Answer:
The margin of error for her confdence interval is of 0.3757.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Standard deviation of 0.55 meters.
This means that [tex]s = 0.55[/tex]
What is the margin of error for her 99% confidence interval?
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]
[tex]M = 0.3757[/tex]
The margin of error for her confdence interval is of 0.3757.
Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.
What is the margin of error for small samples?Suppose that we have:
Sample size n < 30
Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Degree of freedom = n-1Then the margin of error(MOE) is obtained as
Case 1: Population standard deviation is knownMargin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]
where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance
For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.
Then, by the given data, we get:
[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18
The degree of freedom is n-1 = 17
Level of significance = 100% - 99% = 1% = 0.01
The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)
Thus, margin of error for 99% confidence interval for considered case is:
[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]
Thus, the margin of error for the given condition is 3.28 approximately.
Learn more about margin of error here:
https://brainly.com/question/13220147
The mean age of 5 people in a room is 27 years.
A person enters the room.
The mean age is now 35.
What is the age of the person who entered the room?
Answer:
main age = total age/total people
if Main age is = 27
[tex]27 = \frac{ \times }{5} [/tex]
and x = 135
Total age is = 135
then main age is 35
[tex][35 = \frac{y}{6} [/tex]
and y = 210
first main age - second main age = age of the person participating
210 - 135 = 75
the age is = 75HAVE A NİCE DAY
Step-by-step explanation:
GREETINGS FROM TURKEY
Which ordered pairs are in the solution set of the system of linear inequalities?
y > Negative one-thirdx + 2
y < 2x + 3
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (6, 0. Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (negative 3, negative 3) and (0, 3). Everything above the line is shaded.
Options:
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
Answer:
A. (2, 2), (3, 1), (4, 2)
Step-by-step explanation:
Given
[tex]y > -\frac{1}{3}x + 2[/tex]
[tex]y < 2x + 3[/tex]
Required
Solve for x and y
To solve this, we make use of graphical method (see attachment for graph)
All points that lie on the shaded region are true for the inequality
Next, we plot each of the given options on the graph
A. (2, 2), (3, 1), (4, 2)
All 3 points lie on the shaded region.
Hence, (a) is true
Answer:
A. (2, 2), (3, 1), (4, 2)
Step-by-step explanation:
From two points on the same level as the base of a tree, the angles of elevation to the top of the tree are found to be 24° and 46°. If the two points are 42 feet apart and on the same side of the tree, how tall is the tree? (Give your answer to the nearest tenth of an inch.)
Answer:
the answer is 32.8in.
Step-by-step explanation:
(sin 22)/42 = (sin 24)/x
x = 45.60
sin 46 = x/45.60
x = 32.80
32.8in.
hope it helped :)
mark me brainliest!
What is the mode of the data?
Weight of Dogs In the Pet Store
Stem Leaves
0 3, 8
1 0, 1, 4, 7,
2 2, 4, 5
3 5 0 | 3 = 3 pounds
4 0
A. 17
B. 3
C. no mode
D. 40
Answer:
No mode
Step-by-step explanation:
Mode = number that appears the most
No number appears more than 1 time
Hence there is no mode
Answer:Should be no mode tell me if i'I'm wrong
Step-by-step explanation:
If someone can pls give me the answer the would be greatly appreciated :)
Step-by-step explanation:
The Answer Is Provided Below ➳
(2²)² = 2⁴/2⁴ = 2⁰ × 2⁰ = 2⁰/2⁰
when 5 is added to 2 times a number , the results is 45. find the number
Answer:i think its 20
Step-by-step explanation: 20 x 2 is 40 plus 5 is 45
Answer:
✓ x - the number 5 + 2x = 45 2x = 45 - 5 2x = 40 x = 20 5 + 2(20) = 45 5 + 40 = 45 45 = 45 Hope this helps. :-) the answer is 20
Step-by-step explanation: Algebra.com
Is AABC-ADEF? If so, name which similarity postulate or theorem applies.
