how does the graph of f(x)= -3^2x-4 differ from the graph of f(x)=-3^2x-4
Answers
the main difference between the two functions is that the first one has an exponential term with a variable exponent, while the second one has a linear term with a constant coefficient.
what is variable exponent ?
In mathematics, a variable exponent refers to an exponent in an expression that depends on a variable. For example, in the expression , y is the variable exponent because its value can vary depending on the value of x.
In the given question,
The graphs of f(x)= -3²ˣ-4 and f(x)= -3²ˣ-4 are not the same. The difference is in the placement of the exponent.
In the first function, -3 is raised to the power of 2x, and then the negative sign is applied to the result. This means that the exponent 2x is inside the parentheses of the exponentiation, and the negative sign is applied to the result of that exponentiation. So, the function can be rewritten as f(x) = -(3²ˣ)-4.
In the second function, -3 is raised to the power of 2, and then that result is multiplied by x and the negative sign is applied to the entire expression. This means that the exponent 2 is outside the parentheses, and only affects the base of the exponentiation. So, the function can be rewritten as f(x) = (-3²)x - 4, which simplifies to f(x) = -9x - 4.
Thus, the main difference between the two functions is that the first one has an exponential term with a variable exponent, while the second one has a linear term with a constant coefficient. As result, the graphs of these functions will be different.
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Related Questions
4. In your own words describe the difference between the natural breaks, quantile, and equal interval classification schemes that can be used to make a thematic map. Refer to lecture and homework 8.
Answers
The natural breaks, quantile, and equal interval classification schemes are methods used to categorize data for the purpose of creating thematic maps. Each scheme has its own approach and considerations: Natural Breaks, Quantile, Equal Interval.
Natural Breaks (Jenks): This classification scheme aims to identify natural groupings or breakpoints in the data. It seeks to minimize the variance within each group while maximizing the variance between groups. Natural breaks are determined by analyzing the distribution of the data and identifying points where significant gaps or changes occur. This method is useful for data that exhibits distinct clusters or patterns.
Quantile (Equal Count): The quantile classification scheme divides the data into equal-sized classes based on the number of data values. It ensures that an equal number of observations fall into each class. This approach is beneficial when the goal is to have an equal representation of data points in each category. Quantiles are useful for data that is evenly distributed and when maintaining an equal sample size in each class is important.
Equal Interval: In the equal interval classification scheme, the range of the data is divided into equal intervals, and data values are assigned to the corresponding interval. This method is straightforward and creates classes of equal width. It is useful when the range of values is important to represent accurately. However, it may not account for data distribution or variations in density.
In summary, the natural breaks scheme focuses on identifying natural groupings, the quantile scheme ensures an equal representation of data in each class, and the equal interval scheme creates classes of equal width based on the range of values. The choice of classification scheme depends on the nature of the data and the desired representation in the thematic map.
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Determine whether the function f(x) = 2x2 - x + 2 is continuous at x = 2 A. Yes, because the function is defined at x = 2 B. None of these are correct C. Yes, because the function is defined at x = 2 and approaches y = 8 on the left and right sides of x = 2 D. Yes, because the function approaches the same y-value 8 on the left and right sides of x = 2
Answers
The function f(x) = 2x2 - x + 2 is continuous at x = 2, the correct option is C. Yes, because the function is defined at x = 2 and approaches y = 8 on the left and right sides of x = 2.
A continuous function is a type of function in mathematics that has no abrupt changes or breaks in its graph. It is a function where the values change smoothly as the input values vary. In other words, a function is continuous if its graph can be drawn without lifting the pen from the paper.
Given the function f(x) = 2x² - x + 2.
Determine whether the function is continuous at x = 2.
Explanation: For a function to be continuous at x = a, it must satisfy the following conditions:
1. The function must be defined at x = a.
2. The limit of the function at x = a must exist.
3. The limit of the function at x = a must be equal to the value of the function at x = a.
Let us verify these conditions for the given function
f(x) = 2x² - x + 2 at x = 2.
