Consider the following set of numbers:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
What is the probability of drawing an odd number or a
multiple of 3?

Answer:

To solve the equation 3(x+2)=17, we start by simplifying the expression on the left side by distributing the 3:

3(x+2) = 17

3x + 6 = 17

Next, we isolate the variable term by subtracting 6 from both sides:

3x + 6 - 6 = 17 - 6

3x = 11

Finally, we solve for x by dividing both sides by 3:

3x/3 = 11/3

x = 11/3

Therefore, the solution to the equation 3(x+2)=17 is x = 11/3.

To solve the equation 4x+3=2x+15, we start by simplifying the expression by combining like terms:

4x + 3 = 2x + 15

2x + 3 = 15

Next, we isolate the variable term by subtracting 3 from both sides:

2x + 3 - 3 = 15 - 3

2x = 12

Finally, we solve for x by dividing both sides by 2:

2x/2 = 12/2

x = 6

Therefore, the solution to the equation 4x+3=2x+15 is x = 6.

Step-by-step explanation:

Answer 63^(12)

Step-by-step explanation:

7x9=63

8+4=12

have a good day!

To streamline your betting odds and increase your chances of making a profit from your initial 100 scrap, you can use a combination of different betting strategies.

Here are a few possible strategies:

1) Spread your bets: Instead of betting all of your scrap on one number, you can spread your bets across multiple numbers to increase your chances of winning.

For example, you could bet 25 scrap on 1 (yellow), 25 scrap on 3 (green), 25 scrap on 5 (blue), and 25 scrap on 10 (pink). This way, you have a 48% chance of winning on 1 (yellow), a 24% chance of winning on 3 (green), a 16% chance of winning on 5 (blue), and an 8% chance of winning on 10 (pink).

2) Bet on the most likely outcomes: Another strategy is to bet on the numbers with the highest probabilities of winning. For example, you could bet 50 scrap on 1 (yellow) and 50 scrap on 3 (green), which have the highest probabilities of winning at 48% and 24%, respectively.

3) Use a combination of the above strategies: You could also combine the above strategies to increase your chances of winning. For example, you could bet 25 scrap on 1 (yellow), 25 scrap on 3 (green), 25 scrap on 5 (blue), and 25 scrap on 10 (pink), and then also bet an additional 50 scrap on 1 (yellow) and 50 scrap on 3 (green).

Overall, the key to streamlining your betting odds is to spread your bets across multiple numbers and focus on the numbers with the highest probabilities of winning. By using a combination of different betting strategies, you can increase your chances of making a profit from your initial 100 scrap.

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If David paid $1. 25 per drink and purchased 6 drinks, then the total price of drink is option (C) c =$7.50

To solve this problem, we need to first understand what we are looking for - the total price that David paid for all the drinks he purchased. We know that David purchased 6 drinks and paid $1.25 for each drink.

To find the total price, we can multiply the price per drink by the number of drinks. This gives us:

c = 1.25 x 6

Multiply and Simplifying this equation, we get:

c = $7.50

Therefore, the correct option is (C) c =  $7.50

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Answer:

Let's call the larger number "x" and the smaller number "y".

From the problem, we know that:

x + y = 38 (Equation 1)

y = x - 14 (Equation 2)

We can substitute Equation 2 into Equation 1:

x + (x - 14) = 38

2x - 14 = 38

Adding 14 to both sides:

2x = 52

Dividing both sides by 2:

x = 26

Now we can use Equation 2 to find y:

y = x - 14

y = 26 - 14

y = 12

So the two numbers are 26 and 12.

Step-by-step explanation:

Answer:

12 and 26

Step-by-step explanation:

n + b = 38 n < b b = n + 14 n + n + 14 = 38 2n = 24 n = 12 b = 12 + 14 b = 26 Your two numbers are 12 and 26

in essence, which of the two fractions is the larger one, well, let's put both with the same denominator by multiplying each other by the other's denominator.

[tex]12:15\qquad 9:10\hspace{5em}\cfrac{12}{15}\qquad \cfrac{9}{10} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{12}{15}\cdot \cfrac{10}{10}\implies \cfrac{120}{150} ~~ \bigotimes\hspace{9em}\cfrac{9}{10}\cdot \cfrac{15}{15}\implies \cfrac{135}{150} ~~ \textit{\LARGE \checkmark}[/tex]

Answer:9/10

Step-by-step explanation:

90% average vs 80% average

The temperature in degrees Fahrenheit is approximately 77.4°F.

