Answer:
Yes, there is a linear relationship between height and volume.
V = (12π)h. 12π is a constant.
If you rewrite this as y = (12π)x and graph it, you will notice that the graph is a line which goes through the origin.
Which set of numbers has a greatest common factor of 12?
A. 3 and 4
B. 6 and 18
C. 32 and 48
D. 36 and 96
Show your work.
The set of numbers 36 and 96 has a greatest common factor of 12.
Explanation:
The greatest common factor (GCF) of a set of numbers is the largest number that can evenly divide all the numbers in the set. To find the GCF, we can list all the factors of each number and find the largest one they have in common.
For set A, the factors of 3 are 1 and 3, and the factors of 4 are 1, 2, and 4. There is no common factor greater than 1.
For set B, the factors of 6 are 1, 2, 3, and 6, and the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest factor they have in common is 6.
For set C, the factors of 32 are 1, 2, 4, 8, 16, and 32, and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The largest factor they have in common is 16.
For set D, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36, and the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. The largest factor they have in common is 12.
Therefore, set D, consisting of the numbers 36 and 96, has a greatest common factor of 12.
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15. MULTIPLE CHOICE Determine which statement is true given that CBX = SML.
The statement that is true, given that ΔCBX ≅ ΔSML, would be G. XC ≅ ML.
How to find the true statement on congruent triangles ?Given that ΔCBX ≅ ΔSML, we can use the properties of congruent triangles to determine which statement is true. The correspondence between the vertices of the two triangles is as follows:
C ↔ S
B ↔ M
X ↔ L
XC ≅ ML is true because XC corresponds to the side connecting vertices X and C in ΔCBX, and ML corresponds to the side connecting vertices M and L in ΔSML. Since the triangles are congruent, their corresponding sides are congruent.
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Help please I got 5.76 I don’t know if that’s right
Answer:
trust yourself cuh
Step-by-step explanation:
Find the least common multiple of 44 , 18and 4 ?
A 3,168
B 66
C 396
D 792
E none of these answers are correct
Please help!!
Answer:
C. 396
Step-by-step explanation:
You want the LCM of 4, 18, and 44.
LCMYou can find the least common multiple by considering the unique factors to their highest powers.
4 = 2^2
18 = 2·3^2
44 = 2^2·11
The unique factors are 2, 3, 11, and their highest powers are 2, 2, and 1, respectively. The LCM is ...
2² × 3² × 11 = 396
__
Check
396 = 4·99 = 18·22 = 44·9 . . . . . 99, 22, and 9 have no common factors
How do l do this help
Answer:
130
Step-by-step explanation:
Answer: y=130 x=130
Step-by-step explanation:
please help with these 2 questions in math
The correct answer is E (-1,-3). Reflection across the x-axis is a transformation that flips the object across an imaginary line that runs through the center of the x-axis.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
In this case, the x-axis is the line y = 0. The figure ABCD is reflected across this line, resulting in point A being reflected to E.
When a figure is reflected, the x-coordinates remain the same, while the y-coordinates change sign. This means that the x-coordinate of point A (-1) remains the same, but the y-coordinate (3) changes to its opposite (-3). Therefore, the resulting coordinates of point A are (-1,-3).
Reflection across the x-axis is an example of a transformation. Transformations involve changing the position, size or orientation of a figure, but not its shape. This means that the figure ABCD is still the same shape after being reflected, but its position has changed. After being reflected, the figure is now located on the opposite side of the x-axis.
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Me . Lake Bought four dozen apples for her band kids 1/4 of the apples were green and 3/4 or red. How many apples were red
Answer:
36
Step-by-step explanation:
3/4 of 48 is 36
graphing a Quadratic function given in factored from
Answer:
y
Step-by-step explanation:
PLS HELP FASTTTTTTTTTTTTTTTTTTTTTT
Select the correct answer. Which function has an average rate of change of -4 over the interval [-2,2]?
A. x | -2 | -1 | 0 | 1 | 2
m(x) | -12 | -5 | -4 | -3 | 4
B.
C.
D.
Answer:
The correct answer is option B.
To find the function with an average rate of change of -4 over the interval [-2,2], we need to calculate the slope of the function between the two points -2 and 2.
