A total of n bar magnets are placed end to end in a line with random independent orientations. Adjacent like poles repel while ends with opposite polarities join to form blocks. Let X be the number of blocks of joined magnets. Find E(X) and Var(X).
Answers
Answer:
E(x) [tex]= \frac{n+1}{2}[/tex]
Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]
Step-by-step explanation:
Hint x = 1 + x1 + ......... Xn-1
[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]
attached below is the detailed solutioN
usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block
Related Questions
The first common multiple of two number is 6. What is their fourth common multiple?
Answers
Answer:
4th multiple = 24
Step-by-step explanation:
Given
Let the two numbers be represented by m and n
Required
Find the 4th common multiple of the numbers.
From the question, we understand that the first common multiple of m and n is 6.
This can be represented as:
m * n * 1 = 6
mn = 6
Their fourth common multiple can be represented as: m * n * 4
4th multiple = m * n * 4
4th multiple = 4 * mn
Substitute 6 for mn
4th multiple = 4 * 6
4th multiple = 24
Hence, the 4th multiple of both numbers is 24.
Simplify the following expression. (4x − 8)(4x + 8)
Answers
Answer:
16x^2 - 64
Step-by-step explanation:
(4x − 8)(4x + 8)
We recognize that this is the difference of squares
(a-b) (a+b) = a^2 - b^2
=(4x)^2 - 8^2
=16x^2 - 64
Simplify the expression 3-8x3-4
Answers
Answer:
−8x3−1
Step-by-step explanation:
let's simplify step-by-step.
3−8x3−4
=3+−8x3+−4
Combine Like Terms:
=3+−8x3+−4
=(−8x3)+(3+−4)
=−8x3+−1
Answer:
-1 - (2x^3)^3
Step-by-step explanation:
The equation is:
=> 3 - 8x^3 - 4
=> -1 - 8x^3
=> -1 - (2x^3)^3
The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly. (For the following matched samples, let the difference "d" be: d = after - before.)
Salesperson After Before
1 94 90
2 82 84
3 90 84
4 76 70
5 79 80
6 85 80
Answers
Answer:
Since the calculated value of t= 2.249 does not falls in the rejection region we therefore accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the bonus plan has not increased sales significantly.
Step-by-step explanation:
The null and alternative hypotheses as
H0: μd=0 Ha: μd≠0
Significance level is set at ∝= 0.05
n= 6
degrees of freedom = df = 6-1 = 5
The critical region is t ( base alpha by 2 with df=5) ≥ ± 2.571
The test statistic under H0 is
t = d/ sd/ √n
Which has t distribution with n-1 degrees of freedom
Sales Difference
Person After Before d = after - before d²
1 94 90 4 16
2 82 84 -2 4
3 90 84 6 36
4 76 70 6 36
5 79 80 -1 1
6 85 80 5 25
∑ 18 118
d`= ∑d/n= 18/6= 3
sd²= 1/6( 118- 18²/6) = 1/6 ( 118 - 54) = 10.67
sd= 3.266
t= 3/ 3.266/ √6
t= 2.249
Since the calculated value of t= 2.249 does not falls in the rejection region we therefore accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the bonus plan has not increased sales significantly.
a ball is dropped from a height of 512 inches onto a level floor. after the fourth bounce it is still 2 inches off the ground. presuming that the height the ball bounces is always the same fraction of the height reached on the previous bounce. what is that fraction? A) 1/4 B) 3/7 C) 5/9 D)4/7 E)3/5
Answers
Answer:
A. 1/4
Step-by-step explanation:
We know that before the 1st bounce, the height of the ball is 512 inches.
Say the fraction is x.
Then, after the first bounce, the height of the ball is 512 * x = 512x.
After the second bounce, the height is now x * 512x = 512x².
By similar reasoning, the height after the third bounce is 512x³ and after the fourth bounce, it is [tex]512x^4[/tex].
