Data set 2: 23, 47, 16, 26, 20, 37, 31, 17, 29, 19, 38, 39, 41 Provide the summary statistics for data set 2. Q14. What is the mean value? Q15. What is the median value? Q16. What is the sum of square

Answer:

$57.60

Step-by-step explanation:

48 x 0.20 = 9.60

48 + 9.60

57.60

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Given:

\(\Delta FUN\cong \Delta TEA\)

To find:

Identify the congruent corresponding parts of \(\angle N\cong \angle \_\_\).

Solution:

We have,

\(\Delta FUN\cong \Delta TEA\)

We know that corresponding parts of congruent triangles are congruent.

\(\angle F\cong \angle T\)

\(\angle U\cong \angle E\)

\(\angle N\cong \angle A\)

Therefore, the required corresponding part is  \(\angle N\cong \angle A\).

Step-by-step explanation:

1 result(s) found

x  

2

−x−3

Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

STEP

2

:

           x3 + 3x2 - 7x - 12

Simplify   ——————————————————

                 x + 4        

Checking for a perfect cube :

2.1    x3 + 3x2 - 7x - 12  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x3 + 3x2 - 7x - 12  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -7x - 12  

Group 2:  x3 + 3x2  

Pull out from each group separately :

Group 1:   (7x + 12) • (-1)

Group 2:   (x + 3) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = x3 + 3x2 - 7x - 12

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -12.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,12

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -3.00      

     -2       1        -2.00        6.00      

     -3       1        -3.00        9.00      

     -4       1        -4.00        0.00      x + 4  

     -6       1        -6.00        -78.00      

     -12       1       -12.00       -1224.00      

     1       1        1.00        -15.00      

     2       1        2.00        -6.00      

     3       1        3.00        21.00      

     4       1        4.00        72.00      

     6       1        6.00        270.00      

     12       1        12.00        2064.00      

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  x3 + 3x2 - 7x - 12  

can be divided with  x + 4  

Polynomial Long Division :

2.4    Polynomial Long Division

Dividing :  x3 + 3x2 - 7x - 12  

                             ("Dividend")

By         :    x + 4    ("Divisor")

dividend     x3  +  3x2  -  7x  -  12  

- divisor  * x2     x3  +  4x2          

remainder      -  x2  -  7x  -  12  

- divisor  * -x1      -  x2  -  4x      

remainder          -  3x  -  12  

- divisor  * -3x0          -  3x  -  12  

remainder                0

Quotient :  x2-x-3  Remainder:  0  

Trying to factor by splitting the middle term

2.5     Factoring  x2-x-3  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -1 .

     -3    +    1    =    -2  

     -1    +    3    =    2  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Canceling Out :

2.6    Cancel out  (x+4)  which appears on both sides of the fraction line.

Final result :

 x2 - x - 3

Terms and topics

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Polynomial root calculator

Polynomial long division

Related links

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Root Finder -- Polynomials Calculator

How to factor five term polynomial - Yahoo Answers

Long Polynomial Division

Polynomial long division - Wikipedia

Polynomial Long Division

Polynomials - Long Division

Answer:

30 = 140 M&M's I 40 = 120 M&M's I 50 = 100 M&M's

Step-by-step explanation:

Answer:

The answer would be 6

First, order the number set from least to greatest:

3 , 4 , 4 , 7 , 8 , 9 , 12 , 14 , 16 , 20

Mean: You find the mean by combining all the terms, and dividing by the amount of the terms there are in the number set:

(3 + 4 + 4 + 7 + 8 + 9 + 12 + 14 + 16 + 20)/10

(97)/10 = 9.7

Mean: 9.7

Median: You find the median by first ordering the number set from least to greatest, and finding the middle number. Note that if there is a even number of numbers in the set, you find the mean with the two given median digits:

8 & 9 are the median numbers:

(8 + 9)/2 = (17)/2 = 8.5

Median: 8.5

Mode: The mode is the number(s) in the set that shows up the most:

Mode: 4 (shows up one more time than all other numbers)

Range:  The range can be found by subtracting the least number from the greatest number in the number set:

Range: 20 - 3 = 17

Range: 17

~

It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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Answer:

The y-intercept is 5

Step-by-step explanation:

y=mx+b

m is your slope while b is your y-intercept

Therefore your y-intercept is 5

Your Welcome.

Answer:

The y intercept is 5

Step-by-step explanation:

Y=MX+B

B= the y intercept.

5 is in the spot for B

Therefor, 5 is the y intercept.

Hope this helps have a great day. :)

Answer:

The following expression can be used to represent the perimeter of rectangle ABCD: 16x-12

Step-by-step explanation:

Let l be the length of rectangle and w be the width of rectangle.