Average rate of change = (f(2) - f(-2))/(2 - (-2)) = (-4)
Option B has the function qx with values {-4, 0, 0, -4, -12} at x values {-2, -1, 0, 1, 2}. The average rate of change of this function over the interval [-2,2] is indeed -4.
explain the logic in fractions where 1/6+2/3+3/7 becomes 7/42+28/42+18/42
Answer:
Step-by-step explanation:
What are fractions?Fractions are parts or pieces of a complete thing.
In this problem, the fractions start out with varying denominators, and then end with the same denominator. In order to go from different denominators to the same denominator, we must find a common denominator.
What is a common denominator?A common denominator is a number that denominators of fractions can equal when multiplied by something else. Ex: 1/3 + 2/ 7 Multiples of 3: 3, 6, 9, 12, 15, 18, 21 Multiples of 7: 7, 14, 21. Both 3 and 7 have 21 in common, so this would be the common denominator.
A common denominator is needed so fractions with different denominators can be combined. To get from 6, 3, and 7 to 42, the multiples of 2, 3, and 7 must be listed.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 29, 42
Multiples of 7: 7, 14, 21, 28, 35, 42
All three numbers have 42 in common, so that is their common denominator. Whatever was done to the denominator, must be done to the numerator. Now, we must take the number that can be multiplied by the denominator to reach 42 and multiply it by the numerator.
[tex]\frac{1*7}{6*7}}[/tex]
[tex]=\frac{7}{42}[/tex]
[tex]\frac{2*14}{3*14}[/tex]
[tex]=\frac{28}{42}[/tex]
[tex]\frac{3*6}{7*6}[/tex]
[tex]=\frac{18}{42}[/tex]
So, to sum it up, when trying to add fractions with different denominators, find a common denominator by listing multiples of the denominators and multiply the numerator by the number the denominator was multiplied by to get the common denominator.
The logic in this fraction addition problem is to find a common denominator for all the fractions and then add the numerators. In this case, the common denominator is the least common multiple of the denominators, which is 42.
To convert the first fraction, 1/6, to have a denominator of 42, we need to multiply both the numerator and denominator by 7. This gives us 7/42.To convert the second fraction, 2/3, to have a denominator of 42, we need to multiply both the numerator and denominator by 14. This gives us 28/42.To convert the third fraction, 3/7, to have a denominator of 42, we need to multiply both the numerator and denominator by 6. This gives us 18/42.Now that all the fractions have a common denominator of 42, we can add the numerators to get the final answer:
[tex]\begin{aligned} \sf \dfrac{1}{6} + \dfrac{2}{3} + \dfrac{3}{7} = \dfrac{7}{42} + \dfrac{28}{42} + \dfrac{18}{42} = \bold{\dfrac{53}{42}} \end{aligned}[/tex]
Therefore, the sum of the fractions is 53/42.
I hope this helps!
K
Add the fractions. Simplify if possible.
2
9x
+
10
9x
The sum of the given fractions is (2x + 10)/x.
What is fraction ?
A fraction is a way of representing a part of a whole or a ratio between two quantities. It is written in the form of a numerator and a denominator separated by a horizontal line. The numerator represents the number of equal parts under consideration, while the denominator represents the total number of equal parts that make up the whole. For example, the fraction 3/4 represents three equal parts out of a total of four equal parts. Fractions can be added, subtracted, multiplied, and divided to perform various mathematical operations.
According to the question:
The given fractions can be added if they have a common denominator. In this case, the common denominator is 9x.
So, we need to write the fractions with 9x as the denominator:
2/1 * (9x/9x) = 18x/9x
10/1 * (9/9x) = 90/9x
Now, we can add these two fractions:
18x/9x + 90/9x = (18x + 90)/9x = 9(2x + 10)/9x = 2x + 10/ x
Therefore, the sum of the given fractions is (2x + 10)/x.
Q: Find K by Adding the fractions and simplify if possible k=(2*(9x))+(10*(9x))
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Ann thought of a number, n . She multiplied it by 5 and then added 7. Then she told Jim the result, r
Start with the formula you wrote in part (b). Use it to write another formula that could help Jim find Ann’s number, n as soon as he is given the result, r
The formula that could help Jim find Ann’s number, n as soon as he is given the result, r is n = (r - 7) / 5.
