The exponential function that models the population of bluefin tuna after x years is given as follows:
y = 1550(0.96)^x.
The parameters of the exponential function are given as follows:
a = 1550.b = 0.96.How to define the exponential function?An exponential function is defined as follows:
y = a(b)^x.
For which the parameters are given as follows:
a is the initial value.b is the rate of change.When he first started monitoring the population, there were about 1,550 bluefin tuna in the bay, meaning that the parameter a is given as follows:
a = 1550.
One year later, he estimated that the population of bluefin tuna had decreased to about 1,488, hence the parameter b is obtained as follows:
b = 1488/1550 = 0.96.
Hence the function is defined as follows:
y = 1550(0.96)^x.
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Describe a sequence of transformation that maps triangle DOG onto triangle CAT
The transformation of the function is given by reflection along y axis and a translation of 5 units up
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the transformation be represented as A
Now , the equation will be
Let the triangle be represented as ΔODG
Now , the coordinates of ΔODG is
O = O ( -1 , -2 )
D = D ( -5 , -3 )
G = G ( -2 , -4 )
Now , the transformed triangle is ΔACT
The coordinates of ΔACT is
A = A ( 1 , 3 )
C = C ( 5 , 2 )
T = T ( 2 , 1 )
Now , on reflecting the triangle ΔODG along y axis , we get
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse
So , the coordinates of triangle O'D'G' , we get
O' = O' ( 1 , -2 )
D' = D' ( 5 , -3 )
G = G' ( 2 , -4 )
Now , translating the triangle ΔO'D'G' up by 5 units , we get
The y coordinate of the triangle gets incremented by 5
So ,
A = O' ( 1 , -2 + 5 )
C = C ( 5 , -3 + 5 )
T = T ( 2 , -4 + 5 )
And , the coordinates of the triangle ΔACT is
A = A ( 1 , 3 )
C = C ( 5 , 2 )
T = T ( 2 , 1 )
Hence , the transformation is reflection along y axis and followed by translation of 5 units up
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Identify all of the necessary assumptions for a significance test for comparing dependent means.
>Categorical Data
>At least 15 successes and 15 failures in both groups
>Quantitative Data
>Random Samples or Random application of treatments
>n is greater than or equal to 30 OR Population of Differences could be Normally distributed.
>Both sample sizes are greater than 30 or Both population distributions could be Normally Distributed
The correct answer will be:
Quantitative data, both sample sizes are greater than 30 or Both population distributions could be Normally Distributed, Random Samples or Random application of treatments
There should be just one group for each subject. The observations in each category are unrelated to one another. There were no notable outliers in any category.
The following are the presumptions for a percentage significance test: Data come from a random sample [Sample is large enough, which is presumed to be true when. It should be noted that both quantitative and categorical data can be subjected to a significance test for a proportion.
Most parametric tests begin with the underlying presumption of population distribution. The ratio scale or interval scale measurements, easy random extraction, normal distribution of the data, a sufficient sample size, and homogeneity of variance are all prerequisites for performing the t-test.
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A bottle of water is 2/3 full. You drink 1/2 of the water. find the portion of the bottle of water that you drink.
Hannah either walks or cycles to school. The probability that she walks to school is 0.75 If she walks, the probability that she is late is 0.6 If she cycles, the probability that she is late is 0.2 Work out the probability that on any one day Hannah will not be late for school.
If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.
If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.
0.48 + 0.3 = 0.78.
In other words, there is a 78% probability of her not being late.
Need Help! How would I complete this table?
The number of feet is dependent on the number of yards. The table is completed as shown in the attachment.
Dependent variable.A variable whose value can be determined only if another variable's value is known is called a dependent variable. Thus the value of the variable depends on another variable.
In the given question, the number of feet can be known when that of yards is multiplied by a multiplicative factor. The value of the factor can be determined as;
multiplicative factor = 15/ 5
= 3
So that feet is related to that of yards by this expression;
feet = multiplicative factor * yards
Thus,
when yards is 2, then;
feet = 3 * 2
= 6
when feet = 12
12 = 3 * yards
yards = 12/ 3
= 4
Thus the complete table is herewith attached to this answer for more clarifications.
