Juan and Patti decided to see who could read the most books in a month. They began to keep track after Patti had already read 5
books that month. This graph shows the number of books Patti read for the next 10 days.
Number of Books Read
Books
25
20
15
10
5
05
-X
0 1 2 3 4 5 6 7 8 9 10
Day
If Juan has read no books before the fourth day of the month and he reads at the same rate as Patti, how many books will he have
read by day 12?
10
0 15
O 20

Juan And Patti Decided To See Who Could Read The Most Books In A Month. They Began To Keep Track After
Juan And Patti Decided To See Who Could Read The Most Books In A Month. They Began To Keep Track After

Answers

Answer 1

With the help of the given graph, we know that Juan has read 10 books by day 12.

What is a graph?

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.

The points on a graph are typically used to depict the relationships between two or more things.

Making a diagram that shows the link between two or more objects is known as developing a graph.

Create a graph by placing a series of bars on graph paper.

So, for path:
The curve line: y = kx + 5 which passes (4, 10)

10 = 4k + 5, k = 5/4

For Juan:

His reading rate same as Patti's.

Curve line: y = ax + b

a = 5/4

He has not read any book before 4th day.

So, when x = 4, y = 0.

0 = 4a + 5, 4 * 5/4 + b

b = -5

y = 5/4 * -5 (x > 4)

When x = 12, y = 5/4 * 12 - 5 = 15 - 5 = 10

Juan has read 10 books by day 12.

Therefore, with the help of the given graph, we know that Juan has read 10 books by day 12.

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Answer 2

With the help of the given graph, we know that Juan has read 10 books by day 12.

What is a graph?

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.

The points on a graph are typically used to depict the relationships between two or more things.

Making a diagram that shows the link between two or more objects is known as developing a graph.

Create a graph by placing a series of bars on graph paper.

So, for path:
The curve line: y = kx + 5 which passes (4, 10)

10 = 4k + 5, k = 5/4

For Juan:

His reading rate same as Patti's.

Curve line: y = ax + b

a = 5/4

He has not read any book before 4th day.

So, when x = 4, y = 0.

0 = 4a + 5, 4 * 5/4 + b

b = -5

y = 5/4 * -5 (x > 4)

When x = 12, y = 5/4 * 12 - 5 = 15 - 5 = 10

Juan has read 10 books by day 12.

Therefore, with the help of the given graph, we know that Juan has read 10 books by day 12.

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Related Questions

Suppose Lisa wants to glue decorative paper onto the block. What is the total surface area that Lisa would need to cover? Show your work.

Suppose Lisa wants to glue decorative paper onto the block. What is the total surface area that Lisa

Answers

The total surface area that Lisa would need to cover is 2 times the sum of the areas of the top and bottom faces plus 2 times the sum of the areas of the side faces.

To calculate the total surface area that Lisa would need to cover, we need to consider all the faces of the block.

Assuming the block is a rectangular prism, it will have six faces: a top face, a bottom face, and four side faces.

Let's denote the length, width, and height of the block as L, W, and H, respectively.

Top and Bottom Faces:

The top and bottom faces have dimensions of L × W each, so their combined area is 2 × (L × W).

Side Faces:

The side faces consist of four rectangles, two with dimensions of L × H and two with dimensions of W × H. So, the combined area of the side faces is 2 × (L × H) + 2 × (W × H).

Now, we can calculate the total surface area by summing up the areas of all the faces:

Total Surface Area = 2 × (L × W) + 2 × (L × H) + 2 × (W × H)

Therefore, the total surface area that Lisa would need to cover is 2 times the sum of the areas of the top and bottom faces plus 2 times the sum of the areas of the side faces.

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Please help will mark!!!!

Please help will mark!!!!

Answers

Answer:

Right Triangle

Step-by-step explanation:

Answer:Acute triangle

Step-by-step explanation:

Eva deposits $2,000 in a savings account with an interest rate of 5% compounded continuously. She decides not to deposit or withdraw any money after the initial deposit. She uses the formula A = Petto represent her account balance, A, after t years, where r is the rate of interest and P is the beginning balance, or principal. How long will it take for Eva's initial deposit to double?​

Answers

It take 20 years for Eva's initial deposit to double?.

