Step-by-step explanation:
Given:
[tex]A=1.5\:\text{cm}^2×\left(\frac{1\:\text{m}^2}{10^4\:\text{cm}^2}\right)=1.5×10^{-4}\:\text{m}^2[/tex]
[tex]d = 2.0\:\text{mm} = 2.0×10^{-3}\:\text{mm}[/tex]
The charge stored in a capacitor is given by [tex]Q = CV.[/tex] In the case of a parallel-plate capacitor, its capacitance C is given by
[tex]C = \epsilon_0\dfrac{A}{d}[/tex]
where [tex]\epsilon_0[/tex] = permittivity of free space. The amount of charge stored in the capacitor is then
[tex]Q = \left(\epsilon_0\dfrac{A}{d}\right)V[/tex]
[tex]\:\:\:\:\:=\left[\dfrac{(8.85×10^{-12}\:\text{F/m})(1.5×10^{-4}\:\text{m}^2)}{(2.0×10^{-3}\:\text{m})}\right](12\:\text{V})[/tex]
[tex]\:\:\:\:\:=8.0×10^{-12}\:\text{C}[/tex]
Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean
(a) Find endpoints of a t-distribution with 5 % beyond them in each tail if the sample has size n = 12.
(b) Find endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20.
Answer:
a) Hence the endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n=12 is ± 1.796.
b) Hence the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ± 2.539.
Step-by-step explanation:
Here the answer is given as follows,
Graph the complex numbers in the complex plane
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Answer:
see attached
Step-by-step explanation:
The imaginary value is plotted on the vertical axis in the same way that the y-coordinate would be for an ordered pair (x, y). Similarly, the real value is plotted on the horizontal axis.
__
I find it helpful to think of the complex number a+bi as equivalent to the ordered pair (x, y) = (a, b) when it comes to graphing.
The graph of y= -2x + 10 is:
O A. a line that shows only one solution to the equation.
O B. a point that shows the y-intercept.
O C. a line that shows the set of all solutions to the equation.
O D. a point that shows one solution to the equation.
SUBM
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Answer:
C. a line that shows the set of all solutions to the equation.
Step-by-step explanation:
Any graph shows the set of all solutions to the equation being graphed.
The graph of a linear function is a straight line.
I conducted a poll and asked 1012 students how many books they read last year. The data indicates x = 12.1 books and s = 16.6 books. Construct a 90% confidence interval for the number of books the students read. Z = 1.645
Answer:
(11.242 ; 12.958)
Step-by-step explanation:
The confidence interval is obtained using the relation :
C. I = xbar ± Zcritical * s/√n
Given that ::
xbar = 12.1 ;
Standard deviation, s = 16.6
n = 1012
C. I = 12.1 ± 1.645 * (16.6/√1012)
C.I = 12.1 ± 0.8583881
C. I = 11.242 ; 12.958
jope works 42 hours in a 6 day week, calculate the number of hours in a week he is not at work
Answer:
the number of hours in a week Jope, who is not at work, is 102 hours
Step-by-step explanation:
call X is the number of hours in a week Jope is not at work.
=> the number of hours in a week = X + the number of work hours in a week
=> 6*24 = X + 42
=> X = 6*24 - 42
=> X = 102 hours
write an equation for a radical function that has a domain of all real numbers greater than or equal to -2 and a range of all real numbers greater than of equal to 1
[tex] y = 1 + \sqrt{x + 2} [/tex]
the root must at least be 0 to have a solution. the "1+" makes it at least 1 instead of zero
If a house is worth $125,000 and depreciates by 7.5% per year, how much is it worth in two years
Answer:
Solution given;
principal [P]=$125,000
depreciated rate[R]=7.5%
time[t]=2 years
worth price of house [A]=???
we have
Worth price[A]=[tex]\large \bold P(1-\frac{R}{100})^{t}[/tex]
=[tex]125,000(1-\frac{7.5}{100})^{2}[/tex]
=125,000*0.925²
=125,000*0.855625
=106953.125
its worth price is $106953.125ZDAC = ZBAD.
What is the length of CD?
Round to one decimal place.
Answer:
3.4
Step-by-step explanation:
The angle bisector theorem states that for a triangle that is bisected, the ratio between the two edges in each of the triangles that form are proportional to each other.
