in general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect _____ .

Answers

Answer 1

In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect the mean (average) of the data set.

This is because the mean is calculated by summing all the values in the data set and dividing by the total number of values. As the sample size increases, the influence of any individual value on the mean becomes smaller. An extremely large outlier may have a significant impact on the sum of the data set, but if the sample size is large enough, the impact on the mean will be relatively small.

However, adding an extremely large outlier to a data set can substantially affect other measures of central tendency and dispersion, such as the median and standard deviation. These measures are based on the order and spread of the data, rather than the sum of the data, and may be more sensitive to extreme values.

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Related Questions

how to convert 2030 military time?

Answers

2030 military time is equivalent to 8:30 PM in standard 12-hour time notation.

2030 is a military time notation for 8:30 PM in standard 12-hour time notation.

In military time, the 24-hour clock is used, where the first two digits indicate the hour and the last two digits indicate the minutes. The hour digits range from 00 to 23, and the minute digits range from 00 to 59.

To convert 2030 military time to standard 12-hour time notation, you can use the following steps:

Check if the hour digits are greater than 12. If the hour digits are 13 or higher, subtract 12 from the hour digits to get the equivalent hour in standard time notation.

Add "PM" after the hour and minute digits to indicate that it is in the evening.

Using these steps, we can convert 2030 military time to 8:30 PM in standard time notation:

Since the hour digits 20 are greater than 12, we subtract 12 from 20 to get 8.

Add "PM" after 8:30 to indicate that it is in the evening.

Therefore, 2030 is 8.30 PM

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What is the surface area of the right rectangular prism?
Enter your answer in the box.
ft²
8 ft
18 ft
7 ft

Answers

The surface area of the right rectangular prism is 652 ft²

What is the surface area of the rectangular prism?

The surface area of a right rectangular prism is expressed as;

SA = 2( wl + hl + hw )

From the diagram;

Length l = 8ftWidth w = 7ftHeight h = 18ft

Plug the values into the above formula and solve for the surface area.

SA = 2( wl + hl + hw )

SA = 2( (7×8) + (18×8) + 18×7 )

Simplify

SA = 2( 56 + 144 + 126 )

SA = 2( 326 )

SA = 652 ft²

Therefore, the surface area of the prsim is 652 ft².

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The question is whether verbal reinforcement affects response rates. Subjects in
Group 1 were verbally reinforced every time they respond to the instructor’s
questions. Subjects in Group 2 were not. After 2 weeks, the two groups were
compared by gauging the number of students who raised their hand when
questions were asked. The following data were collected.

Group 1: 13, 15, 12, 17, 14, 14,
Group 2: 10, 12, 12, 11, 13, 9

Answers

The results of the study suggest that verbal reinforcement does affect response rates.

The mean number of students raising their hands for Group 1 (14.3) is significantly higher than the mean number of students raising their hands for Group 2 (11). This indicates that verbal reinforcement does lead to higher response rates.

Response rate is a measure of the proportion of people who respond to a given stimulus. For example, in the study mentioned above, the response rate for each group was measured by the number of students who raised their hands when questions were asked. A higher response rate indicates that more people are responding to a given stimulus.

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can somebody help me with this

Answers

Answer:

-4

Step-by-step explanation:

7(-1)³ + 5(-1)² -2 = ?

-7 + 5 -2 = ?

-2 -2 = ?

? = -4

Create a dice rolls application that displays 5 rolls of two dice java exercise 14

Answers

Below is the code required to Create a dice rolls application that displays 5 rolls of two dice in Java.

Here is a Java program that displays 5 rolls of two dice:

import java.util.Random;

public class DiceRolls {

   public static void main(String[] args) {

       Random random = new Random();

       int rolls = 5;

     

        for (int i = 0; i < rolls; i++) {

           int die1 = random.nextInt(6) + 1;

           int die2 = random.nextInt(6) + 1;

           int sum = die1 + die2;

           System.out.println("Roll " + (i+1) + ": " + die1 + " + " + die2 + " = " + sum);

       }

   }

}

Explanation:

We start by importing the Random class from the java.util package, which we will use to generate random numbers for the dice rolls.We then create an instance of the Random class using the new operator.We set the number of rolls we want to display to 5 using an integer variable rolls.We then use a for loop to generate and display each roll.Inside the loop, we generate two random numbers between 1 and 6 (inclusive) using the nextInt method of the Random class, and store them in the die1 and die2 variables.We then compute the sum of the two dice rolls and store it in the sum variable.Finally, we display the roll number (i+1), the individual rolls of each die, and the sum of the two dice rolls using System.out.println() method.

