Based on the given data and the results of the t-test, we have evidence to support the claim that the mean score is above 70 at a 10% alpha level.
To test the claim that the mean score is above 70, we will conduct a one-sample t-test. The null hypothesis is that the mean score is equal to 70, and the alternative hypothesis is that the mean score is greater than 70.
First, we need to calculate the sample mean and standard deviation. The sample mean is (62 + 92 + 75 + 68 + 83 + 95) / 6 = 78.33, and the sample standard deviation can be calculated using the formula:
s = sqrt((1/(n-1)) * sum(xi - xbar)^2)
where n is the sample size, xi is each individual score, xbar is the sample mean. Plugging in the values, we get:
s = sqrt((1/(6-1)) * ((62-78.33)^2 + (92-78.33)^2 + (75-78.33)^2 + (68-78.33)^2 + (83-78.33)^2 + (95-78.33)^2))
s = 12.76
Next, we need to calculate the t-statistic using the formula:
t = (xbar - mu) / (s / sqrt(n))
where mu is the hypothesized population mean, which is 70 in this case. Plugging in the values, we get:
t = (78.33 - 70) / (12.76 / sqrt(6))
t = 1.64
Using a t-distribution table with degrees of freedom equal to n - 1 = 5 and a one-tailed test at a significance level of alpha = 0.10, we find that the critical value of t is 1.476.
Since our calculated t-value of 1.64 is greater than the critical value of t, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean score is above 70 at a 10% alpha level.
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what is the chromatic number of the graph k33, the graph with 33 vertices, each connected to each other
The chromatic number of the graph K33, which is a complete bipartite graph with 33 vertices, each connected to every vertex in the other set, is 2. This means that the graph can be colored using only two colors.
The chromatic number of a graph represents the minimum number of colors needed to color its vertices such that no adjacent vertices have the same color.
In the case of K33, the graph is a complete bipartite graph, which means it can be divided into two sets of vertices, where each vertex in one set is connected to every vertex in the other set. In this specific graph, we have 33 vertices in each set.
To determine the chromatic number, we observe that in a complete bipartite graph, no vertices within the same set are connected to each other. Therefore, we can assign one color to all the vertices in one set and a different color to all the vertices in the other set.
In K33, we can color one set of 33 vertices, let's say set A, with color 1, and the other set of 33 vertices, set B, with color 2. Since no vertices within the same set are connected, there will be no adjacent vertices with the same color.
Hence, we conclude that the chromatic number of the graph K33 is 2, as it can be colored using only two colors.
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Triangle H N K is shown. Angle H N K is 90 degrees. The length of hypotenuse H K is n, the length of H N is 20, and the length of N K is 9.
Law of cosines: a2 = b2 + c2 – 2bccos(A)
What is the value of n to the nearest whole number?
18
22
29
41
Answer:
B just took the test
Step-by-step explanation:
have a good rest of your day
For positive acute angles A and B, it is known that cos A = 8/17 and sin B = 3/5. Find the value of sin(A - B) in simplest form.
The expansion of Cos(A-B) is:
\(\text{Cos(A}-B)=CosACosB+SinASinB\)We are provided with the following:
\(\text{Cos A=}\frac{8}{17},Sin\text{ B=}\frac{3}{5}\)We will have to obtain the values of Cos B and Sin A. Thus, we have:
To be obtain Sin A, we have to get the value of the third side, which is the opposite side, by applying the pythagoras theorem. Thus, we have:
\(\begin{gathered} (\text{Hypotenuse)}^2=(\text{Opposite)}^2+(\text{Adjacent)}^2 \\ 17^2=O^2+8^2 \\ 289=O^2+64 \\ 289-64=O^2 \\ O^2=225 \\ O=\sqrt[]{225} \\ O=15 \\ \text{Thus, Sin A=}\frac{Opposite}{\text{Hypotenuse}} \\ Sin\text{ A=}\frac{15}{17} \end{gathered}\)To be obtain Cos B, we have to get the value of the third side, which is the adjacent side, by applying the pythagoras theorem. Thus, we have:
\(\begin{gathered} \text{Hyp}^2=\text{Opp}^2+\text{Adj}^2 \\ 5^2=3^2+A^2 \\ 25=9+A^2 \\ 25-9=A^2 \\ A^2=16 \\ A=\sqrt[]{16} \\ A=4 \\ \text{Thus Cos B=}\frac{Adjacent\text{ }}{\text{Hypotensue}} \\ \text{Cos B=}\frac{4}{5} \end{gathered}\)Now that we have obtained the values of Cos B and Sin A, we can then go on to solve the original problem.