For this triangle, the bisector splits the triangle into ΔABD and ΔACD. The edges of ΔABD are BD and AB, while the edges of ΔACD are CD and AC. Therefore, we can say that BD/AB = CD/AC . Note that both parts of line that is bisected (BC) are on top, while the other edge sides are on the bottom. *
BD/AB = CD/AC
2.6/4.9 = ? / 6.5
multiply both sides by 6.5 to isolate the ?
2.6 * 6.5 / 4.9 = ? ≈ 3.4
* this can also be rearranged so that AB/BD = AC/CD, but it is vital to ensure that either both sides that are part of the larger triangle are on top or both parts of the bisected line are on top
(d) 320 If the measurement of two angles of a triangle are 72º and 70%, find third ange in degrees. If the measurement of two angles of a triangle are 630 and 100
Out of a total of 10 college textbooks estimate the standard deviation of their ages if the oldest textbook is known to be 7.9 years old and the newest textbook is 1.3 years old.
Answer:
Given that the maximum age of the textbook is 7.9 years and the minimum age of the textbook is 1.3 years.
Using the range rule, the standard deviation is estimated as,
S≈maximum−minimum/4
=7.9−1.3/4
=1.65
The required value of the approximate standard deviation is 1.65.
The standard deviation of the data is 1.65.
What is Standard Deviation?Standard deviation is the measure of the deviation of the data from the mean.
The total college textbooks is 10
The oldest book is 7.9 years old
The newest book is 1.3 years old
The standard deviation of range is equal to one fourth of the difference of maximum to minimum.
The standard deviation = ( 7.9 - 1.3 ) /4 = 1.65
To know more about Standard Deviation
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One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.
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Answer:
90°, 60°, 30°
Step-by-step explanation:
The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.
The first angle is 3 ratio units, or 90°.
The second angle is 2 ratio units, or 60°.
The third angle is half that, or 30°.
The three angles are 90°, 60°, 30°.
Which equation shows a slope of 3 and a y-intercept of (0,7)?
y = 7x + 3
y = −7x + 3
y = 3x
y = 3x + 7
Answer:
[tex]{ \tt{y = 3x + 7}}[/tex]
Step-by-step explanation:
General equation of a line:
[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]
m is the slope, and c is the y-intercept:
m = 3, and c = 7
PLEASE HELP
Write the equation of the line that is perpendicular to the given segment and that passes through the point (-6, -3). A. 1 V=--x-3 2 B. 1 V=--X-6 2 C. y = 2x + 9 D. = 2x-6.
Answer:
C
Step-by-step explanation:
The slope of the line will be (2) and the equation will be C
(A) A small business ships homemade candies to anywhere in the world. Suppose a random sample of 16 orders is selected and each is weighed. The sample mean was found to be 410 grams and the sample standard deviation was 40 grams. Find the 90% confidence interval for the mean weight of shipped homemade candies. (Round your final answers to the nearest hundredth)
(B) When 500 college students are randomly selected and surveyed; it is found that 155 own a car. Find a 90% confidence interval for the true proportion of all college students who own a car.
(Round your final answers to the nearest hundredth)
(C) Interpret the results (the interval) you got in (A) and (B)
The correct answer to the given question is "[tex]\bold{392.47\ < \mu <\ 427.53}[/tex],[tex]\bold{0.28 \ < P <\ 0.34}[/tex], and for Interpret results go to the C part.
Following are the solution to the given parts:
A)
[tex]\to \bold{(n) = 16}[/tex]
[tex]\to \bold{(\bar{X}) = 410}[/tex]
[tex]\to \bold{(\sigma) = 40}[/tex]
In the given question, we calculate [tex]90\%[/tex] of the confidence interval for the mean weight of shipped homemade candies that can be calculated as follows:
[tex]\to \bold{\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{S}{\sqrt{n}}}[/tex]
[tex]\to \bold{C.I= 0.90}\\\\\to \bold{(\alpha) = 1 - 0.90 = 0.10}\\\\ \to \bold{\frac{\alpha}{2} = \frac{0.10}{2} = 0.05}\\\\ \to \bold{(df) = n-1 = 16-1 = 15}\\\\[/tex]
Using the t table we calculate [tex]t_{ \frac{\alpha}{2}} = 1.753[/tex] When [tex]90\%[/tex] of the confidence interval:
[tex]\to \bold{410 \pm 1.753 \times \frac{40}{\sqrt{16}}}\\\\ \to \bold{410 \pm 17.53\\\\ \to392.47 < \mu < 427.53}[/tex]
So [tex]90\%[/tex] confidence interval for the mean weight of shipped homemade candies is between [tex]392.47\ \ and\ \ 427.53[/tex].
