Answer:
a) p=0.154
b) P(X≤2)=0.019
c) He can argue that the proportion of minority jurors is not representative of the proportion of that minority in the population.
Step-by-step explanation:
a) The proportion can be calculated dividing the number of jurors that are from the minority race by the total number of jurors:
[tex]p=X/N=2/13=0.154[/tex]
b) We can model this with a binomial random variable, with sample size n=13 and probability of success p=0.47.
The probability of k minority jurors in the sample is:
[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{13}{k}\cdot0.47^k\cdot0.53^{13-k}[/tex]
We have to calculate the probability that 2 or less minority jurors. This can be calculated as:
[tex]P(x\leq2)=P(x=0)+P(x=1)+P(x=2)\\\\\\P(x=0)=\dbinom{13}{0}\cdot0.47^{0}\cdot0.53^{13}=1\cdot1\cdot0.0003=0.000\\\\\\P(x=1)=\dbinom{13}{1}\cdot0.47^{1}\cdot0.53^{12}=13\cdot0.47\cdot0=0.003\\\\\\P(x=2)=\dbinom{13}{2}\cdot0.47^{2}\cdot0.53^{11}=78\cdot0.221\cdot0.001=0.016\\\\\\\\P(x\leq2)=0.000+0.003+0.016\\\\P(x\leq2)=0.019[/tex]
The probability that 2 or less minority jurors is 0.019.
Please help don't understand this. The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g?
Explanation:
The graph shows that f(x) has the y intercept at -5. This is where the red line crosses the vertical y axis. More specifically, the y intercept is located at the point (0,-5)
We're told that g(x) has a y intercept at -1. So we must move f(x) 4 units up to go from y = -5 to y = -1. This is because -5+4 = -1.
Do this for every point on f(x) and you'll end up with g(x) = f(x)+4. Recall that y = f(x). So saying f(x)+4 is the same as y+4 to indicate "shift up 4 units".
f(x) and g(x) have the same slope, but different y intercepts. So they are parallel lines that never cross.
James plays at the neighborhood basketball court which is enclosed by a circular fence. The circle created by fence has a radius of 50 feet. What is the APPROXIMATE area of the space enclosed by the fence? Use 3.14 for π. 1,962.5 sq ft 7,850 sq ft 157.5 sq ft 314 sq ft
Answer:
7850 feet.sq
Step-by-step explanation:
the area of a cercle is:
A = r²*π where r is the radius
A= 50²*3.14 = 7850 ft²
What is the area of this composite shape? Enter your answer in the box. in²
Answer:
Area = 53 in²
Step-by-step explanation:
area of a box = 8 * 6 = 48 in²
area of a triangle = 1/2 * b * h
b = 6 - 4 = 2 in
h = 13 - 8 = 5 in
area of a triangle = 1/2 * 2 * 5 = 5 in²
total area = area of a triangle + area of a box
total area = 5 in² + 48 in²
total area = 53 in²
A circular post in a cafeteria has a diameter of 3 feet. Which of these is
closest to the circumference of the post?
Answer:
9.42 feet
Step-by-step explanation:
The circumference is π × diameter.
3.14 × 3 = 9.42
The circumference of the circular post is 9.42 feet.
You are ordering softballs for two softball leagues. The Elementary League uses a
larger softball priced at $2.75 each. The Middle School league uses a smaller softball
prices at $3.25 each. You order a total of 80 softballs for $245. What equations
would you use to find out how many of each size of softball you can order. Let L =
the larger softball and let S = the smaller softball.
Answer:L=30 S=50
Step-by-step explanation:
3.25 x 50 = 162.5
245 - 162.5 = 82.5
82.5 divided by 30 equals 2.75.
ten percent of 140,000 = ?