We also know that after the fourth bounce, the height is 2 inches. So, set 2 equal to [tex]512x^4[/tex]:
2 = [tex]512x^4[/tex]
Divide both sides by 512:
[tex]x^4=2/512[/tex][tex]x^4=2/512=1/256[/tex]
Take the fourth root of both sides:
[tex]x=\sqrt[4]{1/256} =1/4[/tex]
Hence, the answer is A.
~ an aesthetics lover
Answer:
A. 1/4.
Step-by-step explanation:
This is exponential decay so we have , where x = the fraction:
512(x)^4 = 2
x^4 = 1/256
x= 1 / (256)^0.25
= 1/4
Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses.
Answers
Answer:
Step-by-step explanation:
1. 4/4+4-4=1
2. 4/4+4/4=2
3. 4+4/4-4=3
4. 4 × (4 − 4) + 4=4
5. (4 × 4 + 4) / 4=5
6. 44 / 4 − 4=6
7. 4+4-4/4=7
8. 4+4+4-4=8
9. 4+4+4/9=9
10. 44 / 4.4=10
Answer:
1 = (4 x 4)/(4 x 4) or (4 + 4)/(4 + 4) or (4 / 4) x (4 / 4) or (4 / 4)/(4 / 4)
2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)
3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4
4 = 4 - (4 - 4)/4
5 = (4 x 4 + 4)/4
6 = 4 + (4 + 4)/4
7 = 4 - (4/4) + 4
8 = 4 + (4 x 4)/4
9 = 4 + 4 + (4/4)
10 - I tried the best. You might need ! or sqrt operator to get 4.
Updated:
I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:
10 = (44 - 4)/4
what does the inverse of f(x)=2x-3 looks like on a graph
Answers
Step-by-step explanation:
To find this inverse of a graph you have to multiply the current equation by -1.
-1(2x-3)
f(x)=-2x+3.
This graph will start at the point (0,3). Then according to the slope the rest of the points will go down two than right one. So the next two point will be (1,1) and (2,-1).
Determine what type of decimal each is.
8.54
Answers
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]8.54 \div 100 = 0.0854[/tex]
(what do you mean by Determine what type of decimal each is: 8.54 because there is only one decimal there )
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Write the expression
using only positive exponents.
-3/x-4
Answers
A study collects samples of water from the tap in Vacaville and from bottled water available from the Nugget stores and samples their pH levels. The results are in the table below. I find a bottle marked #13 but cannot read the label for the type of water. He measures the pH and gets 6.32. What type of water do you think it is?
Answers
Answer:
see below
Step-by-step explanation:
the observed ph is 6.32
the mean pH of Tap water is shown below
sum of observations
Mean (Tap) = -----------------------------------
number of observations
(7.24 +7.05 +7.07 +6.6 +7.28 +7.29 +7.05 +6.7 +7.16 +7.07 +7.12 +6.56
= ---------------------------------------------------------------------------------------------------------
12
= 7.016
then mean pH of bottle water is shown below
sum of observations
Mean (Bottles) = -----------------------------------
number of observations
(5.35 + 5.29 + 5.46 + 5.4 + 5.95 + 6.22 + 5.43 +5.48 +6.06 +5.33 +5.46 +5.41)
= --------------------------------------------------------------------------------------------------------------
12
= 5.57
theoretically.. the higher the pH values should be between 0 to 14.
based from the above results, the mean tap water has an average of 7.016 and by looking at the pH chart... its a neutral or pure water.
while the average pH Bottles has 5.57, this means its more acidic water, or by looking at the pH chart its an acid rain water.
a 6.32pH is below pure water, based on the chart looks like a urine/saliva.
Two sides of a triangle are equal length. The length of the third side exceeds the length of one of the other sides by 3 centimeters. The perimeter of the triangle is 93 centimeters. Find the length of each of the shorter sides of the triangle
Answers
Answer:
30 cm
Step-by-step explanation:
let x be the lenght of the two sides of equal lenghts, so the other is x+3
and the perimeter is x+x +x +3
P=3x+3
P=3(x+1)
93=3(x+1)
31=x+1
x=30
so the shorter sides are of 30 centimeters and the longest is 33
How do you write 30,8608
Answers
Answer:
it should be 308,608. the comma is after every three in this scenario.