\(\begin{gathered} \text{Cos(A}-B)=\text{CosACosB}+\text{SinASinB} \\ Cos(A-B)=\mleft\lbrace\frac{8}{17}\times\frac{4}{5}\mright\rbrace+\mleft\lbrace\frac{15}{17}\times\frac{3}{5}\mright\rbrace \\ \text{Cos(A-B)=}\frac{32}{85}+\frac{45}{85}_{} \\ \text{Cos(A}-B)=\frac{77}{85} \end{gathered}\)Determine if segments AB and CD are parallel, perpendicular, or neither. AB formed by A(3,8) and B(-6,5) CD formed by C(-6,7) and D(-3,8)
Answer:
They are parallel
Step-by-step explanation:
(3,8)(-6,5): do sloe formula (y1-y2 over x2-x1)
AB: 1/3 slope (Full formula y=1/3x+7)
(-6,7)(-3,8) ---> 8-7 over -3-(-6) = 1/3
CD: 1/3 slope (Full formula y=1/3x +9)
They have the same slope so they are parallel
Find the surface area of the cylinder. Round your answer to the nearest tenth.
Answer:
87.9\(m^2\)
Step-by-step explanation:
Surface area of a cylinder: 2*π*r*h + 2*π*\(r^2\)
π = 3.14
r = 2mm
h = 5mm
A = 2*π*r*h + 2*π*\(r^2\)
2*3.14*2*5 + 2*3.14*\(2^2\)(4)
62.8 + 25.12
87.92\(m^2\) rounded to the nearest tenth is 87.9\(m^2\)
Hope this helps!
2.13 use algebraic manipulation to find the minimum sum-of-products expression for the function f = x1x2x3 x1x2x4 x1x2x3x4.
To find the minimum sum-of-products expression for the function f = x1x2x3 x1x2x4 x1x2x3x4 using algebraic manipulation, the following steps need to be followed:
Step 1: Write the SOP expression f = x1x2x3 x1x2x4 x1x2x3x4
Step 2: Create a K-map with the input variables x1, x2, x3, and x4 on the top and left side
Step 3: Identify the minterms using the K-map, which is 2, 5, 6, 7, 8, 9, 10, 11, 12, and 13
Step 4: Plot the minterms on the K-map using 1s
Step 5: Look for groups of 1s on the K-map and combine them to create an SOP expression with the fewest possible terms.
In this case, two groups can be combined:
Group 1 includes minterms 2, 6, 10, and 14.
Group 2 includes minterms 5, 7, 13, and 15.
The minimum sum-of-products expression is thus:
f = (x1'x2'x3'x4) + (x1'x2x3'x4')
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please help I am really stuck on this one!! I would like an explanation with the answer please so I can learn how to do it from now on!!
ANSWER:
x° = 24°
y° = 72°
Analysis on picture hope it helps
The total length of a road trip was 14. 4 hours. if highway signs are posted every 0. 6 hours, including one at the end of the road trip, how many highway signs will there be on the road trip?
There will be 24 highway signs on the road trip.
What is a division in mathematics?
In mathematics, the division is the process of finding the number of times one number, called the divisor, is contained in another number, called the dividend. The division is often represented using the symbol "/" or "÷".
