. Ferric chloride is used as a flux in some types of extraction metallurgy processes. This material is shipped in containers, and the container weight varies. It is important to obtain an accurate estimate of mean container weight. Suppose that from long experience a reliable value for the standard deviation of flux container weight is determined to be 4 lb. How large a sample would be required to construct a 95% two-sided confidence interval on the mean that has a total width of 1 lb1 lb? (Montgomery, 08/2019, p. E-10) Montgomery, D. C. (2019). Introduction to Statistical Quality Control, Enhanced eText, 8th Edition. [[VitalSource Bookshelf version]]. Retrieved from vbk://9781119399308 Always check citation for accuracy before use.
Answer:
The sample size is [tex]n = 246[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 4\ lb[/tex]
The confidence level is C = 95%
The total width is [tex]w = 1 \ lb[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 -95 )\%[/tex]
=> [tex]\alpha = 0.05[/tex]
From the normal distribution table the critical value for [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2}} * \sigma }{E}]^2 [/tex]
Here E is the margin of error which is mathematically represented as
[tex]E = \frac{w}{2}[/tex]
=> [tex]E = \frac{1}{2}[/tex]
=> [tex]E = 0.5 [/tex]
So
[tex]n = [\frac{1.96 * 4 }{0.5}]^2 [/tex]
[tex]n = 246[/tex]
Jerry, Skyler and Kyle were measuring the tank (cylinder) for storing water tower on the hill. Working together Jerry and Skyler
determine the circumference was approximately 295.3 feet. Kyle measured the height to be about 40 feet. What is the potential
volume of the tank? (Round to the nearest tenth)
Answer?
Answer:
277 591.1 ft³
Step-by-step explanation:
First, use the formula for circumference to solve for the diameter.
Circumference = πd
295.3 = πd
295.3/π = d
94 ft = d
Then, divide the diameter by 2 to find the radius.
r = d/2
r = 94/2
r = 47 ft
Now, use the value of the radius with the given height in the formula for volume of a cylinder.
V = πr²h
V = π(47²)(40)
V = 277 591.1 ft³
What are interesting applications of real analysis?dont steal my points
Answer:
Real analysis serves as the basis for measure theory, axiomatic probability, which follow to stochastic processes. Stochastic processes are used in finance, trading, computer and network simulations, modelling, manufacturing, quality control, etc
The graph of f(x) shown below
Answer:
C
Step-by-step explanation:
the "-" sign can't be true, because that would have turned the whole graph of x² upside-down. but it is not.
so, we need a positive sign for the x term.
and the whole graph is shifted to the right. so the functional value of x of F(x) is now the same that happened "earlier" (for smaller x) with G(x). so, the argument "x" is now reduced (by 3 units, as the graph is shifted right by 3 units) in the calculation compared to the original G(x) calculation.
therefore, the ...(x-3)... expression is right.
so, positive sign and "(x-3)" is only in C.
in each linear equation identify the slope (m) and the y-intercept (b)
Answer:
a is D and b is C
Step-by-step explanation:
Slope is always with an x, b is always alone
Hey there!
Please remember that
in slope-intercept form, m is the slope, and b is the y-intercept.Is y=4x-5 written in slope-intercept form (y=mx+b)? Sure! :)
Therefore, the slope, m, is 4, and the y-intercept, b, is -5.
Same with the second equation:
y=2/3-x
or
y=x-2/3
here, the y-intercept, b, is 2/3, and the slope, m, is -1.
Now, what's the equation of the line with a slope of 2 and a y-intercept of -7?
That's right, y=2x-7.
Hope everything is clear.
Let me know if you have any other questions!
#LearningDoesn'tEnd
:-)
Rewrite (123 + 456) + 789 using the Associative Law of Addition
Answer:
123 + (456 + 789)
Step-by-step explanation:
since this is an addition problem, the parenthesis don't matter, and they can be put wherever you want.
(123 + 456) + 789
123 + 456 + 789
(123 + 456 + 789)
123 + (456 + 789)
technically, any of these would work, but I think the kind of answer the problem is looking for is;
123 + (456 + 789)
Help help help! Im stuck please help!
Answer:
1) 8/15
Step-by-step explanation:
When dividing by a number, multiply by its reciprocal.
2/5 ÷ 3/4
2/5 × 4/3
8/15
If
[tex] \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0[/tex]
and
[tex] {x}^{2} + {y}^{2} + {z}^{2} = 25[/tex]
, then x + y + z will be? Z
Answer:
5
Step-by-step explanation:
We would like to find out the value of [tex] x + y + z [/tex] from the given equations , which are ;
[tex]\longrightarrow \dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0[/tex]
[tex]\longrightarrow \\ x^2+y^2+z^2=25[/tex]
Now consider ,
[tex]\longrightarrow \dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0\\[/tex]
[tex]\longrightarrow \dfrac{xy + yz + zx }{xyz }=0\\[/tex]
[tex]\longrightarrow xy + yz + zx = 0(xyz)\\ [/tex]
[tex]\longrightarrow xy + yz + zx = 0\\ [/tex]
[tex]\longrightarrow 2(xy + yz + zx)=0(2)\\[/tex]
[tex]\longrightarrow 2(xy + yz + zx)=0[/tex]
Now recall the identity ,
[tex]\longrightarrow (a + b + c)^2=a^2+b^2+c^2+2(ab + bc + ca)[/tex]
Plug in the values ,
[tex]\longrightarrow (x+y+z)^2= 25 + 0\\ [/tex]
[tex]\longrightarrow (x + y + z )^2=25\\[/tex]
[tex]\longrightarrow (x + y + z)=\sqrt{25}\\[/tex]
[tex]\longrightarrow \underline{\underline{\boldsymbol{ x + y + z = 5}}}{} [/tex]
And we are done !