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Using the special right triangle shortcuts, what is the length of the long leg of a 30-60-90 triangle with a hypotenuse of 14?

Answers

the length of the long leg (the side opposite the 60-degree angle) is x√3, which is:

(7/2)√3 ≈ 6.06

What is the hypotenuse?

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle.

In a 30-60-90 triangle, the ratio of the side lengths is x : x√3 : 2x, where x is the length of the shorter leg, and 2x is the length of the hypotenuse.

Since the hypotenuse of this triangle is 14, we can set 2x = 14 and solve for x:

2x = 14

x = 7/2

Hence, the length of the long leg (the side opposite the 60-degree angle) is x√3, which is:

(7/2)√3 ≈ 6.06

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Solve for the variable.
B.
3x
A
4x - 1
О
F
x2-x-2
D

Answers

The variable x has no true value in the similar shapes

How to solve for the variable

From the question, we have the following parameters that can be used in our computation:

The figure

Using the figure, we have the following ratio

3x : 4x - 1 = 4x - 1 : x² - x - 2

Factorize

3x : 4x - 1 = 4x - 1 : x² + x - 2x - 2

So, we have

3x : 4x - 1 = 4x - 1 : x(x + 1) - 2(x + 1)

This gives

3x : 4x - 1 = 4x - 1 : (x - 2)(x + 1)

Express as fraction

3x/(4x - 1) = (4x - 1)/(x - 2)(x + 1)

So, we have

3x(x - 2)(x + 1) = (4x - 1)(4x - 1)

Using a graphing tool, we have

x = undefined

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Help me with this question please

Answers

16 is the required coordinate of point C

How to determine the position of a point on the number line.

A line is defined as the shortest distance between 2 points

Given the following parameters from the number line

Point M = 2

Point J = 18

The coordinate of point C that is 7/8 of the distance from M to J

C = 7/8 of MJ

C = 7/8 * (18 - 2)

C = 7/8 * 16

C = 14

Hence the point C that is 7/8 of the distance from M to J is 16

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7-4 skills practice solving logarithmic equations and inequalities
Solve each equation.
1. 3x = log6 216 2. x - 4 = log3 243 3. log4 (4x - 20) = 5
4. log9
(3 - x) = log9 (5x – 15) 5. log81 (x + 20) = log81 (6x) 6. log9 (3x2) = log9 (2x + 1)
7. log4(x - 1) = log4(12) 8. log7(5 - x) = log7 (5) 9. logx (5x) = 2
Solve each inequality.
10. log5 (-3x) < 1 11. log6x > log6 (4 - x)
12. log10 (x - 3) <2 13. log2 (x - 5) > log2 (3)
14. log7 (8x + 5) > log7 (6x - 18) 15. log9 (3x - 3) < 1.5
16. log10 (2x - 2) < log10 (7 - x) 17. log9 (x - 1) > log9 (2x)
18. log16 x ≥ 0.5 19. log3 (−x - 34 + 5) > log3 (x + 2)
20. log5 (3x) < log5 (2x - 1) 21. log3 (7 - x) ≤ log3
(x + 19)

Answers

1. 3x = log6 216

3x = 3

x = 1

2. x - 4 = log3 243

x - 4 = 5

x= 9

3. log4 (4x - 20) = 5

4x - 20 = 45

4x = 65

x = 16.25

Describe logarithmic function.

A logarithmic function is a type of mathematical function that relates two quantities by the use of logarithms. In particular, a logarithmic function describes the relationship between the input (or independent variable) and the output (or dependent variable) in terms of the logarithm of the input.

The general form of a logarithmic function is:

f(x) = loga(x)

where f(x) is the output, x is the input, and a is the base of the logarithm The logarithm of a number x with respect to a base a is the power to which a must be raised to obtain x. For example, if a is 10, then log10(100) = 2, because[tex]10^2[/tex] = 100.

Logarithmic functions are useful for expressing quantities that vary over a large range of values, such as the brightness of stars or the acidity of solutions. They can also be used to solve exponential equations or to represent data that follows a certain pattern.