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HELP!!! Find the inverse of the matrix..
Answer:
The matrix does not have an inverse (D)
Step-by-step explanation:
The matrix is singular, therefore doesn't have an inverse
What is the degree of the polynomial 7x 2y 3z 4?
The degree of a polynomial is the highest power of each variable in the equation. In the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Therefore, the degree of this polynomial is 8.
1. Identify the highest power of each variable.
For 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z.
2. Add the highest powers of each variable.
2 + 3 + 4 = 9
3. Subtract 1 from the sum.
9 - 1 = 8
4. The degree of the polynomial is the result of the subtraction.
Therefore, the degree of the polynomial 7x2y3z4 is 8.
The degree of a polynomial is the highest power of each variable in the equation. To calculate the degree of a polynomial, you must identify the highest power of each variable and add them together. Then, subtract 1 from the sum to get the degree of the polynomial. For example, in the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Adding these powers together gives us 9. Subtracting 1 from this sum gives us 8, which is the degree of the polynomial. Therefore, the degree of the polynomial 7x2y3z4 is 8.
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Deshad runs a river tubing company that serves 300 customers a day during sunny, summer days. He knows that 45% of the customers rent life jackets. Suppose that Deshad calculates the daily proportion p ^ on top of customers who rent life jackets from his sample of 300. We can assume the customers each day represent a random sample
Here acccording to the question,We are examining the conditions under which the sampling distributions of the sample proportions given.
What is sampling distribution?
Sampling distribution is a statistic that determines the probability of an event based on data from a small group within a large population. Its primary purpose is to establish representative results of small samples of a comparatively larger population. Since the population is too large to analyze, you can select a smaller group and repeatedly sample or analyze them. The gathered data, or statistic, is used to calculate the likely occurrence, or probability, of an event.
Sampling distribution According to the given ScenarioWe are examining the conditions under which the sampling distributions of the sample proportions appear uniform, roughly normal, skewed to the left or skewed to the right.
When np10 and n(1p)10, where n is the sample size and p is the sample of proportions, are true, we know that the sampling proportions of the sample distributions will have a normal shape.
Aforementioned that our sample size is 300 people and that p = 0.45, we can use the given data to calculate
Successes anticipated: np= 300(0.45) = 135 10
Failures predicted: n(1p)=300 (10.45)=165 10
Since both of these statements are accurate, sample distribution sampling proportions will have a normal shape.
Because we anticipate each sample to have at least 10 successes and 10 failures, we have a normal sampling distribution.
As a result, the sample distribution has a roughly normal shape.
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Select ALL the correct answers.
For AABC, which two relationships are true?
0
0
sin (0) = AE =
cos (0)
cos (8) = A
cos (6)
cos (6)
ACC = sin (90 - 0)
sin (90 - 0)
sin (0)
cos (906)
cos (90 - 0)
=
=
BOCC
sin
(0) = C
sin (0) = A
=
=
=
=
B
(90-8)
Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 - ∅), and cos = AB/AC = sin(90 - ∅).
Describe the trigonometric function.The right triangle's angle serves as the domain input value for the six basic trigonometric operations, which produce a range of numbers as their results.Understanding the trigonometric functions of the four quadrants' graphs, domains, differentiation, and integration will be achievable.
Here,
Sinx = perp./hypo.
Cosx equals base/hypo.
So,
Sin = B/C
A= cos(90 -∅ ) = BC/AC
So,
Cos(90 -∅ ) = Sin(BC/AC)
And,
cos = AC/AB
AB/AC = sin(90 -∅ )
So,
cos AB/AC = sin (90 -∅ )
Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 -∅ ), and cos = AB/AC = sin(90 - ∅).
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Olivia owns a pastry shop, and needs to fill an order for 700 cupcakes
She already has 15 cupcakes made, and she can make 137 cupcakes
hour. How many hours does Olivia need to fill the order?
Olivia needs
more hours.
Answer:
5 hours
Step-by-step explanation:
Olivia needs to make 700 - 15 = <<700-15=685>>685 cupcakes.