1. The function is defined at x = 2.
2. We need to calculate the left-hand limit and the right-hand limit of the function as x approaches 2.
Let us first calculate the left-hand limit:
lim f(x) as x → 2- = lim (2x² - x + 2)
as x → 2- = 2(2)² - 2 + 2
= 6
Now, let us calculate the right-hand limit:
lim f(x) as x → 2+ = lim (2x² - x + 2)
as x → 2+ = 2(2)² - 2 + 2
= 6
Since both the left-hand limit and the right-hand limit of the function exist and are equal to 6, the limit of the function at x = 2 exists and is equal to 6.
3. We need to verify whether the limit of the function at x = 2 is equal to the value of the function at x = 2.
Let us calculate the value of the function at x = 2:
f(2) = 2(2)² - 2 + 2
= 8
Since the limit of the function at x = 2 is equal to the value of the function at x = 2,
we can say that the given function f(x) = 2x² - x + 2 is continuous at x = 2.
Thus, the correct option is C.
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will give brainliest to first correct answer. find missing length indicated
Answers
Helpppppppppppppppppppp
Answers
Answer:
SAS proves that these triangles are congruent.
CC has the following beginning balances in its stockholders' equity accounts on January 1, 2012: Common Stock, $100,000; Additional Paid-in Capital, $4,100,000; and Retained Earnings, $3,000,000. Net income for the year ended December 31, 2012, is $800,000. Court Casuals has the following transactions affecting stockholders' equity in 2012:
May 18 Issues 25,000 additional shares of $1 par value common stock for $40 per share.
May 31 Repurchases 5,000 shares of treasury stock for $45 per share.
July 1 Declares a cash dividend of $1 per share to all stockholders of record on July 15. Hint: Dividends are not paid on treasury stock.
July 31 Pays the cash dividend declared on July 1.
August 10 Reissues 2,500 shares of treasury stock purchased on May 31 for $48 per share.
Taking into consideration all the entries described above, prepare the statement of stockholders' equity for the year ended December 31, 2012.
Answers
Total stockholders’ equity 7,800,000
Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000
Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000
Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000
To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.
The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.
Calculations:Opening balance of common stock = $100,000
Opening balance of additional paid-in capital = $4,100,000
Opening balance of retained earnings = $3,000,000
Net Income for the year ended December 31, 2012 = $800,000
Retained earnings (Opening Balance) = $3,000,000
Add: Net Income for the year ended December 31, 2012 = $800,000
Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000
Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000
Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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I need this answer
ASAP!
Remainder of 52,259 divided by 215
Answers
Answer:
14
Step-by-step explanation:
52,259 divided by 215 is 243.065116279
so we know that the nearest whole number is 243.
243x215 is 52,245
subtract 52,245 from 52,259 which gives you the remainder of 14
Write an equation for a parabola with x-intercept (-3,0) and (2,0) which pae through the point (1,-20)
Answers
An equation for a parabola with x-intercept (-3,0) and (2,0) which pass through the point (1,-20) is "\(5x^2+5x-30\)".
parabola is a major conic section that has wide applications in science and technology. know according to the condition by following intercepts we begin with an equation
\(y=a(x+3)(x-2)\)
where a is any number that restricts the parabola to pass through (1,-20)
know we have to choose a for what the above equation got its require achievements. substitute (1,-20) in \(y=a(x+3)(x-2)\) we get
\(-20=a(1+3)(1-2)\\\\-20=a(4)(-1)\\\\a=5\)
substituting a back in the first equation we get the equation of the parabola. so, the parabola has an equation y= f(x)=\(5x^2+5x-30\).
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Help me please I need this for my test tomorrow pleaseeeee!!!!!!
Answers
Answer:
st
Just substitute in the given values
Step-by-step explanation:
Hey, there!!
You can solve it simply,
1.
Given,
x= 1 , y=2 , z= 3
To solve:
\( = \frac{1}{ {x}^{2} } - \frac{x}{y + z} \)
\( = \frac{1}{ {1}^{2} } - \frac{1}{2 + 3} \)
\( = 1 - \frac{1}{5} \)
Taking LCM,
\( = \frac{5 - 1}{5} \)
Therefore, the final answer is 4/5.
2.
Given,
x= 1 , y= -2, z= -1.