Answer:
14000
Step-by-step explanation:
Of means multiply
10% * 140000
Change to decimal form
.10 * 140000
14000
Answer:
[tex]14000[/tex]
Step-by-step explanation:
[tex]10\% \times 140000[/tex]
[tex]\mathrm{Apply} \: a\% = \frac{a}{100}[/tex]
[tex]\frac{10}{100} \times 140000[/tex]
[tex]\mathrm{Apply} \: \frac{a}{100} \times b = \frac{ab}{100}[/tex]
[tex]\frac{1400000}{100}[/tex]
[tex]\mathrm{Simplify.}[/tex]
[tex]\frac{14000}{1} =14000[/tex]
please please please please help i need to pass please
Answer:
D
Step-by-step explanation:
Solution:-
The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:
f ( x ) = sin ( w*x ± k ) ± b
Where,
w: The frequency of the cycle
k: The phase difference
b: The vertical shift of center line from origin
We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).
We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.
The resulting sinusoidal waveform can be expressed as:
f ( x ) = sin ( 2x ) ... Answer
Question
Gabrielle is
7
years older than Mikhail. The sum of their ages is
91
. What is Mikhail's age?
Answer:
42
Step-by-step explanation:
Since Gabrielle is 7 years older than Mikhail, we subtract 7 from 91. Then we divide it by 2. So 84/2=42. Since Gabrielle is 7 years older we add 7 to 42. She is 49 and Mikhail is 42 years old. To double check our answer we should add both of the ages we got to make sure they add up to 91, so 42+49 is 91.
f(x)={x+1]^2 Determine for each x-value whether it is in the domain of f or not. (-2 y/n} { -1 y/n} {9 y/n}
Answer:
all are "yes"
Step-by-step explanation:
A polynomial is defined for all values of x. None are excluded. Every value listed is in the domain of f(x) = (x +1)².
Answer:
Step-by-step explanation:
You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures: 44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7 Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 98% C.I.
Answer:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
Step-by-step explanation:
For this problem we have the following dataset given:
44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7
We can find the mean and sample deviation with the following formulas:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex]\bar X= 51.278[/tex]
[tex] s= 22.979[/tex]
The confidence interval for the mean is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The degrees of freedom are:
[tex] df=n-1= 9-1=8[/tex]
The confidence would be 0.98 and the significance [tex]\alpha=0.02[/tex] then the critical value would be:
[tex] t_{\alpha/2}= 2.896[/tex]
Ad replacing we got:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
ratio 300 ml to 6 l
Answer:
20
Step-by-step explanation:
fist you convert 6l to ml=6×1000
then,300/300:6000/300
gives you 1:20
A takeaway sells 10-inch pizzas and 12-inch pizzas.
The profit made in week 1 is 0.69 and week 2 is 0.71.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
A takeaway sells 10-inch pizzas and 12-inch pizzas.
From the table
For week 1:
Proportion= 509/ 736 = 0.69
and, week 2:
Proportion= 765/ 1076 = 0.71
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g A CD player with an original price of $380.00 is on sale at 35% off. What is the discount amount and the CD player sale price?
Answer:
Cost: $247
Discount: $133
Step-by-step explanation:
Simply multiply 380 and 35% off together to get your answer:
380(1 - 0.35)
380(0.65)
247
To find the discount amount, simply subtract the 2 numbers to get your answer:
380 - 247 = 133
A farmer wants to take 4 of his animals to a city. He has to select the animals from 5 cows and 5 goats. (a) How many possible selections can he make? (b) In how many of these selections will there be more cows than goats?
Answer:
(a) 210
(b) 55
Step-by-step explanation:
(a) I'm assuming the animals are considered to be unique rather than identical. The order of the animals isn't important, so the number of ways he can choose 4 animals from 10 is:
₁₀C₄ = 210
(b) If there are more cows than goats, then there are either 3 cows and 1 goat:
₅C₃ ₅C₁ = 50
Or there are 4 cows:
₅C₄ = 5
The total number of combinations is 55.
Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals. Function Interval f(x) = 7 − 2x [1, 2]
Answer:
-2n
Step-by-step explanation:
f(x)=7-2x {1,2}
f(1)=7-2(1)=5
f(2)=7-2(2)=3
Slope (m)=3/5
{7-2(1)}-{7-2(2)}=3-5=-2
In terms of n=-2n
The upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3]
Given the function of the graph bounded by the inteval [1, 2] expressed as
f(x) = 7 - 2x
The upper limit of the function is the point where the domain of the function x is 2. Substitute x = 2 into the function, we will have:
f(2) = 7 - 2(2)
f(2) = 7 - 4
f(2) = 3
For the lower limit, the domain of the function is at x = 2:
f(1) = 7 - 2(1)
f(1) = 7 - 2
f(1) = 5
Hence the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3].