In particular, logarithmic functions have the property that they can "undo" exponential functions. That is, if we have an exponential function f(x) =[tex]a^x[/tex], then its inverse function is given by [tex]f^-1(x)[/tex] = loga(x). This property is often used in calculus and other areas of mathematics.

Logarithmic functions can be graphed in a variety of ways, depending on the base and other parameters of the function. The graph of a logarithmic function typically looks like a curve that gets steeper as it moves away from the origin.

In summary, a logarithmic function is a type of mathematical function that relates two quantities by the use of logarithms. They are useful for expressing quantities that vary over a large range of values and can "undo" exponential functions.

1. 3x = log6 216

3x = 3

x = 1

2. x - 4 = log3 243

x - 4 = 5

x= 9

3. log4 (4x - 20) = 5

4x - 20 = 45

4x = 65

x = 16.25

4. log9(3 - x) = log9 (5x – 15)

3 - x = 5x - 15

4x = 18

x = 4.5

5. log81 (x + 20) = log81 (6x)

x + 20 = 6x

5x = 20

x = 4

6. log9[tex](3x^2)[/tex] = log9 (2x + 1)

[tex]3x^2[/tex] = 2x + 1

[tex]3x^2[/tex] - 2x - 1 = 0

(3x + 1)(x - 1) = 0

x = -1/3 or x = 1 (but x = -1/3 doesn't work because it results in a negative argument of the logarithm)

7. log4(x - 1) = log4(12)

x - 1 = 12

x = 13

8. log7(5 - x) = log7 (5)

5 - x = 5

x = 0

9. logx (5x) = 2

5x = [tex]x^2[/tex]

[tex]x^2[/tex] - 5x = 0

x(x - 5) = 0

x = 0 or x = 5 (but x = 0 doesn't work because it results in an undefined logarithm)

10. log5 (-3x) < 1

-3x < 5

x > -5/3

11. log6x > log6 (4 - x)

x > 4 - x

2x > 4

x > 2

12.  log10 (x - 3) < 2

x - 3 < 100

x < 103

13. log2 (x - 5) > log2 (3)

x - 5 > 3

x > 8

14. log7 (8x + 5) > log7 (6x - 18)

8x + 5 > 6x - 18

2x > -23

x > -11.5

15. log9 (3x - 3) < 1.5

3x - 3 < 27

x < 10

16. log10 (2x - 2) < log10 (7 - x)

2x - 2 < 7 - x

3x < 9

x < 3

17. log9 (x - 1) > log9 (2x)

x - 1 > 2x

-x > -1

x < 1

18. log16 x ≥ 0.5

x ≥ √16

x ≥ 4

19. log3 (−x - 34 + 5) > log3 (x + 2)

-x - 29 >

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how to convert 1m to inches?

Answers

One meter is equal to 39.3701 inches

To convert 1 meter to inches, we can use the following formula:

1 meter = 39.3701 inches

The conversion factor is 39.3701

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in meter

Substitute the values in the equation

1 meter = 39.3701 × 1

Multiply the numbers

= 39.3701 inches ( rounded to four decimal places )

Therefore, one meter is 39.3701 inches

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PLEASE HELP!! 100 POINTS!!
Write equations that represent the transformed functions described below:
NOT ANSWER CHOICES
a) f(x)=√x is shifted left 4 units and vertically compressed by a factor of 1/3
b) f(x)=√x is vertically stretched by a factor of 4 and then shifted 3 units up
c) f(x)=√x is shifted left 2 and then shifted 6 units down

Answers

Answer:

a) f(x) = (1/3)√(x-4)

b) f(x) = 4√(x+3)

c) f(x) = 6 - √(x - 2)

What is the value of p in the equation 5/6 (12p-6)=-3/4 (12p+24)

Answers

Step-by-step explanation:

-Multiply inside the brackets

-Add like terms ( Or in this case move it to the others side to find p)

-Add

- Then do some substitution to check for the answers

What is the average rate of change of the function

(

)
f(x) on the interval
2



7
2≤x≤7?

Answers

The formula for the average rate of change to get is:

average rate of change = (y2 - y1) / 5

What is the average rate of change?

The average rate of change means the average rate at which one quantity is changing with respect to something else changing.