How to write formula?Formula 1;
Let the unknown number Ann thought of = n
(n × 5) + 7 = r
5n + 7 = r
If Jim is given Ann's number n if given the results, r
This means Jim will make Ann's number n the subject of the formula;
5n + 7 = r
Subtract 7 from both sides
5n = r - 7
divide both sides by 5
n = (r - 7) / 5
Therefore, the formula written in terms of n is n = (r - 7) / 5
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Perry's patio is 6 meters long and 53 meters wide. What is the area of his patio?
5. Andrew needs to choose a captain creature and a partner creature for his
expedition to a mysterious dungeon. Each creature belongs to the grass,
fire, or water group, and each group has 6 creatures. If the captain and
partner creatures cannot be from the same group, how many ways can
Andrew choose a captain creature and a partner creature?
Andrew needs to choose a captain creature and a partner creature for his expedition to a mysterious dungeon. Each creature belongs to the grass, fire, or water group, and each group has 6 creatures, hence there are 216 ways
If the captain and partner creatures cannot be from the same group, how many ways can Andrew choose a captain creature and a partner creature?" by using combinatorial techniques.
Since Andrew cannot choose a captain and partner creature from the same group, there are 3 choices for the captain creature and 2 choices for the partner creature.
Therefore, the number of ways that Andrew can choose a captain and partner creature is: 3 * 2 * 6 * 6 = 216
Therefore, there are 216 ways that Andrew can choose a captain creature and a partner creature for his expedition to the mysterious dungeon
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Quadrilateral has a vertex (5,2), coordinates after translation (x,y)- (x-1, y+3), followed by a dilation by 2
As a result, after translation and dilation, the initial quadrilateral's apex (5, 2) changes into the vertex (8, 10).
A quadrilateral form is what?One quadrilateral is a circular shape with four sides. These geometric shapes are quadrilaterals: produced by Raphael. a quadrilateral form. There is only one pair of parallel edges to the form, and there are no right angles.
To find the coordinates of the vertices of the quadrilateral after translation and dilation, we can follow these steps:
Translate the vertex (5, 2) by subtracting 1 from the x-coordinate and adding 3 to the y-coordinate to get the new coordinates: (5-1, 2+3) = (4, 5).
Dilate the translated vertex by a factor of 2 with respect to the origin (0, 0) to get the final coordinates: (24, 25) = (8, 10).
Therefore, the vertex (5, 2) of the original quadrilateral is transformed into the vertex (8, 10) after translation and dilation.
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The complete question is: After translating a quadrilateral with a vertex at (5,2) to a new position given by (x-1, y+3) and then dilating it by a factor of 2, what are the coordinates of the new vertices of the quadrilateral?
Answer:
(8,10)
Step-by-step explanation:
The company Sea Esta has ten members on its board of directors. In how many different ways can it
elect a president, vice-president, secretary and treasurer?
Answer:
Step-by-step explanation:
The president, vice-president, secretary and treasurer are four different positions that need to be filled by ten individuals.
Therefore, the number of ways to elect the president is 10. After electing the president, the number of candidates available for the vice-president position reduces to 9. Similarly, after electing the president and the vice-president, the number of candidates available for the secretary position reduces to 8. Finally, after electing the president, vice-president, and secretary, the number of candidates available for the treasurer position reduces to 7.
Using the multiplication principle of counting, we can find the total number of possible combinations for all four positions by multiplying the number of candidates for each position:
Total number of ways to elect all four positions = (number of candidates for president) x (number of candidates for vice-president) x (number of candidates for secretary) x (number of candidates for treasurer)
= 10 x 9 x 8 x 7
= 5,040
Therefore, there are 5,040 different ways that Sea Esta can elect a president, vice-president, secretary, and treasurer from its board of directors.
Ricardo took out a single payment loan for $2500 at 7.8% ordinary interest to pay his federal income tax bill. Find the maturity value of the loan if he had to pay it back after 180 days.
Answer:
Therefore, the maturity value of the loan is $2568.75.
Step-by-step explanation:
To calculate the maturity value of the loan, we need to add the interest to the principal.
First, we need to find out how much interest Ricardo will owe for the 180-day period.
The formula for calculating ordinary interest is:
Interest = Principal x Rate x Time
where:
Principal = $2500
Rate = 7.8% = 0.078 (expressed as a decimal)
Time = 180/360 (since the interest is for a 180-day period and the rate is an annual rate)
Time is expressed as a fraction of a year because the rate is an annual rate. In this case, the time is 180/360 because the loan is for 180 days, which is half of a year.