There are two widely used temperature scales in the world: Celsius and Fahrenheit. The freezing and boiling temperatures of water serve as the foundation for the Celsius scale, commonly referred to as the centigrade scale. According to this scale, the freezing point of water is 0°C, while the boiling point is 100°C.

On the other hand, a German physicist by the name of Daniel Gabriel Fahrenheit created the Fahrenheit scale. While it makes use of different reference points, this scale is similarly based on the freezing and boiling points of water.

The formula of the conversion is given by equation:

25 = 559/9 * (F - 32).

We can solve for F as follows:

25 = 559/9 * (F - 32)

25 * 9/559 = F - 32

F = 25 * 9/559 + 32

F ≈ 77.4

Therefore, the temperature in degrees Fahrenheit is approximately 77.4°F.

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Answer:

1.      2.5

2.    2.5x=y

3.     15

The square based pyramid has a surface area of is 224 mm²

Given that

A square based pyramid

The shapes in the net of a square based pyramid are

The shape's net is attached

To determine the surface area, we use

Area = l² + 2hl

Where

l = length of the square base = 8 mm

h = slant height = 10 mm

By substitution, we have

Area = 8² + 2 * 10 * 8

Evaluate

Area = 224

Hence, the surface area is 224 mm²

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(a)  may not be truly random and representative

(b)  (i)  CV = 54.31%

     (ii)  IQR = 5.9

(c)  right skewed

(d)  -2.54

(a) The measurement of TV rating belongs to the measurement of media reach, which is the proportion of people that have the potential to be exposed to a given message. One limitation of the TV rating survey in Hong Kong based on its sampling method is that the sample may not be truly random and representative of the population, leading to sampling bias and inaccurate results.

(b) (i) The mean of the data set is 6.50 and the standard deviation is 3.54. The coefficient of variation (CV) of the data set is calculated by dividing the standard deviation by the mean and multiplying by 100. Thus, the CV = 54.31%.

(ii) The five-number summary of the data set is: Minimum = 0, Q1 = 3.4, Median = 6.8, Q3 = 9.3, Maximum = 12. The interquartile range (IQR) is calculated by subtracting Q1 from Q3. Thus, IQR = 9.3 - 3.4 = 5.9.

(c) The skewness of the distribution of this data set is right skewed. This is because the mean (6.50) is less than the median (6.8) and the coefficient of skewness is positive (0.36).

Based on the figures, we can conclude that the TV shows in Hong Kong generally have higher ratings than the ones in Korea in 2022. The coefficient of skewness of the data set in Korea is -2.54, which indicates that the data set is significantly skewed to the left and that the majority of the TV shows in Korea are rated lower than average.

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Wei-Ling's fifteenth-generation ancestor is estimated to have around 1,220,703 descendants.

Assuming that each descendant has an average of 2.5 children, we can use the formula:

where n is the number of generations.

In this case, n = 15 (fifteenth-generation), so we can plug in the values and get:

number of descendants = [tex](2.5)^{15}[/tex]= 1,220,703.125

Therefore, Wei-Ling's fifteenth-generation ancestor is estimated to have around 1,220,703 descendants. However, it is important to note that this is just an estimation and may not be entirely accurate due to various factors such as reproductive rates and other variables.

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The correct option is ([tex]H) i.e. a² > b².[/tex]

What is an inequality?

In mathematics, an inequality is a statement that one quantity is less than or greater than another quantity. Inequalities are used to compare values and express relationships between them.

For all integers a < 0 and b < 0, the following inequality must be true:

[tex]H. a² > b²[/tex]

This can be proved as follows:

If a and b are both negative, then a² and b² are both positive. Since a < 0 and b < 0, we have a < b or b < a, which implies that[tex]a² > b² or b² > a².[/tex]

If a and b are both negative and equal (i.e., a = b < 0), then a² = b², which implies that a² > b² and b² > a² are both false.