What is Simple interest?

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

Eva deposits $2,000 in a savings account with an interest rate of 5% compounded continuously.

Here, Principal amount = $2000

Amount = $4000

Interest rate = 5%

Now, We know that;

⇒ Interest = PRT

Substitute all the values, we get;

⇒ 2000 = 2000 × 0.05 × T

⇒ T = 1/0.05

⇒ T = 100/5

⇒ T = 20 years

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a random variable has possible values of 20, 21, 22, 23, and 24 that are equally likely to occur. what is the probability that the random variable is less than 23?

Answers

The probability of the random variables being less than 23 will be 0.6.

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that a random variable has possible values of 20, 21, 22, 23, and 24 that are equally likely to occur.

Total sample = { 20, 21, 22, 23, 24 } = 5

Favourable outcome = { 20,21,22} = 3

The probability will be calculated as,

Probability = 3 / 5

Probability = 0.6

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Riya looks at the temperature in the kitchen. What is the temperature in the kitchen to the nearest division

Answers

Answer:

24 degree Celsius

Step-by-step explanation:

Temperature may be defined as the intensity or the degree of heat that is present in any substance or present in the environment. It is the measure of hotness or coldness of any item or surroundings. Temperature is measured with the help of a comparative scale which shows the how hot or cold the place is or item is.

In the context, Riya uses a comparative scale like the thermometer to measure the temperature of the kitchen. The mercury level on the scale rises and stops at a point indicating the temperature of the kitchen.

Thus the temperature of the kitchen according to the scale is \($24 ^ \circ C$\).

Riya looks at the temperature in the kitchen. What is the temperature in the kitchen to the nearest division

Three friends all live on the same street that runs west to east. Ben lives 7 blocks from Ann. Carol lives 2 from Ben. If the street is represented by a number line and ​Ann's house is located at​ 0, what are the possible locations for ​'s ​house?

Answers

Answer:

Just use your number line for help but you have to figure out if the numbers are positive or negative.

Step-by-step explanation:

If Ann lives at 0 and ben lives 7 blocks from Ann then you would say ben lives a number 7 on the number line and Carol lives 2 blocks from ben then carol would live at 9.

Answer:

-9, -5,5,9

Just use a number line, it's easy.

Can someone help on this? Thank youu;)

Can someone help on this? Thank youu;)

Answers

Answer:

2^(3/7)

Step-by-step explanation:

For these types of questions, what is inside the root is the numerator, and what is on top is the denominator.

3 is in the root, so it is the numerator

7 is outside the root, so it is the denominator

Therefore, The answer is 2^(3/7)

Equivalent or not Equivalent :
5(3t - 6) = 15t - 30

Answers

The two mathematical expressions 5(3t - 6) and 15t - 30 are equivalent.

What are equivalent expressions?

Mathematical expressions are equivalent or equal when they have the same value.

Equivalent expressions work the same way despite their different looks.

We determine that two or more mathematical expressions are equivalent when simplified or yield the same value after substituting the variables.

Equivalent mathematical expressions are usually indicated using the equation symbol (=).

5(3t - 6) = 15t - 30

If t = 3

5(3t - 6) = 15

15t - 30 = 15

Thus, if two algebraic expressions are equivalent, then the two expressions have the same value.

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Find the general solution of the following differential equation. Primes denote derivatives with respect to x. 9x(x + y)y' = 9y(x - 6y) The general solution is (Type an implicit general solution in the form F(x,y) = C, where C is an arbitrary constant. Type an expression using x and y as the variables.)

Answers

The general solution to the given differential equation is\(y = (C_1)/(x(x-6y))\)where C_1 is the constant of integration.

