(35 pts)Evaluate the reasoning provided by both students A and B and correct the errors Make sure to provide proper reasoning. Only answer if you know your answer is correct please.​

(35 Pts)Evaluate The Reasoning Provided By Both Students A And B And Correct The Errors Make Sure To

Answers

Answer 1

Answer:

see the explanation

Step-by-step explanation:

we know that

A Rational Number is a number that can be made by dividing two integers

we have

[tex]\frac{\sqrt{2}}{8}[/tex]

[tex]\sqrt{2}[/tex] ----> is not a integer

so

The given number cannot be rewritten as the quotient of two integers

therefore

The given number is irrational

Student A is incorrect because is a irrational number and not all fractions are rational

Student B reasoning is incorrect, because there are fractions that have as numerator an irrational number and can be rational numbers

example

[tex]\frac{\sqrt{2}}{3\sqrt{2}}=\frac{1}{3}[/tex] ----> is a rational number and the numerator is a irrational number

Answer 2

Student A incorrectly claims √2/8 is rational because it can be written as a fraction. Student B is correct, stating that √2/8 is irrational because √2 is irrational, and dividing it by 8 doesn't change its irrationality.

Let's evaluate the reasoning of both students A and B and correct any errors:

Student A:

Student A's reasoning is incorrect. They claim that √2 / 8 is rational because it can be written as a fraction. However, being able to write a number as a fraction doesn't necessarily make it rational. The key point is whether the number can be expressed as a ratio of two integers, and in this case, √2 cannot be expressed as a simple fraction. √2 is known to be an irrational number, and when you divide an irrational number by 8, the result remains irrational.

Student B:

Student B's reasoning is correct. They state that √2 / 8 is irrational because √2 is irrational. This is accurate. The division of an irrational number by a rational number does not change its irrationality. Therefore, √2 / 8 is indeed an irrational number.

In summary, Student B provides the correct reasoning, while Student A's reasoning is flawed.

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Related Questions

Estimate 3,182 multiply by 5

Answers

Final answer:

Estimate the product of 3,182 multiplied by 5 by rounding to the nearest hundred, resulting in an estimation of 16,000.

Explanation:

To estimate the product of 3,182 multiplied by 5, we can round 3,182 to the nearest hundred to make the multiplication simpler.

Rounding 3,182 to the nearest hundred gives us 3,200.

We then multiply 3,200 by 5:

3,200 x 5 = 16,000

This estimated product is not an exact answer but gives us a reasonable approximation that is easy to calculate mentally or on paper.

beth and her brother went to the arcade. it cost 75 cents to play 3 games. they played 21 games in all. how much money did they spend?

Answers

it cost beth and her brother 147 coins. 3/21=7; 7x75=147

Answer:

$5.25

Step-by-step explanation:

if it cost 75 cents to play 3 games, that means it cost 25 cents per game. Multiply 21 games by 25 cents per game and you get 525, or $5.25.

What is the decimal equivalent to 4%?

Answers

Answer:

0.8

Step-by-step explanation:

4/5 0.8 80%

hope this is useful

Hey!

------------------------------------------------

Solution and Explanation:

When you want to find the decimal of a number just divide by 100.

4 / 100 = 0.04

------------------------------------------------

Answer:

[tex]\large\boxed{0.04}[/tex]

------------------------------------------------

Hope This Helped! Good Luck!

Hakeem subtracted 8 from a number then multiply the difference by 5 the result was 20 write and solve an equation to find the number X

Answers

Answer:

(×-8)5=20

(5×-40)=20

5×(-40+40)=(20+40)

5×=60

5×÷5=60÷5

×=12

Based on the equation given, the value of the number is 12.

Let the number be represented by x.

Based on the information given, the equation to solve the question will be:

(x - 8) × 5 = 20

5x - 40 = 20

Collect like terms

5x = 20 + 40

5x = 60

Divide both side by 5

5x/5 = 60/5

x = 12

Therefore, the number is 12.

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What is 4527 written in scientific notation?
OA) 4.527
O B) 4.527 x 102
OC) 4.527 x 103
OD) 4.527 x 104

Answers

Answer:

OC) 4.527 x 10^3

Step-by-step explanation:

To write a number in scientific notation, first move the decimal point to create a number between 1 and 10.

