The two facts that we can double to find 8 × 4 is (4 and 4) .
The Double Facts are the number that repeat two time .
For Example : 2 × 2 , 4 + 4 .
The two facts of a number that is doubled is represented as :
2 * b = c
the value of c is given as 8*4 = 32 .
2 * b = 32
dividing both sides of the equation 2 * b = 32 by 2 , we get
b = 32/2 ,
Simplifying further ,
we get ,
b = 16 .
which in double can be written as 4 × 4 ,
that means 2(4×4) = 2(16) = 32 .
Therefore , The two facts that we can double to find 8 × 4 is 4 and 4 .
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What are the types of functions?.
There are many types of functions as;
1. Injective function
2. Many – one function.
3. Onto – function (Surjective Function)
4. Into – function.
5. Polynomial function.
6. Linear Function.
7. Identical Function.
8. Quadratic Function.
What is Function?
A relation between a set of inputs having one output each is called a function.
Now,
The name of the functions are;
There are many types of functions as;
1. Injective function
2. Many – one function.
3. Onto – function (Surjective Function)
4. Into – function.
5. Polynomial function.
6. Linear Function.
7. Identical Function.
8. Quadratic Function.
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PLSSS SOMEONE HELP ME I JUST NEED HELP PLEASEE!! IM OFFERING 40 PTS FOR THIS!! IM BEGGING YOU!!
Match each description with its corresponding value for the system below:
y = 4 x + 1 and y = -2 x + 7
-2
-1
-7
-5
The y -intercept of the exponential function.
The y -value of the solution in Quadrant I.
The number of points of intersection.
The y -intercept of the linear function.
The correct responses for the linear and exponential functions are;
The y-intercept of the linear function is 7The y-intercept of the exponential function is 2The number of points of intersection is 1The y-value of the solution in Quadrant I is 5What is an exponential function?An exponential function is one that has the argument as an exponent
1. The functions in the question are;
y = 4ᵃ + 1 and y = -2·x + 7
A linear function is of the form, y = m·x + c
Where;
m = The slope
c = The y-intercept
By comparison, the y-intercept of the linear function is 7
2. The standard form of the exponential function is; y = a·bᵃ + q
Where the y-intercept is a + q
The y-intercept of the exponential function is therefore;
y = 4⁰ + 1 = 1 + 1 = 2
The y-intercept of the exponential function is 2
3. The solution can be obtained from the equation;
4ᵃ + 1 = -2·x + 7, we get;
4ᵃ = -2·x + 7 - 1 = -2·x + 6
When x = 1,
4¹ = -2×1 + 6 = 4
The number of points of intersection obtained by plotting the functions is 1
4. The y-value of the solution is therefore;
y = 4¹ + 1 = 5
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A line in the coordinate plane has a slope of 4, and a distance of 1 unit from the origin. Find the area of the triangle determined by the line and the coordinate axesA line in the coordinate plane has a slope of m=4, and a distance of 1 unit from the origin. => that is a point (1,0)
so, the equation of this line will be:
y-y1=m(x-x1)...plug in given data
y-0=4 (x-1)
y=4x-4
now we know y intercept is at (0,-4)Find the area of the triangle determined by the line and the coordinate axes
the triangle determined by the line and the coordinate axes is right triangle, and its legs are base and altitude
base is 1 unit long, altitude is 4units long
The area of the triangle according to the information given in the question is 17/8.
What is meant by triangle?A triangle is a three-sided polygon that is also known as the trigon.
Angles in a triangle are formed by connecting the three sides end to end at a point.
Consider the following right-angled triangle, with vertices (0,-4), (0.0), and (1,0).
Its legs are 4 and 1 meters long, and its hypotenuse is 42+12=17 meters long.
The height "h" (altitude) of this triangle drawn to the hypotenuse is easily determined.
Based on the area, we get the equation (41)/2=(1/2)17h h=4/17 h=0.970143.
As we can see, it is not a single unit.
It means that the triangle's legs should be 17/4 as long as the original triangle's legs (1 unit and 4 units).
