Answer:
[tex]MoE = 1.645\cdot \frac{13.1}{\sqrt{772} } \\\\MoE = 1.645\cdot 0.47147\\\\MoE = 0.776\\\\[/tex]
Step-by-step explanation:
Since the sample size is quite large, we can use the z-distribution.
The margin of error is given by
[tex]$ MoE = z_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]
Where n is the sample size, s is the sample standard deviation and [tex]z_{\alpha/2}[/tex] is the z-score corresponding to a 90% confidence level.
The z-score corresponding to a 90% confidence level is
Significance level = α = 1 - 0.90= 0.10/2 = 0.05
From the z-table at α = 0.05
z-score = 1.645
[tex]MoE = 1.645\cdot \frac{13.1}{\sqrt{772} } \\\\MoE = 1.645\cdot 0.47147\\\\MoE = 0.776\\\\[/tex]
Therefore, the margin of error is 0.776.
Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 64 + x2 − y2 R = {(x, y): x2 + y2 ≤ 64}
The area of the surface above the region R is 4096π square units.
Given that:
The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]
The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].
To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.
The integral for the area is given by:
[tex]Area = \int\int_R f(x, y) dA[/tex]
To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.
Using polar coordinates, we can parameterize the region R as follows:
x = rcos(θ)
y = rsin(θ)
where r goes from 0 to 8, and θ goes from 0 to 2π.
Now, rewrite the integral in polar coordinates:
[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]
Now, we can integrate with respect to r first and then with respect to θ:
[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]
Integrate with respect to r:
[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]
Now, we can integrate with respect to θ:
[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]
Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))
Area = 4096π + 128(0) - 0
Area = 4096π square units
So, the area of the surface above the region R is 4096π square units.
Learn more about Integration here:
https://brainly.com/question/31744185
#SPJ4
x+15=6 What does x equal?
Answer:
x=-9
Step-by-step explanation:
6-15=-9
Answer:
-9
Step-by-step explanation:
When you add some thing to a negative that means you are actually subtract that number
the product of 12 and K is 84 solve for K K =
Answer: k = 7
Step-by-step explanation:
12k=84
Divide(12)
k=7
Hope it helps <3
Answer:
7Step-by-step explanation:
The product of 12 and k is 84
let's create an equation:
[tex]12k = 84[/tex]
Divide both sides of the equation by 12
[tex] \frac{12 \: k}{12} = \frac{84}{12} [/tex]
Calculate
[tex]k = 7[/tex]
Hope this helps...
Best regards!!
a three dimensional figure with a circular base and a smooth face that diminishes to a single point
Answer:
I believe that the answer is a cone
Step-by-step explanation:
A cone is a three dimensional figure that has a circular base and a smooth face that goes up into a single point.
Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage?
Answer:
The range is found by subtracting the minimum data entry from the maximum data entry.
Step-by-step explanation:
The range is found by subtracting the minimum data entry from the maximum data entry.
It is easy to compute.
It uses only two entries from the data set.
Total length of a pole is 21.3 m. If 0.2m of the length of the pole is inside the ground. Find how much of its length is outside the ground
Answer:
21.1 mStep by step explanation
Total length of pole = 21.3 m
Length of pole inside the ground = 0.2 m
Let length of pole outside the ground be X,
So, according to the Question,
[tex]x + 0.2 = 21.3[/tex]
Move constant to R.H.S and change its sign
[tex]x = 21.3 - 0.2[/tex]
Calculate the difference
[tex]x = 21.1 \: m[/tex]
Hope this helps...
Good luck on your assignment...
Please help with this
Answer:
B
Step-by-step explanation:
Look at the parallelogram ABCD shown below. The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent. Statement Reasons 1 . AB is parallel to DC and AD is parallel to BC - definition of parallelogram 2 . angle 1 = angle 2, angle 3 = angle 4 - if two parallel lines are cut by a transversal then the corresponding angles are congruent 3 . BD = BD - Reflexive Property 4 . triangles ADB and CBD are congruent - if two sides and the included angle of a triangle are congruent to the corresponding sides and angle of another triangle , then the triangles are congruent by SAS postulate 5 . AB = DC, AD = BC - corresponding parts of congruent triangles are congruent Which statement is true about the table? 1. It is not correct because it provides incorrect sequence of statement 2 and statement 4. 2. It is not correct because it does not provide correct reasons for statement 2 and statement 4. 3. It is accurate because it provides the correct sequence of statements. 4. It is accurate because it provides the correct reasons for the statements.
Answer:
Can you add the image so i can anwser?
Step-by-step explanation:
Someone please help! Thxx
Answer:
E, needs more info to be determined
Step-by-step explanation:
We know that Kai takes 30 minutes round-trip to get to his school.
One way is uphill and the other is downhill.
He travels twice as fast downhill than uphill.
This means that uphill accounts for 20 minutes of the round-trip and downhill accounts for 10 minutes of his trip.
However, even with this information, we do not know how far his school is.
In order to figure out how far away his school is, we would need more information about the speed at which Kai is traveling.
Simply knowing that he travels twice as fast downhill is not enough.