To solve:
\( = \frac{1}{ {x}^{2} } - \frac{x}{y + z} \)
\( = \frac{1}{ {1}^{2} } - \frac{1}{ - 2 - 1} \)
Taking LCM,
\( = \frac{ - 3 - 1}{ - 3} \)
\( = \frac{ - 4}{ - 3} \)
Cancelling the minus sign,
\( \frac{4}{ 3} \)
is the final answer.
3.
Given,
x= -3, y= -1, z= 4
To solve:
\( = \frac{1}{ {x}^{2} } - \frac{x}{y + z} \)
\( = \frac{1}{ {( - 3)}^{2} } - \frac{ - 3}{ - 1 + 4} \)
\( = \frac{1}{9} - ( - 1)\)
\( = \frac{1 + 9}{9} \)
Therefore, the answer is 10/9.
4.
Given,
x= 1/2, y=1, z=1.
To solve:
\( = \frac{1}{ {x}^{2} } - \frac{x}{y + z} \)
\( = \frac{1}{ ( { \frac{1}{2}) }^{2} } - \frac{ \frac{1}{2} }{1 + 1} \)
Simplifying them ,
\(1 \times \frac{4}{1} - \frac{1}{2} \times 2\)
\( = 4 - 1\)
Therefore, the answer is 3.
Hope it helps...
If you are paid a salary of $48,240 annually, how much would you expect to make per
month?
0.13
Answers
Answer:
B
Step-by-step explanation:
Answer:
$4.20 Per month = $4.2/1month
Step-by-step explanation:
1 year = 12 months
Proportions:
12 months ⇒ $48.24
1 month ⇒ $P
P = 48.24*1/12
P = $4.2
4 2/3 divided by 1/2 = what plsssss helppp
Answers
Answer:
8.66
Step-by-step explanation:
Answer:
28/3
Step-by-step explanation:
Dividing a fraction is the same as multiplying it by the reciprocal.
First, convert 4 and 2/3 to an improper fraction.
You get 14/3. Multiply that by the reciprocal of 1/2 (2/1) to get your answer.
14/3 * 2/1 = 28/3
Factorise the following
1.1. 6a-21
1.2.
\(6 {x}^{2} + 9x\)
Answers
Answer:
1.1. 3(2a-7)
1.2. 3x(2x+3)
Step-by-step explanation:
Put the common factor on the outside of the parentheses.
1.1. 6a-21
The lowest common factor for 6a and -21 is 3.
3(2a-7)
1.2. \(6x^{2} +9x\)
The lowest common factor for \(6x^{2}\) and 9x is 3x.
3x(2x+3)
12. 3x(2x+3)
Hope it helps
- the mean is 41 inches - the median is 39 inches - the standard deviation is about 9.6 inches - the iqr is 5.5 inches how does each statistic change if the length of the jumps are measured in feet instead of inches?
Answers
Thus, there would be no-static change if the length of the jumps is measured in feet instead of inches.
Now, According to the question:
What is a statistic?
A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer.
Given the data is:
The mean is 41 inches
The median is 39 inches
The standard deviation is about 9.6 inches
The IQR is 5.5 inches
For the conversion of the length from inches to feet would not affect the static data but the values of observation will change with respect to the standard of conversion which is for 1 foot = 12 inches or 1 inch = 1 / 12 feet.
Thus, there would be no-static change if the length of the jumps is measured in feet instead of inches.
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This is a 2 part question. Using the following information South Rim Location: 36.0421∘−111.8261∘ Horizontal distance between: 4500 m Colorado River Location: 36.0945∘−111.8489∘ Horizontal distance between: 7000 m North Rim Location: 36.1438∘−111.9138∘ Part 1. Calculate the rate of incision (using the time of 3.6 million years that it took the river to reach its current position)) from both the South Rim to the Colorado River and the North Rim to the Colorado River. Part 2. Calculate the rate of widening from the river to the South Rim (using the time of 4.8 million years when the Colorado River started to flow in this area) and also the rate of widening from the river to the North Rim. South Rim incision about 400 m/Ma; North Rim incision about 460 m/Ma; South Rim widening about 830 m/Ma; North Rim widening about 1460 m/Ma South Rim incision about 800 m/Ma; North Rim incision about 400 m/Ma; South Rim widening about 800 m/Ma; North Rim widening about 1500 m/Ma South Rim incision about 400 m/Ma; North Rim incision about 800 m/Ma; South Rim widening about 800 m/Ma; North Rim widening about 1150 m/Ma None of the answers listed are even close. Thus, this is the best answer.
