In the following option n log n seems to grow the fastest amongst all according to the size of inputs.
In computer science and mathematics, the running time or complexity of an algorithm is often measured in terms of the size of the input, usually denoted by n. The notation O(f(n)) is used to describe the upper bound on the running time of an algorithm, where f(n) is a function of n.
In the context of comparing growth rates of functions, we usually only consider the highest-degree term of the function. For example, we would say that f(n) = n^2 + n grows as O(n^2), because n^2 grows much faster than n and dominates the running time as n grows larger.
Now, let's consider the functions n, n / log n, n - log n, n log n, and n^2. As n grows, each of these functions grows at a different rate.
1. n grows linearly with n, so it takes more time as the size of the input grows.
2. n / log n grows faster than n, but slower than n log n. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n / log n grows faster.
3. n - log n grows slower than n and n / log n, because log n grows much slower than n, so as n grows larger, n - log n becomes closer to n.
4. n log n grows faster than n, n / log n, and n - log n, but slower than n^2. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n log n grows faster.
5.n^2 grows much faster than n, n / log n, n - log n, and n log n, so as n grows larger, n^2 becomes much larger than any of these functions.
So, of the options given, n log n grows the fastest, meaning that an algorithm that takes time proportional to n log n will become slower faster as the size of the input grows than an algorithm that takes time proportional to n, n / log n, or n - log n.
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Pls help I need this quick thx :D
The steps followed by Nikki are correct. Hence, option 1 is the correct answer.
How to construct parallel line to a given line and passing through a given point?Using a ruler and compass, perform the following procedures to create a line from an exterior point that is parallel to the other line:
Given: A point P that sits outside of line segment AB and line segment AB
to create a line that runs through point P and is parallel to line AB.
Select any point X and connect it to point P on the line segment AB.
Draw an arc with X as the center and any reasonable radius, cutting the line segments PX and AB at points M and N, respectively.
Draw an arc EF with P as the center and the same radius as in the previous step, cutting the line segment PX at point Q.
Draw an arc with Q as the center and the same radius as previously, cutting the arc EF at R.
To create the line segment CD, join R and P.
The necessary parallel to the line segment AB that goes through the point P is the line segment CD.
According to the steps of construction we determine that the steps of construction of Nikki are correct.
Hence, option 1 is the correct answer.
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why is the cutting edge of the knife made very thin ?
Due to the edge's significantly smaller surface area and increased pressure, it is simpler to force your palm through. You don't need to move the butter around as much because the edge is narrower.
What does a knife's cutting edge look like?The blade's edge is its cutting edge. It stretches all the way from the knife's tip to its heel. Heel: Opposite the tip, the heel is the back portion of the edge.
A knife's edge is how thick?Knives should have a thickness of between.013" and.25" to be considered optimum. Kitchen knives are typically slimmer, whereas survival blades are typically thicker.
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The two triangles are similar.
What is the value of x?
The value of x for the similar triangles is equal to 7.
How to calculate for x for the similar trianglesWe have the triangles to be similar, this implies that the length 2x - 2 of the smaller triangle is similar to the length 3x of the larger triangle
and the length 8 of the smaller triangle is similar to the length 6+8 = 14 of the larger triangle
so;
(2x - 2)/3x = 8/14
14(2x - 2) = 8 × 3x {cross multiplication}
28x - 28 = 24x
28x - 24x= 28 {collect like terms}
4x = 28
x = 28/4 {divide through by 4}
x = 7.
Therefore, the value of x for the similar triangles is equal to 7.
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Mr. Abott washed 3 8 of his laundry. His son washed 1 3 of it. Who washed more laundry? How much of the laundry still needs to be washed?
Combine the like terms to create an equivalent expression. 9+a−5b−2
Rewrite vertex form y = 3(x + 5)2 − 11 into standard form.