This question could only be solved by knowing how many miles Kai travels uphill or downhill in a given time.
Evaluate f(x) when x= 9
f(x) = {6x² +2 if 6
112 if 9
No solution
O 110
O 12
56
Answer:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
Step-by-step explanation:
For this problem we have the following function given:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
In which table does y vary inversely with x? A. x y 1 3 2 9 3 27 B. x y 1 -5 2 5 3 15 C. x y 1 18 2 9 3 6 D. x y 1 4 2 8 3 12
Answer:
In Table C, y vary inversely with x.
1×18 = 18
2×9 = 18
3×6 = 18
18 = 18 = 18
Step-by-step explanation:
We are given four tables and asked to find out in which table y vary inversely with x.
We know that an inverse relation has a form given by
y = k/x
xy = k
where k must be a constant
Table A:
x | y
1 | 3
2 | 9
3 | 27
1×3 = 3
2×9 = 18
3×27 = 81
3 ≠ 18 ≠ 81
Hence y does not vary inversely with x.
Table B:
x | y
1 | -5
2 | 5
3 | 15
1×-5 = -5
2×5 = 10
3×15 = 45
-5 ≠ 10 ≠ 45
Hence y does not vary inversely with x.
Table C:
x | y
1 | 18
2 | 9
3 | 6
1×18 = 18
2×9 = 18
3×6 = 18
18 = 18 = 18
Hence y vary inversely with x.
Table D:
x | y
1 | 4
2 | 8
3 | 12
1×4 = 4
2×8 = 16
3×12 = 36
4 ≠ 16 ≠ 36
Hence y does not vary inversely with x.
Find the intervals of convergence of f(x), f '(x), f ''(x), and ∫f(x) dx. (Be sure to include a check for convergence at the endpoints of the intervals. Enter your answer using interval notation.) f(x) = [infinity] (−1)n + 1(x − 8)n n8n n = 1
Answer: See solution and explanations in the attached documents
Step-by-step explanation:
See explanations in the attached documents
For the piecewise function, find the values g(-2), g(3), and g(4).
X +5, for x<3
g(x)=
6- X, for x>3
9(-2)=
g(3)=
9(4)=
Answer:
g(-2)= -2 + 5 =3 ( here we chose the function g(x)= x+5 as x< 3)
Step-by-step explanation:
g(3)= is not defined ( function is defined for x<3 and x>3 but not x=3)
g(4) = 6-4=2 ( here we chose the function g(x)= 6-x as x> 3)
what is this? 15.8 = d/25
Answer:
395
Step-by-step explanation:
15.8=d/25
multiply both sides by 25 to remove the denominator
25×15.8=d
d=395
which of the following is equivalent to the expression below? log2-log14 A. LOG(1/7) B. LOG(-12) C. LOG 12 D. LOG 7
Answer:
The answer is option A.
Step-by-step explanation:
Using the properties of logarithms
that's
[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]
log 2 - log 14 is
[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]
Simplify
We have the final answer as
[tex] log( \frac{1}{7} ) [/tex]
Hope this helps you
Answer:
log ( 1/7)
Step-by-step explanation:
log2-log14
We know that log ( a/b) = log a - log b
log (2 /14)
log ( 1/7)
The measure of ∠1 is 150°. What are the measures of ∠4, ∠3 and ∠2?
Answer:
∠1 is 150°
∠2 is 30°
∠3 is 150°
∠4 is 30°
Step-by-step explanation:
∠1 is vertically opposite to ∠3 so they are equal
360° - (150° + 150°) = 360° - 300° = 60°
∠2 and ∠4 must sum to 60°
Step-by-step explanation:
From the question
∠1 is opposite to ∠ 3 and vertically opposite angles are equal
So
∠1 = ∠ 3
That's
∠ 3 = 150°∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°
So to find ∠4, subtract ∠3 from 180°
That's
∠ 4 = 180 - ∠ 3
∠ 4 = 180 - 150
∠ 4 = 30°Since ∠ 4 and ∠ 2 are opposite they are also equal
That's
∠ 4 = ∠ 2
Therefore
∠ 2 = 30°Hope this helps you
For each sequence, find the common difference.
-6,0, 6, 12,...
8, 15, 22,29, ...
-2,-4, -6, -8,...
2,-1,-4,-7....
Please helpp
Answer:
first is 18
second is 36
third is -10
fourth is -10
write and equation to represent the following statement 28 is 12 less thank K. solve for K K =
Answer:
K = 40
Step-by-step explanation:
As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"
Hope it helps and pls mark as brainliest : )
Answer:
Equation : 28 = k - 12K = 40Step-by-step explanation:
28 is 12 less than k
Let's create an equation:
[tex]28 = k - 12[/tex]
Now, let's solve:
[tex]28 = k - 12[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - k = - 12 - 28[/tex]
Calculate the difference
[tex] - k = - 40[/tex]
Change the signs on both sides of the equation
[tex]k = 40[/tex]
Hope this helps...
Best regards!!
A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age?
Hey there! I'm happy to help!
We see that the father is 60 years old, and the son is half of that age, so this means that the son is 30 years old.
We want to see the age the son was at when the father was four times his age. We know that the father is thirty years older than him, so we can write this equation with s representing the age of the son.
s+30=4s (30 years older than the son is equal to to four times the son's age at the time)
We subtract 30 from both sides.
s=4s-30
We subtract 4s from both sides.
-3s=-30
We divide both sides by -3.
s=10
Therefore, the boy was 10 when his father was four times his age. This is because his father would have been 40 because that is 30 more years than 10, and it is four times ten!
Have a wonderful day! :D
75% letter size paper and 25% legal size paper. What is the ratio of letter size paper to legal size paper
Answer:
3:1
Step-by-step explanation:
75%=[tex]\frac{75}{100}[/tex]=[tex]\frac{3}{4}[/tex]
25%=[tex]\frac{25}{100}[/tex]=[tex]\frac{1}{4}[/tex]
Solve of the following equations for x: 3x = 5
Answer: 1.7
Step-by-step explanation:
5 divided by 3=1.666666667
1.6 and next 6 in line is over 5 so the 6 turns to a 7
3*1.7= 5.1 but when rounded 1 tells 5 to stay down so it = 5
Please help!! Over several years, Stephon gathered data about his age and the time it took him to run two laps on the school track. The scatter plot shows the data he gathered and the line of best fit. The equation of the line of best fit is y = -2.1x + 565.6. Based on the line of best fit, approximately how long will it take Stephon to run two laps on the track when he is 192 months old?
Answer:
It will take Stephon about A: 163 seconds to run two laps when he is 192 months old.
Step-by-step explanation:
To find 163 seconds all I did was eyeball where 192 months is going to be on the x-axis and lined it up with the provided line of fit, then I ran it across the x-axis to the y-axis and I got around 163 seconds.
Given line of best fit is y = -2.1x + 565.6, where x is age in months and y is time in seconds, it take Stephon 162.4 seconds to run two laps on the track when he is 192 months old
A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points.
Given in the question,
x = age in months
y = time in seconds
Here, age of child is independent and time taken to run two laps is dependent variable.
given line of best fit : y = -2.1x + 565.6
given y = 192 months
finding the value of y :
y = -2.1x + 565.6 = -2.1 * 192 + 565.6 = 162.4
Learn more about line of best fit here
https://brainly.com/question/29250235
#SPJ2
if the probability of drawing a red card from a box is 3/8, what are the odds against drawing a red card from the box
Answer: 5/8
Step-by-step explanation:
Simply do 8/8(1)-3/8 to get 5/8
Hope it helps <3
a warehouse had 3 shelves long enough to hold 8 boxes and high enough to hold 4 boxes. all the shelves are full how many boxes are on the shelves all together?
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I think. I just multiplies the 3 numbers. Hope this helps (:
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I just multiplies the 3 numbers.
A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: A=4, B=3, C=2, D=1, and F=0. Compute the grade point average (GPA) and round the result to two decimal places.
Answer:
Computation of Grade Point Average (GPA):
GPA = Total Weighted Points divided by total credit hours
= 45/19
= 2.37 on 4.00 Grade Average
Step-by-step explanation:
a) Data and Computations:
Courses Grade Letters Credit Hours Quality Points Weighted Points
1 B 4 3 12
2 B 5 3 15
3 A 1 4 4
4 C 5 2 10
5 D 4 1 4
Total 19 credit hours 45 Points
b) GPA = Total Weighted Points divided by total credit hours
= 45/19
= 2.37
c) The GPA for this student is the total weighted points (which is a product of the credit hours (loads) and the quality point) expressed as a ratio of the total credit hours for the courses she took. The grade point average ensures that the each point used in calculating the GPA is weighed by the credit hours allocated to the course. The resultant figure of 2.37 implies that out of 4.00 grade points, the student scored 2.37, translating to about 59%.
6th grade math help me, please:D
Answer:
the answer is c...............
What is the value of x in the triangle
Answer:
3
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]x^{2} +b^{2} =(3\sqrt{2} )^{2}[/tex]
[tex]3*3=9[/tex][tex]\sqrt{2} *\sqrt{2} =2[/tex]
[tex]2*9=18[/tex]
9*2=18
x^2=9
b^2=9
x=3
Hi I need this question please asap.
Points A,B,C and D are midpoints of the sides of the larger square. If the smaller square has area 60, what is the area of the bigger square?
Answer:
80
Step-by-step explanation:
13. A hole is drilled in a block of wood as shown in the sketch. The hole is 3/4 of
the total depth of the wood. The total depth of the block of wood is 13/16 in.
How deep is the hole?
Hole
The depth of hole is 0.609 inches.
Given, the total depth of the block of wood is [tex]\frac{13}{16}[/tex] inches.
Since the hole is [tex]\frac{3}{4}[/tex] of the total depth, so the depth of the hole will be,
[tex]D=\frac{3}{4} \times\frac{13}{16}[/tex]
Or, [tex]D=\frac{39}{64}[/tex]
[tex]D=0.609375 \ in[/tex]
Hence the depth of hole is 0.609 inches.
For more details follow the link:
https://brainly.com/question/2263981