75
A. Similar - SSS
B. Similar - AA
0
C. Similar - SAS
D. Cannot be determined
Answer:
B. Similar - AA
Step-by-step explanation:
Two angles in ∆ABC are congruent to two corresponding angles in ∆DEF. Thus, it follows that the third pair of angles of both triangles would also be congruent.
Therefore, the three sides of ∆ABC and corresponding sides of ∆DEF will be proportional to each other.
This satisfies the AA Similarity Criterion. Therefore, ∆ABC ~ ∆DEF by AA.
Three more than twice a number is 35.
Answer:
x = 16, or if you didn't want the value for x,
2x + 3 = 35
Step-by-step explanation:
Three more: +3
Twice a number: 2x
Combined:
2x + 3 = 35.
Get rid of the 3 by subtracting it from both sides:
2x = 32
Get rid of the 2 by dividing it from both sides:
x = 16
Answer:
The number is 16.
Step-by-step explanation:
Let the unknown number be x.
Now we translate the sentence into an equation piece by piece.
Three more than twice a number is 35.
2x
Three more than twice a number is 35.
2x + 3
Three more than twice a number is 35.
2x + 3 = 35
Now we solve the equation.
Subtract 3 from both sides.
2x = 32
Divide both sides by 2.
x = 16
Answer: The number is 16.
P.S. Notice that x was a variable that was introduced solely to solve the problem. The original problem is a word problem, not an equation, and has no x in it. The correct answer makes no reference to x since x was used to solve the equation but is not part of the given problem. The person asking the question has no idea what x is. He just wants a number as an answer.
You bought a car that was $25500 and the value depreciates by 4.5% each year.
How much will the car be worth after 5 years?
How much after 8 years?
Answer:
(a) 20256.15625
(b) 17642.78546
Step-by-step explanation:
(a) There's a formula for this problem y = A(d)^t where, A is the initial value you are given, d is the growth or decay rate and t is the time period. So, in this case, as the car cost is decreasing it is a decay problem and we can write the formula as such; y = A(1-R)^t
So, in 5 years the car will be worth, 25500(1-4.5%)^5 or 20256.15625 dollars
(b) And after 8 years the car will be worth 25500(1-4.5%)^8 or 17642.78546 dollars.
If P = (2,-1), find the image
of P under the following rotation.
270° counterclockwise about the origin
([?], [])
Enter the number that belongs in
the green box.
9514 1404 393
Answer:
P'(-1, -2)
Step-by-step explanation:
The transformation for 270° CCW rotation is ...
(x, y) ⇒ (y, -x)
Then the image of the given point is ...
P(2, -1) ⇒ P'(-1, -2)
Plz help. I’m finding surface area. I need the answer in units. Thank you.
Answer:
C. 17 units
Step-by-step explanation:
Surface area of rectangular prism is given as:
A = 2lw + 2lh + 2wh
A = 930 square units
l = 12 units
h = 9 units
w = ? (We're to find the width)
Plug in the value into the formula
930 = 2*12*w + 2*12*9 + 2*w*9
930 = 24w + 216 + 18w
Add like terms
930 - 216 = 42w
714 = 42w
Divide both sides by 42
714/42 = 42w/42
17 = w
w = 17 units
Q.1 Determine whether y = (c - e ^ x)/(2x); y^ prime =- 2y+e^ x 2x is a solution for the differential equation Q.2 Solve the Initial value problem ln(y ^ x) * (dy)/(dx) = 3x ^ 2 * y given y(2) = e ^ 3 . Q.3 Find the general solution for the given differential equation. (dy)/(dx) = (2x - y)/(x - 2y)
(Q.1)
[tex]y = \dfrac{C - e^x}{2x} \implies y' = \dfrac{-2xe^x-2C+2e^x}{4x^2} = \dfrac{-xe^x-C+e^x}{2x^2}[/tex]
Then substituting into the DE gives
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{2\left(\dfrac{C-e^x}{2x}\right) + e^x}{2x}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{C-e^x + xe^x}{2x^2}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = \dfrac{-C+e^x - xe^x}{2x^2}[/tex]
and both sides match, so y is indeed a valid solution.