Answer :
5⠀
Step-by-step explanation:
Given,
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} = 0}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {x}^{2} + {y}^{2} + {z}^{2} = 25 }}}}[/tex]
⠀
To Find :
[tex]{ \longrightarrow \qquad{ { \sf{ x + y + z }}}}[/tex]
⠀
Solution :
[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} = 0}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ \dfrac{yz + zx + xy}{xyz} = 0}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {yz + zx + xy} = 0}}}}[/tex]
⠀
Multiplying both sides by 2 :
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0.2}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0}}}}[/tex]
⠀
We know,
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + zx) }}}}[/tex]
⠀
As, It is given that,
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {x}^{2} + {y}^{2} + {z}^{2} = 25 }}}}[/tex]
⠀
and as we get,
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ 2( {yz + zx + xy} )= 0}}}} \\ \\{ \longrightarrow \qquad{ { \sf{ 2( {xy + yz + zx} )= 0}}}}[/tex]
⠀
Now, We'll substitute it in the formula :
[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = 25 + 0 }}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {(x + y + z)}^{2} = {25} }}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ {x + y + z}^{} = \sqrt{25} }}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \bf{ \pmb {x + y + z}^{} = {5} }}}}[/tex]
⠀
Therefore,
The value of x + y + z is 5 .Can somebody Help me pls !
Answer:
2.7
Step-by-step explanation:
I hope it helsp if its right pls amrk me as brainliest
Aplumber charges a $75 flat fee for jobs lasting up to an hour and $30 for each hour of labor after the first hour. Which
expression models the cost of a job lasting h hours, when h is greater than 1?
O 75-30h
O 75+ 30(h-1)
O 75h+30
75(h-1)+30
[tex]\longrightarrow \sf 75+ 30(h-1) [/tex]
Solution:-Given that :-
job last for h hours Cost of job lasting more than 1 hour = $30Cost for the first hour = $75[tex]\leadsto[/tex]Remaining hours for which the job will last after first hour= (h-1)
Therefore,
Cost for subsequent hours = 30×(h-1)
= 30(h-1)
Total Cost for job = Cost for 1st hour + Cost for subsequent hours
[tex]\quad\quad\quad\quad\quad\quad\quad\quad\boxed{\sf{= 75+30(h-1)}}[/tex]
write the expressions using exponents b*b*b
Answer:
[tex]b^{3}[/tex]
Step-by-step explanation:
b × b × b = [tex]b^{3}[/tex]I hope this helps!
Solve: -1/2 x +3 = -x+7
Answer:
thats the answer
Step-by-step explanation:
Use Cramer's rule to solve for x
x + 4y - z=-14
5x + 6y + 3z = 4
-2x + 7y + 2z = -17
Answer:
( 2, 3, 4 )
Step-by-step explanation:
Answer:
The answers are below...
IAI = 1 4 -1 IAxI= -14 4 -1
5 6 3 4 6 3
-2 7 2 -17 7 2
IAI = B -120
IAxI = A -240
X = 2
A car salesman sold one car that was
priced $18,298 and one truck that
was priced $35,225. What was the
cost of the car and truck in all?
Answer:
$53,523
Step-by-step explanation:
This is an addition. You must add the two prices.
$18,298 + $35,225 = $53,523
Anyone know the answer to this
the largest perfect square number that is a factor of 75 is?
the largest perfect square number that is a factor of 32 is?
the largest perfect square number that is a factor of 68 is?
Answer:
Step-by-step explanation:
75 = 3 x 25 = 3 x 5²
32 = 2 x 16 = 2 x 4²
68 = 4 x 17 = 2² x 17
So
the largest perfect square number that is a factor of 75 is 25
the largest perfect square number that is a factor of 32 is 16
the largest perfect square number that is a factor of 68 is 4
help me please!!!!!!
A poster is 2 feet wide and 4 feet tall what is the perimeter
Answer:
12
Step-by-step explanation:
P = is you add Length (L) plus Legnth (L) plus Width (W) plus Width (W)
4+4+2+2
)Mrs. Smith bought 6 rolls of foil to use at a bake sale. She used 223 feet of foil and had 77 feet left over. How many feet are on each roll?
Step-by-step explanation:
First you add the number of used and unused feets of foil
223 + 77 = 300
After that you divide the feets of rolls by the total number of foils
that is, 300 / 6 = 50
therefore there are 50 feets in each foil
if this helped pls give brainliest
3
A goalkeeper saves 7 out of 50 penalties.
a
Estimate the probability that a penalty is saved.