None of the other inequalities (F, G, J, K) must be true for all such a and b. For example:

F. a/b > 1 is not necessarily true, since a and b could both be negative and have the same absolute value (e.g., a = b = -1), in which case a/b = 1.

G. ab > 2 is not necessarily true, since a and b could both be negative and have absolute values less than 2 (e.g., a = b = -1), in which case ab = 1 < 2.

J. [tex]a²b³ > 0 is[/tex] not necessarily true, since a and b could both be negative and have different absolute values (e.g., a = -2 and b = -1), in which case[tex]a²b³ = -8 < 0.[/tex]

K. [tex]a^{4} b² > 0[/tex] is not necessarily true, since a and b could both be negative and have the same absolute value (e.g., a = b = -1), in which case [tex]a^{4} b² = 1 > 0[/tex]. However, if we add the condition that a and b have different absolute values, then K would be true, since [tex]a^{4} b²= (|a|)² |b|² > 0.[/tex]

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The mean of the sampling distribution of p is 0.40 and the standard deviation of the sampling distribution of p is 0.0409.

Standard deviation is a measure of how spread out the values in a data set are from the mean. It is calculated by taking the square root of the variance of the data set. It is a commonly used measure to assess the variability in a data set.

The mean of the sampling distribution of p is 0.40, which is the same as the proportion of supporters in the population of Okeechobee County. This is due to the fact that the sample proportion estimates the population proportion. The standard deviation of the sampling distribution of p is equal to the square root of the product of p (0.40) and q (1-p, or 0.60) divided by the sample size (135). In this case, the standard deviation of the sampling distribution of p is 0.0409.

The mean and standard deviation of the sampling distribution of p can be used to understand what values of p are likely when samples of size n = 135 are drawn from the population of Okeechobee County. If a sample is drawn from the population, the sample proportion of supporters is likely to be close to 0.40, which is the mean of the sampling distribution of p. Furthermore, most of the sample proportions of supporters are likely to be within two standard deviations (or 0.0818) of the mean. This means that the sample proportion of supporters is likely to be between 0.3182 and 0.4818 when samples of size n = 135 are drawn from the population.

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Answer:

never true

Step-by-step explanation:

If angles A and B are complementary, their measures add to 90º.

This means that if:

m∠B = 55º,

then:

m∠A = (90 - 55)º = 45º

Using this information, we can make the assertion that because:

55º ≠ 45º,

m∠A ≠ m∠B,

and thus:

sin(A) ≠ sin(B)

because 55º and 45º are NOT coterminal angles.

Therefore, the statement

sin(A) = sin(B)

is never true.

Answer:

y = sine (x + 90 degrees)

Step-by-step explanation:

y = cosine(x) is a curve that crosses the y-axis at y = 1 and completes one cycle at 360 degrees.

sine(x) have the same curve than cosine(x), but translated 90° to the right respect cosine(x)

f(x + c) translates f(x) horizontally c units to the left.

Then, sine(x + 90) is equivalent to cosine(x)

A snail moves at a speed of 1. 2 feet per minute. the snail will move 12 yards in half an hour

There are 60 minutes in an hour, so half an hour is 30 minutes.

The snail moves at a speed of 1.2 feet per minute. Therefore, in 30 minutes, it will travel:

1.2 feet/minute * 30 minutes = 36 feet.

To convert feet to yards, we need to divide by 3 since there are 3 feet in a yard:

36 feet / 3 = 12 yards.

Therefore, .

the snail's speed may seem slow to us, it's important to remember that different animals have different speeds that are adapted to their particular ecological niche.

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Answer:

If you want to derive an equation from the question, you answer is:

3*x+4<-62

If you want the solved equation for x, your answer is:

x<-22

(Depending on what your question is)

Step-by-step explanation:

For the first answer, you can represent the unknown number as x. Three times is equivalent to 3 multiply, so it will look like 3*x, or just 3x. Increased by four is just adding four, so your equation will now look like 3x+4. Less than -62 is just 3x+4<-62. To solve future problems, just carefully look at the words. Does it mention divided by? Maybe decreased? Carefully look and analyze the question and plug in the operators, variables, and numbers.

