Evaluate whether the following argument is correct; if not, then specify which lines are incor- rect steps in the reasoning. Each line is assessed as if the other lines are all correct. So, you are to identify which lines (the minimum number) would you need to fix to get a correct proof. Proposition: If r and y are rational numbers then 3x + 2y is also a rational number. Proof: 1. We proceed by contradiction proof. 2. Assumer and y are irrational numbers. 3. Since r and y are rational, 1 = and y = a, where a, b, c, and d are integers, and b + and d 70. 4. We will show that 3x +2y is a rational number. 5. Plugging in for and į for y into the expression 3x +2y gives: 3x + 2y = 38 + 24 = 6. Since a, b, c, and d are all integers, 3ad + 2bc and bd are also integers. 7. Since b + 0 and d + 0, bd 70. 8. Therefore, 3ad + 2bc and bd contradict the assumption that r and y are irrational numbers, which implies that 3x +2y is irrational is false. 3ad +-2bc bd

Answer: See explanation

Step-by-step explanation:

From the question, we are informed that last month $30 was spent on clothing and that this month, 160% of what was spent last month.

The equation to to model this situation will be:

= 160% × $30

= 160/100 × $30

= 1.6 × $30

= $48

That means $48 will be spent this month.

Answer: a) P=10c b) A=4(c^2)

Step-by-step explanation:

the length of each side is c

a) the perimeter is the border of the whole shape. we can see here there are 4 squares but together. each square has 4 sides however since they are connected, we only count 10 of them for the perimeter. 4 for the top and bottom and 1 on each side (4+4+1+1)=10. so it would be 10c

b) area is width x length. which is c x c or c^2. multiply this by however many squares there are. in this case its 4. so it would be 4 x (c^2) or 4(c^2)

Step-by-step explanation:

Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:

= 10 + (1/2 × 10) = 10 + 5 = 15 feet

Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:

= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet

Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:

= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75

Lola's mom walked x feet, and then half that length again. Total length walked will be:

= x + (1/2 × x) = x + 0.5x = 1.5x

Total feet walked by the whole member of the family will be:

= 15 + 4.5 + 9.75 + 1.5x

= 29.25 + 1.5x

Answer:

turtle: 10 + 5 = 15

brother:  3 + 1 1/2 = 4 1/2

hamster: 6 1/2 + 3 1/4 = 9 3/4

Mom: x + 1/2x = 1 \(\frac{1}{2}\)x

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

And also,PLEASE DONT YELL AT ME/US!!

The variation in assembly times within each assembly method the treatment sum of squares is 2, and the degrees of freedom (df2) for the error sum of squares is 12.

To determine the degrees of freedom (df1) for the treatment sum of squares, we need to consider the number of groups (assembly methods) being compared.

In this case, there are three different ways of assembling the part. Since there are three groups, the degrees of freedom for the treatment sum of squares is calculated as:

df1 = number of groups - 1

= 3 - 1

= 2

To calculate the degrees of freedom (df2) for the error sum of squares, we need to consider the total number of observations and the number of groups.

In this case, there are 5 people assigned to each assembly method, and there are 3 assembly methods in total. so the total number of observations is 5 * 3 = 15.

df2 = total number of observations - number of groups

= 15 - 3

= 12

Therefore, the degrees of freedom (df1) for the treatment sum of squares is 2, and the degrees of freedom (df2) for the error sum of squares is 12.

To know more about degrees of freedom here

https://brainly.com/question/32084981

#SPJ4

The graph of the absolute value function f(x) = |x - 2| is given by the image presented at the end of the answer.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent absolute value function is given as follows:

f(x) = |x|.

Which has the format of the V-graph, with vertex at the origin.

f(x) = |x - 2| is a translation right two units of f(x) = |x|, hence the vertex will be at the point (2,0).

More can be learned about translations at brainly.com/question/28174785

#SPJ1

Answer:

14 or 0.14

Step-by-step explanation:

3 1/2 ÷ 1/4

1/4 = 25

3 1/2 ÷ 25 = 0.14 or 14

This is correct answer can you mark me brainliest

The exact value of tan(α+β) is 323/36.

To find the exact value of tan(α+β) without using a calculator, we need to use trigonometric identities and the given information.

Since α and β are acute angles in quadrant 1, we know that sin(α) and cos(β) are both positive.

From the given information, we have sin(α) = 7/25 and cos(β) = 5/13.

We can use the following trigonometric identity to find tan(α+β):

tan(α+β) = (tan(α) + tan(β)) / (1 - tan(α)tan(β))

First, let's find the values of tan(α) and tan(β):

Since sin(α) = 7/25, we know that sin(α) / cos(α) = 7/25 / cos(α).

