Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly because individuals who deviate too much from the mean have lower fitness. If this is the case, does variance in a trait rise after it becomes less functionally important? Billet et al. (2012) investigated this question with the semicircular canals (SC) of the three-toed sloth (Bradypus variegatus). The authors proposed that since sloths don't move their heads much, the functional importance of SC is reduced, and may vary more than it does in more active animals. They obtained the following measurements of the ratio of the length to width of the anterior SC in 6 sloths. Assume this represents a random sample. In other, more active animals, the standard deviation of this ratio is 0.09.
Answers
Answer:
The 95% confidence interval for the standard deviation is (0.14, 0.54).
Step-by-step explanation:
The complete data and question is:
Sloth CW Ratios ; {1.5 , 1.09 , 0.98 , 1.42 , 1.49 , 1.25}
The 95% confidence interval for the standard deviation of this data is < σ < (two decimals - include the leading zero) .
Solution:
Compute the sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{6}\times 7.73=1.2883\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{6-1}\times 0.2387}=0.2185[/tex]
The (1 - α)% confidence interval for the variance is:
[tex]CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}<\sigma^{2}<\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2}}[/tex]
Confidence level = 95%
⇒ α = 0.05
The degrees of freedom is,
df = n - 1 = 6 - 1 = 5
Compute the critical values of Chi-square:
[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.025,5}=12.833\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{0.975,5}=0.831[/tex]
*Use a Chi-square table.
Compute the 95% confidence interval for the variance as follows:
[tex]CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}<\sigma^{2}<\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2}}[/tex]
[tex]=\frac{5\times (0.2185)^{2}}{12.833}<\sigma^{2}<\frac{5\times (0.2185)^{2}}{0.831}\\\\=0.0186<\sigma^{2}<0.2873\\\\=\sqrt{0.0186}<\sigma<\sqrt{0.2873}\\\\=0.1364<\sigma<0.5360\\\\\approx 0.14<\sigma<0.54[/tex]
Thus, the 95% confidence interval for the standard deviation is (0.14, 0.54).
Related Questions
How do I write the equation of hyperbola in standard form with center (0,0),endpoints of the transverse axis (±6,0) and length of latus rectum is 16?
Answers
Answer:
Length of latusrectum =9=
a
2b
2
⇒b
2
=
2
9a
..... (i)
and e=
4
5
∵1+
a
2
b
2
=
16
25
∴1+
2a
2
9a
=
16
25
[from Eq. (i)]
⇒
2a
9
=
16
9
⇒a=8
On putting the value of a in Eq. (i), we get
b
2
=
2
9×8
=36⇒b=6
∴ Equation of hyperbola is
8
2
x
2
−
6
2
y
2
=1⇒
64
x
2
−
36
y
2
=1
what is the reciprocal of 8
Answers
Answer:
0.125
Step-by-step explanation:
to get the reciprocal of a number we divide the number by 1
in this case it would be 1 divide by 8
1/8 = 0.125
what is 2x-6 >-16 and 3x-10 8
Answers
Answer: 2x-6>-16 = -5
Step-by-step explanation:
add 6 to -16, you get -10.
divide 2x by 10, you get -5
A transportation engineer uses the formula, R = 1600/15+127e, to determine the minimum radius of curvature (R) in meters, for a roadway with a 40 km/hr design speed and a maximum superelevation rate (e). What is the maximum superelevation rate recommended if the radius of curvature is 350 meters? Answer as a decimal, rounded to two decimal places.
Answers
Answer:
The value is [tex] e = 1.92 [/tex]
Step-by-step explanation:
From the question we are told that
The formula for radius of curvature is [tex]R = \frac{1600}{15} +127e[/tex]
The design speed of the roadway is [tex]v = 40 \ km/hr[/tex]
The value of radius of curvature considered R = 350 m
From the equation given e is the superelevation rate
Now making the subject of the formula
[tex] e = \frac{R}{127} - \frac{1600}{1905} [/tex]
At R= 350
[tex] e = \frac{350 }{127} - \frac{1600}{1905} [/tex]
[tex] e = 1.92 [/tex]
Here, we are required to determine the maximum superelevation rate, e (rounded to 2 decimal places) recommended if the radius of curvature, R is 350 meters.