Step-by-step explanation:
Please answer this correctly without making mistakes
Answers
Answer:
7/10 mi
Step-by-step explanation:
The total distance is 3 miles = 30/10 miles.
The other distances added gives 7/10+7/10+9/10 = 23/10
Therefore the last hop from Kingwood to Silvergrove is 30/10 - 23/10 = 7/10
Equivalent means having ___ ___
I need two answer omg pls helppp ;-;
Answers
Answer:
equal value and function
Step-by-step explanation:
The length of a rectangle is twice the width. If the length is increased by 4 inches and the width is decreased by 1 inch, a new rectangle is formed whose perimeter is 198 inches. Find the dimensions of the original rectangle.
Answers
Answer:
Width: 32 inches.
Length: 64 inches.
Step-by-step explanation:
Let's say that the width of the rectangle is x inches, so the length is 2x inches.
If 2x + 4 and x - 1, the perimeter is 198 inches. That means that two times the width plus two times the length is 198 inches.
2(2x + 4) + 2(x - 1) = 198
4x + 8 + 2x - 2 = 198
6x + 6 = 198
x + 1 = 33
x = 32.
That means that the width of the original rectangle is 32 inches, and the length is 32 * 2 = 64 inches.
Hope this helps!
Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 3 trips, and for each trip Lennox gets 300 dollars. On a single trip, a truck delivers 50 packs, and each pack contains 12 kilograms of apples. Overall, Lennox sells 4500 dollars worth of apples in a week. How much does Lennox get for a single kilogram of apples?
Answers
Answer:
$0.50
Step-by-step explanation:
Each trip transports 50 packs at 12 kg each, for a total of 600 kg. That trip nets $300 in income.
Lennox gets paid ($300)/(600 kg) = $0.50/kg, or 50¢ for 1 kg of apples
Answer:5 trucks
Step-by-step explanation: in kahn it’s 4500 divided by 900 because she makes 300 a trip which makes 900$ a truck
Use De Moivre's theorem to find the indicated power of the complex number. Write the answer in rectangular form.[2(cos10∘ + i sin10∘)]^3.
Answers
Answer:
[tex]\bold{4\sqrt3 + i4}[/tex]
Step-by-step explanation:
Given complex number is:
[tex][2(cos10^\circ + i sin10^\circ)]^3[/tex]
To find:
Answer in rectangular form after using De Moivre's theorem = ?
i.e. the form [tex]a+ib[/tex] (not in forms of angles)
Solution:
De Moivre's theorem provides us a way of solving the powers of complex numbers written in polar form.
As per De Moivre's theorem:
[tex](cos\theta+isin\theta)^n = cos(n\theta)+i(sin(n\theta))[/tex]
So, the given complex number can be written as:
[tex][2(cos10^\circ + i sin10^\circ)]^3\\\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3[/tex]
Now, using De Moivre's theorem:
[tex]\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3\\\Rightarrow 8 \times [cos(3 \times10)^\circ + i sin(3 \times10^\circ)]\\\Rightarrow 8 \times (cos30^\circ + i sin30^\circ)\\\Rightarrow 8 \times (\dfrac{\sqrt3}2 + i \dfrac{1}{2})\\\Rightarrow \dfrac{\sqrt3}2\times 8 + i \dfrac{1}{2}\times 8\\\Rightarrow \bold{4\sqrt3 + i4}[/tex]
So, the answer in rectangular form is:
[tex]\bold{4\sqrt3 + i4}[/tex]
When conducting a residual analysis, which plot would you look at to determine if the equal variance assumption is satisfied?
a. Scatter plot of Yhat vs. QN X
b. Scatter Plot of Residuals vs QN X
c. Scatter Plot of Residuals vs Yhat
d. Stem-and-Leaf Plot of the Zresiduals
Answers
Answer:
C.Scatter Plot of Residuals vs Yhat
Step-by-step explanation:
Helppp needed ASAP!!!!