To find tan(α), we can simplify this expression:

tan(α) = sin(α) / cos(α) = (7/25) / (√(1 - sin²(α))) = (7/25) / (√(1 - (7/25)²)) = 7/24

Similarly, for cos(β) = 5/13, we have:

tan(β) = sin(β) / cos(β) = (√(1 - cos²(β))) / cos(β) = (√(1 - (5/13)²)) / (5/13) = 12/5

Now, we can substitute these values into the formula for tan(α+β):

tan(α+β) = (tan(α) + tan(β)) / (1 - tan(α)tan(β))
         = (7/24 + 12/5) / (1 - (7/24)(12/5))
         = (35/120 + 288/120) / (1 - 84/120)
         = (323/120) / (36/120)
         = 323/36

So, the exact value of tan(α+β) is 323/36.

Learn more about trigonometric identities from this link:

https://brainly.com/question/3785172

#SPJ11

Answer:

There is no mode !

Step-by-step explanation:

Hello,

what is the mode of a set of data?

It is the value in the set that occurs most often.

To note that this is also possible to have a set of data with no mode.

in this example, let's order them

7, 8, 11, 12, 13, 14, 15, 20

There is no repetition, right? each value occurs only once.

So, there is no mode!

hope this helps

Answer:

y = -3.5x + 2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

It will be B.

Hope this helps!

Answer:

A.

Step-by-step explanation:

The points are at 3,1 which 3/1=3, 6,2, which 6/2=3/1, and 9,3, which 9/3=3/1.

(hope this helps!)

Answer:

y/4 + x/12

Step-by-step explanation:

The number of working toys = x

The number of broken toys = y

Bert breaks 1/3 of the working toys, that is:

1/3 * x = x/3

The number of broken toys is now:

y + x/3

Ernie then throws away 1/4 of the broken toys. In terms of x and y, the number of broken toys that Ernie threw away is:

1/4 *(y + x/3)

= y/4 + x/12

The largest binary code is on 4 bits, the maximum possible number is binary 1111 or 15. And the maximum decimal number that can be represented with 1 byte is 255 or 11111111.

Binary code:

In math, binary code refers a coding system using the binary digits 0 and 1 to represent a letter, digit, or other character in a computer or other electronic device.

Given,

Here we need to find the largest binary code.

Here we know that, for each digit d in a binary number, starting from the rightmost digit, the value in decimal corresponding to this digit is written as,

=> d2ⁿ + d*2ⁿ⁻¹ .... 0, where n is its position.

For, example would be converting 11001:

Here we start from the right

=> 1*2⁰ + 0*2¹ + 0*2² + 1*2³ + 1*2⁴ = 25.

Therefore, if we have 8 bits, the largest number would be 11111111, That has the value of 255, which is the same result as the conversion above (1+2+4+8+16+32+64+128).

To know more about Binary code here.

https://brainly.com/question/28222245

#SPJ4

Answer:

both of the triangels  have an area of 400

Answer:

m = 4/3

Step-by-step explanation:

The correct answers for the given question are:

1. The remote angles of the triangle are: ∠PQR, ∠PRQ

2. ∠QRU

3. The exterior angle of triangle are : ∠RPS, ∠TQP,  ∠QRU.

4. ∠RPS and ∠QPV are vertically opposite angle. So, ∠RPS = ∠QPV

5. The relation between ∠RPS and ∠RPQ is  ∠RPS + ∠RPQ = 180⁰.

A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices P, Q, and R is represented as △PQR.

Here,

1. The remote angles of the triangle are: ∠PQR, ∠PRQ

2. ∠QRU

3. The exterior angle of triangle are : ∠RPS, ∠TQP,  ∠QRU.

4. ∠RPS and ∠QPV are vertically opposite angle. So, ∠RPS = ∠QPV

5. The relation between ∠RPS and ∠RPQ is  ∠RPS + ∠RPQ = 180⁰.

Learn more about Triangle from:

https://brainly.com/question/2773823

#SPJ1

Answer:

256

Step-by-step explanation:

any number to the 0 power equals 1, so r^0 equals 1

then, you have (4(1))^4

4×1=4

4^4=256

Answer:

3328

Step-by-step explanation:

13(4r^0)^4=13*44= 13*(4

*

4

*

4

*

4

)

=

3328

Answer: 400:18

and 200:9

Step-by-step explanation:

Answer:

3 < x

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Common Sense

Hope it helps???

Danielle will get a better return if she invests in Bank B rather than in Bank A.

Given data are,

Bank A: 2.75% compounded monthly

Bank B: 3.25% compounded semi-annually.

In order to find the better return after 10 years, we need to calculate the final amount at both banks.

Let's calculate the final amount of Bank A using the compound interest formula,

A = P(1 + r/n)nt

Where, P = Principal amount, r = annual interest rate, n = number of times interest is compounded per year, t = time (in years).