The answer is e = 1.92 (rounded to 2 decimal places).
First, from the information given, the minimum radius of curvature, R is related to the maximum superelevation rate, e by the formular;
R = (1600/15) + (127e)
Therefore, to evaluate the value of e for R = 350, we have;
350 - (1600/15) = 127e.
350 - (1600/15) = 127e.350 - 106.667 = 127e
Therefore, 243.333 = 127e.
Therefore, e = 1.9160meters
As a result, The maximum superelevation rate, e recommended if the radius of curvature, R is 350 meters is:
e = 1.92 (rounded to 2 decimal places).Read more:
https://brainly.com/question/21140562
Savannah sells character images online. Small images take one hour to make and she sells them for $15. Large images sell for $25 and take two hours to make. Each week, Savannah can work up to 20 hours making images, and she wants to earn at least $400.
Let x represent the number of small images Savannah makes in a week, and let y represent the number of large images. Which of the following systems of inequalities models the constraints of this situation?
Answers
Answer:
15x + 25y ≥ 400
x + 2y ≤ 20
x ≥ 0, y ≥ 0
Step-by-step explanation:
Here, we are modelling the total number of hours she can use in making images in a week and the total amount that can be earned in a week, considering the given constraints.
Number of small images in a week = x
Number of hrs in making images if it takes 1 hr to make 1 = 1*x = x
Number of large images in a week = y
Number of hrs in making large images if it takes 2 hrs to make 1 = 2*y = 2y
Given that she has up to 20 hrs to make the images, therefore, the inequality that models this situation would be:
x + 2y ≤ 20
This implies that, the hours spent altogether can be less than or equal to 20hrs
Amount for small images = $15
Amount in total for all images made in a week = $15*x = 15x
Amount for large images = $25
Amount in total for all images made in a week = $25*y = 25y
Given that she can earn AT LEAST $400 in a week, therefore, the inequality that models this situation would be:
15x + 25y ≥ 400
This implies that, the amount she wants to make in a week would be $400 or more.
The system of inequalities would be:
x + 2y ≤ 20
15x + 25y ≥ 400
x ≥ 0, y ≥ 0
Describe a transformation that would make quadrilateral ABCD into a square
I NEED URGENT HELP PLEASE
Answers
Answer:
ok, relax and listen I’ve got this ok?
Step-by-step explanation:
You just move it up 4 squares to (2, 9), (10,9)
see?you got this I believe in you!!!
Andrew is showing his work in simplifying (−5.7 + 2.2) − 1.1.
Step 1: (2.2 − 5.7) − 1.1
Step 2: 2.2 − (5.7 + 1.1)
Step 3: 2.2 − (6.8)
Step 4: −4.6
Which statement is true?
In step 1, Andrew used the commutative property.
In step 2, Andrew used the distributive property.
In step 3, Andrew used the associative property.
In step 4, Andrew's answer is incorrect.
Answers
Step 2 i believe im not sure tho.
Please help I don't understand!!!!!!
Answers
Answer:
X-3
Step-by-step explanation:
The graph shifted 3 units to the left so you subtract from the x value.
A sports club tests its players for steroid usage with a test that gives a positive reading 93% of the time when administered to a steroid user and gives a negative reading 96% of the time when administered to a player who does not use steroids. It is known that 8% of the players are steroid users. Draw a probability tree diagram for the given problem.
What is the probability that a player does not use steroids, given that the person had a positive reading on the test? Round your answer to four decimal places.
Answers
Answer:
P(no steroid user / positive reading on test) = 0.3309
Step-by-step explanation:
Computation:
Bayes' Theorem:
P(A / B) = P(A and B) / P(B)
P(no steroid user / positive reading on test) = P(no steroid user and positive) / P(positive)
P(no steroid user / positive reading on test) = (0.92 x 0.04)/(0.08 x 0.93 + 0.92 x 0.04)
P(no steroid user / positive reading on test) = 0.3309
The probability that a player does not use steroids, given that the person had a positive reading on the test is 0.3309.