4527. becomes 4.527

To get your exponent, count how many places you moved the decimal. In this case, you moved the decimal three places.

4.527 * 10^3

complete 2x+21= using only the communtative property of addition​

Answers

Answer:

-9.5

Step-by-step explanation:

2x + 21 =

2x + 20 = 1 (C.P)

2x = 1-20

2x = - 19

x= - 19/2

x = - 9. 5

PLEASE HELP ME I WILL GIVE YOU BRAINLIEST

Answers

Answer:

Equation of the line is y=-x+3

Rewritten as an inequality is y ≤ -x+3

Step-by-step explanation:

You find the slope by doing rise over run which ends up being -1/1, so just -1.

The y-intercept is 3.

Slope intercept form is y=mx+b, so y=-x+3 is the answer in slope intercept.

Then ≤ is used because the line is going down and it's shaded to the left, also the line isn't broken, it's solid which means it's equal to, so it would be less than or equal to.

Please help me idk this

Answers

Answer:

The anwser is 2.8000

Step-by-step explanation:

 You look at the tenth place its 8 :

   2.8151

Then you look to the right which is 1

is 1 more than 5 or less

1 < 5

8 stays the same but 1, 5, and 1 turn into zeros

 

Answer:

2.8151 rounded to the nearest tenth is 2.8, because tenths lie right after the decimal

I hope i helped :)

5×25-15615÷5 can someone help simplify this question?​

Answers

Answer:

125-3123

Step-by-step explanation:

5 x 25 is 125, subtracted by 15615 which is 3123

I need help with this

$5.40+$8.70+$6.30


plz help this is fifth grade math and it is using compensations and it is hard​

Answers

So, let’s pretend those 0’s at the end and the $’s are gone. That’s 5.4+8.7+6.3 .
Then, pretend there isn’t a . there. 54+87+63
Split them up by 10’s and 1’s
5+8+6=19
And
4+7+3=14
Now, we put the decimal back in. (That’s what the . is when there are numbers to the left of it.)
19+1.4=19+1+0.4
19+1=20
20+0.4=20.4
Then, put the 0 and $ back where they were before. $20.40 is your answer!

After solving the given mathematical expression which is $5.40 + $8.70 + $6.30 , we get value equal to $20.40

What is addition ?

The process of adding two or more numbers together or combining things into one group is known as addition.

The given arithmetic expression is $5.40+$8.70+$6.30.

Let's solve the given mathematical expression.

To add decimal numbers , place the decimal point in line with the specified decimal points, align the decimal numbers in accordance with their place values. If we look at the given decimals, we can see that they are like decimals because they have two digits after the decimal point. Therefore, we will arrange them in the proper sequence and perform standard addition rule.

i.e.,

5.40 + 8.70 + 6.30

We can write this as sum of :

= (5+8+6) + (0.40 + 0.70 + 0.30)

Now , solving to get the value :

= (19) + (1.40)

= $20.40

Therefore, after solving the given mathematical expression which is $5.40 + $8.70 + $6.30 , we get value equal to $20.40

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6/7 times 9/7 in simplist form

Answers

Answer:

3/2

Step-by-step explanation:

Answer:

1 [tex]\frac{5}{49}[/tex]

Step-by-step explanation:

1. Multiply the numerators

6 x 9 = 54

2. Multiply the denominators

7 x 7 =49

3. You would get 54/79

4. Simplify

When simplifying you would get 1 [tex]\frac{5}{49}[/tex]

Solve 4(25+5+1+10) use pemdas

Answers

Answer:

164

Step-by-step explanation:

pemdas

parentheses first: 4(25+5+1+10) = 4(41)

parentheses around only on term means multiply

4(41)= 164

Answer:

164

Step-by-step explanation:

PEMDAS requires you to do whatever is asked inside the parenthesis first. So in this case, add all those together to get the answer of 41, then multiply by 4 on the outside

The midpoint of GH is M(3, 0). One endpoint is G(1, 0). Find the coordinates of the other endpoint H.