Answers
Part 1: South Rim incision: 400 m/Ma, North Rim incision: 460 m/Ma.
Part 2: South Rim widening: 800 m/Ma, North Rim widening: 1500 m/Ma.
Part 1: The rate of incision is the change in elevation over time. From the given information, the South Rim incises at a rate of 400 m/Ma (meters per million years), while the North Rim incises at a rate of 460 m/Ma.
Part 2: The rate of widening is the change in horizontal distance over time. Using the provided data, the rate of widening from the river to the South Rim is approximately 800 m/Ma, and from the river to the North Rim, it is about 1500 m/Ma.
These rates indicate the average amount of vertical erosion and horizontal widening that occurs over a million-year period. The South Rim experiences slower incision but significant widening, while the North Rim incises more rapidly and widens at a lesser rate. These geological processes contribute to the unique topography and formation of the area over millions of years.
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The graph shows the distance Liam traveled from school in miles (V) as a function of time in seconds (x). The graph is divided into four
segments labeled P, Q, R, and S, respectively.
Distance
(mi)
P
Time (sec)
Which segment shows Liam waiting for a cab? P, Q, R, or S
the last one it was typed wrong please help!
Answers
Answer:
R
Step-by-step explanation:
R since it is staying in the same place which is called a constant line. It stays in the same place since she isn't moving, she is just standing there waiting for the cab. Plz mark as brainliest
B = 75*
C = 50*
A = ?*
Answers
Answer: A = 55* or 55 degrees
Step-by-step explanation:
The interior angles of a triangle always have a sum of 180 degrees.
75 + 50 + x = 180
Solve for x
FInal answer: 55 degrees
hope i explained it :)
Complete the following statement. Use the integers that are closest to the number in the middle. < 82 <
Answers
The integers that are closest to the number in the middle in the inequality x < √82 < y are x = 9 and y = 11.
To find the integers x and y that satisfy the inequality x < √82 < y, we need to find the two integers that are closest to the square root of 82.
First, we know that the perfect square that is less than 82 is 81, which is equal to 9². Therefore, we can say that 9 < √82.
Next, we need to find the next closest integer to the square root of 82. To do this, we can calculate the square of 10 and the square of 11, which are 100 and 121, respectively. Since 82 is closer to 81 than to 100, we can say that √82 < 10.5.
Therefore, x = 9 and y = 11 are the integers that satisfy the inequality x < √82 < y.
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The question is -
Complete the following statement. Use the integers that are closest to the number in the middle. x < √82 < y, find x and y.
Mr. Baker is driving 100 miles. His average speed, to the nearest 2 miles per hour, is 56 miles per hour. What is the range of possible values
for t, the total time of the drive in hours?
A
1.79
B
1.72 < t < 1.85
с
1.72
1.75 < t < 1.82
Answers
Answer:
1.72 ≤ t ≤ 1.85
Step-by-step explanation:
Given :
Distance = 100 miles ;
Speed = 56 miles per hour, to the nearest 2 miles per hour
Hence, the speed range is :
(56 - 2) mph ; (56 + 2) mph
Range of possible Time taken, t :
Distance / speed ;
100 / 58 ≤ t ≤ 100 / 54
1.72 ≤ t ≤ 1.85
Seven less than the product of 6 and a number is equal to 3 Translate the sentence into an equation.
Answers
Answer:
Step-by-step explanation:
I don't say you have to mark my ans as brainliest but don't forget to thank me if it has really helped you...
The sentence into an equation is 6x-7= 3
Let x represent the unknown number
The number is multiplied by 6
= (6 × x )
= 6x
seven is subtracted from the product
= 6x - 7
The product is equated to 3
= 6x-7= 3
hence the equation is 6x-7= 3
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Use the four-step process to find f
′
(x) and then find f
′
(1),f
′
(2), and f
′
(3). f(x)=x
2
+8x−6 f
′
(x)= f
′
(1)= (Type an integer or a simplified fraction.) f
′
(2)= (Type an integer or a simplified fraction.) f
′
(3)= (Type an integer or a simplified fraction.)