Calculation of the probability:Since A sports club tests its players for steroid usage with a test that gives a positive reading 93% of the time when administered to a steroid user and gives a negative reading 96% of the time when administered to a player who does not use steroids. It is known that 8% of the players are steroid users.
So, here the probability should be
P(no steroid user / positive reading on test) = (0.92 x 0.04)/(0.08 x 0.93 + 0.92 x 0.04)
= 0.3309
Hence, The probability that a player does not use steroids, given that the person had a positive reading on the test is 0.3309.
Learn more about probability here: https://brainly.com/question/24442276
Write the equation of the line that passes
through the points (3, 1) and (-2, 6).
Answers
Answer:
x + y - 4 = 0
Hope this helps, if you need more of an explanation feel free to let me know!
Pattern: 4, 10, 18, 28, 40, 54, 70, 88, 108, 130
Since the second difference is constant in the pattern above, the algebraic
expression will have degree 2. In an expression of degree 2, the largest
exponent is 2. Therefore, we know that the expression for this pattern must
include n^2. What is the algebraic expression for the nth term in this pattern?
Answers
Answer:
The algebraic expression for the nth term in this pattern is n^2 + 3n
Step-by-step explanation:
We want an algebraic expression for the nth term in this pattern.
Like we are told, there must be an expression that includes the term n^2
So therefore;
We need to express each of the terms to include the n^2 term
Kindly note that the n notation will represent the term number of the value we are considering. Let’s take it one after the other.
for 4; 1^2 + 3(1)
For 10; 2^2 + 3(2)
For 18; 3^3 + 3(3)
For 28; 4^2 + 3(4)
For 50; 5^2 + 3(5)
So the nth term will be;
n^2 + 3n
(-12,8), (9,1)
What is the point-slope form of the equation of the line?
Answers
Answer:
y-y1 = m (x-x1)
where
m is the slope
and (x1,y1) is one of the points given.
You have been given 2 points (-12,8) and (9,1). You can call one of them (x1,y1) and the other (x2,y2). It doesn't matter which one is which.
But before we go further, we need to determine the slope.
We can do this from the points as well.
y2-y1
m = ---------
x2-x1
Let's say
(x1,y1) = (-12,8)
(x2,y2) = (9,1)
This gives us a slope of
y2-y1 1-8 -7 -1
m = --------- = ---------- = ---- = ---
x2-x1 9-(-12) 21 3
Now that we have everything we need
y-8 = (-1/3)[x-(-12)]
Distribute the -1/3
y-8 = (-1/3)x -4
If we add 8 to both sides we have the equation in the slope intercept form (y=mx+b)
y = (-1/3)x + 4
Describe your thinking and the steps taken when developing an
algebraic representation for the sum of the first t terms of a
linear sequence.
Answers
Let's see what to do buddy...
_________________________________
Step (1)
Suppose we want to find the sum of numbers from 1 to n.
To do this, we use the following method.
By writing the sum of numbers from 1 to n
, Then we write the sum of numbers n to 1 below it, see :
[tex]s = 1 + 2 + 3 + ... + n[/tex]
[tex]s = n + (n - 1) + (n - 2) + ... + 1 \\ [/tex]
Now we add the sentences of the above two phrases, peer to peer like this :
[tex]1 + n = n + 1 \\ [/tex]
[tex]2 + n - 1 = n + 1[/tex]
[tex]3 + n - 2 = n + 1[/tex]
And the others.....
So we have :
[tex]2s = ( n + 1) + (n + 1) + ... + (n + 1) \\ [/tex]
We had n numbers to sum so we have :
[tex]2s = n \times (n + 1)[/tex]
Divided the sides of the equation by 2
[tex]s = \frac{n \times (n + 1)}{2} \\ [/tex]
Remember this step I will use it again.
_________________________________
Step (2)
What does the linear sequence mean ?
The linear sequence is the sequence which any terms created by the sum of previous term with constant.
I name that constant value d.