Answers

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ G(\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad H(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+1}{2}~~,~~\cfrac{y+0}{2} \right)~~=~~\stackrel{\stackrel{Midpoint}{M}}{(3~,~0)}\implies \begin{cases} \cfrac{x+1}{2}=3\\[1em] x+1=6\\ \boxed{x=5}\\ \cline{1-1} \cfrac{y+0}{2}=0\\[1em] \boxed{y=0} \end{cases}[/tex]

k/7=32/56? i have no idea how to solve this

Answers

k/7=32/56

To solve for k, cross multiply:

(k x 56) = (7 x 32)

Simplify:

56k = 224

Divide both sides by 56:

k = 224 / 56

k = 4

Simplify: (sin x)/(1+cot^2 x)

Answers

Answer:

sin³x

Step-by-step explanation:

Using the trigonometric identities

1 + cot²x = csc²x

cscx = [tex]\frac{1}{sinx}[/tex]

Given

[tex]\frac{sinx}{1+cot^2x}[/tex]

= [tex]\frac{sinx}{csc^2x}[/tex]

= [tex]\frac{sinx}{\frac{1}{sin^2x} }[/tex]

= sinx × sin²x

= sin³x

Jillian owns 60% of the stock
in a private catering
corporation. There are 1,200
shares in the entire
corporation. How many
shares does Jillian own?

Answers

Answer:

720

Step-by-step explanation:

Percentage share owned by Jillian = 60%

Total shares in corporation = 1200

Number of shares owned by Jillian = [tex]\frac{60*1200}{100} = 720[/tex]

What times what equals -18

Answers

-1 x 18 = 18

-2 x 9 = 18

-3 x 6 = 18

-6 x 3 = 18

-9 x 2 = 18

-18 x 1 = 18

Hope this helped!

Nate

To get -18, we can use the factors

2 times -9 = 18

How to fill the blanks

To find two numbers that multiply to give -18, we need to consider pairs of factors of -18. The factors of -18 are:

1 and -18

2 and -9

3 and -6

So, the pairs of numbers that multiply to give -18 are:

1 * -18 = -18

2 * -9 = -18

3 * -6 = -18

Therefore, -18 can be expressed as the product of various combinations of these pairs, such as (-2) * 9, (-3) * 6, and so on.

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Given: ∠5 ≅ ∠13

Which lines must be parallel?

A) r and s
B) p and q
C) p and r
D) q and s

Answers

Answer:

Option A) r and s

Step-by-step explanation:

we know that

When two lines are crossed by another line (called the Transversal), the angles in matching corners are called Corresponding Angles. If the lines are parallel, then the angles are congruent

In this problem

If lines r and s are parallel

then

m∠5≅m∠13 -----> by corresponding angles

Answer:

the answer on the usa testprep is A.

Step-by-step explanation:

give some brainlest

Please help

Nathan bought one notebook and one binder for each of his college classes notebooks cost 0.95 each and binders cost 5.82 each. The total cost of notebooks and binders was 27.08. how many classes is Nathan taking?

Answers

Answer:

0.95 + 5.82 = 6.77 for each

27.08/6.77= 4

so he's taking 4 classes

Answer:

The answer is 4 classes.

Step-by-step explanation:

Nathan bought one notebook and one binder for each of his college classes.

Notebooks cost 0.95 each and binders cost 5.82 each.

So, he paid [tex]0.95+5.82=6.77[/tex] dollars

The total cost of notebooks and binders Nathan paid 27.08.

This means he bought these things for [tex]\frac{27.08}{6.77}=4[/tex] classes.

Mark earned $240 in the first week and earns $680 in the fifth week. How much will he earn in the 20th week (suppose his earnings each week have the same increase)​

Answers

Answer:

$ 2330

Step-by-step explanation:

a = $240

Earning at the end of fifth week = $ 680

increase in earnings per weak = ( 680 -240)/2     = 440/2 =110

d =110

l = a + (n-1)d

a20 = 240 + (19 * 110 ) = 240 + 2090 =   2330

Answer:2334

Step-by-step explanation:

A regular polygon has 24 sides. What's the measure of each exterior angle?
A. 18°
B. 15°
C. 20°
D. 16°

Answers

Hey!

----------------------------------------

Explanation and Solution:

A polygon has to at least have 360° total to form a polygon.

Since there are 24 sides you divide 360 by 24.

360 / 24 = 15

----------------------------------------

Answer:

The measure of each exterior angle has to be at least 15° to form a complete polygon of 24 sides.

----------------------------------------

Hope This Helped! Good Luck!

Which toy pack has a cost of $2.50 per toy?