Given that:

\(l = 5x+1\\w = 3x-7\)

The perimeter of a rectangle is given by the expression:

\(P = 2(l+w)\)

Putting the values of length and width, we get

\(P = 2\{(5x+1)+(3x-7)\}\\P = 2\{5x+1+3x-7\}\\P = 2(8x-6)\\P = 16x-12\)

Hence,

The following expression can be used to represent the perimeter of rectangle ABCD: 16x-12

Statistical procedures that summarize and describe a series of observations are called descriptive statistics.

Descriptive statistics involve various techniques and measures that aim to summarize and describe the key features of a dataset. These procedures include measures of central tendency, such as the mean, median, and mode, which provide information about the typical or average value of the data. Measures of dispersion, such as the range, variance, and standard deviation, quantify the spread or variability of the data points.
In addition to these measures, descriptive statistics also involve graphical representations, such as histograms, box plots, and scatter plots, which provide visual summaries of the data distribution and relationships between variables. These graphical tools help in identifying patterns, outliers, and the overall shape of the data.
Descriptive statistics play a crucial role in providing a concise summary of the data, enabling researchers and analysts to gain insights, make comparisons, and draw conclusions. They form the foundation for further statistical analysis and inferential techniques, which involve making inferences about a population based on a sample.

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The answer is (1,400)  because its 400 jump ropes per hour.

Answer:

Step-by-step explanation:

x -4  , 3x-11 , 5x - 18 ,.......

first term = a = x -4

Common difference (d) = second term  - first term

                                =  3x -11 - [ x - 4]

                                = 3x - 11 - x + 4

                                = 3x - x - 11 + 4

                                 = 2x - 7

nth term = a + (n-1)*d

12th term = x - 4 + 11*(2x - 7)

               = x - 4 + 11*2x  - 7 *11

                = x - 4 + 22x - 77

                =x + 22x - 4 - 77

                = 23x - 81

Answer:

104

Step-by-step explanation:

Let x = the unknown second number.  2/5 of [the sum of] two numbers is 56. One of the numbers is 36:

(2/5)(36+x) = 56

Multiply both sides by 5/2:

36 + x = 56*5/2

36 + x = 140

x = 104

Check:

(2/5)(36+104)=56

(2/5)(140)=556

280/5 = 56

56 = 56

Check!

The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

According to the statement

we have to show the square root function as a equation in the graphical representation.

So,

we know that the definition of a

Graph a diagram showing the relation between variable quantities, typically of two variables and it also show the relation between more than two variables.

Now, we know that the definition of Equation is a mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

And the equation obtained from the graph is a y=√x-2 by a some calculations in the graph.

So, The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

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Answer:

number of kilometers travelled by cavalier-86.4

he used 6litres for the journey. take number of kilometers divide by number of litres

86.4/6=14.4

Answer:

Total length of the road = 6 3/4 miles.

Each markers are spaced at a distance = 1/8 of a mile.

Step-by-step explanation:

Total length of the road ÷ each marker space =

a) 6 3/4 ÷ 1/8.

b) In order to solve it, we need to convert that fraction into improper fraction:

6 3/4 = 27/4

6 3/4 ÷ 1/8 = 27/4 ÷ 1/8

We need to convert division sign into multiplication sign and flip the second fraction.

27/4 × 8/1

then simplify to get

27  × 2 = 54.

There would be total number of 54 markers of lengths (1/8) of a mile.

Answer:

three thousand one hundred and two

Step-by-step explanation:

Step-by-step explanation:

three point seven two five eight

brainiest please

Answer:

A

Step-by-step explanation:

Put '0' in for 's' and solve :

0 = -p^2 + 75 p + 1200

 Use Quadratic Formula with a = -1      b=75      c = -1200

      to find p = ~ 24  OR  52       THE LEAST NUMBER WOULD BE 24

Answer: Corresponding Angles

Step-by-step explanation:

When two lines are crossed by another line (The Transversal), the angles in matching corners are called Corresponding Angles.

Answer:

\(y = -\frac{1}{2} x+4\)

Step-by-step explanation:

Standard form for equation of line: y = mx + c

where m = gradient or slope

c = y-intercept

From the question we know that,

x = 2

y = 3

m = - 0.5

We will substitute these values into the equation to find c.

3 = (-0.5)(2) + c

3 = - 1 + c

c = 3 + 1 = 4

Therefore the equation of this line is \(y = -\frac{1}{2} x+4\)

Answer:

C) 15 cm is the best estimate.

Step-by-step explanation:

The exact answer is not there, so 15 is the best estimate.

You can use this equation to help you:

d=C/π

Where d is the diameter.

C is the circumference.

And the last one is Pi.

You know that C = 45, so divide that by Pi (3.14).

45/3.14159 = 14.32

The closest answer is 15.

Hope this helps! Have a great day!

Answer:

Step-by-step explanation:

Conclusion:

Therefore, the best estimate of the circle's diameter is 15cm.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

x=260 texts

Step-by-step explanation:

85=0.25x+20

Subtract 20 from each side.