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What is 1 standard deviation on a
normal curve?
A. Another name for the mean.
B. Another name for the inflection point.
C. The distance from the mean to the bottom of the
curve.
D. The distance from the mean to an inflection point.
Answer:
D. The distance from the mean to an inflection point
Step-by-step explanation:
We rarely encounter the actual formula for the normal PDF. It is ...
[tex]p(x)=\dfrac{1}{\sqrt{2\pi}}e^{-\dfrac{x^2}{2}}[/tex]
In fact, the inflection points are at x = ±1, where the curve changes from being concave downward to concave upward.
So, one standard deviation is the distance from the mean to an inflection point.
What is 3 1/2 times 4?
Answer:
14
Step-by-step explanation:
3 1/2 × 4
Convert 3 1/2 to an improper fraction.
7/2 × 4
7/2 × 4/1
Multiply.
(7× 4) / (2 × 1)
28 / 2
= 14
Answer: 14
Step-by-step explanation: To multiply a mixed number times a whole number, first write each of them as an improper fraction.
So we can rewrite 3 and 1/2 as the improper fraction 7/2
and we can write 4 as the improper fraction 4/1.
If you've forgotten how to write a mixed number as an improper fraction, feel free to ask me below and I will review this with you.
So now we have 7/2 × 4/1.
When we're multiplying fractions, we want to
cross-cancel first whenever possible.
So here, notice that we can cross-cancel 2 and 4 to 1 and 2.
So we have 7/1 × 2/1.
Now we just multiply across the numerators and multiply across the denominators and we have our answer, 14/1 or just 14.
Evaluate the spherical coordinate integral
u=x+y , v= -2x + y;
∫ ∫ (-3x + 4y) dx dy
R
where R is the parallelogram bounded by the lines y = -x + 1, y = -x + 4, y = 2x + 2, y = 2x + 5
Rewrite the equations of the given boundary lines:
y = -x + 1 ==> x + y = 1
y = -x + 4 ==> x + y = 4
y = 2x + 2 ==> -2x + y = 2
y = 2x + 5 ==> -2x + y = 5
This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.
Compute the Jacobian determinant for this change of coordinates:
[tex]J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3[/tex]
Rewrite the integrand:
[tex]-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3[/tex]
The integral is then
[tex]\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}[/tex]
Any polygon can be the base of a prism. A. True B. False
Answer:
true
Step-by-step explanation:
A prism is a solid with parallelogram sides (usually rectangles) and a polygon for the 2 bases. Any polygon can be the base.
Answer:
Hello!
__________________
Your answer would be (A) True.
Step-by-step explanation: Hope this helped you!
Any polygon can be the base of a prism so the answer is true.
Suppose there are 100 people at airport security, 45 passengers were flying to Dallas of which 30 were men. 55 Passengers were flying to Portland of which 12 where men.
a. What is the probability that a randomly selected person is a man flying to Dallas?
b. Are the events flying to Dallas' and being a man' independent events? Explain.
c. Are the events 'flying to Dallas' and being a man' mutually exclusive events? Explain.
Answer: A: 30% B: Yes they are independent events because they can both happen without the other one. C: No they are not mutually exclusive events because both of them can happen at the same time
Step-by-step explanation:
45 / 100 = .45 = 45%
.45 x 2/3 = .3
.3= 30%
Can someone teach me how to solve this problem please:)
Answer:
x= -3, y= -5
or x= 5, y=3
Step-by-step explanation:
① Label the 2 equations
x² +y²= 34 -----(1)
3x -3y= 6 -----(2)
From (2):
x -y= 2 -----(3)
Notice that (x-y)²= x² -2xy +y²
Thus, (equation 3)²= (equation 1) -2xy
Squaring (3):
(x -y)²= 2²
(x -y)²= 4
Expand terms in bracket:
x² -2xy +y²= 4
x² +y² -2xy= 4 -----(4)
subst. (1) into (4):
34 -2xy= 4
2xy= 34 -4 (bring constant to 1 side)
2xy= 30 (simplify)
xy= 30 ÷2 (÷2 throughout)
xy= 15 -----(5)
From (3):
x= y +2 -----(6)
I'll rewrite 2 of the equations.