According to above :
[tex]t(2) = t(1) + d[/tex]
And
[tex]t(3) = t(2) + d [/tex]
[tex]t(3) = t(1) + d + d[/tex]
[tex]t(3) = t(1) + 2d[/tex]
I have a question ;
[tex]3 - 1 = 2[/tex]
Is it correct ?
If it is correct we have :
[tex]t(3) = t(1) + (3 - 1)d[/tex]
WOW we found a thing ;
Put n instead of 3 :
[tex]t(n) = t(1) + (n - 1)d[/tex]
_________________________________
Step (3)
Stop right here.
Let's go to find the sum of the n first terms of the linear sequence.
Do you remember what did we do in step(1) ? Of course you do.
Let's do it again.
[tex]s = t(1) + t(2) + t(3) + ... + t(n) \\ [/tex]
[tex]s = t(n) + t(n - 1) + t(n - 2) + ... + t(2) + t(1) \\ [/tex]
According to the thing what we found in step(2) we have :
[tex]s = t(1) + ( \: t(1) + d \: ) + ( \: t(1) + 2d \: ) + ... + ( \: t(1) + (n - 1)d \: ) \\ [/tex]
[tex]s = ( \: t(1) + (n - 1)d \: ) + ( \: t(1) + (n - 2)d \: ) + ... + t(1) \\ [/tex]
Sum the two above equation's terms like this:
[tex]t(1) + t(1) + (n - 1)d = 2t(1) + (n - 1)d \\ [/tex]
And
[tex]t(1) + d +t(1) + (n - 2)d = 2t(1) + d(n - 2 + 1) = 2t(1) + (n - 1)d \\ [/tex]
And the others like this.
We had n terms so we sumed n terms.
So we have :
[tex]2s = n \times ( \: 2t(1) + (n - 1)d \: )[/tex]
Divided the sides of the equation by 2
[tex]s(n) = \frac{n}{2} \times ( \: 2t(1) + (n - 1)d \: ) \\ [/tex]
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Greg ran 12 miles a day on 18 different days last month. How many miles did he run?
Answers
Answer:
216
Step-by-step explanation:
12*18=216
hope this helps :3
if it did pls mark brainliest
1 meter is equal to 37.3701 inches. What is 37.3701 inches rounded to the nearest tenth?
Answers
Answer:
37.4
Step-by-step explanation:
the number places after the column go as followed ; tenth, hundredths, thousandths, ten thousandths
Suzi starts her hike at 200 feet below sea level. When she reaches the end of the hike, she is
still below sea level at -190 feet. What was the change in elevation from the beginning of
Suzi's hike to the end of the hike?
Answers
Hope this helps
A recipe for 1 batch of spice mix says, “Combine 3 teaspoons of mustard seeds, 5 teaspoons of chili powder, and 1 teaspoon of salt." How many batches are represented by the diagram? mustard seeds (tsp) chili powder (tsp) salt (tsp)
Answers
you need to put a picture again
sorry i cant answer because it doesnt show diagram
What is the value of -2 7/12 divided -1/6
Answers
Answer:
15.5
Step-by-step explanation:
-2 7/12 = -31/12
-31/12 ÷ -1/6 = 15 1/2 or 15.5
Find the value of x in the following ratio 3:15=x:30
b) x :9 =4=36
Answers
A machine made 4 1/2 pencils in 3 1/3 minutes. How many pencils did the machine make in one minute?
Answers
Given parameters:
Number of pencils = [tex]4\frac{1}{2}[/tex] pencils
Time taken = [tex]3\frac{1}{3}[/tex] minutes
Unknown:
Number of pencils produced in 1 minute;
Solution:
To solve this problem, let us first find the rate of the machine;
Rate of machine = [tex]\frac{number of pencils }{time taken}[/tex]
Rate of machine = [tex]\frac{\frac{9}{2} }{\frac{10}{3} }[/tex] = [tex]\frac{9}{2} x \frac{3}{10}[/tex] = [tex]\frac{27}{20}[/tex] pencils/minute
Now, number of pencils produces in 1 minute;
Number of pencils = rate of machine x time taken
Number of pencils = [tex]\frac{27}{20}[/tex] pencils/ min x 1 min
Number of pencils = [tex]\frac{27}{20}[/tex]pencils
The number of pencils produced in 1 minute is [tex]\frac{27}{20}[/tex]
convert 3250 ml to L
Answers
Answer:
3250 milliliters transfers into 3.25 liters.