To find the number of highway signs on the road trip, we need to divide the total length of the road trip (14.4 hours) by the interval between signs (0.6 hours).
The number of highway signs on the road trip is:
14.4 hours / 0.6 hours/sign = 4.4/0.6=24 signs
Hence, there will be 24 highway signs on the road trip.
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or write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. at a community barbecue, mrs. dotson and mr. kent are buying dinner for their families. mrs. dotson purchases 2 hot dog meals and 3 hamburger meals, paying a total of $33. mr. kent buys 1 hot dog meal and 3 hamburger meals, spending $27 in all. how much do the meals cost? hot dog meals cost $ each, and hamburger meals cost $ each.
Let's use the variables x and y to represent the cost of a hot dog meal and a hamburger meal, respectively.
Then, we can write the following system of equations to describe the situation:
2x + 3y = 33 (Mrs. Dotson's purchases)
1x + 3y = 27 (Mr. Kent's purchases)
To solve this system of equations using elimination, we can multiply the second equation by 2 and subtract it from the first equation:
2x + 3y = 33
-2x - 6y = -54
0x - 3y = -21
Simplifying the equation, we get:
y = 7
Substituting this value of y into either equation, we can solve for x:
2x + 3(7) = 33
2x + 21 = 33
2x = 12
x = 6
Therefore, hot dog meals cost $6 each, and hamburger meals cost $7 each.
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Fill in the blanks with the answer to each question based on information provided.Two toy robots are having a race. Robot A can go 14 meter in 15 seconds. Robot B can go 1 meter in 50 seconds.1) If Robot A continues at that same speed, how long will it take to go 1 meter? Remember units! __________2) How long for Robot A to go 4 meters at that speed? Remember units! _________
Answer:
1 1/14 seconds4 2/7 secondsStep-by-step explanation:
We are being asked for times, so we can express the rate in terms of seconds per meter.
(15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter
__
1) It will take Robot A 1 1/14 seconds to go 1 meter.
2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)
7.006 x 10^-3 in standard notation
Answer:
7.006*10⁻³ = 0.007006
Step-by-step explanation:
7.006*10⁻³ = 0.007006
what is x−10=4 pls help me
Answer:
Step-by-step explanation: 14 = x
Answer:
The answer to your question would be 14
Step-by-step explanation:
Simple equation
14 - 10 = 4
I hope this helps and have a wonderful day!
Where is the graph of f(x)=4[x-3]+2 discontinuos
Answer:
Below
Step-by-step explanation:
4 [x-3] + 2 = y is not discontinuous anywhere
However 4 / [x-3] + 2 DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!
intr-o florarie sunt 840 flori:lalele trandafiri crizanteme.Stiind ca daca impartim numarul lalelelor la nr total de trandafiri si crizanteme obtinem catul 3,restul 8 si ca nr trandafirilor este cu doi mai mare decat nr crizantemelor, sa se afle nr flori
Răspuns:
Trandafiri = 105
Lalele = 632
Crizanteme = 105
Explicație pas cu pas:
Lăsa :
Trandafiri = x
Lalea = y
Crizanteme = z
x + y + z = 840
x = z + 2
y / (z + z + 2) = 3 r 8
y / (2z + 2) = 3 restul 8
y = (2z + 2) (3) + 8
y = 6z + 6 + 8
y = 6z + 14
x = z + 2
y = 6z + 14
x + y + z = 840
Înlocuiți x și y în ecuația:
z + 2 + 6z + 14 + z = 840
8z + 16 = 840
8z = 840 - 16
8z = 824
z = 824/8
z = 103
x = z + 2
x = 103 + 2
x = 105
y = 6z + 14
y = 6 (103) + 14
y = 632
the ratio of dogs to cats seen at the veterinarian's office is 7:3. If the veterinarian sees 15 cats, how many dogs do they see?