Answers
Answer:
The two missing sides are : 79.54m and 58.62m
Step-by-step explanation:
first we look for the missing angle in the triangle
sum of angle in a triangle = 180°let make the missing angle be A 180 = A + 25 + 35180 = A + 60A = 180 - 60A = 120°so now we use sine rules:
a/(sin A) = b/(sin B) = c/(sin C)Let us make:
The side facing 35° be called bThe side facing 25° be called cThe side facing 120° be called aso :
120/(sin 120°) = b/(sin 35°)120/(0.866) = b/0.574138.57 = b/0.574b = 138.57 x 0.57479.54mso the side facing 35° = 79.54m
b/(sin B) = c/(sin C)79.54/(sin 35) = c/(sin 25)79.54/ (0.574) = c/(0.423)138.57 = c/(0.423)c = 138.57 x 0.423c = 58.62mTo find the area of this triangle
The length of a rectangle is a inches. Its width is 5 inches less than the length. Find the area and the perimeter of the rectangle.
Answers
Answer:
[tex]Area = 5a - a^2[/tex] [tex]inches\²[/tex]
[tex]Perimeter = 10\ inches[/tex]
Step-by-step explanation:
Given
Length = a
Width = 5 - a
Required
Determine the Area and Perimeter;
Calculating Area
Area is calculated as thus;
[tex]Area = Length * Width[/tex]
Substitute values for Length and Width
[tex]Area = a * 5 - a[/tex]
[tex]Area = a * (5 - a)[/tex]
Open Bracket
[tex]Area = 5a - a^2[/tex]
Calculating Perimeter
Perimeter is calculated as thus;
[tex]Perimeter = 2 (Length + Width)[/tex]
Substitute values for Length and Width
[tex]Perimeter = 2 (a + 5 - a)[/tex]
Collect Like Terms
[tex]Perimeter = 2 (5 + a- a)[/tex]
[tex]Perimeter = 2 (5)[/tex]
Open Bracket
[tex]Perimeter = 10\ inches[/tex]
“Type ‘equal, supplementary, complementary, or vertical in the space provided’”
Answers
Answer:
Supplementary
Step-by-step explanation:
When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.
<AOB (40°) and <BOC (140°) are not equal angles.
<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.
<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.
<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.
what is 12x^3-9x^2-4x+3 in factored form?
Answers
Answer: (3x^2-1)(4x-3)
============================
Work Shown:
Use the factor by grouping method
12x^3-9x^2-4x+3
(12x^3-9x^2)+(-4x+3)
3x^2(4x-3)-1(4x-3)
(3x^2-1)(4x-3)
here is my question hope this works now
Answers
Answer:
[tex]\boxed{x=1}[/tex] and [tex]\boxed{x=7}[/tex]
Step-by-step explanation:
This quadratic is already factored down to its factors (x - 1) and (x - 7).
Set these equal to zero and solve for x by adding 1 or 7 to both sides of the equation.
[tex]x-1=0\\\\\boxed{x=1}[/tex]
[tex]x-7=0\\\\\boxed{x=7}[/tex]
What kinds of people actually read printed information on the packaging before purchasing a product? As part of a larger study on the influence of product packaging on purchase decisions, a survey of 250 citizens of Sarajevo asked if they observed printed information before purchasing a product (Poturak, 2014). Assume that the sample was a simple random one.
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
[tex]X = 1.2857[/tex]
Step-by-step explanation:
Generally from the table the contribution to the chi-square statistic of the number of individuals in the survey aged 20 - 22 who strongly disagreed about whether they observe packing information before purchasing items is mathematically represented as
[tex]X = \frac{(10 - 7)^2 }{7}[/tex]
[tex]X = 1.2857[/tex]
Evaluate −x^2−5 y^3 when x = 4 and y = 1
Answers
Answer:
Simplify:
[tex]-4^2-5(1^3)[/tex]
So you get:
[tex]-21\\[/tex]
Answer:
[tex]\huge\boxed{-21}[/tex]
Step-by-step explanation:
-x²-5y³
Given that x = 4, y = 1
[tex]-(4)^2-5(1)^3[/tex]
[tex]-16-5(1)\\-16-5\\-21[/tex]
Find y. A. √22 B. 8 C. √42 D. 4
Answers
Answer:
[tex]\Large \boxed{\mathrm{D. \ 4}}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions to solve the problem.
tan θ = opp/adj
tan 30 = y/(4√3)
y = 4√3 tan 30
y = 4
Is 55/22 a rational
Answers
Answer:
The fraction [tex]\displaystyle \frac{55}{22}[/tex] is indeed a rational number.