For the second solution, since we've already translated the question to an equation from above, we can solve the equation we've derived, which is 3x+4<-62. Subtract four on both sides. The equation will look like this: 3x+4-4<-62-4. Simplifying, we get 3x<-66. Next, we divide both sides of the equation by 3, and we will get x<-22.

Good luck on your studies!

(I may be young but I know stuff so you can trust me :) )

According to given conditions, the biggest number is 46.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

Let the two numbers in the first ratio be 3x and 5x, where x is some constant of proportionality.

According to the problem, if we subtract 9 from each number, the new ratio is 12:23. So, we have:

(3x - 9) : (5x - 9) = 12 : 23

We can cross-multiply to get:

23(3x - 9) = 12(5x - 9)

Simplifying this equation, we get:

69x - 207 = 60x - 108

9x = 99

x = 11

So, the two numbers in the first ratio are 3x = 33 and 5x = 55.

To find the biggest number, we need to determine which of these numbers is larger after subtracting 9.

33 - 9 = 24

55 - 9 = 46

Therefore, according to given conditions, the biggest number is 46.

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The equal monthly payments for a car costs $22,000 with a down payment of $4,000 based on each scenario are:

Let's discuss each scenario we have.

5. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.

The amount of the down payment is $4,000.

The total cost of the car is $22,000.

Hence the balance is:

Balance = Total cost of the car − Down payment

Balance = $22,000 − $4,000 = $18,000

Now we can calculate the amount of each payment.

The payment is to be made in 48 equal monthly installments.

The interest rate is 12% per year.

We need to convert this into the monthly interest rate by dividing by 12.

Hence:

Monthly interest rate = 12% / 12 = 1% = 0.01

Let x be the amount of each monthly payment. Then the equation that represents the above conditions is given by:

18000=x(1−(1+0.01)−48)/0.01

Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:

18000=x(1−(1+0.01)−48)/0.01x

=18000/28.95x

≈621.92

Hence the amount of each equal monthly payment is approximately $621.92.

6. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.

The amount of the down payment is $4,000.

The total cost of the car is $22,000.

Hence the balance is:

Balance = Total cost of the car − Down payment

Balance = $22,000 − $4,000 = $18,000

Now we can calculate the amount of each payment.

The payment is to be made in 60 equal monthly installments.

The interest rate is 12% per year.

We need to convert this into the monthly interest rate by dividing by 12.

Hence:

Monthly interest rate = 12% / 12 = 1% = 0.01

Let x be the amount of each monthly payment.

Then the equation that represents the above conditions is given by: 18000=x(1−(1+0.01)−60)/0.01

Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:

18000=x(1−(1+0.01)−60)/0.01x

=18000/35.643x

≈505.01

Hence the amount of each payment is approximately $505.01.

7. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.

The amount of the down payment is $4,000.

The total cost of the car is $22,000.

Hence the balance is:

Balance = Total cost of the car − Down payment

Balance = $22,000 − $4,000 = $18,000

Now we can calculate the amount of each payment.

The payment is to be made in 72 equal monthly installments.

The interest rate is 12% per year.

We need to convert this into the monthly interest rate by dividing by 12.

Hence:

Monthly interest rate = 12% / 12 = 1% = 0.01

Let x be the amount of each monthly payment.

Then the equation that represents the above conditions is given by:

18000=x(1−(1+0.01)−72)/0.01

Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:

18000=x(1−(1+0.01)−72)/0.01x

=18000/46.869x

≈383.63

Hence the amount of each payment is approximately $383.63.

8. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.

The amount of the down payment is $4,000.

The total cost of the car is $22,000.

Hence the balance is:

Balance = Total cost of the car − Down payment

Balance = $22,000 − $4,000 = $18,000

Now we can calculate the amount of each payment.

The payment is to be made in 48 equal monthly installments.

The interest rate is 18% per year.

We need to convert this into the monthly interest rate by dividing by 12.

Hence:

Monthly interest rate = 18% / 12 = 1.5% = 0.015

Let x be the amount of each monthly payment.

Then the equation that represents the above conditions is given by:

18000=x(1−(1+0.015)−48)/0.015

Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:

18000=x(1−(1+0.015)−48)/0.015x

=18000/25.525x

≈704.26

Hence the amount of each payment is approximately $704.26.