As a result, the area of the seeking triangle is (1/2)(17/4)(417/4) = (1/2)(17/4) =17/8
As a result, the area of the triangle in the question is 17/8.
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liz has two pieces of string, one 18cm long and the other 24cm long. she wants to cut them up to produce smaller pieces of string that are all of the same lengths, with no string leftover. What is the greatest length, in cm, that she can make
The GCF of a set of values (typically two) is the greatest factor that applies to every number.
Solving the QuestionWe must find the GCF of 18 and 24:
List the factors of both values:
18: 1, 2, 3, 6, 9, 1824: 1, 2, 3, 4, 6, 8, 12, 24Let's identify the common factors between 18 and 24:
18: 1, 2, 3, 6, 9, 1824: 1, 2, 3, 4, 6, 8, 12, 24Therefore, the GCF is 6.
AnswerThe greatest length that Liz can make using the strings is 6 cm.
angle a is corresponding to angle b the measure of angle b is 2x+60 and the measure of angle a is x what is the measure of both angles
The measure of both angles is 60 and 180 degrees respectively.
What are corresponding angles?In a literal sense, corresponding means pairwise angles. Like the right corner angles of two triangles etc. But usually, we take them as:
For two similar figures, the pair-by-pair similar angles of those two similar figures are called corresponding angles. They are of the same measurement.
Given that angle a is corresponding to angle b the measure of angle b is 2x+60 and the measure of angle a is x.
Since both the angles are equal then;
Angle A = Angle B
x = 2x + 60
Solving for x;
2x - x = -60
x = -60
Therefore, the measure of both angles is 60 and 180 degrees.
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A chord of length 24cm i 13cm from the centre of the circle. Calculate the radiu of the circle
The radius of the circle is approx. 17.692
What is a radius?
In traditional geometry, the radius of a circle or sphere is any line segment that connects the object's center to its perimeter; in more modern usage, the radius also refers to the length of those segments.
To put it another way, the radius of a circle is the distance between any two points on the circle's circumference. Usually, "R" or "r" is used to indicate it.
Solution Explained:
Given,
Length of cord = 12cm
Length from the center of the circle = 13cm
We use the formula,
r = [tex]\sqrt{12^2 + 13^2}[/tex]
= [tex]\sqrt{144 + 169}[/tex]
= [tex]\sqrt{309}[/tex]
≈ 17.692
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find an equation for the parabola that has its vertex at the origin and satisfies the given conditions. opens upward with focus 6 units from the vertex
The equation of parabola that open upwards with focus 6 units is x²=24y.
A parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. A parabola is a curve where any point at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface is also Parabola.
The general equation of Parabola is given by
y = a(x-h)²+ k
where (h,k) is the vertex of parabola.
And the equation of parabola open upward is,
(x-h)² = 4a(y-k)
where (h,k) is vertex and a is focus unit.
⇒ (x-0)² = 4(6)(y-0)
⇒ x² = 24y
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find the missing side of each triangle GIVE STEP BY STEP PLEASE!!!
Answer:
1. C) [tex]3.6 \, \textrm{cm}[/tex]
2. A) [tex]4\sqrt{10}[/tex]
Step-by-step explanation:
Utilize the Pythagorean Theorem for both problems:
[tex]a^2+b^2=c^2[/tex]
where [tex]a[/tex] and [tex]b[/tex] are the right triangle's legs (short sides adjacent to the right angle) and [tex]c[/tex] is its hypotenuse.
1) Form an equation using the above formula.
[tex]8.7^2 + x^2 = 9.4^2[/tex]
Next, isolate x.
[tex]x^2 = 9.4^2 - 8.7^2[/tex]
[tex]x = \sqrt{9.4^2 - 8.7^2}[/tex]
Finally, plug the square root into a calculator and round the result to get:
C) [tex]3.6 \, \textrm{cm}[/tex]
2) Form an equation using the Pythagorean Theorem.
[tex]6^2 + x^2 = 14^2[/tex]
Next, isolate x.