The standard form is y= 3x^2+114+30x.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given;
y = 3(x + 5)^2 − 11
y= 3(x^2+25+10x)-11
y= 3x^2+125+30x-11
y= 3x^2+114+30x
Therefore, the equation will be y= 3x^2+114+30x
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What percent is modeled by the grid? A grid model with 100 squares. 33What percent is modeled by the grid? A grid model with 100 squares. 33 squares are shaded. 23% 30% 33% 40% squares are shaded. 23% 30% 33% 40%
Answer:
33%
Step-by-step explanation:
There are 33 squares out of 100 that are shaded
33/100
Percent means out of 100
33%
Or
A ratio that compares a number to 100 can be written as a percent. So in this problem, since the figure has 33 out of 100 boxes shaded, we have the ratio 33/100 which can be written as 33%.
prove that 32^5-16^5+2^19 is divisible by 63
Answer:
see below
Step-by-step explanation:
32^5 - 16^5 +2^19 = (2*16)^5 - 16^5 +2^19
= 2^5 *16 ^ 5 - 16^5+ 2^19
=32* 16 ^ 5 - 16 ^ 5 + 2^19
=31 * 16^5 + 2^19
=31 *2 ^(4*5) + 2^19
= 31 *2^20 + 2^19
= 62 *2^19 + 2^19
=63*2^19
so it's dvisible by 63
I'm fifty years old it's a discreet or continuous variable justify the answer
I'm fifty years old the sentence is a discrete variable and not continuous variable as age is counted in concrete numbers and it does not involve complex numbers.
What is discrete and continuous data?Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted. Complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.
Numerical information that is continuous refers to the unspecified number of measurements that could be made between two realistic sites.
Despite the fact that these numbers are frequently gathered via accurate measurements, they are not necessarily neat and orderly as those in discrete data. Measuring a specific issue repeatedly enables us to establish a defined range, within which we can predictably gather more data.
I'm fifty years old the sentence is a discrete variable as age is counted in concrete numbers and it does not involve complex numbers.
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what is the index notation of 4*4
Answer:
The index notation of 4^4 (4 raised to the power of 4) is written as 4^4 = 256.
Step-by-step explanation:
In mathematics, an exponent is a symbol indicating the number of times a quantity is multiplied by itself. In index notation, the number being raised to a power is written as the base and the power it's being raised to is written in superscript. So, in this case, 4 is being raised to the power of 4, which means 4 is being multiplied by itself 4 times. So, 4 * 4 * 4 * 4 = 256.
fill in the blank. ___ refers to whether or not an estimator tends to overestimate or underestimate a parameter. refers to how much the estimate varies from sample to sample.
Bias refers to whether an estimator tends to overestimate or underestimate a parameter, while variance refers to how much the estimate varies from sample to sample.
Bias is a measure of the difference between an estimator's expected value and the true value of the parameter being estimated. An estimator is said to be biased if it systematically overestimates or underestimates the parameter. Variance is a measure of how much the estimate of the parameter varies from sample to sample. High variance implies that the estimator is not consistent and can be unreliable. Low variance implies that the estimator is consistent and reliable. Therefore, it is important to consider both bias and variance when assessing the quality of an estimator. Bias and variance work together to form the overall accuracy of an estimator, and so it is important to consider both when evaluating the performance of an estimator.
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find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x= 1+4t-t^2, y= 2-t^3 at t=1. dy/dx = -3/2 at t=1. where do i go from here?
The equation of the tangent to the curve at the point corresponding to the given value of the parameter is y= (-3/2)x + 7
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
find value of x and y :
x= 1+4t-t²
Substitute t=1
x= 1+4(1)-1² =1+4-1 = 4
y= 2-t³
Substitute t=1
y= 2-1³ = 2-1 = 1
Given slope, m= -3/2
point slope form of line :
y-y1=m(x-x1)
y-1=-3/2(x-4)
=>2(y-1) = -3(x-4)
=> 2y-2 = -3x+12
=> 2y = -3x+12 + 2
=> 2y = -3x+14
=> y= (-3/2)x + 7
The equation of the tangent to the curve at the point corresponding to the given value of the parameter is y= (-3/2)x + 7
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The equation of the tangent to the curve at the point corresponding to the given value of the parameter is y= (-3/2)x + 7
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
find value of x and y :
x= 1+4t-t²
Substitute t=1
x= 1+4(1)-1² =1+4-1 = 4
y= 2-t³
Substitute t=1
y= 2-1³ = 2-1 = 1
Given slope, m= -3/2
point slope form of line :
y-y1=m(x-x1)
y-1=-3/2(x-4)
=>2(y-1) = -3(x-4)
=> 2y-2 = -3x+12
=> 2y = -3x+12 + 2
=> 2y = -3x+14
=> y= (-3/2)x + 7
The equation of the tangent to the curve at the point corresponding to the given value of the parameter is y= (-3/2)x + 7
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13. Kenny sets up his own waving business. He charges $2 each time he waves graciously at someone, and $3 each time he waves vigorously with zeal. Smiles cost extra. All the waving causes tendonitis in his elbow and he must pay a $150 bill for his doctor's visit. If he completed 125 gracious waves and 300 10 vigorous waves, how much money did he make?
