Evaluate the following integral (Calculus 2) Please show step by step explanation!
Answers
Answer:
[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x=-\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
Using Integration by parts:
[tex]\textsf{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]
[tex]\textsf{Let }\dfrac{\text{d}v}{\text{d}x}=x^{-8} \implies v=-\dfrac{1}{7}x^{-8+1}=-\dfrac{1}{7}x^{-7}=-\dfrac{1}{7x^7}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x & = -\dfrac{1}{7x^7}\ln x- \int -\dfrac{1}{7x^7} \cdot \dfrac{1}{x}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7x^8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7}x^{-8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}-\dfrac{1}{7 \cdot 7}x^{-8+1}+\text{C}\\\\& = -\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $\ln x$}\\\\If $y=\ln x$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
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Substitute [tex]y=\ln(x) \iff e^y = x[/tex] and [tex]dy=\frac{dx}x[/tex] to get
[tex]\displaystyle \int \frac{\ln(x)}{x^8} \, dx = \int ye^{-7y} \, dy[/tex]
Integrate by parts with
[tex]u = y \implies du = dy[/tex]
[tex]dv = e^{-7y} \, dy \implies v = -\dfrac17 e^{-7y}[/tex]
Then
[tex]\displaystyle \int u\,dv = uv - \int v\,du \\\\ \implies \int y e^{-7y} \, dy = -\dfrac17 ye^{-7y} + \frac17 \int e^{-7y} \, dy + C \\\\ ~~~~~~~~~~~~ = -\frac17 ye^{-7y} - \frac1{49} e^{-7y} + C \\\\ ~~~~~~~~~~~~ = \boxed{-\frac{\ln(x)}{7x^7} - \frac1{49x^7} + C}[/tex]
Related Questions
A graph titled Speed as a Function of Time with horizontal axis time (seconds) and vertical axis speed (meters per second). A straight orange line labeled A starts at 0 seconds 4 meters per second and runs to 6 seconds 7 meters. A straight blue line labeled B starts at 0 seconds 4 meters and upward to 6 seconds 4 meters. A straight green line starts at 0 seconds 4 meters and runs to 4 seconds 0 meters.
Use the graph of speed versus time to answer the questions about acceleration.
Which of the cars is speeding up?
Which of the cars is slowing down?
Which of the cars is maintaining a constant speed?
Answers
From the attached speed versus time graph, it can be seen that the orange or first or car is speeding up. The third or green car is slowing down, and the blue or second car is maintaining a constant speed.
Speed Analysis from the Graph
The graph in the attachment shows the linear increase in speed of the first car over time. Therefore, we can say that it is accelerating at a certain rate.
The graph shows how the speed of the third car is decreasing with time. This demonstrates that the green vehicle is de-accelerating.
The graph shows a straight line for the second car. It displays that the speed does not alter as seconds or minutes pass. We might infer that the blue car is continuing to travel at its current pace as a result.
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Answer:
A C B
Step-by-step explanation:
Which of the cars is speeding up?
A
Which of the cars is slowing down?
C
Which of the cars is maintaining a constant speed?
B
The diameter of the wheel in wades el camino is 15 inches. If the wheel made 5 complete revaluations how far would the wheel have rolled? Round your answer to the nearest hundredth of an inch
Answers
Step-by-step explanation:
solution
here
15×5
=75inches
Identify if the question is
statistical or non statistical.
"How many students at your
school play soccer?"
Answers
Answer: Statistical
Step-by-step explanation:
I think its statistical because its quantitative data, meaning you can count it.
Determine the unknown length or angle measurement. Round each answer to the nearest whole number.
Answers
Answer:
a) 52
b)115
Step-by-step explanation:
Solid rock is an unlevered firm with an ebit of $10 million and an unlevered cost of capital of 12 percent. if the tax rate is 40 percent, what is the value of the firm?
Answers
The value of the firm is $50 million
How to determine the value of the firm?The given parameters are:
EBIT = $10 million
Tax Rate, Tc = 40%
Unlevered cost of capital, RU = 12%
The value of the firm is calculated as:
Value = EBIT*(1 - Tc)/Ru
This gives
Value = 10 million *(1 - 40%)/12%
Evaluate the expression
Value = 50 million
Hence, the value of the firm is $50 million
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Which is the inequality in factored form that represents the region greater than or equal to the quadratic function with zeros –3.5 and 11.5 and includes the point (8.5, –54) on the boundary?