Step-by-step explanation:
A number [tex]x[/tex] is rational if and only if there exist two integers [tex]p[/tex] and [tex]q[/tex] (where [tex]q \ne 0[/tex]) such that [tex]x = \displaystyle \frac{p}{q}[/tex].
[tex]\displaystyle \frac{55}{22}[/tex], the number in question here is already written in the form of a fraction. The two integers [tex]p = 55[/tex] and [tex]q = 22[/tex] ([tex]q \ne 0[/tex]) meet the requirement that [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]. Therefore, [tex]\displaystyle \frac{55}{22}\![/tex] is indeed a rational number.
Side note: the [tex]p[/tex] and [tex]q[/tex] here ([tex]q \ne 0[/tex]) don't have to be unique. For example:
because [tex]\displaystyle \frac{55}{22} = \frac{5 \times 11 }{2 \times 11} = \fraac{5}{2}[/tex], both of the following pairs could satisfy [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]:
[tex]p = 55[/tex] and [tex]q = 22[/tex];[tex]p = 5[/tex] and [tex]q = 2[/tex].Ana drinks chocolate milk out of glasses that each holds 1/8 fraction of a liter. She has 7/10 fraction of a liter of chocolate milk in her refrigerator. How many glasses of chocolate milk can she pour?
Answers
Answer:
6 glasses
I hope this helps!
Answer:
28/5
Step-by-step explanation:
looked up on khan
Assume that women's heights are normally distributed with a mean given by mu = 64.3 inches, and a standard deviation given by sigma= 2.2 inches.
A) If a woman is randomly selected, find the probability that her height is less than 65 inches.
B) If 34 women are randomly selected, find the probability that they have a mean height less than 65 inches.
Answers
Answer:69
Step-by-step explanation:
A polling company reported that 53% of 1018 surveyed adults said that secondhand smoke issecondhand smoke is "very harmful.""very harmful." Complete parts (a) through (d) below.
a. What is the exact value that is 53% of 1018?
b. Could the result from part (a) be the actual number of adults who said that secondhand smoke issecondhand smoke is "very harmful" question mark "very harmful"? Why or why not?
c. What could be the actual number of adults who said that secondhand smoke issecondhand smoke is "very harmful" question mark "very harmful"?
d. Among the 10181018 respondents, 260260 said that secondhand smoke issecondhand smoke is "not at all harmful.""not at all harmful." What percentage of respondents said that secondhand smoke issecondhand smoke is "not at all harmful" question mark "not at all harmful"?
Answers
Answer:
a. 539.54
b. No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.
c. 540
d. 25.54%
Step-by-step explanation:
Given that:
A polling company reported that 53% of 1018 surveyed adults said that secondhand smoke is "very harmful."
Complete parts (a) through (d) below.
a. What is the exact value that is 53% of 1018?
The 53% of 1018 is :
=[tex]\dfrac{53}{100} \times 1018[/tex]
= 0.53 × 1018
= 539.54
b. Could the result from part (a) be the actual number of adults who said that secondhand smoke is ''very harmful"? Why or why not?
No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.
c. What could be the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful"?
Since, a count of people must result into a whole number, the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful" can be determined from the approximation of the exact value into whole number which is 539.54 [tex]\approx[/tex] 540.
d. Among the 1018 respondents, 260 said that secondhand smoke is is "not at all harmful.'' What percentage of respondents said that secondhand smoke is "not at all harmful"?
Since 260 respondents out of 1018 respondents said that the second hand smoke is not harmful, then the percentage of the 260 respondents is :
= [tex]\dfrac{260}{1018} \times 100 \%[/tex]
= 25.54%