[tex]x^2 = 14^2 - 6^2[/tex]
[tex]x^2 = 196 - 36[/tex]
[tex]x^2 = 160[/tex]
[tex]x = \sqrt{160}[/tex]
Finally, use prime factorization to simplify the square root.
[tex]x = \sqrt{10 \cdot 16[/tex]
[tex]x = \sqrt{(2 \cdot 5) \cdot 2^4}[/tex]
[tex]x = 2^2 \sqrt{2 \cdot 5}[/tex]
A) [tex]4\sqrt{10}[/tex]
What are not exponential functions?.
It is not of exponential order for h(t) = et2. F is of exponential order and has order. F is piecewise continuous. No function's Laplace transform is possible. g(t) = eat, where t [0,.
Non-exponential form:
To represent a scientifically notated number as a non-exponential quantity: • Remove the exponential component of the number by moving the decimal point the same number of places as the exponent's value. The decimal is moved to the right by the same number if the exponent is positive.
Here are a few instances of functions other than exponential ones. y = 3 1 x as a result. n = 0 3 p as a result. Because y = ( 4) x. Since b = 1, y = 6 0 x.
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The scale on a map is stated as
1/200 000
A main road connects two towns which are 28 kilometres apart.
How far will it be on the map, in centimetres, between the two towns along the main road?
Answer:
2,800,000 Centimeters.
Step-by-step explanation:
Multiply by 100,000. (works for any kilometers to centimeters conversion. For example, 2 kilometers is 200,000 centimeters. *2 x 100,000*)
HELP QUICK PLEASE THANK YOU
To make a volume of 320mL mixture that contains 8% vinegar, use 64mL of the first brand and 256mL of the second brand.
How to solve simultaneous equation word problems?Let F be the volume of the first brand and let S be the volume of the second brand.
Now, we want the total mixture to be 320mL so: F + S = 310
Also, you want the total mixture to contain 12% vinegar so:
0.08F + 0.13S = 0.12(320)
Now, we can solve the system of equations using substitution method.
F + S = 320 -----(1)
0.08F + 0.13S = 0.12(320) -----(2)
F = 320 - S [solve 1st equation for F]
0.08(320 - S) + 0.13S = 0.12(320) [substitute into 2nd equation]
25.6 - 0.08S + 0.13S = 38.4
0.05S = 12.8
S = 256 mL
F + 256 = 320 [substitute answer for S back into original equation]
F = 320 - 256
F = 64 mL
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tammy works as a tutor for an hour and as a waitress for an hour. this month, she worked a combined total of hours at her two jobs.
Answer:
What is the question?!
Step-by-step explanation:
Use the alternating series estimation theorem to determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001. 1 2 (-1)n +1 n=1 (n+31n) ( or more terms should be used to estimate the sum of the entire series with an error of less than 0.001.
To determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001, we can use the alternating series estimation theorem.
What is the series estimation theorem?A mathematical technique called the series estimation theorem is used to estimate a mathematical series' value. An endless string of integers that can be put together to produce a total is referred to as a mathematical series. According to the theory, if a series possesses a characteristic called absolute convergence, its value may be calculated by adding the first few terms rather than adding all of them together. This can be a helpful tool for estimating the value of a series without having to sum all the terms, which is sometimes difficult or even impossible. For example, the series estimation theorem could be used to approximate the value.
How to solve?
In this case, the series is alternating and decreasing, so we can use the alternating series estimation theorem to determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001. We can do this by finding the first neglected term in the series that is less than 0.001, and then determining how many terms are needed to get to that point in the series.
In general, to determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001, we would need to find the first neglected term in the series that is less than 0.001 and then determine how many terms are needed to get to that point in the series. This would give us the minimum number of terms that should be used to estimate the sum of the entire series with an error of less than 0.001
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if a car gets 13 kilometers per liter of gasoline, how many miles per gallon of gasoline would it get?