The given differential equation is \(9x(x+y)y'=9y(x-6y)\)

Step 1: We can simplify this equation to get y' and dy/dx by dividing both sides by

9xy(x−6y) = (x−6y)dy/dx + y

=> dy/dx = y/[x(x−6y)] − 1/(x−6y)

Now, we can rewrite the differential equation as dy/dx = y/[x(x−6y)] − 1/(x−6y)

Step 2: This is a separable differential equation.

We can write it in the form

dy/dx + 1/(x−6y) = y/[x(x−6y)] Multiplying by the integrating factor μ(x) = e∫(1/(x−6y))dx gives us

\(\mu(x)dy/dx + [\mu(x)/(x-6y)] = \mu(x)y/[x(x-6y)]\)

We can simplify this as \(d/dx[\mu(x)y] = \mu(x)y/[x(x-6y)]\)

Integrating both sides, we get

ln|y| = ∫μ(x)/(x(x−6y)) dx + C where C is the constant of integration

Step 3: Now, we need to find the integrating factor μ(x). We can writeμ(x) = e∫1/(x−6y) dxSo, we substitute x−6y = t and get dx = dt + 6dy

So,

\(\mu(x) = e\int1/(x-6y) dx\)

= e∫1/t dt

= e^(ln|t|)

= |t|

= |x−6y|

Step 4: Substituting for μ(x) and simplifying the integral, we get

\(ln|y| = -(1/6)ln|x-6y| - (1/6)ln|x| + C'\)

=> \(ln|y| = ln((C_1)/(x(x-6y)))\)

=> \(y = (C_1)/(x(x-6y))\)

Where C_1 = e^C' is a new constant of integration \(y = (C_1)/(x(x-6y))\)

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3 Consider the line y= 3/4x+3. Find the equation of the line that is perpendicular to this line and passes through the point (-8, 6).

Answers

ANSWER

\(y\text{ = -}\frac{4}{6}x\text{ - }\frac{14}{3}\)

EXPLANATION

We have to find the equation of the line perpendicular to the given line:

\(y\text{ = }\frac{3}{4}x\text{ + 3}\)

and passes through the point (-8, 6)

A line perpendicular to another line has a slope that is the negative inverse of the line.

The slope of the given line is 3/4, so the slope of the line we are looking for is -4/3

Now, we use the point slope method to find the equation:

y - y1 = m(x - x1)

where m = slope

(x1, y1) = point the line passes through

So, we have:

\(\begin{gathered} y\text{ - 6 = -}\frac{4}{3}(x\text{ - (-8))} \\ y\text{ - 6 = -}\frac{4}{3}(x\text{ + 8)} \\ y\text{ - 6 = -}\frac{4}{3}x\text{ + (-}\frac{4}{3}\cdot8) \\ y\text{ - 6 = -}\frac{4}{3}x\text{ - }\frac{32}{3} \\ \Rightarrow\text{ y = -}\frac{4}{3}x\text{ - }\frac{32}{3}\text{ + 6} \\ y\text{ = -}\frac{4}{6}x\text{ - }\frac{14}{3} \end{gathered}\)

That is the equation of the line.

Can someone help me on this?? Im really struggling

Answers

\(Question \: please.\)

1) back at basketball practice, Haley's coach is impressed with the improvement in her scoring ability over the past month. She went from scoring 12 points per game last month to scoring 18 points per game this month. He exclaims, "Haley, you have made a 100% improvement in your average points per game!"
a. If Haley increased her average points per game by 100%, how many points per game would she be scoring this month?

b. If she had increased her average points per game by 25%, how many points would she be scoring this month?

d. What portion of her points per game for last month does that increase represent? By what percent did Haley improve her average points per game?

P.S I did c

Answers

Answer:

A: It would be 24 points per game.