(Q.2)
[tex]\ln\left(y^x\right)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
This DE is separable, since you can write [tex]\ln\left(y^x\right)=x\ln(y)[/tex]. So you have
[tex]x\ln(y)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
[tex]\dfrac{\ln(y)}y\,\mathrm dy = 3x\,\mathrm dx[/tex]
Integrate both sides (on the left, the numerator suggests a substitution):
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 + C[/tex]
Given y (2) = e ³, we find
[tex]\dfrac12 \ln^2(e^3) = 6 + C[/tex]
[tex]C = \dfrac12 \times3^2 - 6 = -\dfrac32[/tex]
so that the particular solution is
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 - \dfrac32[/tex]
[tex]\ln(y) = \pm\sqrt{3x^2 - 3}[/tex]
[tex]\boxed{y = e^{\pm\sqrt{3x^2-3}}}[/tex]
(Q.3) I believe I've already covered in another question you posted.
Can someone answer these?
Answer: hello there here are your answers:
5.d associate property of addition
6.b multiplicative identify
7. c Additive identify
Step-by-step explanation:
5) they are just changing up the number in the ()
6) Its the same number or equation on both sides just wrote different
7) that in a given mathematical system leaves unchanged any element to which it is added.
hope this help have a good day bye!
suppose y varies inversely with X, and y = 48 when x = 3. What is the value of x when y = 24?
NO LINKS OR ANSWERING YOU DON'T KNOW.
a. 3
b. 12
c. 6
d. 24
Answer:
C. 6
Step-by-step explanation:
Recall that inverse variation is given by:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
We know that y = 48 when x = 3. Substitute:
[tex]\displaystyle (48)=\frac{k}{(3)}[/tex]
Solve for k:
[tex]k=3(48)=144[/tex]
Hence, our equation is:
[tex]\displaystyle y=\frac{144}{x}[/tex]
We want to find x when y = 24. Substitute:
[tex]\displaystyle \frac{24}{1}=\frac{144}{x}[/tex]
Cross-multiply:
[tex]24x=144[/tex]
Divide both sides by 24. Hence:
[tex]x=6[/tex]
Our answer is C.
Insert a digit in place of each “…” to make numbers that are divisible by 6 if it
is possible:
4…6
?
Answer: Either 2, 5, or 8
This means the number 426 is divisible by 6. So are 456 and 486
===============================================================
Explanation:
A number is divisible by 6 if both of the following are true
The number is divisible by 2The number is divisible by 3This is simply because 6 = 2*3. So if 6 is a factor of a number, then 2 and 3 must be factors.
To have 2 be a factor, the units digit must be in the set {0,2,4,6,8} which is the case here (the units digit is 6 in this case). Therefore we know the number is a multiple of 2 regardless of what the other digits are. To have 3 be a factor, the digits must add up to a multiple of 3. Through trial and error, we see that 0 doesn't work because 4+0+6 = 10 which is not a multiple of 3. Same goes for 4+1+6 = 11, but 4+2+6 = 12 is a multiple of 3.Therefore, 426 is a multiple of 6
Increment that middle digit 2 by 3 and we jump from 426 to 456. Those three digits add to a multiple of 3 as well (4+5+6 = 15). Following that line of logic, we go from 456 to 486 as the last possible three digit number that has these conditions of having 4 first and 6 last, and the number is a multiple of 6.
-------------------------------
In short,
The numbers 426 and 456 and 486 are all multiples of 6 since they are multiples of 2 and 3 at the same time.
So we could replace that middle digit with either 2, 5 or 8.
The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of June. Determine the lower class limits.
Answer:
79.5, 110.5, 141.5, 172.5, 203.5, 234.5
Step-by-step explanation:
Given
The attached distribution
Required
The lower class limits
To do this, we simply subtract 0.5 from the lower interval
From the attached distribution, the lower intervals are:
80.0, 111.0, 142.0, 173,0 .......