If a car gets 13 kilometers per liter of gasoline, miles per gallon of gasoline would it get is 40 miles.
if a car gets 13 kilometers per liter of gasoline,
We need to find the number of miles per gallon of gasoline would it get
1 gallon of gasoline = 3.78541 liters of gasoline
In 1 liters of gasoline car travels = 13 kilometers
In 3.78541 liters of gasoline, the car travels 13 x 3.785 = 49.2kilometers
1,60934 kilometer = 1 mile
49.2 kilometers = (1/1.60934) x 49.2 = 40 miles
Therefore, if a car gets 13 kilometers per liter of gasoline, miles per gallon of gasoline would it get is 40 miles.
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at the terminal of a certain airline, records disclose that 10% of their flights arrive early, 70% arrive on time, 12% arrive somewhat late, and 8% arrive very late. use the formula for the multinomial distribution to determine the probability that in six randomly selected flights, one will arrive early, three will arrive on time, two will be somewhat late, and none will be very late. express your answer as a decimal rounded to 2 decimal places.
The required probability by using multinomial distribution is 0.03.
The multinomial distribution is the kind of probability distribution used in finance to assess factors like the likelihood that a company would declare earnings that are greater than anticipated while rivals report disappointing results. In a multinomial distribution, a process has a set of k potential outcomes (X1, X2, X3,..., Xk) and corresponding probabilities (p1, p2, p3,..., pk) such that Σpi = 1. Due to the certainty of one of the outcomes, the probabilities must add up to 1.
Given that at the terminal of a certain airline, records disclose that 10% of their flights arrive early, 70% arrive on time, 12% arrive somewhat late, and 8% arrive very late.
Multinomial probability P = [ n! / ( n1! * n2! * ... nk! ) ] * ( p1n1 * p2n2 * . . . * pknk )
= [ 6! / ( 1! x 3! x 2! x 0! ) ] * ( 0.10^1 x 0.70^3 x 0.12^2 x 0.08^0)
=60*0.000494
=0.02964
Therefore the required probability = 0.03
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Help please I’ve been stuck on this for 1 week
The equation 5x - (3 - 2x) = -(-x- 7) + 6x is an equation with no solution. It simplifies to 0 = 10
How to simplify an equation with no solution?
An equation with no solution is a type of equation that is never true, no matter what we replace the variable with e.g. 6x + 10 = 6x - 10. This equation has no solution because is no value that will ever satisfy this type of equation
Given: the equation 5x - (3 - 2x) = -(-x- 7) + 6x
5x - (3 - 2x) = -(-x- 7) + 6x
Clear the parenthesis:
5x - 3 + 2x = x + 7 + 6x
Add/subtract like terms:
7x -3 = 7x + 7
Collect like terms:
7x -7x = 7 + 3
0 = 10
Since 0 is not equal to 10, therefore this expression has no solution
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A bag contain 5 kg of rice. 1500 gm have been taken out for cooking. What is the ratio of the amount taken out to the amou
Answer:
1500 : 5000
Step-by-step explanation:
Answer:
The ratio is 3: 7
Step-by-step explanation:
You turn the 5 kg into grams so they are both the same unit. So that's 5,000 grams. 1,500 grams was the amount taken out. Then what is left is 3,500. So it makes the ratio 1,500: 3,500. Then you simplify it to 3:7.
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a circle has a circumference of 16 feet. what is the radius of the circle, in feet? individual question 4 8 16 32
The correct answer is the radius of the circle is 2.54648 ft.
The circumference of a circle or ellipse in geometry is known as its perimeter. That is, if the circle was opened up and straightened out to a line segment, the circumference would be said the length of the arc.
The curve length around any closed figure is more commonly referred to as the perimeter.
We know that Circumference = [tex]2\pi r[/tex] and [tex]\pi[/tex] ≈ 3.14159,
Circumference = [tex]2\pi r[/tex]
16 = [tex]2\pi r[/tex] (after substituting)
16/2[tex]\pi[/tex] = 2[tex]\pi[/tex]r/2[tex]\pi[/tex] (remove 2[tex]\pi[/tex] by dividing both sides with the mentioned term)
r = 8/[tex]\pi[/tex]
r = 8/[tex]\pi[/tex] (ft.)