Answer: Kenny made 125 * $2 = $250 from 125 gracious waves.
He made 300 * $3 = $900 from 300 vigorous waves.
So, he made a total of $250 + $900 = $1150.
After paying the doctor bill, he has $1150 - $150 = $1000 left.
Step-by-step explanation:
The amount of money that Kenny made after completing the number of gracious waves and vigorous waves would be = $1000.
How to calculate the total amount of money made by Kenny?The amount that Kenny charges for gracious waves= $2
The amount of money that he charges for vigorous wave = $3.
The total number of completed gracious waves = 125
The amount made for gracious waves = 2× 125 = $250
The total number of completed vigorous waves = 300
The amount made for vigorous waves = 3×300 = $900
The total amount made in both waves = 250+900= $1,150
The bill to be payed to doctor = $150
The amount left = 1,150- 150 = $ 1000
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Reflect the point in the x-axis followed by the y-axis
Please do graph too ty.
Answer:
A(-3, 4) reflected across x-axis ==> A'(-3, -4)
A'(-3, -4) reflected across y-axis ==> A"(3, -4)
Graph attached
Step-by-step explanation:
The point is (-3, 4) shown as point A on attached graph
When reflected across the x-axis to point A' the x-coordinate does not change but the y-coordinate is the negative of the original y-coordinate
Therefore A (-3, 4) ⇒ A' (-3, -4)
When A' is reflected across the y-axis to A" the x-coordinates change sign but y-coordinates stay unchanged
A'(-3, -4) ⇒ A" (3, -4)
So the final point is A"(3, -4)
To help restart the economy growth, government is offering simple interest loans to small business at a rate 1.5%.
Say, you obtain one of these loans of $90,000 for 5 years. Determine the amount of money you must repay the government after 5 years.
Answer:
96750
Step-by-step explanation:
s.i=p×r×t
=90000×5×15/10 all divided by 100
9000×5×15 divided by 100
=90×5×15
=6750
amount=s.i+principal
=6750+90000
=96750
∠A=8x+74
∘
start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 8, x, plus, 74, degrees, end color #11accd
∠
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=
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6
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∠B=2x+56
∘
start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, 2, x, plus, 56, degrees, end color #28ae7b
Encuentra el valor de
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∠
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∠Bstart color #1fab54, angle, B, end color #1fab54:
what do you mean by
∠B=2x+56
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Encuentra el valor de
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∠Bstart color #1fab54, angle, B, end color #1fab54:
let xy be the last two digits of your id number. find the rfc with number 6601 xy (i.e., if your id number is 001234567, the rfc number is 6601 67
The 13-digit RFC number is composed of the prefix (6601), the date of birth (XY), and the homoclave (calculated using the 10-digit RFC).
The RFC (Registro Federal de Contribuyentes) number is a unique identifier that is assigned to taxpayers in Mexico. The 13-digit RFC number is composed of several components. The first four digits, "6601," are the fixed prefix assigned to all Mexican taxpayers. The next six digits represent the date of birth of the taxpayer, in the format of "YYMMDD," so the last two digits of your ID number (XY) would represent the day of birth. The last three digits are a homoclave, a three-digit code that is assigned based on an algorithm and a verification digit. The calculation for the homoclave starts with the concatenation of the first ten digits of the RFC and then applying the following formula:
(11-(∑(D1x4 + D2x3 + D3x2 + D4x7 + D5x6 + D6x5 + D7x4 + D8x3 + D9x2))mod11)mod10
where D1-D9 are the first nine digits of the RFC. The result of the formula is the last three digits of the RFC, the homoclave. In summary, the 13-digit RFC number is composed of the prefix (6601), the date of birth (XY), and the homoclave (calculated using the 10-digit RFC).
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ANSWER ASAP IM BEGGING BRO
Part A: slope = 1
Part B: slope = 1
Part C: Slope values becomes equal.
What is slope?Slope, An evaluation of a line's inclination with respect to the horizontal using numbers. The slope of any line, ray, or line segment in analytical geometry is defined as the proportion of the vertically to the horizontally distance between the two points on the line ("slope equals rise over run").