So, the lower class limits are:
[tex]80.0-0.5 = 79.5[/tex]
[tex]111.0-0.5 = 110.5[/tex]
[tex]142.0-0.5 = 141.5[/tex]
[tex]173.0-0.5 = 172.5[/tex]
[tex]204.0-0.5 = 203.5[/tex]
[tex]235.0-0.5 = 234.5[/tex]
what is the correct equation ?
Answer:
B
Step-by-step explanation:
B is the correct equation
Can someone do eight nine one and two ?
Answer: hello there here are your answers:
8) B multiplication property of zero
9) C additive identify
1) 8
2) -2a-7
Step-by-step explanation:
1) [tex]\frac{3+u}8^{2} \\u=5 \\so\\ \frac{3+5}8^{2} \\3+5=8^{2} \\8^{2} =\\64 \\\\ 64/8=\\\\\\8 \\there.\\\\\\[/tex]
2)[tex]-2(a-7)\\\\-2(a)(-7)\\\\=-2a+14\\\\\\there[/tex]
The total mass of 8 identical dictionaries is 9.92 kilograms. What is the mass, in kilograms, of one dictionary? Enter your answer in the space provided
A student-faculty government committee of 4 people is to be formed from 20 student
volunteers and 5 faculty volunteers.
a. If one person from the group of volunteers is chosen at random to draw the names
out of a hat, what is the probability that the person drawing the names is a student?
b. How many ways can the committee of four be formed if there are no restrictions on
composition.
C. How many ways can two of the students be chosen?
d. How many ways can 2 faculty be chosen?
e. What is the probability that the random selection of the four-person committee will
result in two students and two faculty?
the answer is c i just had this question your welcome
100 POINTS!!
Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Your friend claims that the only solution to the equation sin(x)=1 is x=90 degrees. Is your friend correct? If there are more solutions, explain how to determine additional solutions.
......hope it helps......
Answer:
yes,.to obtain sinx as 1 the angle must be 90degrees
so the answer is correct
but there are more solutions like when the cosine angle is 45 the answer is 1
and when x is 450 still sinx = 1..that is to say sin450= 1
(x-5)(X+12)=-70
[tex](x - 5)(x + 12) = - 70[/tex]
Answer:
[tex]x = - 2[/tex]
[tex]x = - 5[/tex]
Step-by-step explanation:
Give
[tex](x - 5)(x + 12)[/tex]
Apply FOIL Method
[tex]x {}^{2} + 7x - 60 = - 70[/tex]
Add 70 on both sides
[tex] {x}^{2} + 7x + 10[/tex]
Factor
[tex](x + 2)(x + 5)[/tex]
So our roots are
x=-2
x=-5
Answer:
dtet
Step-by-step explanation:
dgbyn
Suppose the random variables X, Y, and Z have the following joint probability distribution. x y z f ( x , y , z ) 1 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 2 0.20 2 1 1 0.20 2 1 2 0.15 2 2 1 0.10 2 2 2 0.05 Determine the conditional probability distribution of X given that Y
Answer:
Determine the conditional probability distribution of X given that Y = 1 and Z = 2. Round your answers to two decimal places (e.g. 98.76).
answer:
Given that Y = 1 : 2/5
Given that Z = 2 : 3/5
Step-by-step explanation:
The conditional probability distribution of X F x | yz^( x )
Given that Y = 1
F x | yz . ( x | yz ) = 2/5
Given that z = 2
= 3/5
attached below is the detailed solution
Please help me i will give you brainlest
Answer:
Step-by-step explanation:
5 ) c
6) c
7) b
8) a
Sebastian is going to choose the color pattern
Answer:
use blue red blue red
Step-by-step explanation:
If f(1) =160 and f(n+1)=-2f(n),
What is f(4)?
Answer:
f(n+1=-2f(n)
f(x)=-2f(n)
f(4)
f(4)=-2f(4)
Answer:
f(4) = - 1280
Step-by-step explanation:
Using the recursive rule and f(1) = 60 , then
f(2) = - 2f(1) = - 2 × 160 = - 320
f(3) = - 2f(2) = - 2 × - 320 = 640
f(4) = - 2f(3) = - 2 × 640 = - 1280
Find the area of the following figure with the indicated dimensions.use pi.