[tex]\pi[/tex] ≈ 3.14159 (value of [tex]\pi[/tex])
Hence, the radius of the circle when its circumference is 16 feet is r ≈ 2.54648 ft. which is the approximate value.
Checking our work:
Circumference = 2[tex]\pi r[/tex]
Circumference = 2 (3.14159) (2.54648)
Circumference = 15.999
Circumference ≈ 16 ft.
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compute the best possible upper estimate for the distance he travels over this period when dividing [0, 5] into 5 equal subintervals and using endpoint sample points
The best possible Upper Estimate for the distance travelled is 69 .
In the question ,
a graph is given ,
we have to estimate the possible upper estimate ,
the time period [0,5] is divided into 5 sub intervals ,
that is (0,1) , (1,2) ,(2,3) , (3,4) and (4,5) .
From the graph we see that ,
the upper limit of the distance in the interval (0,1) is = 20 .
the upper limit of the distance in the interval (1,2) is = 17 .
the upper limit of the distance in the interval (2,3) is = 13 .
the upper limit of the distance in the interval (3,4) is = 10 .
the upper limit of the distance in the interval (4,5) is = 9 .
adding all the upper limit ,
we get ,
upper estimate is = 20 + 17 + 13 + 10 + 9 = 69
Therefore , the upper estimate of the distance is 69 .
The given question is incomplete , the complete question is
compute the best possible upper estimate for the distance he travels over this period when dividing [0, 5] into 5 equal subintervals and using endpoint sample points .
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Use the power property to rewrite log3x9. 3 log subscript 9 baseline x 9 log subscript 3 baseline x 3 log x 2 + log subscript 3 baseline x.
By using the power property, the resultant answer when we rewrite log3x9 is (B) 9log3x.
What is power property?Multiply the exponents to determine the power of the power.
This is a development of the powers property.
Consider raising a number to a power and repeatedly multiplying the entire phrase by itself.
According to the power of a powerful formula, you can multiply two exponents together if one is increased to a power.
How many times to multiply two numbers together is indicated by an exponent.
For instance, 42 instructs you to multiply by 4 and 4. Alternatively, multiply four by two.
So, we have: log3x9
We have the following for logarithm properties:
loga (x ^ b) = b * loga (x)
As a result of this property, in this instance, we have:
log3 (x ^ 9) = 9log3 (x)
Therefore, by using the power property, the resultant answer when we rewrite log3x9 is (B) 9log3x.
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Correct question:
Use the power property to rewrite log3x9.
A) 3log9x
B) 9log3x
C) 3logx
D) 2 + log3x
Is 15 a multiple of 5 yes or no?.
Solve x2−x−3=0 by completing the quare. If the olution are real rational number, lit from leat to greatet eparated by a comma. If the olution are not real number, write your anwer in the form a ± bi. If the olution are irrational, write your anwer in implified radical form, uing ± to expre both olution
The solution of the equation x²-x -3 = 0 are x = (1±√13) /2.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Here we are given the equation x²-x -3 = 0 ---(i) which is a quadratic equation which we can solve using Sri Dharacharya Method.
Sri Dharacharya Formula: For a quadratic equation ax² + bx + c = 0
The value of x is x= (-b ± [tex]\sqrt{b^{2}-4ac }[/tex]) /2a.
Using this formula in (i), we get
x = (-(-1) ± [tex]\sqrt{(-1)^{2} -4*1*(-3)}[/tex]) /2*1
⇒ x = (1±√13) /2.
The solution of the equation are irrational which are x = (1±√13) /2.
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a shirt is on sale for 40% off. after the discount, the customer paid $12. a) what was the original price of the shirt?
Answer:
$20
Step-by-step explanation:
→ Rewrite percentage as multiplier
0.6
→ Divide the amount by multiplier
12 ÷ 0.6 = $20
What determines where the graph will cross the x-axis?.
The graph will cross the x-axis if the multiplicity of the real root is odd.
What is polynomial?
In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Main body:
For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)
(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)
(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)
(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.