To find the average rate of change of a function f(x) over an interval [a, b], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, we are given the function f(x), but we don't have a formula for it. Instead, we are given the interval [2, 7] over which we want to find the average rate of change. So, we can use the values of the function at x = 2 and x = 7 to compute the average rate of change.

Let's assume that we have the function f(x) and evaluate it at x = 2 and x = 7 to get:

f(2) = y1

f(7) = y2

Then, we can use the formula for the average rate of change to get:

average rate of change = (f(7) - f(2)) / (7 - 2) = (y2 - y1) / 5

So, to find the average rate of change of f(x) over the interval 2 ≤ x ≤ 7, we need to know the values of f(2) and f(7). If these values are given or can be calculated, we can use the formula above to find the answer.

Hence,  the formula for the average rate of change to get is:

average rate of change = (y2 - y1) / 5.

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How many square feet in 1 ⁄ 4 acre?

Answers

There are 10,890 square feet in 1/4 acre depending on the relation between the two.

The square feet and acres are the units to represent the area covered by any land. These units are related to each other by the formula -

1 acre of an area is similar to square feet by the quantity 43,560. So, we need to perform calculations for 1/4 acre, which are done here.

1 acre = 43,560

1/4 acre = 43,560/4

Performing division on Right Hand Side of the equation

The area covered by 1/4 acre = 10,890 square feets

Hence, the area covered in square feet is 10,890.

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Answer Clue 3!!

Ignore the things above clue 3!!

Answers

Answer:

4.6 Years

Step-by-step explanation:

Exponential Function :

f(x) = a(1 - r)^x

f(x) = 24,885(1 - 0.14)^x


half of original amount : 12442.50


In 5 years the car will be worth half of its original price

Jada collects data on the number of letters people receive in the mail each week. The distribution of the population is shown on the dot plot.
Which of the following dot plots is likely to represent the means of the samples of size 10 from this population? Explain why.
dot plot 1
dot plot 2

Answers

Dot plot 2, on the other hand, is skewed and does not have a symmetrical distribution, which may not be a good representation of the sample means.

What is normal distribution ?

Normal distribution is a statistical concept that describes a symmetrical, bell-shaped curve that is characterized by its mean and standard deviation. It is a continuous probability distribution that represents the probability of a random variable taking on a certain value.

As per the Central Limit Theorem, the sample means of a sufficiently large sample size taken from any population tend to follow a normal distribution, regardless of the shape of the population distribution. Therefore, the dot plot that is likely to represent the means of the samples of size 10 from this population is dot plot 1 because it has a more symmetrical distribution, which is more similar to a normal distribution.

Hence, Dot plot 2, on the other hand, is skewed and does not have a symmetrical distribution, which may not be a good representation of the sample means.

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the median age of the u.s. population in 1980 was 30.0 years. in 1991, the median age was 33.1 years. (a) what does it mean for the median age to rise? a rising median age in a population usually indicates that the population is becoming younger. a rising median age in a population usually indicates an aging population. a rising median age in a population usually indicates that more babies are being born. a rising median age in a population usually indicates a dying population. a rising median age in a population usually indicates that people are dying at a younger age. correct: your answer is correct. (b) give reasons why the median age could rise. (select all that apply.) the median age could rise due to an increase in deaths over time. the median age could rise due to a decrease in births over time. the median age could rise due to an increase in births over time. this trend could be observed if there were an increased lifespan and thus a decreased number of deaths. this trend could be observed if there were an increased lifespan and an increased number of deaths. incorrect: your answer is incorrect.

Answers

The options A,B,C are incorrect because the rise of population increase median also increases.

what is median ?

In statistics, the median is the middle value of a dataset when the values are arranged in order. Specifically, if the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values. The median is a measure of central tendency that is less affected by extreme values (outliers) than the mean.

Given by the question:

(a) A rising median age in a population usually indicates an aging population.

(b) The median age could rise due to a decrease in births over time, and this trend could be observed if there were an increased lifespan and thus a decreased number of deaths.

(c) In what ways might a rising median age affect a society? (Select all that apply.)

A rising median age might increase the burden on the healthcare system, as older people tend to have more health issues.A rising median age might increase the need for retirement benefits and social security, as more people will be retiring and living longer.A rising median age might lead to a decrease in the workforce, as older people retire and are not replaced by younger workers.A rising median age might lead to a decrease in economic growth, as older people tend to spend less and save more.A rising median age might lead to changes in social and cultural norms, as the needs and preferences of an older population may differ from those of a younger population.