x= y +2 -----(6)
xy= 15 -----(5)
Subst. (6) into (5):
y(y+2)= 15
y² +2y= 15
y² +2y -15= 0
(y +5)(y -3)=0
y+5= 0 or y-3=0
y= -5 or y= 3
Subst. into (6):
x= -5 +2 or x= 3 +2
x= -3 or x= 5
Answer:
y=-5, y=3
x=-3., x=5
Step-by-step explanation:
x^2+y^2=34
3x-3y=6
isolate x in te equation
3x-3y=6
x=3/3 y+6/3
x=y+2
plug the y+2 in the equation:
x^2+y^2=34
(y+2)^2+y^2=34
y^2+4y+4+y^2=34
2y^2+4y=34-4
2y^2+4y=30 divide by 2
y^2+2x-15=0 factorize
(y+5)(y-3)=0 eiter y+5=0 ten y=-5 or y-3=0 then y=3
now plug the solution in the equation
3x-3y=6
3x-3(-5)=6
3x=6-15
x=-9/3=-3
for y=3
3x-3y=6
3x-9=6
3x=15
x=5
Identify whether the given value is a discrete random variable, a continuous random variable, or if it is not a random variable:
1) A college basketball player's height that is reported in the game-day program
2) The color of a student's car
3) The exact weight of an airline passenger's carry-on bag
Answer:
1. continuous random variable
2. not a random variable
3. a continuous random variable
Step-by-step explanation:
The classifications are as follow
a) The height of the player reported in the game day program is treated as a continuous random variable as these values could be determined through measuring them
b) The color of student car is not a random variable as it does not contain any quantitative data or we can say numerical data
c) The exact weight of the bag is a continuous variable as it is lie between the range
A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the standard deviation to be 1.8. She thinks the mean is 5.7 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.12 at the 85% level of confidence? Round your answer up to the next integer.
Answer:
The sample size 'n' = 242
Step-by-step explanation:
Step(i):-
Given mean of the sample = 5.7
Given standard deviation of the sample (σ) = 1.8
The Margin of error (M.E) = 0.12
Level of significance = 0.85 or 85%
Step(ii):-
The margin of error is determined by
[tex]M.E = \frac{Z_{\alpha }S.D }{\sqrt{n} }[/tex]
The critical value Z₀.₁₅ = 1.036
[tex]0.12 = \frac{1.036 X 1.8 }{\sqrt{n} }[/tex]
Cross multiplication , we get
[tex]\sqrt{n} = \frac{1.036 X 1.8}{0.12}[/tex]
√n = 15.54
Squaring on both sides, we get
n = 241.49≅ 241.5≅242
Conclusion:-
The sample size 'n' = 242
The graphed line shown below is y = 3 x minus 1. On a coordinate plane, a line goes through (0, negative 1) and (1, 2). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y + 1 = 3 x y = negative 3 x + 1 y = 3 x + 1 y minus 3 x = negative 3
Answer:
y + 1 = 3x
Step-by-step explanation:
In order for there to be an infinite number of solutions, the two lines need to be the same.
y+1 = 3x
y=3x-1 are both the same
Answer:
a)y + 1 = 3x
Step-by-step explanation:
. At the 5% significance level, has average salary gone down from 2008 to 2010? Reject H0; there is evidence that the average starting salary of college graduates has declined from 2008 to 2010. Reject H0; there is not sufficient evidence that the average starting salary of college graduates has declined from 2008 to 2010. Do not reject H0; there is evidence that the average starting salary of college graduates has declined from 2008 to 2010. Do not reject H0; there is not sufficient evidence that the average starting salary of college graduates has declined from 2008 to 2010.
Answer:
Reject H0; there is evidence that the average starting salary of college graduates has declined from 2008 to 2010.