Answer:
The answer is "47.5354".
Step-by-step explanation:
In the given graph it is a half-circle and a triangle.
So, the diameter of the circle is 6.2 so the radius is 3.1
[tex]\text{Area of a circle}= \pi r^2\\\\\text{Area of a triangle}= \frac{1}{2} b h\\\\[/tex]
Calculating the total area of the shape:
[tex]= \pi r^2+\frac{1}{2} \times b\times h\\\\ = 3.14 \times 3.1^2+\frac{1}{2} \times 6.2 \times 5.6\\\\ = 3.14 \times 3.1^2+\frac{1}{2} \times 6.2 \times 5.6\\\\=3.14 \times 9.61+\frac{1}{2} \times 34.72\\\\=3.14 \times 9.61+\frac{1}{2} \times 34.72\\\\= 30.1754+17.36\\\\=47.5354\\\\[/tex]
pls help will give brainliest, 5* and thanks
trolls will get reports
Answer:
1.
M = 20 degrees
n =28.74
p = 20.12
2.
B = 73.65 degrees
C = 43.35 degrees
c = 30.05
3.
F = 21 degrees
G = 124 degrees
g = 23.13
Step-by-step explanation:
the law of sines is for a triangle ABC
a/sin(A) = b/sin(B) = c/sin(C)
1.
the sum of all angles in a triangle is always 180 degrees.
so, M = 180 - 125 - 35 = 20 degrees
m/sin(M) = n/sin(N)
12/sin(20) = n/sin(125)
sin(125) = sin(180-125) = sin(55)
n = 12×sin(55)/sin(20) = 28.74
p/sin(P) = m/sin(M)
p/sin(35) = m/sin(20)
p = m×sin(35)/sin(20) = 12×sin(35)/sin(20) = 20.12
2.
a/sin(A) = b/sin(B)
39/sin(63) = 42/sin(B)
sin(B) = 42×sin(63)/39 = 14×sin(63)/13
B = 73.65 degrees
therefore,
C = 180 - 63 - 73.65 = 43.35 degrees
c/sin(43.35) = 39/sin(63)
c = 39×sin(43.35)/sin(63) = 30.05
3.
e/sin(E) = f/sin(F)
16/sin(35) = 10/sin(F)
sin(F) = 10×sin(35)/16 = 5×sin(35)/8
F = 21 degrees
therefore,
G = 180 - 35 - 21 = 124 degrees
g/sin(124) = 16/sin(35)
sin(124) = sin(180-124) = sin(56)
g/sin(56) = 16/sin(35)
g = 16×sin(56)/sin(35) = 23.13
The time that it takes to fold 1,000 origami cranes varies inversely with the number of people folding the cranes. If a class of 25 students work together to fold the 1,000 cranes, it will take 3 hours. Write an equation to show the relationship between time (t) and the number of people (n) folding cranes.
ASAP!!!!
Answer:
t = [tex]\frac{75}{n}[/tex]
Step-by-step explanation:
Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]
Replace y with t, and replace x with n, since those are the variables in this situation:
t = [tex]\frac{k}{n}[/tex]
Plug in 3 as t and 25 as n, and solve for k:
3 = [tex]\frac{k}{25}[/tex]
75 = k
Create the equation by plugging in 75 as k:
t = [tex]\frac{75}{n}[/tex]
So, the equation is t = [tex]\frac{75}{n}[/tex]
Given that m∠abc=70° and m∠bcd=110°. Is it possible (consider all cases): Line AB intersects line CD?
The line AB and CD are parallel. Then it is impossible that the line AB intersects the line CD.
What are parallel lines?When the distance between the lines is constant, then the lines are called parallel lines. The lines do not intersect when they are separated from each other. And the slope of the lines is equal.
Given that ∠ABC = 70° and ∠BCD = 110°.
Then the line AB and the line CD makes the same angle with the line BC.
Hence, the line AB and CD are parallel.
Then it is impossible that the line AB intersects the line CD.
More about the parallel lines link is given below.
https://brainly.com/question/16701300
#SPJ1