These are just a few examples, and the effects of a rising median age can be complex and varied depending on the specific circumstances of a society.

Therefore, The options A,B,C are incorrect because the rise of population increase median also increases.

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Increase 85g by 120%​

Answers

The value of 85g increased by 120% is equal to 187g.

What is Percentage ?

In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage. When determining a percentage of a number, we should first divide it by 100 before multiplying the result by 100. As a result, the proportion refers to a component per 100. The word "percent" denotes a percentage. The letter "%" stands for it.

Now in the given question ,

To increase 85g by 120%, we need to find 120% of 85g and add it to 85g.

To find 120% of 85g, we can first convert 120% to a decimal by dividing by 100:

120% = 120/100 = 1.2

Then we can multiply 1.2 by 85g:

1.2 x 85g = 102g

So, increasing 85g by 120% gives us:

85g + 102g = 187g

Therefore, 85g increased by 120% is equal to 187g.

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Solve this system of equations using any method.

y=5x + 4

y = 6x + 1

Question 6 options:

(3,19)


(5,-4)


(-3,-6)


(3,4)

Answers

The solution to the system of equation y = 5x + 4 and y = 6x + 1 is (3,19).

What is the solution to the system of equation?

Given the system of equation in the question;

y = 5x + 4

y = 6x + 1

To solve the system of equation, first plug equation one into equation two and solve for x.

y = 6x + 1

Plug in y = 5x + 4

5x + 4 = 6x + 1

Solve for x

6x - 5x = 4 - 1

x = 3

Now, plug x = 3 into equation one and solve for y.

y = 5x + 4

Plug in x = 3

y = 5( 3 ) + 4

y = 15 + 4

y = 19

Therefore, the value of x is 3 and y is 19.

Option A) (3,19) is the correct answer.

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in observational studies, the variable of interest:_____.

Answers

In an experimental study, the variable of interest is a changing quantity that would be measured. A number of these different factors, known as the original study factors, are monitored so that information on how the factors impact some other interesting as the predictor variables, or merely the response, can be obtained.

Is the variable under consideration an independent variable?

Interesting outcome variable

This is also referred to as a regression model or an interest component. It is a "input" variable that serves as a factor that what a researcher is able within a contained way to test this same impact of changing the amounts of the predictor variables on the overall result measured. An observation falls under the category of data collection case.

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what is longer 2.218 inches or 2.21 inches?

Answers

The first digit in both numbers is 2, so we can move to the next digit. In 2.218, the digit in the second decimal place is 2, while in 2.21, the digit in the second decimal place is 1. Since 2 is greater than 1, 2.218 is longer than 2.21.

Comparing the Length of Two Decimal Numbers

When comparing the length of two decimal numbers, it's important to consider the value of each digit in the number. Let's take the example of 2.218 inches and 2.21 inches.

To begin, we can compare the first digit of each number, which is 2 in both cases. Since the first digit is the same, we need to look at the next digit to determine which number is longer. In 2.218, the second digit is 2, while in 2.21, the second digit is 1. The second digit in a decimal number represents the tenths place, so we can conclude that 2.218 is longer than 2.21.

It's important to note that this method of comparing decimal numbers applies to numbers with the same number of decimal places. If we were comparing 2.218 inches to 2.2 inches, for example, we wouldn't be able to simply look at the second digit. Instead, we would need to compare the numbers digit by digit, starting from the leftmost digit.

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evaluate the integral. (assume a ≠ b. remember to use absolute values where appropriate. use c for the constant of integration.) 8 (x a)(x b) dx

Answers

∫ 8 (x+a)(x+b) dx = (8/3)x³ + 4x²(a+b) + 8x(ab) + c

The antiderivative of 8 (x+a)(x+b) with respect to x is (8/3)x³ + 4x²(a+b) + 8x(ab) + c.