Using the formula above, we can calculate the interest as follows:
Interest = $2500 x 0.078 x 180/360 = $68.75
Therefore, Ricardo will owe $68.75 in interest for the 180-day period.
To find the maturity value of the loan, we add the interest to the principal:
Maturity Value = Principal + Interest = $2500 + $68.75 = $2568.75
Therefore, the maturity value of the loan is $2568.75.
Pudge has three times as many apples as Ace, and Ace has twice as many as Christi. How many apples does each
have if Pudge has 12 more than both Ace and Christi together?
Can you work the problem out please? I’m really having a hard time putting it into a formula.
Answer: Ace has 8 apples Christi has 4 and Pudge has 24
Step-by-step explanation:
Ace has 2 twice as much as Christi has, and 4 x 2 is 8. Pudge has 3 times more than Ace has and 8 x 3 is 24. Pudge has 12 more than Christi and Ace combined. 8 + 4 = 12. 12 + 12 = 24. I hope I explained it right.
Please help i’ll give brainlist!!
Solve each proportion.
Answer: 12, 32/11
Step-by-step explanation:
3 12
4 32/11
Katya is going on a 7-night trip. She is staying in a hotel that costs $129 per night and her airfare is $375. If she budged $2.000 for the trip, how much money will she have left for the trip?
A. $672
B. $686
C.$704
D.$722
Answer: D. $722
Step-by-step explanation:
$2,000 - $375 (initial airfare cost which will only be once)
= 1,625
7 x 129 = 903 (cost of the 7 nights in a hotel)
1,625 - 903 = 722
$722 left for the trip
mHJ
measure of arc HJ:
96
29°
1
Answer:
Step-by-step explanation:
To convert the mixed angle measure 96° 29' 1" to decimal degrees, we can use the following formula:
decimal degrees = degrees + (minutes / 60) + (seconds / 3600)
Using this formula, we have:
decimal degrees = 96 + (29 / 60) + (1 / 3600)
decimal degrees = 96.4836111
Therefore, mHJ = 96.4836111 degrees (rounded to seven decimal places).
While the earth’s orbit (path) about the sun is slightly elliptical, it can be approximated by a circle with a radius of
miles.
How far does the earth travel in one orbit about the sun? That is, what is the approximate circumference of the earth’s path?
Approximately how fast is the earth traveling in its orbit in space? Calculate your answer in miles per hour.
The radius of the Earth's orbit around the sun is approximately 93 million miles.
To calculate the circumference of the Earth's orbit, we can use the formula:
C = 2πr
where C is the circumference and r is the radius. Plugging in the value for the radius, we get:
C = 2π(93,000,000) = 584,336,000 miles
So the Earth travels approximately 584,336,000 miles in one orbit around the sun.
The speed of the Earth in its orbit around the sun can be calculated using the formula:
v = 2πr/T
where v is the velocity, r is the radius, and T is the period (the time it takes for the Earth to complete one orbit). The period of the Earth's orbit is approximately 365.25 days, or 31,557,600 seconds.
Plugging in the values, we get:
v = 2π(93,000,000)/(31,557,600) = 29,784 miles per hour
So the Earth travels at approximately 29,784 miles per hour in its orbit around the sun.
11) m/EFG=132°, m/CFG=x+111,
and m/EFC=x+23. Find mLEFC.
Applying the angle addition postulate, the value of x in the image given is calculated as: 49.
What is the Angle Addition Postulate?The Angle Addition Postulate states that for any angle, the sum of its adjacent angles is equal to the angle formed by combining them.
Therefore, we have:
x + 11 + x + 23 = 132
Combine like terms to find the value of x:
2x + 34 = 132
2x = 132 - 34
2x = 98
2x/2 = 98/2
x = 49
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fruit punch is made up for a party by mixing 2 and 1/2 quarts of apple juice 1 1/2 quarts of cranberry juice and 3 quarts of grape juice of the punch made 6 quarts are poured into a jug to serve to the guest
Answer: To find the proportions of each type of juice in the 6 quarts of fruit punch, we need to use ratios:
For every 2.5 quarts of apple juice, we need (6/8) x 2.5 = 1.875 quarts of apple juice.
For every 1.5 quarts of cranberry juice, we need (6/8) x 1.5 = 1.125 quarts of cranberry juice.
For every 3 quarts of grape juice, we need (6/8) x 3 = 2.25 quarts of grape juice.