B: It would be 15 points per game

C: 33.33%

Step-by-step explanation:

A explanation:

100% of 12 is 24

12 + 12 = 24

B explanation:

25% of 12 = 3

12 + 3 = 15

C explanation:

12/18 = 66.66%

100 - 66.66 = 33.33%

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When a biased coin is tossed, heads is three times as likely to come up as tails. Rearrange the following procedure in the correct order to find the probability that should be assigned to the outcome of heads and tails?
1. p(T) = 1/4 and p(H) = 3/4
2. since heads and tails are the only two outcomes p(H) + p(T) = 1.
3. p(H) = 3p(T)
4. 3p(T) + p(T) = 1
5. 4p(T) = 1

Answers

Answer: 1

Step-by-step explanation:

If heads is 3 more likely to come up than tails, then there are 3 heads for every tails.  

Hope it helps <3

(4) Suppose that the x-intercepts of the graph ofy = f (x) are -8and 1.
What are the x-intercepts of the graph ofy = f(x+4) ? Explain.

Answers

The x - intercepts of the graph f ( x + 4 ) are 12 and 3

The x-intercepts of the graph of y = f (x) are -8and 1. We need to calculate the x - intercepts of y = f(x + 4)

Factors of the function f ( x ) are:

f ( x ) = ( x + 8 ) ( x - 1 ) = x²  -  x + 8 x - 8 =  x² + 7 x - 8

x - intercepts of this function are - 8 and 1

f ( x + 4 ) = ( x + 4 )²+ 7 ( x + 4 ) - 8 = x² + 8 x + 16 + 7 x + 28 - 8 =

= x² + 15x + 36

x² + 15 x + 36 = x² + 12 x + 3x + 36 = x ( x + 12 ) +3 ( x + 12 ) = ( x + 12 ) ( x + 3 )

Therefore x - intercepts of the graph f ( x + 4 ) are 12 and 3

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0.7x-y=5.16 and 2-0.8x=0.4y round to the nearest hundredth? does anyone know this answer?

Answers

Step-by-step explanation:

What is the question? You have not stated the question.

What value of z* should be used to construct a 97 confidence interval of a population mean?

Answers

The value of z* should be used to construct a 97 confidence interval of a population mean is 2.17.

What is confidence interval?

A degree of uncertainty and certainty in a sample process is measured by confidence intervals. They can choose from a variety of probability limitations, the most frequent becoming a 95% or 99% confidence level.

Some characteristics of confidence interval are-

Statistical tools, such as the t-test, are used to compute confidence intervals.Confidence intervals are used by statisticians to quantify uncertainty in such a sample variable. A researcher, for example, may randomly select multiple samples drawn from the same population and compute a confidence interval for every sample to determine how well it might represent the real value of a population variable. The generated datasets are all unique; some intervals contain the genuine population parameter while others do not.

Now, according to the question;

The confidence level is given 97%.

Thus, the crucial value of z for a 97% confidence interval is 2.17, as determined by a z score table, which is as follows:

\(P(-2.17 < Z < 2.17)=0.97\)

Therefore the obtained probability for the z-score of 2.17 is 0.97.

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What is the value of y?

What is the value of y?

Answers

8√2
using pythageoran theoram you can find out that the answer you selected- 8sqrt2 is correct.

A family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

Answers

Answer:

the probability is 1/2

Step-by-step explanation:

the probability of a child being a boy is 1/2, if at least one of them is already a boy, then the probability of both being boys, which amounts to saying that the other is also a boy, is 1/2

When conducting a significance test in practice, how should you choose the alpha level?.

Answers

Use a larger alpha when the consequences of mistakenly rejecting the null hypothesis are more serious. Always use alpha=0.05 since it's the most appropriate for every situation.

The significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant. The researcher determines the significance level before conducting the experiment.

The significance level is the probability of rejecting the null hypothesis when it is true.

For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.

Use significance levels during hypothesis testing to help you determine which hypothesis the data support. Compare your p-value to your significance level. If the p-value is less than your significance level, you can reject the null hypothesis and conclude that the effect is statistically significant. In other words, the evidence in your sample is strong enough to be able to reject the null hypothesis at the population level.