As we know,
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Part A:
(x₁ , y₁) = (0, -4)
(x₂, y₂) = (-2, 2)
m = (2 - 4) / (-2 - 0)
m = -2 / -2
m = 1
Part B:
(x₁ , y₁) = (0, -4)
(x₂, y₂) = (-4, 1)
m = (-4 - 0) / ((-4 - 0)
m = -4 / -4
m = 1
Part C:
As we pick different points to calculate slope for Part A and Part B, conclude that slope values are equal. It means that lines are parallel to each other and they have different y-intercepts.
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A container holds 6 pounds of peanuts. How many ounces of peanuts are in the container? (1 pound = 16 ounces)
12 ounces
16 ounces
54 ounces
96 ounces
Step-by-step explanation:
Good Afternoon! Your Answer would be 96!
16 x 6 = 96
How do we find this answer?
16 + 16 = 32
And 32 would be 16 twice!
32 + 32 = 64
And 64 would be 16 four times!
So now time to get the answer, 64 + 32 = 96.
Have An Amazing day.
what percent is represented by the region that is shaded?
the answer is not 333% or 333.33% or 333.3%
466.66%? Theres four whole circles and one that is two thirds. Unless 466.66% is correct, can you give more info?
If the interval size is decreased from $200 to $100, which of the following must remain the same on the newhistogram?a) The height of the bars will decrease.b) The total number of bars will decrease. c) The width of the bars will increase. d) Each bar will represent more data items than before.
If the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.
How is this determined?The height of the bars will decrease if the interval sizes in a histogram are reduced while the scale remains constant. When the intervals are compressed,
For a particular set of data, there will be more histogram bars, but fewer data points will make up each interval. Reducing the interval size will also reduce the height of the histogram's bars because the height of the bars represents the number of items in each interval.
Hence, if the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.
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In the figure below, the segments AB and AC are tangent to the circle centered at O. Given that AC=9 and OA= 10.6, find OB.
6.1 is the value of OC in right triangle .
What is a right-angle triangle, exactly?
Any angle that is a right angle or has one of its internal angles equal to 90 degrees is considered to be in a right-angled triangle.
In light of this, this triangle is sometimes referred to as the right triangle or the 90-degree triangle.
Triangles AOB and AOC are right triangles
In the right triangle AOC
OC = OB
OA² = OC² + AC²
10.9² = OC² + 9²
OC² = 118.81 - 91
= 37.81
OC = 6.1
OB = OC = 6.1
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Is the ordered pair (4,1) a solution of the system of linear equations:
-x + y = -3
x + 3y = 6
a. yes
b. no
Answer:
no
Step-by-step explanation:
-x+y=-3
-4+1=-3
which is correct
x+3y=6
4+3×1=6
4+3=6
which is incorrect because 4+3=7
What is the range of the data set?
Work Shown:
range = max - min
range = 44 - 33
range = 11
The range is one way to measure how spread out the data set is.
An investor has two bonds in his portfolio. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity equal to 8.2%. One bond, Bond C, pays an annual coupon of 10%; the other bond, Bond Z, is a zero coupon bond. Assuming that the yield to maturity of each bond remains at 8.2% over the next 4 years, what will be the price of each of the bonds at the following time periods? Assume time 0 is today. Fill in the following table. Round your answers to the nearest cent.
T Price of Bond C Price of Bond Z
0 $
$
1
2
3
4
Answer:
Step-by-step explanation:
The price of Bond C at time t can be calculated using the formula:
P_C = (C / (1 + r)^t) + (F / (1 + r)^(n))
where C is the coupon payment, r is the yield to maturity, t is the time period, n is the number of years until maturity, and F is the face value.
Similarly, the price of Bond Z at time t can be calculated using the formula:
P_Z = F / (1 + r)^(n + t)
Substituting the values:
C = 100 (10% of $1,000)
r = 0.082
n = 4
F = $1,000
T Price of Bond C Price of Bond Z
0 $1,000 $1,000
1 $1,082 $961.67
2 $1,167.24 $926.58
3 $1,259.51 $893.63
4 $1,360.29 $862.54
The prices are rounded to the nearest cent.
Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem?a. 10X1+5X2−2X3≥20b. X1−2X22≤100c. 5X1+3≥25d. X1+0.5X2≤30e. 6X1+2X2∗X3≥10
The constraints that are not linear or cannot be included as a constraint in a linear programming problem are b. X1−2X2²≤100.
What is linear constraint?A linear constraint in linear programming occurs when linear components are added or subtracted and the resulting expression must either rise, decrease, or be exactly equal to a right-hand side value.
A constraint is referred to as linear if all of its terms are of the first order.