Here, P = $5,000, r = 2.75% = 0.0275, n = 12 (monthly), t = 10 years.

So, the final amount at Bank A, A = 5000(1 + 0.0275/12)(12×10) = $6,906.90

Now, let's calculate the final amount of Bank B using the formula,

A = P(1 + r/n)nt

Here, P = $5,000, r = 3.25% = 0.0325, n = 2 (semi-annually), t = 10 years.

So, the final amount at Bank B,

A = 5000(1 + 0.0325/2)(2×10) = $7,322.36

Therefore, the better return after 10 years would be at Bank B.

That is, Danielle will get a better return if she invests in Bank B rather than in Bank A.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ11

The options are analyzed as follows:

1: The overline 0.729 means:

This is a non- terminating recurring decimal hence it is rational.

2: The nuumber 0.0195347... is a non terminating and non recurring decimal hence it is irrational.

3. The number -12 is rational since it is an integer.

4.The number 4.565656... is a non terminating recurring decimal hence it is rational.

5. The number given by:

Since square root of 2 is irrational and 3 is rational the product is irrational.

Also the decimal is non terminating non recurring hence it is irratonal.

So the options 2 and 5 are irrational.

Therefore , the solution of the given problem of percentage comes out to be y = e(t + ln(1.03) - 1) - 1.

In mathematics, a number or number stated as a portion of 100 is referred to as a percentage. Also occasionally used are the abbreviations "pct.," "pct," as well as "pc." However, the "%" sign that is used to denote it is frequently used. The % sum is flat; there are no dimensions. Since percentages have a numerator of 100, they are basically fractions.

Here,

a)

We must determine the derivative of y with regard to t in order to determine the slope of the tangent line:

=> (Y+1)/(2t) = dy/dx

The following can be written using the chain rule:

Dy/dt = Dy/dx + Dy/dt

We can differentiate t with respect to itself to discover dx/dt and obtain dx/dt = 1 by doing so.

Consequently, (y+1)/(2t) = dy/dt = dy/dx * dx/dt = dy/dx.

Now that we have this equation, we can change t = 1 and y = 0.03 to obtain the slope of the tangent line:

dy/dt = (0.03+1)/(2√1) = 0.515

The tangent line to the y-axis graph at time t = 1 has the following expression as a result:

y - 0.03 = 0.515(t - 1) (t - 1)

We can use the tangent line equation with t = 1.2 to roughly calculate the proportion of the colony afflicted at that time:

y - 0.03 = 0.515(1.2 - 1) (1.2 - 1)

y - 0.03 = 0.257

y = 0.287 or 28.7% (estimate) (approx)

Consequently, 28.7% of the population was infected at time t = 1.2.

b) We can rewrite the given differential equation as y+1 = e(t + ln(1.03) - 1) in order to directly find y in terms of t.

If we condense this phrase, we get:

y = e^(√t Plus ln(1.03) - 1) - 1

As a result, the formula for the colony's infection rate as a function of time t is y = e(t + ln(1.03) - 1) - 1.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ4

Answer:

Im not sure about a but, b= 38

Step-by-step explanation

b: 90 - 52 = 38

*90 because it is a right angle

Answer:

Length=153 yards

Width=54 yards

Hope this helps! :)

Step-by-step explanation: (153*=306, 54*2=108, 306+108=414)

P=2l+2w                                              

P=414

L=3w-9

W=w

414=2(3w-9)+2w

414=6w-18+2w

414=8w-18

+18      +18

432=8w

/8

54=w

L=3(54)-9

L=162-9

L=153

we know that

Supplementary angles sum 180 degrees

so in this problem

120 and 60and 60

Using the side-side-side (SSS), ΔRST ≅ ΔLKJ as shown in the proof below.

If we show that two triangles have three pairs of corresponding sides that are congruent to each other, then the two triangles can be stated to be congruent to each other based on the side-side-side (SSS) congruence theorem.

Given the two triangles in the diagram, the proof that shows that ΔRST ≅ ΔLKJ is shown below:

Statement                                     Reason                                      

1. Line RS ≅ side KL                     1. Given

2. Line ST ≅ side JK                    2. Given

3. Line RT ≅ side JL                    3. Given

4. ΔRST ≅ ΔLKJ                           4. Side-side-side (SSS)

Learn more about the side-side-side (SSS) on:

https://brainly.com/question/24079210

#SPJ1

Answer:

see explanation

Step-by-step explanation:

consecutive even numbers have a difference of 2

let the consecutive even numbers be n and n + 2, thus

(n + 2)² - n² ← expand (n + 2)² using FOIL

= n² + 4n + 4 - n² ← collect like terms

= 4n + 4

= 4(n + 1) ← which results in a multiple of 4