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what is the solution to the system of equations ? 3r+2y=45 4r-y=5 1. r=5 y=10 2.r=15 y=10 3.r=5 y=15 4. r=15 y=5

Answers

Answer:

The solution to the system of equation is;

\(\begin{gathered} r=5 \\ y=15 \end{gathered}\)

Explanation:

Given the system of equations;

\(\begin{gathered} 3r+2y=45\text{ -----------1} \\ 4r-y=5\text{ ----------2} \end{gathered}\)

Let us solve by elimination, multiply equation 2 by 2 and add to equation 1 to eliminate y;

\(\begin{gathered} 4r(2)-y(2)=5(2) \\ 8r-2y=10\text{ -----------3} \end{gathered}\)

adding to equation 1;

\(\begin{gathered} 3r+8r+2y-2y=45+10 \\ 11r=55 \\ r=\frac{55}{11} \\ r=5 \end{gathered}\)

we can now use the value of r to solve for y;

\(\begin{gathered} 3r+2y=45 \\ 3(5)+2y=45 \\ 15+2y=45 \\ 2y=45-15 \\ 2y=30 \\ y=\frac{30}{2} \\ y=15 \end{gathered}\)

Therefore, the solution to the system of equation is;

\(\begin{gathered} r=5 \\ y=15 \end{gathered}\)

Maureen rolls a fair dice and flips a fair coin.
What is the probability of obtaining a 6 and a head?

Answers

1/6 times 1/2 = 1/12

The probability of obtaining a 6 and a head is 1/12 if Maureen rolls a fair dice and flips a coin.

What is a probability?

It is a likeliness of happening an event. It lies between 0 to 1 .

Probability= Number of events/number of outcomes

How to calculate probability?

When Maureen rolls a fair dice then probability of obtaining a six is 1/6

When Maureen flips a fair coin then probability of obtaining a head is 1/2

So the probability of obtaining a six and a head is 1/6*1/2

=1/12

Hence the probability of obtaining a six and a head is 1/12

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When testing the difference between two dependent population means, the test statistic is based on a ________.

Answers

When testing the difference between two dependent population means, the test statistic is based on a standard deviations of the differences.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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Solve.

24 + d = 30

d =

Answers

Answer:

I think d = 6 because 24 + 6 = 30

Answer:

d=6

Step-by-step explanation:

An online movie service offers an unlimited plan and a limited plan.
• Last month, 3500 new unlimited plans were purchased and 4700 new limited plans were purchased.
• This month, the number of new unlimited plans purchased increased by 55% and the number of new limited plans decreased by 25%.

Part A
To the nearest whole percentage, what was the overall percent change in the number of new plans? Enter the answer in the box. __%

Part B
Was the overall change a percent increase or a percent decrease?
A. percent decrease
B. percent increase

Answers

Answer:

8%

percent increase

Step-by-step explanation:

Last month:

3500 unlimited

4700 limited

total: 8200

This month:

unlimited 3500 × 1.55 = 5425

limited 4700 × 0.75 = 3525

total: 8950

Part A:

8950/8200 = 1.0848484

% change = 8%

Part B:

The total number went up from 8200 to 8950, so it's an increase.

B. percent increase

If triangle pts is congruent to triangle pqr find the value of x

Answers

Answer:

Its 8

Step-by-step explanation:because u add then divide and subtract

Consider a line process with 3 processing stages. The production requires each unit to go through Stage A through Stage C in sequence. The characteristics of the Stages are given below: Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100% Determine the system capacity. Which stage is the bottleneck? What is the utilization of Stage 3.

Answers

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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What is the domain of the function on the graph?
LO
4+
3+
2-
1 +
Nw
O all real numbers
O all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
all real numbers greater than or equal to -3
-5 4 3 2 1
1 2 3 4 5 X
-2
-3
4-
-5-

What is the domain of the function on the graph?LO4+3+2-1 +NwO all real numbersO all real numbers greater

Answers

Answer:

Its D

Step-by-step explanation:

rewrite the expression(16x^3y^2)-24x^4y^4 as a product of the greatest common factor multiplied by a binomial

Answers

The expression (16x^3y^2) - (24x^4y^4) can be written as the product of the greatest common factor (8x^3y^2) and the binomial (2 - 3x^1y^2).