65=0.25x

Divide both sides by 0.25.

260=x

260 texts plus the $20 flat fee will cost $85.

Therefore, the 99% confidence interval for the population mean is 305 - 30 to 305 + 30, which is between 275 and 335 pages.

The correct interpretation of the 99% confidence interval is that we estimate with 99% confidence that the true population mean is between 275 and 335 pages. This is because the confidence interval is based on the sample mean and the standard deviation of the sample, and it provides a range of values within which we can be reasonably confident that the true population mean lies. The fact that the sample was randomly selected helps to ensure that the estimate is representative of the overall population of books in the library. The population standard deviation of 45 pages is used to calculate the standard error of the mean, which in turn is used to construct the confidence interval.
We estimate with 99% confidence that the true population mean is between 275 and 335 pages.

Explanation:
1. A random sample of 15 books is taken from the library.
2. The sample mean (305 pages) is calculated from the random sample.
3. The population standard deviation is given as 45 pages.
4. To construct a 99% confidence interval for the population mean, we need to use the standard deviation and the sample mean.
5. The formula for the margin of error in a confidence interval is: Margin of Error = Z-score * (Standard Deviation / \(\sqrt{SampleSize}\))
6. For a 99% confidence interval, the Z-score is approximately 2.576.
7. Margin of Error = 2.576 * (45 / √15) ≈ 30
8. The confidence interval for the population mean is: (Sample Mean - Margin of Error) to (Sample Mean + Margin of Error)
9. Therefore, the 99% confidence interval for the population mean is 305 - 30 to 305 + 30, which is between 275 and 335 pages.

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the correct interpretation of the 99% confidence interval is:

"We estimate with 99% confidence that the true population mean is between 275.08 and 334.92 pages."

Based on the given information, we can calculate the 99% confidence interval for the true population mean of pages per book in the library.

Here are the steps to calculate the confidence interval:
Identify the given information:

population standard deviation \((\sigma) = 45\) pages, sample size \((n) = 15\) books, and sample mean \((\bar x) = 305\) pages.
Calculate the standard error (SE) of the sample mean:

\(SE = \sigma / \sqrt n = 45 / \sqrt 15 \approx 11.62.\)
The critical value (z) for a 99% confidence level:

\(z \approx 2.576\) (from a standard normal distribution table or using a calculator).
Calculate the margin of error (ME):

\(ME = z \times SE \approx 2.576 \times 11.62 \approx 29.92.\)
Determine the confidence interval:

\((\bar x - ME, \bar x + ME) = (305 - 29.92, 305 + 29.92) \approx (275.08, 334.92).\)

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The side lengths of the real object will be 50 inches and 60 inches.

The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.

The given scale factor is 5:1, which means that the dimensions of the scale drawing are 1/5 of the dimensions of the real object.

To find the side lengths of the real object, we can use the ratio of the dimensions in the scale drawing and the real object.

For example, the length of the real object can be found by multiplying the length of the scale drawing by the scale factor:

Real object length = Scale drawing length x Scale factor

Real object length = 10 in x 5

Real object length = 50 in

Similarly, the width of the real object can be found using the same method:

Real object width = Scale drawing width x Scale factor

Real object width = 12 in x 5

Real object width = 60 in

Therefore, the side lengths of the real object are 50 inches and 60 inches.

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Option B is correct, Rob's number of pets is 3 standard deviations to the right of the mean.

We need to calculate the number of standard deviations away from the mean Rob's number of pets is.

Given:

Mean (μ) = 4

Standard Deviation (σ) = 2

Number of pets owned by Rob = 10

To calculate the number of standard deviations (z-score) away from the mean, we use the formula:

z = (x - μ) / σ

where x is the value we want to measure.

For Rob's number of pets:

z = (10 - 4) / 2

z = 6 / 2

z = 3

Therefore, Rob's number of pets is 3 standard deviations to the right of the mean.

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Answer:

300

Step-by-step explanation:

I = interest earned

P = Principal

R = interest rate

T = Months

plug in all the numbers which would be...

45 = P x 0.03 x 5 *Note that 0.03 is 3% in decimal form

0.03 x 5 = 0.15

45 = P x 0.15

to make the P by itself you have to divide 0.15 to both sides

45/0.15 = 300

P = 300

The transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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

The functions f(x) and g(x)

Where, we have

f(x) = x²

The translation 6 units left and 4 units up means that

g(x) = f(x + 6) + 4

So, we have

g(x) = (x + 6)² + 4

This means that the transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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Answer:

2 : 3

Step-by-step explanation:

You need to show the ratio using the smallest whole numbers possible.

Multiply both numbers by 3.

2/3 : 1

2/3 × 3 : 1 × 3

2 : 3