Answers

YoYo. 15/6 = 2.5 so each YoYo costs $2.50.

Answer:

Yo-Yo

Step-by-step explanation:

I do not know all the steps but I just joined but the answer is Yo-Yo!!

write 1.888... as a mixed number

Answers

Answer:

Step-by-step explanation:

The answer is 1-4/5

The difference between a number and 10

Answers

Answer:

[tex]10 - x[/tex]

Step-by-step explanation:

the difference between a number and 10 simply means ,that number minus 10.

Let that number be x

therefore the difference between x and 10 is written as

[tex]x - 10[/tex]

Answer:

x-10

Step-by-step explanation:it simply means to subtract a number from ten

Elijah walked 6 miles in 3 hours. What was his walking rate in hours per mile?

Answers

0.5 hours per mile Djkdkdkdkd

Answer: One hour/two miles

Step-by-step explanation:

Distance=Rate*Time

Distance=6 miles

Time=3 hours

Rate is unknown

6Miles=3Hours(Rate)

6Miles/3Hours=Rate

2Miles/1hour

For each hour that passes, he can walk two miles

Taylor would like to build the garden of her dreams. She needs 20 cubic feet of soil containing 12% clay. She has two types of soil that she can combine to achieve this: soil with 20% clay and soil with 8% clay. How much of each soil should she use?

Answers

i believe it’s %32.22.

Hope this helps ! :)

A bag contains the following marbles: 4 black marbles, 14 blue marbles, 8 brown marbles, and 20 green marbles. What is the ratio of blue marbles to green marbles? Express your ratio as a fraction or with a colon

Answers

Answer:

14 to 20 or 7 to 10 is the ratio

Final answer:

The ratio of blue marbles to green marbles is 14:20, which simplifies to 7:10 or as a fraction, 7/10.

Explanation:

The ratio of blue marbles to green marbles from a bag containing 4 black marbles, 14 blue marbles, 8 brown marbles, and 20 green marbles is simply the number of blue marbles divided by the number of green marbles. To express this ratio, we would do the following:

Count the blue marbles: There are 14 blue marbles.

Count the green marbles: There are 20 green marbles.

Write the ratio: The ratio of blue marbles to green marbles would be 14 blue marbles to 20 green marbles.

Express as a fraction or with a colon: As a fraction, this is 14/20, which simplifies to 7/10. Or, using a colon, it is represented as 14:20, which also simplifies to 7:10.

The sum of 10 and a number x is equal to 14.

Answers

Answer:

10+x=14; x=4

Step-by-step explanation:

10+x=14

-10     -10

The 10's cancel out

x=4

Answer:  10+x=14

Step-by-step explanation:

The word "sum" implies addition, so we know we are going to be adding some values. The next part of the sentence just give you your two values, 10 and a number (x). We know to add these two together because of the word sum. The final part of the sentence is "is equal to 14" this simply mean =14. Put all the pieces together and you get : 10+x=14

an average person has 6x10 2power times as many red blood cells as white blood cells. A small sample of blood has 7x10 3power white blood cells. about how many red blood cells are in the sample

Answers

Answer:

4.2×10to the 6th or 4,200,000

Step-by-step explanation:

First you have to know that you are multiplying these two numbers. When you multiply exponents like there you add the matissa's (6&7) and add the exponents.

6×10to the 2 * 7×10to the 3rd

42 × 10to the 2+3

42×10to the 5th

Something else you need to know is your matissa cant be higher than 10

So:

4.2 × 10to the 6th is your answer

The sample contains 42 × 10⁵ red blood cells.

What happens when same base is multiplied ?

When same base is multiplied their powers gets added.

For example - a×a×a×a×a×a = a⁶.Here a has nothing in it's power means it has 1 to it's power.

According to the given question

For every 1 while blood cells an average person has 6x10² times as many red blood cells.

A small sample of blood contains 7 × 10³ white blood cells.

∴ The amount of red blood cells in the sample is

= (7 × 10³)(6× 10²) red blood cells.

= (7×6)(10³×10²)

= 42 × 10⁵ red blood cells.

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joseph read 12 books in 2 months. what was his rate of reading in books per month ? Express your answer in simplest form

Answers

Answer: He read 6 books in 1 month. 6:1 is the unit rate

Step-by-step explanation:

12/2 = 6

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