Answer:
Step-by-step explanation:
7 of 50 calculate percentage= 7/50x 100 = 14% =14/100.
Simplify 14/100= \frac{7}{50} probability.,
Maggie keeps track of daily bird sightings. The table shows the number and types of swans that were seen in one day.
Types of swans:
Mute swans 5
Trumpeter swans 34
Tundra swans 2
Maggie incorrectly says that the percent of mute
swans is equivalent to 5
36. Explain her likely error.
What percent of the swans were mute swans? Round to the nearest
whole percent.
Answer:
first we need to add all of the swans together, then from there you take the amount of mute swans and divide it by the sum of all the swans! finally, multiply by 100 to convert into a percent and round it to 12.2%
Step-by-step explanation:
Answer:
8%
Step-by-step explanation:
First, add the total of all the swans together
5+34+2=41
Next, take the total and divide it by the number of mute swans there are
41÷5=8.2
Finally round 8.2 to the nearest whole percent
8.2=8
The answer is 8%
Please Help! I will give brainlest! It locks in an Hour!
Answer:
0 and 2π/3
3rd and 4th
Step-by-step explanation:
In the figure, parallel lines r and s are cut by line t
What is the value of x in this figure?
Answer:
x = 49
Step-by-step explanation:
Since the line is parallel, the value of 2x - 8 is equal to 90.
=> 2x - 8 = 90
=> 2x = 98
=> x = 49
Answer:
x = 49
Step-by-step explanation:
2x - 8 and the right angle are corresponding angles and are congruent , then
2x - 8 = 90 ( add 8 to both sides )
2x = 98 ( divide both sides by 2 )
x = 49
A^2 = 4 and B^2 = 3. What is C^2 × 15?
Answer:
105
Step-by-step explanation:
Assuming A^2 + B^2 = C^2:
C^2 = 4 + 3 = 7
So,
C^2 * 15 = 49(15) = 105
Note: Since the relationship between A, B, and C isn't known, it cannot be said for certain that 105 is the answer.
Step-by-step explanation:
there is no C in the first 2 equations. There is no A or B in the last expression. I do not think you can solve this.
HELP I GIVE 15 POINTS
Please help with angle b.
Answer:
b = 133
Step-by-step explanation:
If 7 books cost Rs. 300 more
than 5 books, find the cost of a
book.
Answer:
150
Step-by-step explanation:
If 7-5=2 books cost 300 and you want to find the cost of 1 book, you would need to divide that 300 by 2.
300÷2=150
Answer:
Step-by-step explanation:
Which part of the proof does the fourth statement and reason represent?
Given: AB ≅ BC
BC ≅ EF
Prove: EG = AB + FG
A line contains point A, B, C.
A 2-column table has 6 rows. Column 1 is labeled Statements with entries line segment A B is-congruent-to line segment B C, line segment B C is congruent to line segment E F, line segment A B is-congruent-to line segment E F, A B = E F, E G = E F + F G, E G = A B + F G. Column 2 is labeled reasons with entries given, given, transitive property, definition of congruent segments, segment addition, and substitution.
It is part of the given information.
It is part of the argument.
It is the conclusion.
It is an assumption.
Answer:
It is part of the argument.
Step-by-step explanation:
AB + BC = AC.
So, the line segment EG , F lies on the line segment;
Therefore, by segment addition postulates we have below:
EG = EF + FG
By substitution AB=EF
EG = AB + FG
~~~~~~~~~~~~~~~~~~~~
Given: AB ≅ BC
BC ≅ EF
Prove: EG = AB + FG
~~~~~~~~~~~~~~~~~~~~~~
~lenvy~
Answer:
It is part of the argument.
Step-by-step explanation:
The answer above is correct.
When six times the larger of two numbers is added to seven times the smaller, the result is 114. Ten times the larger less nine times the smaller is 66. Determine the numbers.
Answer:
Step-by-step explanation:
Let the larger number = x
Smaller number = y
6x + 7y = 114 ------------(I)
10x - 9y = 66 ------------(II)
Multiply equation (I) by 9 and multiply the equation (II) by 7. After that add the two equations. So that, y will be eliminated and we can find the value of x
(1)*9 54x + 63y = 1026
(II)*7 70x - 63y = 462 {Now add}
124x = 1488 {Divide both sides by 124}
x = 1488/124
x = 12
Plugin x = 12 in any of the equation. Here, We are substituting in equation (I)
6*12 + 7y = 114
72 + 7y =114
7y = 114 - 72
7y = 42
y = 42/7
y = 6
The numbers are 12 , 6
PLEASE HELP ME WITH THIS QUESTION
ILL GIVE YOU A BRAINLY
In a toy store, the ratio of the number of dolls to the number of teddy bears is . If the store has 240 dolls, how many teddy bears are in the store? Use pencil and paper. Describe the mental math steps you use to solve this problem.
Answer:
Since you did not list the ratio, i will tell you what to do. say the ration is 5:6, meaning for every 5 teddy bears there are 6 dolls. I would divide 240 by 6, then multiply by 5.