Step-by-step explanation:
To be able to reject the null hypothesis, it means the researcher has sufficient statistical evidence to reject the null hypothesis (claiming no difference or association between specified populations).
The null in this case is that the average starting salary of college graduates has not declined from 2008 to 2010.
Thus, in this case study, to conclude that the average salary has gone down from 2008 to 2010, we reject H0 as there is evidence that the average starting salary of college graduates has declined from 2008 to 2010.
my dad is designing a new garden. he has 21 feet of fencing to go around the garden. he wants the length of the garden to be 1 1/2 feet longer than the width. how wide should he make the garden?
Answer:
21=2w+2w+3 18=4w w=4.5
You are flying a kite while standing 80 ft from a
fence. If the kite string makes a 50° angle with
the ground, how much string, in feet, is let out
when the kite is directly above the fence?
Answer:
124.5 ft
Step-by-step explanation:
Draw a figure. It is a triangle.
Kite
B | \
| \
| \
| \ string
| \
| \
| \
| \
| __ 50 deg \
C |----|---------------------------------------- A
fence 80 ft you are here
You are at point A. The kite is at point B. The fence is at point C. Angle C is a right angle.
The length of the string is the hypotenuse of the triangle, side AB. The bottom side of the triangle, side AC, the ground, is the adjacent leg for angle A.
The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.
[tex] \cos A = \dfrac{adj}{hyp} [/tex]
[tex] \cos 50^\circ = \dfrac{AC}{AB} [/tex]
[tex] \cos 50^\circ = \dfrac{80}{AB} [/tex]
[tex] AB \cos 50^\circ = 80 [/tex]
[tex] AB = \dfrac{80}{\cos 50^\circ} [/tex]
[tex] AB = 124.5 [/tex]
Answer: 124.5 ft
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 421 randomly selected adults showed that 65% of them would erase all of their personal information online if they could. Find the value of the test statistic.
Answer:
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.65 -0.5}{\sqrt{\frac{0.5(1-0.5)}{421}}}=6.16[/tex]
Step-by-step explanation:
Information given
n=421 represent the random sample taken
[tex]\hat p=0.65[/tex] estimated proportion of adults that would erase all of their personal information online if they could
[tex]p_o=0.5[/tex] is the value that we want to test
z would represent the statistic
Hypothesis to test
We want to check if Most adults would erase all of their personal information online if they could, then the system of hypothesis are :
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.65 -0.5}{\sqrt{\frac{0.5(1-0.5)}{421}}}=6.16[/tex]
From the information given, it is found that the value of the test statistic is z = 6.16.
At the null hypothesis, we test if it is not most adults that would erase all of their personal information online if they could, that is, the proportion is of at most 50%, hence:
[tex]H_0: p = 0.5[/tex]
At the alternative hypothesis, we test if most adults would, that is, if the proportion is greater than 50%.
[tex]H_1: p > 0.5[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.In this problem, the parameters are: [tex]p = 0.5, n = 421, \overline{p} = 0.65[/tex].
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.65 - 0.5}{\sqrt{\frac{0.5(0.5)}{421}}}[/tex]
[tex]z = 6.16[/tex]
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A manufacturing company measures the weight of boxes before shipping them to the customers. Assume that the weights of boxes are normally distributed with mean 90 lbs and standard deviation 24 lbs. a) Find the probability that a randomly selected box will exceed 94 lbs. b) If a sample of 36 boxes is randomly selected, find the probability that the average of the boxes exceeds 94 lbs.
Answer:
24
Step-by-step explanation:
heres a list of numbers 3 6 9 7 4 6 7 0 7 Find median,mean,range and mode
median=order them and find the middle=6
mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4
range= the difference between the smallest and largest number=9-3=6
mode= the one that appears the most= 7
The median, mean, range and mode will be 6, 5.4, 9 and 7.
The median is the number in the middle when arranged in an ascending order. The numbers will be:
0, 3, 4, 6, 6, 7, 7, 7, 9.
The median is 6.
The range is the difference between the highest and lowest number which is: = 9 - 0 = 9
The mode is the number that appears most which is 7.
The mean will be the average which will be:
= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.
= 49/9
= 5.4
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