Answer:
35 dogs
Step-by-step explanation:
let dogs ratio be 7x
let cats ratio be 3x
7x/3x = a/15
15÷3 = 5
so, 7×5 = 35
can someone help please?
∠1 and ∠4 are vertical interior angle.
∠1 ≅ ∠5 follows Transitive property of congruence
g ║h by corresponding angle theorem
How to find angles ?The diagram is to prove alternate interior angles converse.
Therefore,
∠4 ≅ ∠5 (Alternate interior angles)
By, the vertical interior angle congruence, ∠1 ≅ ∠4
Vertically opposite angles are congruent. Vertically opposite angles share the same vertex.
Then by the Transitive property of congruence, ∠1 ≅ ∠5.
So, by the corresponding angles theorem, g ║h
Corresponding angles are usually congruent.
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Find the area of the shaded portion.
6
120
Answer:
A = 36√3 - 12π
Step-by-step explanation:
Make 2 identical 30-60-90 triangles out of the "wedge"
For each 30-60-90 triangle:
Since the short leg is 6 the long leg is 6√3
short leg is the base and long leg is the height
a = (1/2)bh
a = (1/2)(6)(6√3)
a = 3(6√3)
a = 18√3
Since there are 2 triangles
a = 36√3
--------------------------------
Then subtract off the area of the 120º sector
a = (120/360)πr^2
a = (1/3)π(6^2)
a = (1/3)π(36)
a = 12π
Shaded area
a = 36√3 - 12π
Step-by-step explanation:
we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).
since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.
basically, the area of a triangle is
1/2 × b×c × sin(A)
A being the angle between the 2 sides b and c. for any 2 sides of the triangle.
one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.
we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.
remember, the sum of all angles in a triangle is 180 degrees.
so, via the law of sines we can then calculate all sides :
a/sin(A) = b/sin(B) = c/sin(C)
with the angles being opposite of the sides.
6/sin(30) = baseline/sin(90)
6/0.5 = baseline/1
12 = baseline
top side² + 6² = 12²
top side² = 12² - 6² = 144 - 36 = 108
top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)
we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.
the area of the 2 triangles is then
6×sqrt(3)×6×sin(90) = 36×sqrt(3)
and the circle segment to be deducted is
pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12
so, the complete answer is
A = 36×sqrt(3) - 12×pi
Learn with an example
53 ft.
45 ft.
b
What is the length of the missing leg? If necessary, round to the nearest tenth.
Jerry filled a pitcher up 1/3 full then poured 5/7 of the pitcher into a glass. What fraction of the total pitcher did he pour into the glass?
Answer:
5/21
hope this helps
Solve the system of equations. \begin{aligned} &-9y+4x - 20=0 \\\\ &-7y+16x-80=0 \end{aligned} −9y+4x−20=0 −7y+16x−80=0
Answer:
(5 , 0)
Step-by-step explanation:
7 * (−9y+4x−20)=0
9 * (−7y+16x−80)=0
-63y + 28x -140 = 0 ......a
-63y + 144x -720 = 0 .....b
b-a: 116x - 580 = 0
116x = 580
x = 5
y = (4x-20)/-9 = 0/-9 = 0
solve the following equation for D. be sure to take into account whether a letter is capitalized or not.
hD=m
Answer:
b
Step-by-step explanation:
The expression in terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The expression is:
hD = m
To solve for D make the subject as D
As we know the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
Divide by h on both the sides:
hD/h = m/h
Here h ≠ 0
D = m/h
Thus, the expression in terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.
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Which of the following options have the same value as 65% of 20?
B
...........................