B)
[tex]\to \bold{(n) = 500}[/tex]
[tex]\to \bold{(X) = 155}[/tex]
[tex]\to \bold{(p') = \frac{X}{n} = \frac{155}{500} = 0.31}[/tex]
Here we need to calculate [tex]90\%[/tex] confidence interval for the true proportion of all college students who own a car which can be calculated as
[tex]\to \bold{p' \pm Z_{\frac{\alpha}{2}} \times \sqrt{\frac{p'(1-p')}{n}}}[/tex]
[tex]\to \bold{C.I= 0.90}[/tex]
[tex]\to\bold{ (\alpha) = 0.10}[/tex]
[tex]\to\bold{ \frac{\alpha}{2} = 0.05}[/tex]
Using the Z-table we found [tex]\bold{Z_{\frac{\alpha}{2}} = 1.645}[/tex]
therefore [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is
[tex]\to \bold{0.31 \pm 1.645\times \sqrt{\frac{0.31\times (1-0.31)}{500}}}\\\\ \to \bold{0.31 \pm 0.034}\\\\ \to \bold{0.276 < p < 0.344}[/tex]
So [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is between [tex]0.28 \ and\ 0.34.[/tex]
C)
In question A, We are [tex]90\%[/tex] certain that the weight of supplied homemade candies is between 392.47 grams and 427.53 grams.In question B, We are [tex]90\%[/tex] positive that the true percentage of college students who possess a car is between 0.28 and 0.34.Learn more about confidence intervals:
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Find the formula for the geometric sequence 1, 5, 25, 125, .
1. Write the polynomial function that models the given situation.A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
Answer:
1. (12 - 2x)(11 - 2x)x
2. 4(11 - 2x)²(x + 1)
3. π(x³ + 15x² + 63x + 81)
Step-by-step explanation:
1. Write the polynomial function that models the given situation.
A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
Since the length of the rectangle is 12 units and its width 11 units and squares of x by x units are cut from its corners, it implies that a length x is cut from each side. So, the length of the open box is L = 12 - 2x and its width is w = 11 - 2x.
Since the cut corners of the rectangle are folded, the side x which is cut represents the height of the open box, h. so, h = x
So, the volume of the open box V = LWh = (12 - 2x)(11 - 2x)x
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
Since the square has sides of 24 units and squares of x + 1 by x + 1 units are cut from its corners, it implies that a length x + 1 is cut from each corner and the length 2(x + 1) is cut from each side. So, the length of side open box is L = 24 - 2(x + 1) = 24 - 2x - 2 = 24 - 2 - 2x = 22 - 2x = 2(11 - x)
Since the cut corners of the square are folded, the side x + 1 which is cut represents the height of the open box, h. so, h = x + 1
Since the area of the base of the pen box is a square, its area is L² = [2(11 - 2x)]²
So, the volume of the open box V = L²h = [2(11 - 2x)]²(x + 1) = 4(11 - 2x)²(x + 1)
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
The volume of a cylinder is V = πr²h where r = radius and h = height of cylinder.
Given that r = x + 6 and h is 3 units more than r, h = r + 3 = x + 6 + 3 = x + 9
So, V = πr²h
V = π(x + 3)²(x + 9)
V = π(x² + 6x + 9)(x + 9)
V = π(x³ + 6x² + 9x + 9x² + 54x + 81)
V = π(x³ + 15x² + 63x + 81)
Hi !I need help with this question
I have doubt it be 270 degrees.
What is the value of the 2 in 4.502?
Answer:
0.002
Step-by-step explanation:
2 in 4.502 is in the thousandths place
Value is 0.002
write your answer in simplest radical form
Answer:
s = 17
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17\sqrt{3} }{s}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by s )
s × [tex]\sqrt{3}[/tex] = 17[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
s = 17
what is the uniqueness of comeplex integration from line integaration?
in a standard normal model which values of z cut off the middle 96
Answer:
-2.053 to 2.053 is ± .48 from z=0
Step-by-step explanation:
In one year, a government collected $6770 per person in taxes. If the population was 220,000,000, how much did the government collect in taxes that year?
Answer:
$1,489,400,000,000
Step-by-step explanation:
Multiply to get the solution.