So the proportions of apple, cranberry, and grape juice in the 6 quarts of fruit punch are approximately:
1.875 quarts of apple juice
1.125 quarts of cranberry juice
2.25 quarts of grape juice
Note that these proportions are approximate because we rounded the amounts of each juice to two decimal places.
Step-by-step explanation:
Find the unknown dimension of a rectangle if its perimeter is 254 meters and one
dimension measures 6 meters. Use labeled sketches and equations to model and
solve this problem. Show your work. Label your answer with the correct units.
The perimeter does indeed equal 254 meters, which confirms that our answer is correct.
What in mathematics is the perimeter?Any two-dimensional closed shape's perimeter is defined as the entire distance encircling it. The perimeter of a rectangle, such as the following: Square perimeter equals the sum of its four edges. Rectangle perimeter equals the sum of its four edges.
Let's call the rectangle's unidentified size x.
P = 2l + 2w, where l is the length and w is the breadth, gives the perimeter of a rectangle.
So that we can create an equation:
254 = 2l + 2(6)
Simplifying the right side:
254 = 2l + 12
Subtracting 12 from both sides:
242 = 2l
Dividing both sides by 2:
121 = l
Consequently, the rectangle's undetermined measurement (length) is 121 metres.
We can compute the perimeter using both variables to confirm our conclusion:
P = 2(121) + 2(6) = 242 + 12 = 254
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A local doctor wants to test the effects of a new diet she decided to lower triglycerides on 10 randomly selected patients. The triglyceride level of each patient is checked twice, once before they start the diet, and again at three weeks after that time. The results are in the table below, (the photo). All data is in milligrams per deciliter (mg/dL).
The Noel and alternative hypothesis for the study are (in the photo)
Please let me know which one of the answers in the photo is correct ! Thank you , 100 points!!
With a significance level of 0.05, the. option that shows the correct test statistic, P- value, and conclusion is A. Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
What is a significance level?In statistics, the significance level (denoted by α) is the probability of making a Type I error, which is rejecting a true null hypothesis. In other words, it is the maximum allowable probability of observing a result as extreme as or more extreme than the one observed, assuming the null hypothesis is true.
The significance level is typically set by the researcher before conducting a hypothesis test and is usually set to 0.05 (5%) or 0.01 (1%). If the p-value of the test is less than or equal to the significance level, the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the significance level, the null hypothesis is not rejected.
The correct option is A.
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With a significance level of 0.05, which of the following shows the correct test statistic, P- value, and conclusion?
Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, = 0.3619; P-value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, -1.952; P-value, 0.0509. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Test statistic, t=0.3651; P-value, 0.6425. There is insufficient evidence to reject the null hypothesis of
no difference between the triglyceride test levels.
Write numbers to make an expression equivalent to 5x - 4
Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4
How numbers to make an expression equivalent to 5x - 4To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.
Here are some examples of how we can do this:
5(x - 4/5)
In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.
5x - 20/5
Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.
(25x - 20)/5
In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.
10x/2 - 8/2
This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.
3(5x/3) - 4
In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.
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2. Solve based on the diagram below.
What is the value of angle x? How do you know (what type of angle pairs are they)?
Answer: 160
Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.
Question content area top
Part 1
Assume the hold time of callers to a cable company is normally distributed with a mean of 3.7 minutes and a standard deviation of .6 minute. Determine the percent of callers who are on hold between 2.6 and 3.9 minutes.
Approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.
What Is a Normal Distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
First, we standardize the value of 2.6 as follows:
z = (x - μ) / σ
where x is the value of 2.6, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:
z = (2.6 - 3.7) / 0.6 ≈ -1.83
z = (x - μ) / σ
where x is the value of 3.9, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:
z = (3.9 - 3.7) / 0.6 ≈ 0.33
We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can find the area as follows:
P(-1.83 < Z < 0.33) ≈ 0.6068
Therefore, approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.
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Approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.
What Is a Normal Distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
First, we standardize the value of 2.6 as follows:
z = (x - μ) / σ
where x is the value of 2.6, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:
z = (2.6 - 3.7) / 0.6 ≈ -1.83
z = (x - μ) / σ
where x is the value of 3.9, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:
z = (3.9 - 3.7) / 0.6 ≈ 0.33
We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can find the area as follows:
P(-1.83 < Z < 0.33) ≈ 0.6068
Therefore, approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.
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