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Answer:

1. Make a table to organize the data:

(The table is in the image that is provided, if you cannot see it; I've written it down below)

Time (t): 10, 15

Number of bottles (b): 4, 6

The table shows the time it takes the machine to fill a certain number of bottles of juice. To determine if the relationship is proportional, we can look at the ratios of time to number of bottles for the different data points.

If the ratios are the same for all data points, then the relationship is proportional. In this case, we have:

Ratio for the first data point: 10/4 = 2.5

Ratio for the second data point: 15/6 = 2.5

Since the ratios are the same, we can conclude that the relationship is proportional.

The terms used in this context are: proportional relationship, table, ratio, and equivalent ratios.

So the answer is yes, the relationship between the time it takes the machine to fill a certain number of bottles of juice and the number of bottles filled is a proportional relationship.

Hopefully this helped, If not I'm sorry! If you need more help, ask me! :]

Answer:

u = 4 , v = 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the tangent and sine ratios in the right triangle and the exact values

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{u}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

u = 2 × 2 = 4

and

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2}{v}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

v = 2[tex]\sqrt{3}[/tex]

Answer:

34$

Step-by-step explanation:

Answer: monkey jungle conclusion of 10-4=21

Step-by-step explanation:

The United States Declaration of Independence, officially The unanimous Declaration of the thirteen united States of America, is the pronouncement and founding document adopted by the Second Continental Congress meeting at Pennsylvania State House, which was later renamed Independence Hall, in Philadelphia, Pennsylvania, on July 4, 1776. Enacted during the American Revolution, the Declaration explains why the Thirteen Colonies at war with the Kingdom of Great Britain regarded themselves as thirteen independent sovereign states and no longer subject to British colonial rule. With the Declaration, the 13 states took a collective first step in forming the United States and, de facto, formalized the American Revolutionary War, which had been ongoing since April 1775.

The Declaration of Independence was signed by 56 of America's Founding Fathers who Second Continental Congress delegates from New Hampshire, Massachusetts Bay, Rhode Island and Providence Plantations, Connecticut, New York, New Jersey, Pennsylvania, Maryland, Delaware, Virginia, North Carolina, South Carolina, and Georgia. The Declaration became one of the most circulated and widely reprinted documents in early American history.

The Committee of Five drafted the Declaration to be ready when Congress voted on independence. John Adams, a leading proponent of independence, persuaded the Committee of Five to charge Thomas Jefferson with authoring the document's original draft, which the Second Continental Congress then edited. The Declaration was a formal explanation of why the Continental Congress had voted to declare its independence from Great Britain, a year after the American Revolutionary War broke out. The Lee Resolution for independence was passed unanimously by the Congress on July 2.

After ratifying the text on July 4, Congress issued the Declaration of Independence in several forms. It was initially published as the printed Dunlap broadside that was widely distributed and read to the public. Jefferson's original draft is currently preserved at the Library of Congress in Washington, D.C., complete with changes made by Adams and Benjamin Franklin, and Jefferson's notes of changes made by Congress. The best-known version of the Declaration is the signed copy now displayed at the National Archives in Washington, D.C., which is popularly regarded as the official document. This engrossed copy was ordered by Congress on July 19 and signed primarily on August 2, 1776.[2][3]

The sources and interpretation of the Declaration have been the subject of much scholarly inquiry. The Declaration justified the independence of the United States by listing 27 colonial grievances against King George III and by asserting certain natural a

Answer:

The solution is (2,10). None of the above answers are correct.

Step-by-step explanation:

[tex]6y = 12x + 36\\15y = 45x + 60\\\\[/tex]

Now, reduce the equations.

[tex]y = 2x + 6\\y = 3x + 4[/tex]

Solve for x by subtracting the equations

[tex]y = 2x + 6\\- (y = 3x+4)\\-x + 2 = 0\\x=2[/tex]

Now plug in x into either of the original equations.

[tex]6y = 12(2)+36\\6y=24+36\\6y=60\\y=10[/tex]

Solution: (2,10)

Answer:

x = -22/3

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ (3x/2) + 12 = 1

Then the value of x will be,

→ (3x/2) + 12 = 1

→ (3x/2) + (24/2) = 1

→ (3x + 24)/2 = 1

→ 3x + 24 = 1 × 2

→ 3x + 24 = 2

→ 3x = 2 - 24

→ 3x = -22

→ [ x = -22/3 ]

Hence, value of x is -22/3.