To evaluate the integral, we can use the distributive property to expand the expression in the integrand:

8 (x+a)(x+b) dx = 8(x² + (a+b)x + ab) dx

We can then integrate each term separately using the power rule of integration:

∫ 8(x² + (a+b)x + ab) dx = (8/3)x³ + 4(a+b)x² + 8abx + c

We can simplify this result by factoring out the constant 8/3 from the first term and using the distributive property to factor out the common factor of 4x from the last three terms:

(8/3)x³ + 4(a+b)x² + 8abx + c = (8/3)x³ + 4x²(a+b) + 8x(ab) + c

We can check our answer by taking the derivative of the result to see if it matches the original integrand. The derivative of (8/3)x³ is 8x², the derivative of 4x²(a+b) is 8x(a+b), the derivative of 8x(ab) is 8ab, and the derivative of the constant c is 0. Adding these terms together, we get the original integrand of 8(x+a)(x+b) dx, so our answer is correct.

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Complete question:

Evaluate the integral. (assume a ≠ b. remember to use absolute values where appropriate. use c for the constant of integration.) 8 (x+a)(x+b) dx

Please help me if your good at Geometric Congruence! The questions are in each photo, please answer them all! Thanks

Answers

Rhombus question:

Opposite sides are equal so we will set x+25 and 3x-55 equal to each other.

x+25=3x-55

Subtract x to both sides:

25=2x-55

Add 55 to both sides:

2x=80

Divide 2 to both sides:

x=40

Now we will find the value of y. Remember a triangle adds up to 180 degrees, so we will add all 3 angles and set it equal to 180. The square means 90 degrees.

40+25+90+y=180

Combine like terms:

155+y=180

Subtract 155 to both sides:

y=25


Rectangle question:

Given that AE=x+16 and EC=2x-4. To solve this, you will add these two given lines together because AE+EC=AC.

x+16+2x-4

Combine like terms:

3x-12


l & m, solve for x:

Using alternate angles, we will know that 95 and x are supplementary, so they add up to 180.

95+x=180

Subtract 95 to both sides:

x=85


n & m:

Use alternate angles, think about zig zag:

1=8, 2=6, 4=5, 3+5=180


l & m solve for y:

First we will need to find the x value to solve for y. Using alternate angles, the two expressions are equal. So set the equal.

29x+2=30x-1

Subtract 29x to both sides:

2=x-1

Add 1 to both sides:

x=3

Now we will solve for y. Using alternate angles, both expressions are equal to y, we can pick any.

30x-1=y

Substitute:

30(3)-1=y

Calculate:

90-1=y

Calculate:

y=89


hope this helped!

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What conversion can be achieved if a 72 l pfr is followed in series by a 24 l cstr

Answers

The converted to product four times as much in the CSTR than it was in the PFR that is 400%.

Conversion is a term used to describe the process of transferring a reactant into a product.

In this case, the reactant is being transferred from a 72 l plug flow reactor (PFR) to a 24 l continuous stirred tank reactor (CSTR). The conversion achieved by this process can be determined by calculating the ratio of product to reactant in the CSTR.

Specifically, if the PFR has a conversion of x%, then the conversion achieved in the CSTR will be x/(1-x), where x is the conversion in the PFR.

Therefore, if the PFR has a conversion of 80%, then the CSTR will have a conversion of 80/(1-80) = 400%.

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Please answer all I will give brainlly

Answers

After getting the product, and simplifying it the correct statement should be: [tex](3^4) \times (2^3) = 648[/tex]

Describe Simplification?

In mathematics, simplification refers to the process of simplifying an expression or equation without affecting its fundamental meaning or value. Using mathematical tools and rules to simplify an equation makes it simpler to manipulate or solve.

In algebra, simplification might take the form of factoring out common factors, grouping like concepts, or distributing multiplication across addition or subtraction. For instance, merging two like terms will simplify the formula 2x + 4x to 6x. The same strategy can be used to reduce the expression 3(x + 2) - 2(x - 1) to 3x + 4 by spreading out the multiplication and combining related terms.

1. The error is in the simplification of the product of the two terms. The correct way to simplify it is to multiply the coefficients and add the exponents of x.

The correct solution is:

[tex](3x^2)(-2x^4) = (3 \times -2)x^{(2+4)} = -6x^6[/tex]

Therefore, the error is in the sign of the result, which should be negative instead of positive. The correct answer is[tex]-6x^6.[/tex]

2. The error is in the distribution of the exponent on the coefficient 4. The correct way to simplify the product is to add the exponents of a and then multiply by the coefficient 4.