Answers
The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).
What is the expression of the quadratic inequality?
Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic equation by solving this system of linear equations:
(x₁, y₁) = (- 3.5, 0)
12.25 · a - 3.5 · b + c = 0 (1)
(x₂, y₂) = (11.5, 0)
132.25 · a + 11.5 · b + c = 0 (2)
(x₃, y₃) = (8.5, - 54)
72.25 · a + 8.5 · b + c = - 54 (3)
The solution of the system is a = 3.6, b = - 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:
y ≥ 3.6 · (x² - 15 · x + 40.25)
y ≥ 3.6 · (x - 11.5) · (x + 3.5)
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Find tan 0 if csc 0 = -√5/2 is in the third quadrant.
A. 1/2
B.-2
C.-1/2
D. 2
Answers
Answer:
D. 2
Step-by-step explanation:
soh cah toa rule
sine equals opposite over hypotenuse,
cosine equals adjacent over hypotenuse, and
tangent equals opposite over adjacent
csc is 1/sin which is hypotenuse over opposite
if csc is -√5/2 then
hypotenuse is -√5
opposite is 2
3rd quadrant on a graph is bottom left
both x and y values are negative
hypotenuse means its a triangle
pythagorean theorem
a^2 + b^2 = c^2
a^2 + 2^2 = (-√5)^2
a^2 + 4 = 5
a = 1 = adjacent
tangent equals opposite over adjacent
tan is 2 / 1 which is 2
third quadrant means it's still positive
because tan is positive in quadrant 3
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Santaniago has a rope that measures 205.95 centimeters.write this number in expanded form
Answers
This number in expanded form 200 + 5 + 5/10 + 9/100 .
What is expanded form in math example?
It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. For example, the expanded form of the number 1572 is 1000+500+70+2.Given : 205.95 centimeters.
the number in a expanded form.
200 + 5 + 9/10 + 5/100
we have given 205.95 centimeters.
We can see 2 is at hundred place = 200.
0 is at tens place = 00.
5 is at ones place = 5.
9 after decimal is at tenth place = [tex]\frac{9}{10}[/tex].
5 is at hundredth place = [tex]\frac{5}{100}[/tex] .
Therefore , Expanded form : 200 + 5 + 5/10 + 9/100 .
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Classify the expression: 5x 2. linear expression quadratic expression cubic expression quartic expression
Answers
The given expression is a (A) linear expression.
What are linear expressions?A linear expression is an algebraic expression in which each term is a constant or a variable raised to the first power. To put it another way, none of the exponents may be greater than 1. x2 is a variable raised to the second power, whereas x is a variable raised to the first power. A constant is represented by the number 5.Reduce the equation as much as feasible to the form y = mx + b. Examine your equation for exponents. It is nonlinear if it has exponents. Your equation is linear if it contains no exponents.2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x - y + z = 3 are some instances of linear equations.Therefore, the given expression is a (A) linear expression.
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The correct question is given below:
Classify the expression: 5x 2.
(A) linear expression
(B) quadratic expression
(C) cubic expression
(D0 quartic expression
Jane has 8 toy cats and 4 baskets. If she wants to arrange 2 toy cats in each basket, how many different ways can she arrange the toy cats?
Answers
Step-by-step explanation:
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
The number of combinations of n objects taken r at a time is determined by the following formula:.
nCr = n! / (n-r)! r!
n = total number of objects in the set
r = number of choosing objects from the set
so here , Jane has 8 toys and first she wants to take 2 toys ....
so , 8C2 = 8! / 6! 2! = 28 ways
so , she selected 2 toys ,,, After she wants to take 2 toys among 6 toys ....
so , 6C2 = 6! / 4! 2! = 15
next , picking 2 toys out of 4
So , 4C2 = 4! / 2! 2! = 6
next , 2C2 = 2! / 0! 2! = 1
total ways to pick toys = 28 × 15 × 6 × 1
= 2520 different ways ..
request :- Sorry if there are some mistakes in my English.