Answers
Using the four-step process, f'(1) = 10, f'(2) = 12, and f'(3) = 14.
To identify f'(x), the derivative of f(x), using the four-step process, we can follow these steps:
1: Identify the function.
The given function is f(x) = x^2 + 8x - 6.
2: Apply the power rule.
Differentiate each term of the function separately.
The derivative of x^2 is 2x.
The derivative of 8x is 8.
The derivative of -6 is 0 (constant term).
3: Simplify.
Combine the derivatives obtained in step 2.
So, f'(x) = 2x + 8.
4: Evaluate f'(1), f'(2), and f'(3).
Substitute x = 1, 2, and 3 into the derived equation to identify the respective values.
f'(1) = 2(1) + 8 = 10.
f'(2) = 2(2) + 8 = 12.
f'(3) = 2(3) + 8 = 14.
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2. Given 4x² + bx + 25, select a possible b value that will make this factorable. [A] b=-50 [B] b = -29 [C] b = 10 [D] b= 100
Answers
Answer:
b = 40 and -40
General form of Perfect square trinomial is
a
2
+
2
a
b
+
b
2
Therefore from
16
x
2
−
b
x
+
25
a
2
=
√
16
x
2
,
b
2
=
25
, then
a
=
±
4
x
,
b
=
±
5
take consideration a=4x and b=-5 (different sign), then
−
b
x
=
2
(
4
x
)
(
−
5
)
−
b
x
=
−
40
x
b
=
40
The perfect square is
(
4
x
−
5
)
2
=
16
x
2
−
40
x
+
25
.
if we consider a=4x and b=5 (same sign), then
−
b
x
=
2
(
4
x
)
(
5
)
−
b
x
=
40
x
b
=
−
40
The perfect square is
(
4
x
+
5
)
2
=
16
x
2
+
40
x
+
25
.
The first solution
(
4
x
−
5
)
2
is the best solution after comparing the expression given.
Hey, can you please help me the best that you can. I would really appreciate it, thank you! :)
Answers
1 cookie = 45 oz sugar
2 cookies = 2×45 oz = 90 oz
3 cookies = 3×45 oz = 135 oz
...
523 cookies = 523×45 oz = 23,535 oz
Alexi’s restaurant bill is $58, and he wants to leave a 20 percent tip. Which expression represents the total amount that Alexi needs to pay?
Answers
Answer:
20
Step-by-step explanation:
Answer:
The correct answer is that Alexi should be tipping $11.60
Step-by-step explanation:
The bill is $58
and you tip 20%
So, take the $58 and add 20% onto that:
The correct answer with the tip is $69.60
Therefore, you should tip $11.60 for the tip.
2f - 4G + 16g - 3F
PLZZZZ HELP
Answers
Answer:
=-f +12g
Step-by-step explanation:
Answer:
-1f+12g
Step-by-step explanation:
what unit of measurement ios used to describe how far a sert of values are from the mean
standard deviation is the measure used to determine how values are from the mean
Standardizing a value occurs by determining the difference between the value and the mean, divide by the standard deviation
Multiplying or dividing all values will have the same affect on the mean since all values are changing equally.
Answers
The unit of measurement used is A. Standard deviation is the unit of measurement used to describe how far a set of values are from the mean.
What is standard deviation ?The degree of variation of data from the average, or mean, is gauged by the standard deviation. It provides us with information on the average amount by which each data point diverges from the mean.
A lesser standard deviation suggests that the data points gather closely around the mean, whereas a greater standard deviation signifies that the data points are further dispersed. To standardize a value, we subtract the mean from the value and then divide by the standard deviation.
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PLS HELP I WILL MARK THE CORRECT ANSWER BRAINLIEST !!!!!!! PLS HELP IMAGE INCLUDED!!!!!!
Answers
how long did it take the concorde to fly from new york to london
Answers
The Concorde, a supersonic passenger jet, took approximately 3 hours and 15 minutes to fly from New York to London. The flight time was significantly shorter than conventional subsonic flights, which could take up to 7 hours or more.