Answer:

[tex] \sqrt{192 {s}^{2} } = s \sqrt{192} = s \sqrt{64 \times 3} = s \sqrt{64} \sqrt{3} = 8s \sqrt{3} [/tex]

Sarah buys 834/0.7 = 1191.4 pens. Since she cannot buy a fraction of a pen, we round down to get: Sarah buys 1191 pens.

Let's start by setting up the equations for the given information:

Sarah buys x pens and 2 rulers, so the cost of her purchase is:

0.7(12) + 0.65(2) + 0.7x = 0.7(12 + x) + 0.65(2)

Note that we multiply the cost per item (0.7 cents for pens, 0.65 cents for rulers) by the number of items purchased.

Tanya buys 3 more pens than Sarah and no rulers, so the cost of her purchase is:

0.7(x + 3)

The total cost of both purchases is $11.80, or 1180 cents, so we can set up the equation:

0.7(12) + 0.65(2) + 0.7x + 0.7(x + 3) = 1180

Simplifying the equation, we get:

8.4 + 1.3 + 1.4x = 1180 - 2.1

9.7 + 1.4x = 1177.9

1.4x = 1168.2

x = 834

Therefore, Sarah buys 834/0.7 = 1191.4 pens. Since she cannot buy a fraction of a pen, we round down to get: Sarah buys 1191 pens.

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The complete question is :

12 Pens cost 70 cents each and ruler cost 65 cents each. Sarah buys x pens and 2 rulers. Tanya buys 3 more pens than Saruth and no rulers They spend $11.80 in total. Form an equation in x and solve it to find the number of pens sarah buys.

Using logarithmic identities and quadratic equation, the value of lg a * lg c is 4/3

Using logarithmic identities, we can rewrite the given equations as:

logₐa + log_b c = 4

log_b b + logₐ c = 3

Simplify the first equation using the fact that logₐa = 1/log_aₐ = 1, and simplify the second equation using the fact that log_b b = 1:

1 + log_b c = 4

1 + logₐ c = 3

Solve for log_b c and logₐ c:

log_b c = 3

logₐ c = 2

Now we can use the fact that logₐ c = logₐ (a · c)/a = logₐ a + logₐ c/a to write:

logₐ a + logₐ c/a = 2

Substitute logₐ c = 2 into this equation to get:

logₐ a + 2/a = 2

Multiply both sides by a to get:

logₐ a · a + 2 = 2a

Rearrange this equation as a quadratic equation:

logₐ a · a - 2a + 2 = 0

This quadratic has a maximum value when the coefficient of logₐ a is zero, i.e., when:

a = 2^(2/3)

Substituting this value of a into the equation logₐ c = 2, we get:

log₂ c = log₂ a^2 = 2/3 · log₂ 2^2 = 4/3

Therefore, logₐ c = log₂ c/log₂ a = (4/3) / (2/3) = 2

Finally, we can find the maximum value of logₐ a · logₐ c by multiplying logₐ a and logₐ c:

logₐ a · logₐ c = log₂ a/log₂ a · log₂ c/log₂ a = log₂ c = 4/3

Therefore, the maximum value of logₐ a · logₐ c is 4/3.

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Answer:

(i) xy² +xy +y +1 can be factorized by grouping:

xy² + xy + y + 1

= xy(x + y) + 1(x + y)

= (xy + 1)(x + y)

Therefore, xy² +xy +y +1 = (xy + 1)(x + y).

(ii) x² -7x +12 can be factorized by finding two numbers that multiply to 12 and add up to -7. These numbers are -4 and -3, so we can write:

x² - 7x + 12 = (x - 4)(x - 3)

Therefore, x² -7x +12 = (x - 4)(x - 3).

(iii) x² - 144 is a difference of squares, and can be factorized as:

x² - 144 = (x + 12)(x - 12)

Therefore, x² - 144 = (x + 12)(x - 12).

Answer:

x²-7x+12

X²+(4+3)x+12

x²-4x+3x+12

x (x+4) +3 (x+4)

(x+3) (x+4)