The graphs: (a) black, (b) red, (c) green
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The lope of i 4. Point F i located at (2,3). Which could be the coordinate of point G?
The coordination of point G is (3,7).
What is a slope?
A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.
Here, we have
Given
Slope = 4
Slope of line = (y₂ - y₁)/ (x₂ - x₁) ... (1)
F is located at (2,3), which implies x₁ = 2 and y₁ = 3
Now, substituting the value in equation 1, we get
4 = y₂ - 3 / x₂ - 2
4x₂ - y₂ = 5.... (2)
let us do the hit-and-trial method in order to find the answer.
secondly, let us take option B) 3,7
similarly, we get,
4* 3 - y₂ = 5
12 - 5 = y₂
y₂ = 7
Hence, the coordination of point G is (3,7).
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The sum of three consecutive odd integers is -63. Find the value of the middle of the three.
-Thanks!
Answer:
- 21
Step-by-step explanation:
consecutive odd numbers have a difference of 2 between each one
let the three consecutive odd integers be
n , n + 2 , n + 4
then
n + n + 2 + n + 4 = - 63
3n + 6 = - 63 ( subtract 6 from each side )
3n = - 69 ( divide both sides by 3 )
n = - 23
n + 2 = - 23 + 2 = - 21
n + 4 = - 23 + 4 = - 19
the three odd integers are - 23, - 21, - 19
with middle one - 21
Answer:
first integer
19
second integer
21
third integer
23
Step-by-step explanation:
The sum of the three consecutive odd integers is
63
, so your equation is:
(x)+ (x+2)+(x+4)=63
Then solve for
x:
(x)+(x+2)+(x+4)=63
x+x+2+x+4=63
3x+6=63
3x+6
−
6=63 −63x=57
3x÷3=57÷3x=19
Now that you know your first integer has a value of
19, substitute x=19 into x+2 and x+4
to find the values of the second and third integers.
Now that you know your first integer has a value of
19
Now that you know your first integer has a value of
19
, substitute
x=19 into x+2 and x+4 to find the values of the second and third integers
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a boat travels upstream for 36 miles in 4 hours and returns in 3 hours traveling downstream in a river. what is the rate of the boat in still water and the rate of the current?
Answer:
rate of the boat is 10.5 and the rate of the current is 1.5
Step-by-step explanation:
Distance = rate x time
Let r = rate of the boat
Let c = current
Upstream:
Rate: r -c
Time: 4 hours
Distance: 36
36 = 4(r-c) Divide both sides of the equation by 4
9 = r - c
Downstream:
Rate: r + c
Time: 3 hours
Distance: 36
36 = 3(r+c) Divide both sides by 3
12 = r -c
Combine the two bold equations:
9 = r - c
12 = r + c
21 = 2r Divide both side's by 2
10.5 = r This is the rate of the boat.
Rate of the current:
4(10.5 - c) =36
42 - 4x = 36 Subtract 42 from both sides
-4x = -6 Divide both sides by -4
x = 3/2 or 1.5
negative charge -q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin. find the x- and y-components of the net electric field at the origin.
The x and y components of net electric field at origing is [tex]E_{x}=E_{y}=(\frac{2kq}{\pi a^2})\text{ or }(\frac{q}{2\pi^2 a^2\epsilon_{o}})[/tex].
In the given question, negative charge -q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin.
We have to find the x- and y-components of the net electric field at the origin.