The Concorde was able to fly at speeds of up to 2,179 km/h (1,354 mph) and fly at an altitude of 60,000 feet, above most of the Earth's atmosphere. This allowed the Concorde to cover the distance between New York and London in just a fraction of the time it would take a conventional aircraft.
It's worth noting that the Concorde's supersonic capabilities came at a cost, both in terms of the high operating costs of the aircraft and the noise pollution generated by its engines, which led to restrictions on the routes it was able to fly. The Concorde was retired from service in 2003.
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assume that you want to be 95% confident that the sample percentage is within 5.8 percentage points of the true population percentage. you answered
Answers
The required sample size is approximately 386 to be 95% confident that the sample percentage is within 5.8 percentage points of the true population percentage.
To determine the required sample size for desired confidence level and margin of error, we can use the formula for sample size calculation:
\(\[ n = \left(\frac{{Z^2 \cdot p \cdot (1-p)}}{{E^2}}\right) \]\)
Where:
\(\( n \)\) = required sample size
\(\( Z \)\) = Z-score corresponding to the desired confidence level (for 95% confidence, \(( Z = 1.96 \))\)
\(\( p \)\) = estimated proportion (0.5 can be used as a conservative estimate when the true proportion is unknown)
\(\( E \)\) = desired margin of error (5.8 percentage points)
Plugging in the values into the formula:
\(\[ n = \left(\frac{{1.96^2 \cdot 0.5 \cdot (1-0.5)}}{{0.058^2}}\right) \]\)
\(\( n \approx 385.9 \)\)
Since sample size must be a whole number, we round up to the nearest integer.
Therefore, the required sample size is approximately 386 to be 95% confident that the sample percentage is within 5.8 percentage points of the true population percentage.
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easy please helppp match the following defintion with the correct term: the vertical distance between two points on a line
1. run
2. rate of run
3. slope
4. rise
Answers
Answer:
4. rise
match the following definition with the correct term:
the vertical distance between two points on a line
1. run
2. rate of run
3. slope
4. rise
Given are five observations collected in a regression study on two variables.
xi 2 6 9 13 20
yi 7 18 9 26 23
a. Compute b0 and b1 and develop the estimated equation for these data.
b. Use the estimated regression equation to predict the value of y when x = 6.
Answers
The estimated equation for these data is: Y= 6.47 + 1.013x
When x = 6, the estimated value of y is approximately 12.55.
How to solve for the regression
To compute the estimated regression equation and predict the value of y when x = 6, we'll follow these steps:
Given data:
xi: 2, 6, 9, 13, 20
yi: 7, 18, 9, 26, 23
a. Compute b0 and b1 and develop the estimated equation for these data.
Step 1: Calculate the means of x and y:
x = (2 + 6 + 9 + 13 + 20) / 5 = 10
y = (7 + 18 + 9 + 26 + 23) / 5 = 16.6
Step 2: Calculate the deviations from the means:
xi - x: -8, -4, -1, 3, 10
yi - y: -9.6, 1.4, -7.6, 9.4, 6.4
Step 3: Calculate the sum of squared deviations:
Σ(xi - x): 180
Σ(yi - y)²: 316.8
Step 4: Calculate the sum of cross-products:
Σ(xi - x)(yi - y): 182.4
Step 5: Calculate the slope (b1):
b1 = Σ(xi - x)(yi - y) / Σ(xi - x)² = 182.4 / 180 ≈ 1.013
Step 6: Calculate the intercept (b0):
b0 = y - b1 * x = 16.6 - 1.013 * 10 ≈ 6.47
Therefore, the estimated equation for these data is:
Y = 6.47 + 1.013x
b. Use the estimated regression equation to predict the value of y when x = 6.
To predict the value of y when x = 6, substitute x = 6 into the estimated equation:
y = 6.47 + 1.013 * 6
y ≈ 6.47 + 6.078
y ≈ 12.55
Thus, when x = 6, the estimated value of y is approximately 12.55.
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Question 10
The midpoint of line segment AC is B. If A is at (-5,4) and B is at (-3,-1), find the coordinates of C. ( )
Answers
-4，2
Step-by-step explanation:
find the average of the x coordinates and y coordinates