So she needs to work for 685 / 137 = <<685/137=5>>5 hours
A linear function is shown on the graph.
A linear function beginning with open circle at negative 3 comma negative 5 and ending with an open circle at 3 comma 7.
What is the domain of the function?
{y | −5 ≤ y ≤ 7}
{y | −5 < y < 7}
{x | −3 ≤ x ≤ 3}
{x | −3 < x < 3}
Answer: D
Step-by-step explanation:
In this problem, we are asked to find the domain of the function. Domain is finding the interval of the function of the x value.
Since we are finding domain, we can eliminate A and B because those are looking at y interval, or range.
This leaves us with C and D. They are almost the same except for the ≤ in C and < in D. The difference between ≤ and < is the fact that ≤ includes and touches the point, and < doesn't.
The function has open circles at x=-3 and x=3. That means they don't touch and include x=-3 and x=3. The function only get's really close to those points, but not include them. This tells us that D is the answer.
The domain of the function is {x | −3 < x < 3}. Thus, Option D holds the truth.
The domain of a function refers to the interval of the x values of the function.
In this case, we are asked to find the domain of a linear function that is shown on a graph. The graph starts at an open circle at negative 3, negative 5 and ends at an open circle at 3, 7.
To find the domain, we need to look at the x interval of the function. Options A and B refer to the y interval or range and can be eliminated.
The remaining options, C and D, are similar, except for the fact that C includes and touches the point with "≤", while D doesn't with "<". The open circles at x=-3 and x=3 indicate that the function only gets close to these points, but does not include or touch them.
Thus, the correct answer is option D, {x | −3 < x < 3}.
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Hello good morning do anyone think they could help please
Answer:2
Step-by-step explanation:
A triangle has sides with lengths of 12 feet, 16 feet, and 18 feet. Is it a right triangle?
Answer:
Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.
Answer:
No, it is not a right triangle.
Step-by-step explanation:
Right triangle fulfill the pythagorean theorem:
[tex]a^2+ b^2 = c^2[/tex]
Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.
[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 25, 150, 900, ... Find the 9th term.
Answer:80
Step-by-step explanation:by5 will be this and 20 by 10 mulltiply 60 by 9
Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.
What is the approximate average fuel consumption rate, between the 100th kilometer and 400th kilometer?
Between the 100th and 400th kilometers, the average fuel consumption rate is 5/6 liters per kilometer.
What is the rate of change?A consequence of dividing the variation in a variable's function by the variation in the variable. For example The rate at which a distance changes in relation to time is known as velocity.
Given, Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.
Since in the domain [100, 400] graph shows somewhat linear properties.
from the graph Fuel consumption at 100 = 375 liters
Fuel consumption at 400 = 125 liters
rate in a linear function between two points = (y₂ - y₁)/ (x₂ - x₁)
thus rate between [100, 400] = (375-125)/400-100
rate between [100, 400] = 250/300
rate between [100, 400] = 5/6litere per kilometer
therefore, the average fuel consumption rate, between the 100th kilometer and 400th kilometer is 5/6 liters per kilometer.
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In our class there are 40 boys. 22 students are girls write a ratio comparing girls to boys
Answer:
Its 22:40
Step-by-step explanation:
Answer: 22:40
Pretty simple
Step-by-step explanation:
Can you help me with this
==========================================================
Explanation:
Pick any two points on the line to apply the slope formula.
I'll select (-5,1) and (5,-1)
[tex](x_1,y_1) = (-5,1) \text{ and } (x_2,y_2) = (5,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - 1}{5 - (-5)}\\\\m = \frac{-1 - 1}{5 + 5}\\\\m = \frac{-2}{10}\\\\m = -\frac{1}{5}\\\\[/tex]
The slope as a fraction is -1/5
A slope of -1/5 means " go down 1, then to the right 5 units".