The figure of the given question is given below:
Linear charge density of a quarter circle is given by,
λ=(-q)/l
From the figure, the length of the quarter circle is;
l = πa/2
From the above two equations,
λ=(-q)/(πa/2)
λ=(-2q)/πa
The small amount of the charge is given by,
dq=λdl
dq=(-2q)/πa dl
Magnitude of electric field due to elemental length if given by,
dE = k|dq|/a^2
dE = k|(-2q)/πa dl|/a^2
dE = (2kq/πa^3)dl
The electric field at origin due to elemental length is given by,
[tex]\vec{dE}[/tex] = dEcosθ[tex]\hat{i}[/tex] + dEsinθ[tex]\hat{j}[/tex]
[tex]\vec{dE}[/tex] = {(2kq/πa^3)dl}cosθ[tex]\hat{i}[/tex] + {(2kq/πa^3)dl}sinθ[tex]\hat{j}[/tex]
[tex]\vec{dE}[/tex] = {(2kq/πa^3)(adθ)}cosθ[tex]\hat{i}[/tex] + {(2kq/πa^3)(adθ)}sinθ[tex]\hat{j}[/tex]
[tex]\vec{dE}[/tex] = (2kq/πa^2)cosθdθ[tex]\hat{i}[/tex] + (2kq/πa^3)sinθdθ[tex]\hat{j}[/tex]
The net electric field at origin is given by,
[tex]\vec{E}=\int\limits^{\pi/2}_0 \, \vec{dE}[/tex]
[tex]\vec{E}=\frac{2kq}{\pi a^2}(\int\limits^{\pi/2}_0 \, \cos\theta {d\theta})\vec{i}+\frac{2kq}{\pi a^2}(\int\limits^{\pi/2}_0 \, \sin\theta {d\theta})\vec{j}[/tex]
[tex]\vec{E}=\frac{2kq}{\pi a^2}(1-0)\vec{i}+\frac{2kq}{\pi a^2}(0-(-1))\vec{j}[/tex]
[tex]\vec{E}=(\frac{2kq}{\pi a^2})\vec{i}+(\frac{2kq}{\pi a^2})\vec{j}[/tex]
or
[tex]\vec{E}=(\frac{2(\frac{1}{4\pi \epsilon_{o}})q}{\pi a^2})\vec{i}+(\frac{2(\frac{1}{4\pi \epsilon_{o}})q}{\pi a^2})\vec{j}[/tex]
[tex]\vec{E}=(\frac{q}{2\pi^2 a^2\epsilon_{o}})\vec{i}+(\frac{q}{2\pi^2 a^2\epsilon_{o}})\vec{j}[/tex]
Therefore, the x and y components of net electric field at origing is;
[tex]E_{x}=E_{y}=(\frac{2kq}{\pi a^2})\text{ or }(\frac{q}{2\pi^2 a^2\epsilon_{o}})[/tex]
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In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. a. The standard error of the mean is b. With a 0.95 probability, the margin of error is approximately c. If the sample mean is 9 hours, then the 95% confidence interval is
The standard error of the mean is e = 0.2 and the 95% confidence interval is 9 ± 0.392.
Given:
In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours.
a.
σ = 1.8
n = 81
we know that,
standard error of the mean e = σ/[tex]\sqrt{n}[/tex]
= 1.8/[tex]\sqrt{81}[/tex]
= 1.8/9
= 18/10/9
= 18*1/10*9
= 2*1/10
= 2/10
= 0.2
b.
confidence interval CI = x ± Z*s/√n
= 9 ± 1.9600*1.8/√81
= 9 ± 0.392
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given here are a set of sample data: 12.0, 18.3, 29.6, 14.3, and 27.8. the sample standard deviation for these data is:
The required value of the sample standard deviation of given data is 62.895.
What is standard deviation?A standard deviation (or σ) is a proportion of how distributed the information is comparable to the mean. Low standard deviation implies information are grouped around the mean, and exclusive expectation deviation demonstrates information are more fanned out.
Using the formula:
Where: xi = sample value; μ = sample mean; n = sample size
Calculate the mean first:
μ = 12.0 + 18.3 + 29.6 + 14.3 + 27.8 / 5
= 102 / 5
μ = 20.4
Then, Using the mean, calculate (xi - μ)² for each value:
(12.0 - 20.4)² = 70.56
(18.3 - 20.4)² = 4.41
(29.6 - 20.4)² = 84.64
(14.3 - 20.4)² = 37.21
(27.8 - 20.4)² = 54.76
Sum the squared differences and divide by n - 1.
μ = 70.56 + 4.41 + 84.64 + 37.21 + 54.76
= 251.58 / 5-1
μ = 62.895
Thus, required the sample standard deviation for these data is 62.895.
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