Answer:
It is A and D
Step-by-step explanation:
65% of 20 is also
.65 * 20 or
65/100 * 20
I did Khan Academy too :)
f the nxn matrices E and F have the property that EF = I, then E and F commute. Explain why Select the correct choice below. 1 A. According the Invertible Matrix Theorem, E and F must both be identity matrices. So FI and E = 1; therefore, FE = EF Thus, E and F commute.B. According the Invertible Matrix Theorem, E and F must be invertible and inverses. So FE = I and I = EF. Thus, E and F commute. C. According the Invertible Matrix Theorem, E and F must not be invertible and therefore cannot be inverses. So FE = I and I = EF. Thus, E and F commute. D. According the Invertible Matrix Theorem, E and F both have columns that span R" So FE = EF. Thus, E and F commute.
Since these two operations cancel each other out, the order in which we apply them does not matter, which is why E and F commute.
The correct choice is B. According to the Invertible Matrix Theorem, if EF = I, then both E and F are invertible matrices with inverses F⁻¹ and E⁻¹ respectively. This is because if EF = I, then both E and F are one-to-one and onto, which implies that they have inverses.
Since E and F are invertible matrices, it follows that FE = E⁻¹(EF)F⁻¹ = E⁻¹IF⁻¹ = F⁻¹E⁻¹ = (EF)⁻¹ = I⁻¹ = I. Therefore, we have shown that E and F commute.
To explain this result, note that if two matrices A and B commute, then AB = BA. In other words, the order in which we multiply A and B does not matter. In this case, we have shown that EF = I implies that FE = I, which means that the order in which we multiply E and F does not matter.
Intuitively, we can think of E and F as performing opposite operations that cancel each other out. When we apply E and then F, we get back to where we started, which is the identity matrix I.
Similarly, when we apply F and then E, we also get back to I.
Since these two operations cancel each other out, the order in which we apply them does not matter, which is why E and F commute.
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A jar contains 39 marbles of which 7 is blue and 22 are red and the rest are green what is the ratio of blue marbles to green marbles?
Leah runs M miles everyday during the week except for Wednesday or Sunday. A. write an algebraic expression that represents the total number of miles leah runs each week B. there are 52 weeks in a year. write an algebraic expression that represents the total number of miles leah runs in a year
A. The algebraic expression that represents the total number of miles Leah runs each week is 5*M.
B. The algebraic expression that represents the total number of miles Leah runs in a year is 260*M.
Leah runs M miles everyday during the week except for Wednesday or Sunday.
We need to write the algebraic expression that represents the total number of miles Leah runs each week. Leah runs for 5 days in a week. The total number of miles run in a week is 5*M.
We need to write the algebraic expression that represents the total number of miles Leah runs in a year. Leah runs 5*M miles in a week. The total number of miles run in a year is (5*M)*52 = 260*M.
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Solve the equation a = m – n for the variable n
Answer:
a=m-n
(Add n to both sides)
a+n=m-n+n
(The -n and +n cancel out, on the right side of the equation)
a+n=m
(Now subtract a from both sides)
a+n-a=m+a
(The +a and -a cancel out, on the right side of the equation)
n=m+a
Answer:
\(\huge \boxed{n=-a+m}\)
Step-by-step explanation:
\(a=m-n\)
Adding \(n\) to both sides.
\(a+n=m-n+n\)
\(a+n=m\)
Subtracting \(a\) from both sides.
\(a+n-a=m-a\)
\(n=m-a\)
Which of these are components of DNA? Select five options. deoxyribose sugar molecules ribose sugar molecules adenine phosphate molecules uracil cytosine thymine
Answer:
A. deoxyribose sugar molecules
C. adenine
D. phosphate molecules
F. cytosine
G. thymine
Step-by-step explanation:
I got it correct
DNA is a biomolecule that is made up of, deoxyribose sugar, phosphate group, and nitrogenous base cytosine, thymine, and adenine.
What is the structure of the DNA?DNA is a double helix structure, in which hydrogen bonds between purines and pyrimidines, making the material for storage of the genetic information.
DNA stands for deoxyribonucleic acid, it is a polynucleotide made by repeated units of nitrogenous base attach by a glycosidic bond with the sugar and this repeated nucleoside unit is attached to the phosphate group-making nucleotide.