220,000,000 × 6770 = 1,489,400,000
Help me please --------------------
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Answer:
139.39 in
Step-by-step explanation:
The length of a semicircle of diameter D is ...
C = (1/2)πD
For the given diameter of 27 inches, the length of the curved edge of the figure is ...
C = 1/2(3.14)(27 in) = 42.39 in
__
The perimeter of the figure is the sum of the side lengths. Clockwise from left, that sum is ...
P = 27 + 35 + 42.39 + 35 = 139.39 . . . inches
The perimeter of the figure is 139.39 inches.
I NEED HELP PLEASE AND THANK YOU!!! ASAP
Answer:
71
Step-by-step explanation:
Initial angle lies in 4th quadrant
Find the length of the arc round your answer to the nearest 10th
Answer:
45
Step-by-step explanation:
The length of the arc is equal to the central angle it sees.
Subtract (−4m2+5mw−12w2) from (−10m2−11mw−7w2).
Answer:
-6m² - 16mw + 5w²
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
(-10m² - 11mw - 7w²) - (-4m² + 5mw - 12w²)
Step 2: Simplify
[Distributive Property] Distribute negative: -10m² - 11mw - 7w² + 4m² - 5mw + 12w²Combine like terms: -6m² - 16mw + 5w²Answer:
-6m² - 16mw + 5w²
Step-by-step explanation:
(−10m2−11mw−7w2)−(−4m2+5mw−12w2)=−10m2−11mw−7w2+4m2−5mw+12w2
Use the commutative property to bring the like terms together and simplify.
−10m2−11mw−7w2+4m2−5mw+12w2=−10m2+4m2−11mw−5mw−7w2+12w2=−6m2−16mw+5w2
8
6
4
2
6
8
-8 -6 -4 -2 0-3
21
.
-6
-8
O A. y -[x]-2
OB. y -[x]+3
O C. y = (x) - 3
O D. y = [x]+2
The required equation of the line is y = [x]+2
From the graph shown, we can see that the line dotted points forms a straight line. We are to find the required equation of the line formed.
The formula for calculating the equation of a straight line is expressed as
y = mx+b where
m is the slope b is the y-intercept
Get the slope 'm'
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the coordinate points (2, 0) and (4, 2)
[tex]m=\frac{2-0}{4-2}\\m=\frac{2}{2}\\m=1[/tex]
Get the y-intercept 'b'
Substitute m = 1 and (2, 0) into y = mx+b as shown;
[tex]2=1(0)+b\\2=0+b\\b=2[/tex]
Get the required equation. Recall that y = mx+b, hence;
[tex]y = 1x + 2\\y=x+2[/tex]
Hence the required equation of the line is y = [x]+2
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Write the number 16,107,320 expanded form.
Answer:
Sixteen million, one hundred and seven thousand, three hundred twenty
Step-by-step explanation:
A cricket bat is bought for $330. Later, it is sold with a loss of 15%.
How much is the oricket bat sold for?
After selling the cricket bat, how much money has been last?
Give your answer to two decimal places because it is a currency.
Answers:
Discount price = 280.50 dollarsAmount lost = 49.50 dollars================================================
Explanation:
If it's sold at a loss of 15%, then the store owner loses 0.15*330 = 49.50 dollars
So it was sold for 330- 49.50 = 280.50 dollars
----------------------------
An alternative method:
If the store owner loses 15%, then they keep the remaining 85% since 15%+85% = 100%.
85% of 330 = 280.50 dollars is the discount price
This means 330-280.50 = 49.50 dollars is the amount lost.
Find 0.2B
B=[50 10
25 15]
Multiplying a matrix by a scalar results in every entry in a matrix get multiplied by that scalar, as defined,
[tex]a\begin{bmatrix}b&c\\d&e\\\end{bmatrix}=\begin{bmatrix}ab&ac\\ad&ae\\\end{bmatrix}[/tex]
So in our case, ([tex]0.2=\frac{1}{5}[/tex]
[tex]\frac{1}{5}\begin{bmatrix}50&10\\25&15\\\end{bmatrix}=\begin{bmatrix}\frac{50}{5}&\frac{10}{5}\\\frac{25}{5}&\frac{15}{5}\\\end{bmatrix}=\boxed{\begin{bmatrix}10&2\\5&3\\\end{bmatrix}}[/tex]
Hope this helps :)