We know that the degree of the linear constraint is one, hence the constraint that does not have a degree of one is not a linear constraint.
Thus, option b X1−2X2²≤100 has a degree of two and it cannot be used as constraint in a linear programming problem.
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50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 which of the following histograms is the best representation of the data?
The best way to represent histograms is by decreasing to increasing order.
The mean is the arithmetic mean and is calculated by adding a group of numbers and dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
Given the values:
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45
We have that:
(22+24+28+28+30+31+31+32+32+35+36+37+38+41+42+42+44+44+45+46+46+47+47+49+50)/25=37.88.
The average age that a large construction company wants to know is 38.
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I need to proportion and what theorem it is please help
The missing side is AJ and the theorem is, the ratio of corresponding sides of a similar triangle are equal
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
The corresponding sides are FJ , AJ and CF and AC
The ratio of these corresponding sides are equal. i.e
FJ/AJ = CF/AC
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Angles BAE and FAC are straight angles. What angle relationship best describes angles BAC and EAF?
Adjacent angles
Complementary angles
Supplementary angles
Vertical angles
Answer: Vertical Angles
Step-by-step explanation:
Took The test!
Angles BAC and EAF are vertically opposite angles .
Given,
Angles BAE and FAC are straight angles.
Here,
∠BAC + ∠FAC = 180° (Linear pair angles).
Now ,
∠BAC and ∠EFA are vertically opposite to each other .
Thus,
∠BAC = ∠EFA.
Thus these angles are vertically opposite angles and are equal .
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a) The biologists who collected the flower length data compared the two varieties using statistical methods based on the mean and standard deviation. Find the mean and standard deviation for each flower variety. Do this by hand, using a calculator (do not use Stata). You may check your answer afterwards by putting the data into Stata and using the summarize function if you wish.
b) Many standard statistical methods that you will study in this course are intended for use with distributions that are fairly symmetric and have no outliers. Do the distributions appear suitable for use of the mean and standard deviation as summaries?
The answer is:
a) The following formula must be used to get the mean and standard deviation for each flower variety:
Mean is the average of all values (number of values)
Sqrt((sum of squared deviations from the mean) / (number of values - 1)) is a formula for calculating standard deviation.
We have the following information on the first variety:
6.2, 6.3, 5.8, 6.4, 6.0, 6.9, 6.7, 6.1, 6.5, 6.4
Mean = (6.2 + 6.3 + 5.8 + 6.4 + 6.0 + 6.9 + 6.7 + 6.1 + 6.5 + 6.4) / 10 = 6.35
To find the deviations from the mean for each number, we must first compute the standard deviation:6.2 - 6.35 = -0.15
6.3 - 6.35 = -0.05
5.8 - 6.35 = -0.55
6.4 - 6.35 = 6.2 - 6.35 = -0.15
6.3 - 6.35 = -0.05
5.8 - 6.35 = -0.55
6.4 - 6.35 = 0.05
6.0 - 6.35 = -0.35
6.9 - 6.35 = 0.55
6.7 - 6.35 = 0.35
6.5 - 6.35 = 0.15
6.4 - 6.35 = 0.05
We now square each deviance and add them all up:
[tex]((-0.15)^2 + (-0.05)^2 + (-0.55)^2 + (0.05)^2 + (-0.35)^2 + (0.55)^2 + (0.35)^2 + (-0.25)^2 + (0.15)^2 + (0.05)^2) = 1.15[/tex]
The square root is then calculated by dividing the number of values by the number minus one:
Sqrt(1.15 / 9) 0.38 is the standard deviation.
As a result, for the first flower variety, the mean and standard deviation are 6.35 and 0.38, respectively.
b) We have the following information for the second variety: 5.1, 5.4, 5.1, 5.8, 5.0, 5.6, 5.7, 5.3, 5.5, 5.2
Mean = (5.1 + 5.4 + 5.1 + 5.8 + 5.0 + 5.6 + 5.7 + 5.3 + 5.5 + 5.2) / 10 = 5.43
To find the deviations from the mean for each number, we must first compute the standard deviation:
5.1 - 5.43 = -0.33
5.4 - 5.43 = 0.03
5.1 - 5.43 = -0.33s
5.8 - 5.43 = 0.37
5.0 - 5.43 = -0.43
5.6 - 5.43 = 0.17
5.7 - 5.43 = 0.27
5.3 - 5.43 = -0.13
5.5 - 5.43 = 0.07
5.2 - 5.43 = -0.
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