

Step-by-step explanation: 1.39 x 102 = 141.78