The correct solution is:

[tex]4a^2 \times 3a^5 = (4 \times 3) a^{(2 + 5)} = 12a^7[/tex]

Therefore, the error is in the addition of the coefficients instead of multiplying them, and the incorrect distribution of the exponent on the coefficient 4. The correct answer is [tex]12a^7.[/tex]

3. There is no error in this simplification.

The product of[tex]x^6, x, and $ x^3 $[/tex] is equivalent to [tex]x^{(6+1+3)} = x^{10}[/tex]

However, the answer given in the question, x^9, is incorrect.

4. The given statement is incorrect.

The product of[tex](3^4) and (2^3)[/tex] can be simplified as follows:

[tex](3^4) \times (2^3) = 81 \times 8 = 648[/tex]

Therefore, the correct statement should be:

[tex](3^4) \times (2^3) = 648[/tex]

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Thor, Rosa and Belvedere went walking in an enchanted forest and found 104 magic pencils. They split them up into 4:6:3. How many pencils did Thor receive?

Answers

Answer: Thor got 32 magic pencils

Step-by-step explanation: The ratio say it is 4:6:3 which means that we have to add them together to get the total. 4+6+3=13. Now that we know we have 13 parts we need to divide by 104 to get the answer, 104/13=8, Thor got 4 parts, as we know from the problem so we multiply 8 by 4 and we get 32.

Using the special right triangle shortcuts, what is the length of the leg of a 45-45-90 triangle with a hypotenuse of 6√2?

Answers

The length of the leg of the 45-45-90 triangle is 6.

What is the hypotenuse?

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle.

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

In a 45-45-90 triangle, the length of each leg is equal to x, and the length of the hypotenuse is √2 times the length of a leg.

So if the hypotenuse is 6√2, then each leg has length:

x = (6√2)/√2 = 6

Hence, the length of the leg of the 45-45-90 triangle is 6.

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1- What is the connection between exponential function and geometric sequence.

Answers

Exponential functions and geometric sequences are closely related, as the terms in a geometric sequence can be expressed using an exponential function.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio. For example, a geometric sequence starting with 2 and with a common ratio of 3 would be: 2, 6, 18, 54, 162, ...

The general formula for a geometric sequence is:

a_n = a_1 * r^(n-1)

Where:

a_n is the nth term of the sequence.a_1 is the first term of the sequence.r is the common ratio.n is the number of terms.

Exponential functions have the general form:

f(x) = a * b^x

Where:

a is a constant.b is the base.x is the exponent.

If we take the formula for a geometric sequence and rewrite it as an exponential function, we get:

a_n = a_1 * r^(n-1) = a_1 * (1 + (r-1))^(n-1)

Using the binomial expansion formula, we can simplify this to:

a_n = a_1 * (1 + (r-1))^(n-1) = a_1 * (1 + (r-1)*(n-1))

This is an exponential function with base (1 + (r-1)) and exponent (n-1). Therefore, the terms of a geometric sequence can be expressed using an exponential function.

Conversely, if we have an exponential function of the form f(x) = a * b^x, then we can find a geometric sequence by evaluating the function for a range of values of x. For example, if we take f(x) = 2 * 3^x and evaluate it for x = 1, 2, 3, 4, we get the geometric sequence 6, 18, 54, 162.

~ Zeph

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3

Answers

What is quadratic expression ?
A quadratic expression is a polynomial expression of degree two, meaning that it contains one or more terms in which the variable is raised to the second power (or squared). The general form of a quadratic expression is:

ax^2 + bx + c

Explanation:
The following steps could be used to solve the quadratic equation 8x^2 + 16x + 3 = 0:

Rewrite the equation in standard form: 8x^2 + 16x + 3 = 0.

Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 8, b = 16, and c = 3.

Substitute the values of a, b, and c into the quadratic formula and simplify
Therefore, the three options provided are not completely accurate. Here are the corrected versions:

Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 8, b = 16, and c = 3.

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Change the following fraction to a decimal. (Carry the division for three places as indicated. Do not round your answer.)
1/64 =

Answers

1/64 fraction is equal to 0.015625 in decimal form.

To change the fraction 1/64 to a decimal, we need to perform division.

1 divided by 64 can be written as:

0.015625

----------

64 | 1.000000

   0

  10

   0

The result of the division is 0.015625. This means that 1/64 is equal to 0.015625 in decimal form.

Note that in this case, we carried the division out to six decimal places, but the question specified that we should carry it out to three decimal places. In that case, we would round the answer to 0.016.

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