An example of this motion is when going from (-5,1) to (0,0)
Another example would be going from (0,0) to (5,-1)
----------
The "down 1, right 5" motion is because
slope = rise/run = -1/5rise = -1 = go down 1run = 5 = go to the right 5Jim and Tim share money in the ratio 6:1 if Tim gets 54 how much does Jim get
The amount of money owned by JIm is $9
How to determine the amount owned by JImFrom the question, we have the following parameters that can be used in our computation:
The ratio of the amount owned by Tim tohe ratio of the amount owned by Jim is 6 : 1
This means that
Tim : Jim = 6 : 1
Also from the question, we have
Tim gets $54
This means that
Tim = 54
Substitute the known values in the above equation, so, we have the following representation
54 : Jim = 6 : 1
Multiply by 9
54 : Jim = 54 : 9
So, we have
Jim = 9
Hence, the amount is $9
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Item 4 Greg has a piece of rope 18 ft long. He wants to cut it into two pieces so that the longer piece is 2 ft less than 3 times the length of the shorter piece. How long will each piece of rope be
The length of the shortest piece is 5, and the longest piece is 13 feet by solving the equations.
The length of the shortest piece is 5, and the longest piece is 13 feet.
the solution is as follows,
Greg has a piece of rope that is 18 ft long.
He wants to cut it into two pieces so that the longer piece is 2 ft less than three times the length of the.
Let the length of the shorter piece be x.
And the length of the longer piece is 3x -2.
Greg has a piece of rope that is 18 ft long.
Then,
longest piece+ shorter piece = 18
x + 3x -2 = 18
4x - 2 =18
4x = 18+2
4x = 20
x= 20/4
x = 5.
Therefore,
The length of the shorter piece is x =5.
And the length of the longer piece = 3x -2 = 3(5)-2 = 15-2 = 13
Hence, the length of the shortest piece is 5, and the longest piece is 13 feet.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)
How to determine the correct representationsFrom the question, we have the following expression that can be used in our computation:
–3(2x – 5) < 5(2 – x)
Divide bot sides of the inequality by -1
So, we have the following representation
3(2x – 5) > -5(2 – x)
Next, we open the brackets
This gives
6x – 15 > -10 + 5x
Hence, the representation is 6x – 15 > -10 + 5x
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Complete question
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
(a) 6x – 15 > -10 + 5x
(b) 6x – 15 < -10 + 5x
(c) 3(2x – 5) > -5(2 – x)
(d) 3(2x – 5) < -5(2 – x)
Factor expression 12p-28 factored using GCF is?
Answer:
4(3p - 7)
Step-by-step explanation:
First find the factors of 12 and 28:
12: 1, 2, 3, 4, 6, 12
28: 1, 2, 4, 7, 28
Notice any common factors: 1, 2, 4
Now, out of these factors, 4 is the GCF since it is the greatest common factor, so divide 12 and 28 by 4:
12/4 = 3. 28/4 = 7.
Hence, 12p-28 = 4(3p - 7)
which answer is this
A.43
B.38
C.61
D.81
How do you know if its linear or linear?
Linear equations are equations that can be written in the form ax + b = c, where a, b, and c are real numbers and a ≠ 0.
The equation can be solved for the variable x by subtracting b from both sides and then dividing both sides by a. This will give the solution for x, which is x = (c - b) / a.
For example, consider the equation 2x + 4 = 10. This is a linear equation since it can be written in the form ax + b = c, where a = 2, b = 4, and c = 10. To solve for x, subtract b from both sides to get 2x = 6, and then divide both sides by a to get x = 3. Therefore, the solution to the equation is x = 3.
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I NEED ANSWERS ASAP!!!!!!!!!!!
If WY is 4. 6, what is MZ? Round your
answer to the nearest tenth. Write NA if there
is not enough information given.
NA (There is not enough information given to determine the value of MZ)
In this question, we are given that WY is 4.6 for us to find the value of MZ We need more information to be in a position to answer this. More information includes maybe we know the value of M or at least having some relationship between WY and MZ for us to draw a conclusion and come up with the value of MZ. If at all we had a common value in WY and MZ say M then it could be easier to come to a conclusion and finally get the value of MZ.
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Write an equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5).
y =
The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5) is 2x+y = -2.
The line between these locations' slopes must equal the negative reciprocal of the bisector's slope. It must go through the segment midway.
The slope of the line through the given points :
m = (y2 -y1)/(x2 -x1) = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2
Then, The slope of the required bisector: m = -1/(1/2) = -2
The midpoint of the given segment:
((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)
Then the point-slope form of the equation of the bisector:
y -y1 = m(x -x1)
y -2 = -2(x -(-2))
y = -2x -4 +2
y = -2x -2 . . . . . . . slope-intercept form equation
2x +y = -2 . . . . . . .standard form equation
Thus, The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5) is 2x+y = -2.
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Identify the root of f(x)=-2(x+9)(x-1)
Answer:
(-9,0) and (1,0)
Step-by-step explanation:
Study the example showing a function. Then solve
problems 1-6.
Example
The table and graph show the
relationship between the length
of the sides of a square, in feet, and
the perimeter of the square in feet.
Side Length (input) 1 2 3 4 S
Perimeter (output) 4
812 16 20
The relationship is a function because
there is only one output value for
each input value.
Perimeter (output)
20
18
16
14
12
10
8
6
4
2
Perimeters of Squares
0 1 2 3 4 5 6 7 8 9
Side Length (input)
1 Describe the relationship between the input and output
values in the example.
2 Can you represent the function in the example with an
equation? If so, what equation can you write? If not,
why not?
Vocabulary
function a rule that
The relationship between the input and output is that the perimeter of a square is always equal to four times the length of one of its sides.
What is the perimeter of square?The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S
1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.
2.Yes, the function can be represented with an equation. The equation would be:
Perimeter = 4 × Side Length.
Side Length (input) 1 2 3 4 5
Perimeter (output) 4 8 12 16 20
This equation states that the perimeter of a square is equal to four times the length of one of its sides.
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Which expressions are equivalent to (1/3x+2x−5/3x)−(−1/3x+5) ?
Select all correct expressions.
Responses
−4x+5+3x
negative 4 x plus 5 plus 3 x
5−x
5 minus x
x−5
x minus 5
4x−5−3x
Answer:
Both x - 5, and 4x-5-3x are equivalent to (1/3x+2x−5/3x)−(−1/3x+5)
Step-by-step explanation:
Let's reorganize the given expression:
(1/3x+2x−5/3x)−(−1/3x+5)
1/3x+2x−5/3x + 1/3x-5 [Expand the parentheses]
2/3x+2x−5/3x -5 [Combine like terms]
-3/3x+2x -5
-x + 2x - 5
x - 5 One of the equivalent expressions
The option 4x-5-3x also reduces to x - 5
Jada earns $7 dollars per hour mowing her neighbors’ lawns. Name the two quantities in Jada’s situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works (independent variable) and the amount of money she earns (dependent variable).
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works and the amount of money she earns. The number of hours worked is the independent variable because it is the variable that affects the amount of money earned. The amount of money earned is the dependent variable because this is the variable that is dependent on the number of hours worked.If she works 8 hours, she would earn $56.Jada earns $7 per hour, so if she works 3 hours, she would earn
$21 (3 x 7 = 21).
If she works 5 hours, she would earn
$35 (5 x 7 = 35).
If she works 8 hours, she would earn
$56 (8 x 7 = 56).
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Complete the stemplot for the following data. 34 53 66 52 48 42 41 58 36 50 40 59 49 35 30 40 43 35 61 43 49 39 44 43 34 42 68 46 46 39 Enter the numbers for the last row. Do not enter commas or other symbols, just numbers.
The stem plot for the given data is 3 4 5 6.
A stem and leaf plot, also known as a stem and leaf diagram, is a technique to arrange data such that it is simple to see how frequently certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
Arranging the given data in ascending order,
30, 34, 34, 35, 35, 36, 39, 39, 40, 40, 41, 42, 42, 43, 43, 43, 44, 46, 46, 48, 49, 49, 50, 52, 53, 58, 59, 61, 66, 68
The stem plot = 3 4 5 6
Calculated Statistics:
Minimum:30
Maximum:68
Range:38
Count:30
Sum:1365
Mean:45.5
Median:43
Mode:43
Standard Deviation:9.616
Variance:92.47
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