To rewrite the expression (16x^3y^2) - 24x^4y^4 as a product of the greatest common factor multiplied by a binomial, we need to find the greatest common factor of the two terms. The greatest common factor of 16x^3y^2 and 24x^4y^4 is 8x^3y^2.

We can factor out 8x^3y^2 from both terms to get:

(16x^3y^2) - (24x^4y^4) = 8x^3y^2(2 - 3x^1y^2)

Therefore, the expression (16x^3y^2) - (24x^4y^4) can be written as the product of the greatest common factor (8x^3y^2) and the binomial (2 - 3x^1y^2).

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PLEASE ANSWER QUICK Part A: If (62)x = 1, what is the value of x? Explain your answer. (5 points) Part B: If (60)x = 1, what are the possible values of x? Explain your answer. (5 points)

PLEASE ANSWER QUICK Part A: If (62)x = 1, what is the value of x? Explain your answer. (5 points) Part

Answers

Answer:

The first one is 0, the second one is ARN (All real numbers)

Step-by-step explanation:

1. Anything raised to the "zeroth" power is always 1

2. Because 7 is being raised to the zeroth power, the number inside the parentheses becomes 1. Now x can equal anything, 1 times itself will always equal 1, no matter how many times you multiply them.

Equations can have one, zero or infinitely many solutions.

a: The value of x is 0b: x has infinitely many solutions

\((a)\ (6^2)^x = 1\)

Express 1 as \(6^0\)

\((6^2)^x = 6^0\)

Express 0 as 2 x 0

\((6^2)^x = 6^{2 \times 0}\)

Open the bracket

\(6^{2 \times x} = 6^{2 \times 0}\)

Cancel out 6 on both sides

\(2 \times x =2 \times 0\)

Divide both sides by 2

\(x =0\)

Hence, the value of x is 0

\((b)\ (6^0)^x = 1\)

Express \(6^0\) as 1

\(1^x = 1\)

Express \(1^x\) as 1

\(1 = 1\)

Both sides of the equation are the same

This means that:

x has infinitely many solutions

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You are required to determine the relationship between Gibbs-Duhem equation and the activity coefficient of a selected binary chemical mixture (chemical A and chemical B ) in chemical industrial process. The following model is represented the excess Gibbs energy for the selected binary chemical mixture (chemical A and chemical B ). RT
G E
=X 1
lnγ 1
+X 2
lnγ 2
The Gibbs-Duhem equation says that, in a mixture, the activity coefficients of the individual components are not independent of one another but are related by a differential equation. In a binary mixture the Gibbs-Duhem relation is; x 1
( ∂x 1
∂lnγ i
) T,P
=x 2
( ∂x 2
∂lnγ 2
) T,P

Answers

The Gibbs-Duhem equation relates the activity coefficients of the individual components in a mixture. It states that the activity coefficients are not independent of each other but are related by a differential equation.

In the case of a binary mixture (chemical A and chemical B), the Gibbs-Duhem relation can be written as:

x1 * (∂x1/∂lnγ1)T,P = x2 * (∂x2/∂lnγ2)T,P

Here, x1 and x2 represent the mole fractions of chemical A and chemical B, respectively. The activity coefficients for chemical A and chemical B are denoted as γ1 and γ2, respectively.

The equation shows that the change in mole fraction of one component (x1) with respect to the change in the logarithm of its activity coefficient (lnγ1) is proportional to the change in mole fraction of the other component (x2) with respect to the change in the logarithm of its activity coefficient (lnγ2).

This relationship helps us understand how changes in the activity coefficients of the components affect each other in a binary mixture. By studying this relationship, we can gain insights into the behavior of the mixture and make predictions about its properties.

For example, let's consider a mixture of ethanol (chemical A) and water (chemical B). If the activity coefficient of ethanol (γ1) decreases, the Gibbs-Duhem equation tells us that the mole fraction of ethanol (x1) will also decrease. Similarly, if the activity coefficient of water (γ2) increases, the mole fraction of water (x2) will increase.

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