Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 10 (newly deceased) adults, the mean failure strain (%) was 24.0, and the standard deviation was 3.2.
Required:
a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
In an experiment, you choose to have two randomly assigned groups. In one, you take measurements both pretest and posttest; with the second, a posttest-only measure. This describes which task of conducting an experiment
Answer:
The answer is "Specific treatment levels".
Step-by-step explanation:
When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.
The height of a triangle is 4 yards greater than the base. The area of the triangle is 70 square yards. Find the length of the base and the height of the triangle.
9514 1404 393
Answer:
base: 10 yardsheight: 14 yardsStep-by-step explanation:
Let b represent the length of the base. Then (b+4) is the height and the area of the triangle is ...
A = 1/2bh
70 = 1/2(b)(b+4)
b² +4b -140 = 0 . . . . . multiply by 2, put in standard form
(b +14)(b -10) = 0 . . . . factor
b = 10 . . . . the positive solution
The base of the triangle is 10 yards; the height is 14 yards.
Algebra 2, please help! thank you
The function y = 2 cos 3(x + 2π∕3) +1 has a phase shift (or horizontal shift) of
A) –2π∕3
B) 3
C) 1
D) 2
Answer:
-2pi/3
Step-by-step explanation:
y = 2 cos 3(x + 2π∕3) +1
y = A sin(B(x + C)) + D
amplitude is A
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
We have a shift to the left of 2 pi /3
Answer:
A
Step-by-step explanation:
The standard cosine function has the form:
[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]
Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.
We have the function:
[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]
We can rewrite this as:
[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]
Therefore, a = 2, b = 3, c = -2π/3, and d = 1.
Our phase shift is represented by c. Thus, the phase shift is -2π/3.
Our answer is A.
Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red then blue).
Answer:
4/27
Step-by-step explanation:
total number of marbles=9
probability of red=4/9
since you returned the first marble, the total number of marbles remains the same
prob(Blue)=(3/9)=1/3
P(red then blue)=(4/9)*(1/3)
=4/27
-1/5y+7=7
What is the value of y?
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
1/10 + 3/5
ANSWER QUICK PLS FIRST ANSWER GETS BRAINLIEST
Please help me determine the general equation for the graph above as well as solve for a. Thank you.
Observe that the x coords of the roots of a polynomial are,
[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]
Which can be put into form,
[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
with data
[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]
Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,
[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]
and a will be "lost" in the process.
If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.
Hope this helps :)
The whole number 23 is an example of a ____ number.
prime or composite?
The answer is prime! I hope this helps you out!
Answer:
23 is a prime number. Reason: Prime number are those numbers which are divisible by 1 and itself. Example: 5 is divisible by 1 and 5 only.
A line is perpendicular to the line y = 4x - 3 and has x-intercept (2,0). Which of the following is an equation of the line?
Answer:
y = -1/4x+1/2
Step-by-step explanation:
y = 4x - 3
This is in slope intercept form, y = mx+b where the slope is m
The slope is 4
Perpendicular lines have slopes that are negative reciprocals
-1/4 is the slope of the perpendicular line
y = -1/4x+b
Using the point (2,0)
0 = -1/4(2)+b
0 = -1/2+b
b = 1/2
y = -1/4x+1/2
please help !!!!
i would really appreciate it
Answer: A
Step-by-step explanation: x=-2, y=3, z=-3
Answer:
A. -2, 3, -3
Step-by-step explanation:
x = 7 - 2y + z
y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =
= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z
13y = 63 + 8z
y = (63 + 8z)/13
2x + 2y - 3z = 11
2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11
2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11
14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11
-2×(63 + 8z)/13 - z = -3
-2×(63 + 8z) - 13z = -39
-126 - 16z - 13z = -39
-29z = 87
z = -3
y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3
x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2
Write an explicit formula for the sequence.
-4,7,-10,13,-16
Step-by-step explanation:
Sequence is
4
,
7
,
10
,
13
,
16
,
.
.
.
a
1
=
4
,
a
2
=
7
,
a
3
=
10
,
.
.
.
If it is Arithmetic sequence,
a
2
−
a
1
=
a
3
−
a
2
=
a
4
−
a
3
& so on
In the given sum,
a
2
−
a
1
=
7
−
4
=
3
a
3
−
a
2
=
10
−
7
=
3
a
4
−
a
3
=
13
−
10
=
3
Since the difference between the successive terms is same and
hence
common difference
d
=
3
I will give brainliest if you answer properly.
Answer:
See below
Step-by-step explanation:
a)
[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]
[tex]\therefore x=\dfrac{4\pi }{3}[/tex]
But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution
Therefore,
[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]
This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.
Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]
b)
[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]
Once
[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]
As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
[tex]\therefore x=-\dfrac{\pi }{6}[/tex]
c)
[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]
Therefore,
[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]
[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
The solutions are
[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
HELP ME OUT ASAPPP PLSSS
Answer:
https://linksharing.samsungcloud.com/ul5cX9oOmhzt
I need help ASAP please please please
Answer:
n=39/5
Step-by-step explanation:
24=5(n-3)
24=5n-15
-5n= -15-24
-5n=39
n= 39/5
The expression y + y + 2y is equivalent to ??
because ??
Answer:
4y
They would have the same value if a number was substituted for y
Step-by-step explanation:
y+y+2y =
Combine like terms
4y
These are all like terms
They would have the same value if a number was substituted for y
Let y = 5
5+5+2(5) = 5+5+10 = 20
4(5) =20
If a $6 per unit tax is introduced in this market, then the new equilibrium quantity will be
Answer:
soory i dont know just report me if you angry
Find the missing side round your answer to the nearest tenth
Answer:
x=13.2
Step-by-step explanation:
cos(43)=x/18
x=18×cos(43)
x=13.2
Answered by GAUTHMATH
What is the product of 2/5 × 3/4?
Answer:
3/10
Step-by-step explanation:
2/5*3*4
=6/20
=3/10
solve for x please help (show ur work)
Answer:
x = -3
Step-by-step explanation:
12 -4x-5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from each side
12-9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
Answer:
x = -3
Step-by-step explanation:
12 - 4x - 5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from both sides
12 - 12 - 9x = 39 - 12
-9x = 27
Divide both sides by -9
-9x/-9 = 27/-9
x = -3
A simple random sample of 400 individuals provides 112 Yes responses. (a) What is the point estimate of the proportion of the population that would provide Yes responses
Answer:
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
Step-by-step explanation:
Point estimate of the proportion of the population that would provide Yes
The sample proportion of yes responses.
In the sample:
112 yes responses in the sample of 400, so:
[tex]p = \frac{112}{400} = 0.28[/tex]
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
simplify the following without using calculator
√50 + √98
Answer:
The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8
Step-by-step explanation:
√50 + √98 = √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2
Nasa is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before the launch and has a diameter of 4.7 feet. What is the total weight in pounds?
Answer:
Step-by-step explanation:
What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? (5 points)
Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
The distribution of SAT scores is approximately normal with a mean of 1500.
If 1628 is the 90th percentile, what is the standard deviation?
Answer:
Hello,
Answer
[tex]\sigma=457,95...[/tex]
Step-by-step explanation:
p(z<a)=0.9
p(z<1.29)=0.9015
p(z<1.28)=0.8997
using linear interpolation: with 4 decimals
p(z<1.282)<0.9
[tex]\dfrac{1628-1500}{\sigma} =1.282\\\\\sigma =\dfrac{1628-1500}{1.282}\\\\\sigma=457,95...\\[/tex]
what us 10 to the power of two
the answer is
10² ( ten square )
step by step :
10² = 10 × 10
= 100
Answer: 100
Step-by-step explanation: 10*10=100
Carmen Abdul and David sent a total of 78 text messages over their cell phones during the weekend . Abdul sent 10 fewer messages then Carmen . David sent two times as many messages as Abdul how many messages did they each send?
Answer:
Carmen:27
Abdul:17
David=34
Step-by-step explanation:
Carmen+Abdul+David = 78
Carmen-Abdul=10
David=2Abdul
Carmen=Abdul+10
Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78
4Abdul=68
Abdul = 68/4=17
Carmen = 17+10=27
David = 2 * 17 = 34
27+17+34=78
Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)
The equation has 2 valid solutions; no extraneous solutions
The given equation is:
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
First, we determine the solutions
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
Add 5 to both sides
[tex]\sqrt{x - 1} = x - 8 + 5[/tex]
[tex]\sqrt{x - 1} = x - 3[/tex]
Square both sides
[tex]x - 1 = (x - 3)^2[/tex]
Expand
[tex]x - 1 = x^2- 3x - 3x + 9[/tex]
[tex]x - 1 = x^2- 6x + 9[/tex]
Collect like terms
[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]
[tex]x^2 - 7x + 10 = 0[/tex]
Expand again
[tex]x^2 - 2x-5x + 10 = 0[/tex]
Factorize
[tex]x(x - 2) -5(x -2)= 0[/tex]
Factor out x - 2
[tex](x - 5)(x -2)= 0[/tex]
Split
[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]
[tex]x= 5[/tex] or [tex]x = 2[/tex]
The above values are valid values of x.
Hence, the equation has 2 valid solutions; no extraneous solutions
Read more about equations at:
https://brainly.com/question/2396830
Answer:
That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.
Step-by-step explanation:
for plato users
What is the formula for the volume of a pyramid?
V = πr2h
V = 3/4πr2h
V = 1/3πr2h
V = 1/3Bh