Help asap
bdndndnejejdjdjdjdjdjdjdjdjdjejdjs
Answers
Answer:
no
Step-by-step explanation:
two points cant be on the same line in a vertical pattern
60% of blank = 300
60 out of 300 = blank %
Answers
Answer:
500 = 100%
20% = 60
Step-by-step explanation:
300 = 60%
50 = 10%
500 = 100%
100% = 300
10% = 30
20% = 60
Hope this helps!
Answer:
60% of 750 = 300
60 out of 300 = 20%
I hope that this can help you ^‿^
The juice dispenser in the cafeteria holds 21 1/4 pints of juice. The glasses in the cafeteria only hold 1/4 of a pint of juice. How many full glasses can be served at breakfast?
Answers
Answer:
85 can
Step-by-step explanation:
21 x 4 = 84
Then you add one more because there is still 1/4 of a pint left and each cup can hold that much too.
The ratio of the number of Andy's seashells to the number of seashells Ben has is 4:9. Andy has 100 seashells. How many does Ben have?
Answers
Answer:
Ben has 225
Step-by-step explanation:
100 ÷ 4 = 25
25 × 9 = 225
11.
April is going to the bakery to purchase donuts and cinnamon rolls for the office personnel. She must purchase at least 30 items. She has collected only $30, so total cost must be no more than $30. If d represents donuts that cost $0.75 each and r represents cinnamon rolls that cost $1.25 each, which system of inequalities can be used to represent the region for the number of donuts and cinnamon rolls April could purchase?
A.d + r ≥ 30
0.75d + 1.25r ≤ 30
B. d + r ≥ 30
1.25d + 0.75r ≤ 30
C. d + r ≤ 30
0.75d + 1.25r ≥ 30
D. d + r ≤ 30
1.25d + 0.75r ≥ 30
Please answer quickly :)
Answers
The system of inequalities that can be used to represent the region for the number of donuts and cinnamon rolls April could purchase is $0.75d + $1.25r ≤ $30
April cannot spend more than $30. Thus, the inequality sign that would be used is ≤ (the less than or equal to sign).
April wants to purchases two items, cinnamon rolls and donuts. The donuts cost $0.75 per dollar and cinnamon rolls cost $1.25 per dollar.
The total amount April can spend on donuts = $0.75 x d = $0.75d
The total amount April can spend on cinnamon rolls = $1.25 x r = $1.25r
The sum of $0.75d and $1.25r has to be less than $30
This can be represented with this inequality: $0.75d + $1.25r ≤ $30
A similar question was solved here: https://brainly.com/question/18649886?referrer=searchResults
2.1÷6 long division
Answers
Answer:
0.35
Step-by-step explanation
6 ) 2.1 ( 0.35 <------- Quotient.
18
30
30
...
Running 7/4 miles in 11 minutes how many miles per minutes
Answers
x miles in 1 minute
Cross multiply we will get:
7/4 = 11x
7/4 x 1/11 = x
7/44 = x
So 7/44 miles per minute is the answer
Answer:
it is either 10 or 6.67 minutes per hour
Step-by-step explanation:
if you ran 3 miles basically in 30 minutes :30 minutes divided 3 miles = 10 minutes per mile pace or 6.67 minutes per hour
simplify this algebraic expression.
y-3/3+12
A.y+11
B.y-5
C.y+13
D.y-11
Answers
Answer:
A. y+11
Step-by-step explanation:
-3/3 = -1
12 + ( -1 ) = 11
y + 11
hope this helped :)
Explain how you can use compatible numbers to estimate the quotient of 925/29.
Answers
Answer: the corrects answer is 31
Step-by-step explanation: