The alternating current (AC) breakdown voltage of an insulating liquid indicates its dielectric strength. The article "Testing Practices for the AC Breakdown Voltage Testing of Insulation Liquids" gave the accompanying sample observations on breakdown voltage (kV) of a particular circuit under certain conditions.
62 50 53 57 41 53 55 61 59 64 50 53 64 62 50 68
54 55 57 50 55 50 56 55 46 55 53 54 52 47 47 55
57 48 63 57 57 55 53 59 53 52 50 55 60 50 56 58
a) Construct a boxplot of the data and comment on interesting features.
b) Calculate and interpret a 95% Confidence Interval for true average breakdown voltage μ. Does it appeas that μ has been precisely estimated? Explain.
c) Suppose the investigator believes that virtually all values of breakdown voltage are between 40 and 70. What sample size would be appropriate for the 95% Confidence Interval to have a width of 2kV (so that μ is estimated to within 1 kV with 95% confidence?)
Answers
Answer:
Step-by-step explanation:
Hello!
Given the variable
X: breakdown voltage of an insulating liquid under certain conditions.
a)
Graphic in attachment.
Box: The median is closer to the third quartile than the first quartile showing skewness to the left.
The black dot in the middle of the box represents the sample mean (X[bar]) as you can see it is also moved to the right side of the distribution, affected by the presence of an outlier.
Whiskers:
The upper whisker is smaller than the lower one and there is a value that can be considered an outlier.
Altogether you can say that the distribution of the data set is skewed to the left.
b)
To estimate the population mean you need the population to be at least normal. The box plot shows that the distribution is not symmetrical but, considering that the sample size is n= 48 you can apply the Central Limit Theorem and approximate the sampling distribution to normal.
X[bar]≈N(μ;σ²)
As the distribution is approximate, using the sample standard deviation (since we don't know the population value) for the distribution standard deviation is also valid ⇒ \(Z= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } }\)
X[bar] ± \(Z_{1-\alpha /2}\) * \(\frac{S}{\sqrt{n} }\)
∑X= 2626 ∑X²= 144950 n= 48
X[bar]= ∑X/n= 2626/48= 54.71
S²= 1/n[∑X²- (∑X)²/n]= 1/47[144950-(2626)²/48]= 27.36
S= 5.23
\(Z_{1-\alpha /2}= Z_{0.975}= 1.96\)
54.71 ± 1.96 * \(\frac{5.23}{\sqrt{48} }\)
[53.22; 56.18]kV
c)
95% CI
amplitude a=2 kV i.e. semi amplitude d= 1 kV
The semi amplitude or margin of error for the CI can be calculated as:
d= \(Z_{1-\alpha /2}\) * \(\frac{S}{\sqrt{n} }\)
From this formula you can clear the sample size
\(\frac{d}{Z_{1-\alpha /2}} = \frac{S}{\sqrt{n} }\)
\((\frac{d}{Z_{1-\alpha /2}} )*\sqrt{n} = S\)
\(\sqrt{n} = S* (\frac{Z_{1-\alpha /2}}{d} )\)
\(n = (S* (\frac{Z_{1-\alpha /2}}{d} ))^2\)
\(n= (5.23*(\frac{1.96}{1} ))^2= 105.08= 106\)
Related Questions
Masud rode his bike 48 miles in 6 days. He rode the same number of miles
each day. How many miles did he ride each day?
A 7
B 8
C 9
D 42
Answers
please help with this question
Answers
Answer:
B. xy(y - x) (y + x)
Step-by-step explanation:
Step by step
Original
xy^3 - x^3y
First factor out xy
xy (y^2 - x^2)
We know that (y^2 - x^2) is a perfect square so
Factor out (y - x)( y + x )
(xy) (y -x ) ( y + x) is your answer
It’s the 2nd one on your attachment
The midpoint of \overline{\text{AB}} AB is M(7, -7)M(7,−7). If the coordinates of AA are (8, -6)(8,−6), what are the coordinates of BB?
Answers
Using the formula for the midpoint of the line with given points A and B as the end points of the line, the coordinates of the point B is (6,-8).
How do you find the midpoint of a line segment?To find the midpoint of a line segment, you must first find the coordinates of the two endpoints of the segment. Then, take the average of the x-coordinates and the y-coordinates to find the x and y coordinates of the midpoint. This can be done by adding the x-coordinates and y-coordinates of the two endpoints together and then dividing by 2.
What is the formula for finding the midpoint of a line segment?
The formula for finding the midpoint of a line segment is:
Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )
Where (x1,y1) and (x2,y2) are the coordinates of the two endpoints of the line segment.
Using the given coordinates of point A(8,-6) and the midpoint M(7,-7) of the line, and using the midpoint formula for a line AB,
Midpoint(M) = \((\frac{x1+x2}{2},\frac{y1+y2}{2} )\)
where x1, y1 are coordinates of point A , and x2, y2 are the coordinates of point B
so , (7,-7) = \((\frac{8+x2}{2} , \frac{-6+y2}{2})\)
equating the corresponding points,
7 =(8+x2)/2
therefore, x2 = 6
and , -7 = (-6+y2)/2
therefore , y2 = -8
Hence the coordinates of B is , (x2,y2 ) = (6,-8)
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4x-5 2x+7 Find the value of x
answers should be from
27
37
47
57
Answers
4x - 5 = 2x + 7
First, let's simplify the equation by combining like terms:
4x - 2x = 7 + 5
2x = 12
Next, divide both sides of the equation by 2 to solve for x:
x = 12 / 2
x = 6
Therefore, the value of x that satisfies the equation is 6. None of the provided answer options (27, 37, 47, 57) are equal to 6.
I need help solving this
Answers
The cylinder has a volume of 150.796 in³. The cylinder has a surface area of 175.929 in².
What's volume of cylinder ?The quantity of three-dimensional space that an object or closed surface occupies is referred to as volume in mathematics. The cubic units of volume are m³, cm³, in³, and so on.
How does surface area work?The sum of all of an object's faces is its surface area in three dimensions. Wrapping, painting, and finally building things to achieve the best possible design are examples of real-world applications of the concept of surface areas.
Evaluating :Given that a volume of cylinder = h × r² × π
h = 12 in
r = 2 in
volume = ?
Volume of cylinder = h × r² ×π
= =12 × 3.14×(2)²
=37.68 × 4
=150.796 in³
B). Surface area of cylinder= 2πr² + 2πrh
=2× 3.14 × (2)²+2× 3.14× 2×12
=175.929in²
The formula V=r²(h) can be used to determine a cylinder's volume. Simply multiplying the area of the circular base shape by the height is all that is required to determine a cylinder's volume.
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What is the area of the square that measures 3.1 m on each side
Answers
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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A biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road. How much more does he need to travel? (distance)
Answers
The biker needs to travel 45 km more to complete his journey.
Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,
Let the total distance of the road be x,
So,
2x/5 - 5 = 3x/8
2x/5 - 3x/8 = 5
Solving for x,
Multiply by 40 to both sides,
16x-15x = 200
x = 200
Therefore, the total distance of the road is 200 km.
Since, he travelled =
200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km
Therefore, he needs to travel 200-155 = 45 km more.
Hence, the biker needs to travel 45 km more to complete his journey.
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A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answers
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
70+20=90
90+20=110
110+20=130
A map is drawn to the scale 1:4,000.
(a) The length of a road on the map is
3.5 cm. Find its actual length in meters.
Answers
Answer:
Original length of the road = 14,000 meter
Step-by-step explanation:
Given Scale;
1 cm = 4,000 meter
The length of road on map = 3.5 cm
Find:
Computation:
Original length of the road
Original length = Length on drawing x scale factor
Original length of the road = The length of road on map x scale factor
Original length of the road = 4,000 x 3.5
Original length of the road = 14,000 meter
What is half of £15.90?
I need exact answer really quick!
PLEASE HELPPPPPPP!
Answers
Answer:7.95
Step-by-step explanation:
15.90/2
Answer:
£7.95
Step-by-step explanation:
Here
The difference between the areas of the figures is less than 4.
An absolute value inequality that represents this situation is ___
The solution of the inequality is ___
Thank you!
Answers
The second one is
4=x-4
-x=-4-4
X=8
Find the midpoint between the pair of points. (-1, -5) and (-5, 9)
Answers
Answer:
Step-by-step explanation:
(-1-5)/2 = -6/2= -3
(-5+9)/2 = 4/2 = 2
(-3, 2)
Which of the following scatterplots below does the correlation r=0•8 match
Answers
Answer:
Step-by-step explanation:
Determine wether y varies directly with x. If so find the constant of variation k and write the equation
Answers
The given data is incorrect, k does not constitute a constant, but rather y does not varies directly to x.
What is defined as the direct variation?A simple connection between two variables is described by direct variation. If y=kx, we say it varies significantly with x (or even as x in some textbooks) for some constant k, known as the constant of variation or the constant of proportionality.Because y varies directly with x, it would fit a equation y=kx for each and every point with in set.We may have 11=7k for the initial point, implying that k=11/7.
Again for second point, we'd have 13=8k, which means k=13/8.
Using proportions, we can see that 11/7 doesn't really equal 13/8: cross multiply and you get 11*8=7*13, or 88=91.
Thus, this is incorrect, k does not constitute a constant, but rather y does not varies directly to x.
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The complete question is-
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
x y
7 11
8 13
9 15
10 17
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 20 miles per hour slower than the westbound train. If the two trains are 360 miles apart after 2 hours, what is the rate of the eastbound train?
Answers
Answer:
Westbound = x;
Eastbourne = x-20;
So they will have the common rate: 360/2 = 180;
x+x-20 = 180
2x = 200;
x = 100;
So Eastbourne will be 100-20 = 80 miles per an hour;
Angle A and Angle B are supplementary, mZA = (6x + 72) and mZB = (2x + 28)". Find x, the
mZA and the mZB.
Answers
Answer:
x = 10
m<A = 132 degrees
m<B = 48 degrees
Step-by-step explanation:
Supplementary = angles that make up 180 degrees
We know <A and <B are supplemntary, so 2x+28+6x+72 = 180.
8x + 100 = 180
8x = 80
x = 10
I input 10 into the equations to solve for the measures of the angles
Tracy is cleaning up after tilling a bathroom. there's are 2 open boxes of tile. each box has 5/8 of the tiles remaining.how many boxes of tiles lComplete the calculations to show how you found your answer . express your final answer in the simplest form.
Answers
When we multiply a fraction by a number, it is the same as multiplying the numerator by this number, therefore, our calculation can be rewritten as
\(2\times\frac{5}{8}=\frac{2\times5}{8}=\frac{10}{8}=\frac{5}{4}=1\frac{1}{4}\)Find the equation of a line parallel to y=x−1 that contains the point (−3,−2). Write the equation in slope-intercept form.
Answers
Answer:
y = x + 1
Step-by-step explanation:
Parallel lines have same slope.
y = x - 1
Compare with the equation of line in slope y-intercept form: y = mx +b
Here, m is the slope and b is the y-intercept.
m =1
Now, the equation is,
y = x + b
The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,
-2 = -3 + b
-2 + 3 = b
\(\boxed{b= 1}\)
Equation of line in slope-intercept form:
\(\boxed{\bf y = x + 1}\)
The equation is :
↬ y = x + 1Solution:
We KnowIf two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.
We shouldn't forget about a point on the line : (-3, -2).
I plug that into a point-slope which is :
\(\sf{y-y_1=m(x-x_1)}\)
Slope is 1 so
\(\sf{y-y_1=1(x-x_1)}\)
Simplify
\(\sf{y-y_1=x-x_1}\)
Now I plug in the other numbers.
-3 and -2 are x and y, respectively.
\(\sf{y-(-2)=x-(-3)}\)
Simplify
\(\sf{y+2=x+3}\)
We're almost there, the objective is to have an equation in y = mx + b form.
So now I subtract 2 from each side
\(\sf{y=x+1}\)
Hence, the equation is y = x + 1someone please help
Answers
Answer:
28
Step-by-step explanation:
78
Simplify -3 p3 + 5 p + (-2 p2 ) + (-4) - 12 p + 5 - (-8 p3 ). Select the answer in descending powers of p . 1 - 7 p - 2 p2 + 5 p3 1 + 7 p + 2 p2 - 5 p3 5 p3 - 2 p2 - 7 p + 1 -5 p3 + 2 p2 + 7 p + 1
Answers
Step-by-step explanation:
Let's simplify step-by-step.
−3p3+5p−2p2−4−12p+5−−8p3
=−3p3+5p+−2p2+−4+−12p+5+8p3
Combine Like Terms:
=−3p3+5p+−2p2+−4+−12p+5+8p3
=(−3p3+8p3)+(−2p2)+(5p+−12p)+(−4+5)
=5p3+−2p2+−7p+1
Answer:
=5p3−2p2−7p+1
I need help understanding this problem,
In a right triangle, one angle measures x°, where sinx° = 4/5. What is cos(90° - x)?
Answers
In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, if sinx° = 4/5, we can label the opposite side of angle x as 4 and the hypotenuse as 5.
Using the Pythagorean theorem, we can find the length of the adjacent side of angle x:
a^2 + b^2 = c^2
where c is the hypotenuse, a is the adjacent side, and b is the opposite side.
Plugging in the values we know, we get:
a^2 + 4^2 = 5^2
a^2 + 16 = 25
a^2 = 9
a = 3
So the adjacent side of angle x is 3.
Now, we need to find cos(90° - x). Using the cosine formula, we know that:
cos(90° - x) = sinx°
Substituting sinx° = 4/5, we get:
cos(90° - x) = 4/5
Therefore, cos(90° - x) is equal to 4/5.
Hope this helped (:
Rewrite the following without an exponent. 1 1 - 4 4 D 0 DB x 5 ?
Answers
Explanation:
Negative exponents tells us that the number has to be in the numerator (if it's in the numerator it has to be in the denominator):
\(\frac{1}{4^{-4}}=4^4\)Now we just have to solve:
\(4^4=4\times4\times4\times4=256\)Answer:
The result is 256
what is h^2-3gh+7g+g^2+5g+3h+h-gh-4gh-9+h^2+10g if g is -1 and h is 4 and how you solve it?
Answers
Answer:
48
Step-by-step explanation:
Plug in all the number and solve!
Can I have brainliest!
Answer:
48
Step-by-step explanation:
A community would like to add a brick paver border around their swimming pool. They created the following image to represent the pool with the border. A large rectangle with a length of 48 feet and a width of 28 feet. Inside of it is another rectangle with a length of 32 feet and a width of 12 feet. Part A: Find the total area of the brick paver border that surrounds the 12 ft by 32 ft pool. Show your work. (2 points) Part B: If brick pavers cost $8 per square foot, what is the total cost of the brick pavers needed for this project? Explain. (2 points)
Answers
Part A: The total area of the brick paver border is \(960\) square feet.
Part B: The total cost of the brick pavers needed for this project is $\(7,680\).
Part A: To find the total area of the brick paver border, we need to subtract the area of the pool from the area of the larger rectangle. The area of the pool is \(32\) feet multiplied by 12 feet, which is equal to \(384\)square feet.
The area of the larger rectangle is \(48\) feet multiplied by \(28\) feet, which is equal to \(1,344\) square feet. Therefore, the area of the brick paver border is \(1,344\) square feet minus \(384\) square feet, which equals \(960\) square feet.
Part B: If brick pavers cost $\(8\)per square foot, we can calculate the total cost by multiplying the cost per square foot by the total area of the brick paver border. The total area of the brick paver border is \(960\) square feet, and the cost per square foot is $\(8\).
Therefore, the total cost of the brick pavers needed for this project is $\(8\)multiplied by \(960\) square feet, which equals $\(7,680\).
Note: The calculations provided assume that the border consists of a single layer of brick pavers.
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Help show work pls :) ill mark brainliest
Answers
Answer:
52.2
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24÷2²(-3)-7-2²-2(3-6) step by step please and thank you!
Answers
Answer:
\(24 \div {2}^{2} ( - 3) - 7 - {2}^{2} - 2(3 - 6) \\ 24 \div 4( - 3) - 7 - 4 - 6 - 12 \\ 24 \div ( - 12) - 3 - 6 - 12 \\ - 2 - 3 - 6 - 12 \\ - 5 - 6 - 12 \\ - 11 - 12 \\ = - 23\)
please help me I rlly do need help
Answers
A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
Complete the table to show the relationship between the amounts of salt and water in the stew recipe. Enter a number in each box.
Can someone please help me quickly!! And also let me know if I got the first 2 correct
Answers
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
What is the amount of salt?A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
There is a ratio issue here.
As X is to three, 3 is to 4.
3 : 4 :: X : 3
To eliminate the fractions, multiply each integer in the ratio by 12.
9 : 12 :: 9X : 12
This is a portion of what is
9 / 12 = 9X / 12
to obtain, cross-multiply.
9 / 12 = 3 teaspoons of salt,
Check: 3 cup of flour yields 3 cups, which is a 4x increase.
The amount of salt in 9/12 tablespoons is four times that of 3 tablespoons.
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
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2 and 1/3 devided by 2/3
Answers
Answer:
3/5 , 7/2 , 3 1/2
Step-by-step explanation:
Step 1 -Two Plus One - Third
2 + \(\frac{1}{3}\)
Make Both Fractions-
\(\frac{2}{1}\) + \(\frac{1}{3}\)
Make Same Denominator ( Bottom # Of Fraction )-
\(\frac{2}{1}\) * \(\frac{3}{3}\) = \(\frac{6}{3}\)
New Equation-
\(\frac{6}{3}\) + \(\frac{1}{3}\)= \(\frac{7}{3}\)
Step 2-Seven - Thirds Divided By Two-Thirds.
\(\frac{7}{3} / \frac{2}{3}\)
Divide In Parts-
7 / 2 = 3.5
Final Answer of '2 and 1/3 divided by 2/3 is 3.5, 7/2, 3 1/2! Don't Forget To Rate Brainiest! -AslinaSolve with explanation please
Answers
Answer:
Length of the rectangular lot = 60 meters
Width of the rectangular lot = 30 meters
Step-by-step explanation:
Let the width of the rectangular lot be x meters.
So, Length of the same = 2x metres.
\(A(rectangular \:lot) = (2x)(x)\)
\(\implies A(rectangular \:lot) = 2x^2\)
When length is increasEd by 40 m and width by 6 m. Then....
New length = \((2x + 40) \:m\)
New width =\((x + 6) \:m\)
According to the question:
\((2x + 40)(x + 6) = 2(2x^2)\)
\(\implies 2x(x + 6) + 40(x + 6) - 4x^2=0\)
\(\implies 2x^2+12x + 40x + 240 - 4x^2=0\)
\(\implies 2x^2- 4x^2+12x + 40x + 240 =0\)
\(\implies -2x^2+52x + 240 =0\)
\(\implies 2(x^2-26x - 120) =0\)
\(\implies x^2-26x - 120=0\)
\(\implies x^2-30x+4x - 120=0\)
\(\implies x(x-30)+4(x - 30)=0\)
\(\implies (x-30)(x+4)=0\)
\(\implies x-30=0,\: x+4=0\)
\(\implies x=30,\: x=-4\)
Since, x represents the side length, so its value can't be negative.
\(\implies x=30\)
\(\implies 2x=2(30)=60\)
Thus,
Length of the rectangular lot = 60 meters
Width of the rectangular lot = 30 meters