This structure of DNA is best suited for the storing of genetic information, on the other hand, RNA is a single-stranded molecule, which is not stable as DNA.
Therefore, DNA consists of deoxyribose sugar, adenine, phosphate molecules, cytosine, and thymine.
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Moon Software Inc. is planning to issue two types of 25-year, noncallable bonds to raise a total of $6 million, $3 million from each type of bond. First, 3,000 bonds with a 10% semiannual coupon will be sold at their $1,000 par value to raise $3,000,000. These are called "par" bonds. Second, Original Issue Discount (OID) bonds, also with a 25 -year maturity and a $1,000 par value, will be sold, but these bonds will have a semiannual coupon of only 7.75%. The OID bonds must be offered at below par in order to provide investors with the same effective yield as the par bonds. How many OID bonds must the firm issue to raise $3,000,000 ? Disregard flotation costs, and round your final answer up to a whole number of bonds.
3,776
3,096
3,927
2,870
4,456
Moon Software Inc. must issue approximately 3,927 OID bonds to raise $3,000,000.
The par bonds have a coupon rate of 10% and a par value of $1,000. To raise $3,000,000, Moon Software Inc. needs to issue 3,000 par bonds since $3,000,000 divided by $1,000 equals 3,000.
The OID bonds have a semiannual coupon rate of 7.75% and a par value of $1,000. Since these bonds need to provide investors with the same effective yield as the par bonds, they must be offered at a discount. To calculate the number of OID bonds required, we need to determine the discount needed to match the effective yield of the par bonds.
The effective yield of the par bonds is 10%. The OID bonds have a coupon rate of 7.75%, so the discount needed to match the effective yield is 10% - 7.75% = 2.25%.
To raise $3,000,000 with OID bonds, we divide the amount by the discount rate: $3,000,000 / 2.25% = $133,333,333.33.
Since each OID bond has a par value of $1,000, we divide the total amount by $1,000: $133,333,333.33 / $1,000 = approximately 133,333.33 bonds.
Since we need a whole number of bonds, we round up to the nearest whole number, which gives us 133,334 bonds.
Therefore, Moon Software Inc. must issue approximately 133,334 OID bonds to raise $3,000,000.
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Two step equation help me pls step by step
The questions 36 and 37
Answer:
Step-by-step explanation:
SOLVING
================================================================
Question 36
6=-2(7-c)
Use distribution to multiply -2 by parenthesis
6=-14+2c
Add to both sides 14
20=2c
Divide 2 into both sides
10=c
Question 375(h-4)=8
Use distribution to multiply 5 by the parenthesis
5h-20=8
Add to both sides 20
5h=28
Divide 5 into both sides
\(h=\frac{28}{5}\)
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The UCL and LCL for an x-bar chart are 25 and 15 respectively. The central line is 20, and the process variability is considered to be in statistical control. The results of the next six sample means are 18, 23, 17, 21, 24, and 16. What should you do? A. Explore the assignable causes because there is a run. B. Nothing; the process is in control. C. Explore the assignable causes because there is a trend. D. Explore the assignable causes because there is an oscillation. E. Explore the assignable causes because the second, fourth, and fifth samples are above the mean.
Option E should be chosen, which is to explore the assignable causes because the second, fourth, and fifth samples are above the mean.
In an x-bar chart, the control limits (UCL and LCL) are based on the process variability and are used to determine if the process is in control. The central line represents the mean of the process.
Looking at the given sample means of 18, 23, 17, 21, 24, and 16, we can see that the second, fourth, and fifth samples are above the mean of 20. This suggests a potential shift or deviation from the expected process mean.
In an x-bar chart, if any sample mean falls outside the control limits or exhibits a non-random pattern, it indicates the presence of assignable causes, which are factors that can be identified and addressed to improve the process. Since the second, fourth, and fifth samples are above the mean, it is advisable to explore the assignable causes, as stated in option E.
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