Identify a possible explicit rule for the nth term of the sequence 2, 8, 26, 80, 242.
Answers
The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.
According to the given statement
we have to find the explicit rule for the nth term of the given sequence,.
So, For this purpose
The given sequence is :
2, 8, 26, 80, 242.
And according to the ap series formula
[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]
If we put the terms in it then we get the exact value as the value in the sequence.
So,
[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]
For [tex]a_{2}[/tex]
[tex]a_{2}[/tex] [tex]= a_{1} *3 +2[/tex]
[tex]a_{2}[/tex] [tex]= 2*3 + 2[/tex]
[tex]a_{2}[/tex] [tex]= 8[/tex]
and by this way we get all the values as same as the sequence.
So, The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.
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Which algebraic expression represents the following: the sum of four times a number and six? (1 point) 4x + 6
Answers
Answer:
4x +6
Step-by-step explanation:
No explanation
Straight answer
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The correct representation of the inequality is -6x + 15 < 10 - 5x and an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
What is inequality?In mathematical concept, an inequality is a representation of an order linking two numbers or algebraic expressions together. These orders are called inequality signs such as greater than (>), less than (<), greater than or equal to(≥), or less than or equal to(≤). Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.
From the given information, we are given the inequality:
= -3(2x - 5) < 5(2 -x)
Open brackets, we get:
= -6x + 15 < 10 - 5x
Subtract 15 from both sides, we have:
= -6x + 15 - 15 < 10 - 5x - 15
= -6x < -5x - 5
Add 5 to both sides
= -6x + 5 < -5x - 5 + 5
= -6x + 5 < -5x
= -x < - 5
= x < 5
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How many different 2-digit numbers are there with the following property:the tenth digit is greater than the units digit?
Answers
Answer:
45
Step-by-step explanation:
Simply start by listing out the numbers from smallest to largest.
We start out with the smallest number following this information being the number 10. The next are 21 and 20. The next are 32, 31, and 30. We can start to see a pattern. If the ten's digit is n, then there are n numbers within that ten-group that have a greater 10's digit than unit's digit. The largest ten-group (90 to 98) has 9 integers following the rules established. Thus, the number of 2-digit integers that have ten's digits greater than units digit is 1+2+3+...+9=45
The length of a rectangle is 5 mm longer than the width. If the area of the rectangle is 24 mm^2, what is the width of the rectangle?
Answers
Answer:
8
Step-by-step explanation:
This question is asking you to solve for the following system of equations, let x be width and y be height of the rectangle.
[tex]\left \{ {{x=y+5} \atop {x*y=24}} \right.[/tex]
Since the former is already equal to x lets set the second equation to x
[tex]x*y=24[/tex]
[tex]x=24/y[/tex]
Now we have the following system of equations:
[tex]\left \{ {{x=y+5} \atop {x=24/y}} \right.[/tex]
Now that the two equations are equal, we can solve for y:
[tex]y+5=24/y[/tex]
Divide both sides by y
[tex]y^2+5y=24[/tex]
Subtract 24 from the right side setting it to 0:
[tex]y^2+5y-24=0[/tex]
Solve for y using quadratic formula:
[tex]y=\frac{-5\pm \sqrt{5^2-4\cdot \:1\cdot \left(-24\right)}}{2\cdot \:1}[/tex]
[tex]y=3,-8[/tex]
Given the y-values lets plug them into our original equations to find the intersections.
[tex]x=3+5\\x=8[/tex]
Giving intersection vector (8,3)
[tex]x=-8+5\\x=-3[/tex]
Giving intersection vector (-3,-8)
Since both the width and length of the rectangle must be positive lets use the first vector (8,3) as our solution.
The x value being 8 means the width must be 8, y value being 3 the height must be 3, these variable correlate to our original definitions of making the x value equal to the width of the carpet and y value the height of the carpet.
Answer:The width is 3mm
Step-by-step explanation:
Length= 5mm + width
Let the width be represented by W
Area=24mm^2
Since area= length x width
24=(5+ W) x W
24=5W +[tex]W^{2}[/tex]
[tex]W^{2}[/tex] +5W-24=0
The factors are 8 and -3
[tex]W^{2}[/tex]+8w-3w-24=0
Factorise
W(w+8)-3(w+8)=0
(w-3)=0 or (w+8)=0
W=3 0r w= -8
The width cannot be negative.
Hence,W=3mm
The sector area of a region of a circle is 23 mi². The central angle, 0 (theta), is 25°. What is the radius?
Answers
The radius of the sector is 10.27 miles
How to find the radius of a sector?The area of a sector can be represented as follows;
area of a sector = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
∅= 25 degrees
area of the sector = 23 miles²
area of a sector = ∅ / 360 × πr²
23 = 25 / 360 × πr²
cross multiply
23 × 360 = 25πr²
8280 = 25πr²
divide both sides by 25
πr² = 8280 / 25
πr² = 331.2
r² = 331.2 / 3.14
r² = 105.477707006
r = √105.477707006
r = 10.2702336877 miles
Therefore, the radius of the sector is 10.27 miles
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Which expression is equivalent to StartRoot StartFraction 128 x Superscript 5 Baseline y Superscript 6 Baseline Over 2 x Superscript 7 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y > 0.
Answers
The equivalent expression of the expression is 128x^5y^6/2x^7y^5
How to determine the equivalent expression?The expression is given as:
128x^5y^6/2x^7y^5
Divide 128 by 2
64x^5y^6/x^7y^5
Apply the law of indices
64y^(6-5)/x^(7-5)
Evaluate the differences
64y/x^2
Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5
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PLEASE HELP!!
Part C
What is the difference of the x-coordinate of point A and the x-coordinate of point B?
Answers
The difference of the x-coordinate of point A and the x-coordinate of point B is 0
Coordinates of a pointThe coordinate of a point on an xy-plane is written in the form (x, y). The given figures are circles A and B where the circle A is greater than circle B.
The position of the dots in both sides are positioned at the centre and as such the coordinate point at the centre of both circle will be the origin (0, 0)
According to the question, we are to find the difference of the x-coordinate of point A and the x-coordinate of point B
x-coordinate of pint A = 0
x-coordinate of point B = 0
Take the difference
Difference = 0 - 0
Difference = 0
Hence the difference of the x-coordinate of point A and the x-coordinate of point B is 0
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in a given figure if o is the centre of circle and oabc is a parallelogram find the value of abc
Answers
From the given information, we get the value of ABC = 120°.
How to estimate the value of ABC?
Given: In the figure, O exists the center of the circle and OABC exists as a parallelogram.
Now, the radius of the circle exists
OA = OB = OC
Opposite sides of a parallelogram are equal
AB = OC and OA = BC
In ∆OAB,
OA = OB = AB and,
In ∆OCB,
OC = OB = BC
Therefore, ∆OAB and ∆OCB exist in equilateral triangles.
All angles of an equilateral triangle are equivalent to 60°.
Hence, ∠ABC = ∠OBA + ∠OBC
∠ABC = 60° + 60°
∠ABC = 120°
Therefore, the value of ∠ABC = 120°.
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In the power function f(x) = -2x, what is the end behavior of f(x) =3^-x 2 as x goes to [infinity]?
Answers
The end behavior of the power function is as x tends to infinity, f(x) tends to zero.
In this question,
The power function is [tex]f(x)=3^{-x}2[/tex]
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The graph below shows the behavior of the function f(x).
The above equation has the degree of 1, which is odd and the leading coefficient has the positive coefficient.
Then the end behavior is
As x -> ∞,
⇒ [tex]\lim_{x \to \infty} f(x)[/tex]
⇒ [tex]\lim_{x \to \infty} 3^{-x}2[/tex]
⇒ [tex]2\lim_{x \to \infty} 3^{-x}[/tex]
⇒ [tex]2\lim_{x \to \infty} 3^{-\infty}[/tex]
⇒ 2(0)
⇒ 0
Thus as x → ∞, f(x) → 0.
Hence we can conclude that the end behavior of the power function is as x tends to infinity, f(x) tends to zero.
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one end of a tent is a triangle. the height of the triangle is 1.5 m and the base is 2.5 m. what is the area of the triangle?
Answers
Answer:
1.5×2.5/2=1.875.
Step-by-step explanation:
We all know that area of triangle is base into hight upon 2.
A school dance committee has 14 volunteers. Each dance requires 3 volunteers at the door, 5 volunteers on the floor, and 6 floaters. If two of the volunteers, Christine and Samuel, cannot work together since they are new, in in how many ways can the volunteers be assigned?
Answers
There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.
Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.
We are required to find the number of ways in which the volunteers can be assigned.
Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.
n[tex]C_{r}[/tex]=n!/r!(n-r)!
Number of ways in which the volunteers can be assigned is equal to the following:
Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.
Number of ways =14[tex]C_{12}[/tex]
=14!/12!(14-12)!
=14!/12!*2!
=14*13/2*1
=91 ways
Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.
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determine the rate of change of the function.
decreasing at increasing rate
increasing at a decreasing rate
decreasing at a decreasing rate
increasing at an increasing rate
Answers
Deceasing at a decreasing rate
The purpose of statistical inference is to make estimates or draw conclusions about a.
Answers
When we make estimates of or draw conclusions about one or more characteristics of a population based upon the sample, we are using the process of statistical inference.
To estimate this sample to sample variance or uncertainty is the goal of statistical inference.What is the purpose of statistical inferences ?
To be able to make inferences about a population based on data from a sample is the goal of statistical inference. The process of statistical inference involves selecting a sample, gathering data from that sample, calculating a statistic from the data, and drawing conclusions about the population from that statistic.How is statistical inference used to draw conclusions?
Estimation and hypothesis testing are components of statistical inference (evaluating a notion about a population using a sample) (estimating the value or potential range of values of some characteristic of the population based on that of a sample).
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PLEASE HELP ME!! I'M TIMED
All the digits of a number A are different. A number can be formed using digits that are each larger than the digits of A by one. What is the largest such number of A?
Answers
Answer: 87,654,321
Step-by-step explanation: All the digits of the number A are different so the max length of the number A is 10 digits. But, then you realise that 9 can't be used because 9+1 = 10. So, A is only 9 digits long. If we arrange them from largest to least it would be 87,654,321.
Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)
Answers
The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.
In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.
In the given expression, a = 1, b = -4, and c = -21.
Thus, ac = -21.
The numbers having a product 21 are:
1*21 = 21,
3*7 = 21.
Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.
Thus, the expression can now be shown as:
x² - 4x - 21
= x² + (3 - 7)x - 21
= x² + 3x - 7x - 21
= x(x + 3) - 7(x + 3) {By taking common}
= (x - 7)(x + 3) {By taking common}.
Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
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Which power of Congress is the most important?
Select one:
O a. the authority to regulate commerce
O b. the authority to establish the federal courts.
O c. the authority to make laws
O d. the authority to coin money
Answers
Pls answer I’ll mark brainliest if first person is correct
Answers
Based on these data, it is better to describe the centers of distribution in terms of: B. median for both coffee shops because the data distribution is not symmetric.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Next, we would calculate the mean and median for the two coffee shops as follows.
For coffee shop A, we have:
Mean = [F(x)]/n
Mean = [12+15+33+45+46+51+52+57]/8
Mean = [311]/8
Mean = 38.875.
Median = (45+46)/2
Median = 91/2
Median = 45.5.
For coffee shop B, we have:
Mean = [F(x)]/n
Mean = [17+16+36+35+12+9+34+15]/8
Mean = [174]/8
Mean = 21.75.
Median = (16+17)/2
Median = 33/2
Median = 16.5.
Since both the mean and median are not close, we can infer and logically deduce that the data distribution isn't symmetric for both coffee shops A and B.
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Answer:
Step-by-step explanation:
A(n) _____is a type of group design in which the species of animals within the study constitutes one of the independent variables.
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A comparative design is a type of group design in which the species of animals within the study constitutes one of the independent variables.
A group of animals, plants, or other living things that all have similar traits and are categorized as one species are considered to be living organisms. All humans are one species, for instance.
It is essential for both biologists and the general public to comprehend what species are and how to recognize them. As species disappear, biological variety is lost, and the only way to influence the social, political, and economic factors that influence conservation efforts is to understand the nature of species.
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