Answer:
x = 11
Step-by-step explanation:
You are solving for the solution of the variable given (x). Set each parenthesis equal to 0 and simplify:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 11 to both sides:
x - 11 = 0
x - 11 (+11) = 0 (+11)
x = 0 + 11
x = 11
Do the same for the other set:
x - 11 = 0
x - 11 (+11) = 0 (+11)
x = 0 + 11
x = 11
~
WILL GIVE BRAINLIEST HELP ASAP
Answer:
x = -3
Step-by-step explanation:
1.8 - 3.7x = -4.2x +.3
Add 4.2x to each side
1.8 - 3.7x +4.2x= -4.2x+4.2x +.3
1.8 +.5x = .3
Subtract 1.8 from each side
1.8 +.5x -1.8 = .3 -1.8
.5x = -1.5
Divide each side by .5
.5x/.5 = -1.5/.5
x = -3
Answer:
x=-3
Step-by-step explanation:
In order to solve this equation, we have to isolate x. Perform the opposite of what is being done to the equation. Remember to perform everything to both sides.
1.8-3.7x= -4.2x +0.3
3.7x is being subtracted from 1.8 (-3.7x). The inverse operation of subtraction is addition. Add 3.7x to both sides.
1.8-3.7x+3.7x= -4.2x+3.7x+0.3
1.8= -4.2x+3.7x+0.3
1.8= -0.5x+0.3
0.3 is being added to -0.5x. The opposite of addition is subtraction. Subtract 0.3 from both sides.
1.8-0.3= -0.5x+0.3-0.3
1.8-0.3 = -0.5x
1.5=-0.5x
-0.5 and x are being multiplied (-0.5*x= -0.5x). The opposite of multiplication is division. Divide both sides by -0.5.
1.5/-0.5=-0.5x/-0.5
1.5/-0.5=x
-3=x
Find the SURFACE AREA of this composite solid.
FINDING THE SURFACE AREA OF A COMPOSITE SOLID
About "Finding the surface area of a composite solid"
Finding the surface area of a composite solid :
A composite solid is made up of two or more solid figures.
To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Finding the surface area of a composite solid - Examples
Example 1 :
Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?
Solution :
Step 1 :
Identify the important information.
• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.
• One face of each prism is not on the surface of the figure.
Step 2 :
Find the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
Step 3 :
Find the area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Step 4 :
Find the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Step 5 :
Add. Then subtract twice the areas of the parts not on the surface.
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
The surface area before the hole was drilled was 3,720 sq.cm.
The surface area before the hole was drilled was; 3,720 sq.cm.
What is composite solid?A composite solid is made up of two or more solid figures.
To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
The bottom is a rectangular prism with h = 18 cm.
The base is a 30 cm x 24 cm rectangle.
One face of each prism is not on the surface of the figure.
Then the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
The area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Now the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Now,
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
Learn more about the area;
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The data represents the heights of eruptions by a geyser. Use the heights to construct a stemplot. Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest.
Height of eruption
62 33 50 90
80 50 40 70
50 63 74 53
55 64 60 60
78 70 43 82
Required:
Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. The values closest to the middle are_________inches and_______inches.
Answer:
[tex] Median = \frac{60+60}{2}=60[/tex]
And we see that the closest values to 60 are 62 and 63 and then the answer would be:
The values closest to the middle are 62 inches and 63 inches.
Step-by-step explanation:
We have the following dataser given:
62 33 50 90 80 50 40 70 50 63 74 53 55 64 60 60 78 70 43 82
We can sort the values from the lowest to the highest and we got::
33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78 80 82 90
Now we see that we have n=20 values and the values closest to the middle and we can use the middle as the median and for this case the median can be calculated from position 10 and 11th and we got:
[tex] Median = \frac{60+60}{2}=60[/tex]
And we see that the closest values to 60 are 62 and 63 and then the answer would be:
The values closest to the middle are 62 inches and 63 inches.
The values closest to these middle elements are 60 and 63 inches
The dataset is given as:
62 33 50 90 80 50 40 70 50 63 74 53 55 64 60 60 78 70 43 82
Next, we sort the data elements in ascending order
33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78 80 82 90
The length of the dataset is 20.
So, the elements at the middle are the 10th and the 11 elements.
From the sorted dataset, these elements are: 60 and 62
Hence, the values closest to these middle elements are 60 and 63
Read more about median at:
https://brainly.com/question/14532771
What is the slope of a line that is perpendicular to the line y = -1/2x + 5?
the answer choices are
-2
-1/2
1/2
2
Answer:
2
Step-by-step explanation:
as you can see the slope of the line y = -1/2x + 5 is -1/2
the slope m of any line perpendicular to it should verify : -1/2×m = -1
-1/2×m = -1
→ multiply both sides by -2
m = 2
Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________. Group of answer choices
Answer:
(71.28, 78.72)
Step-by-step explanation:
We have the following information from the statement:
mean (m) = 75
sample standard deviation (sd) = 5
Sample size (n) = 13
Significance level (alpha) = 1 - 0.98 = 0.02
Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12
The critical value would be:
t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)
Margin of error equals:
E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:
E = 2,681 * 5/13 ^ (1/2)
E = 3.72
Therefore, the interval of 98% confidence interval would be:
75 + 3.72 = 78.72
75 - 3.72 = 71.28
(71.28, 78.72)
Terrance is 3.5 years older than Stephanie. Stephanie is 22.5 years old.
Answer:
Terrance is 25.5
Step-by-step explanation:
Answer:
Hello There. The correct answer is 26
T = 3.5 + 22.5 = 26
Hope It Helps!
help *URGENT* PLZ..........
Answer:
2, -1/2
Step-by-step explanation:
2m²-3m-2=0
2m² - 4m + 1m - 2=0
2m(m-2)+(m-2)=0
(2m+1)(m-2)=0
2m+1=0 ⇒ m= -1/2
m-2=0 ⇒ m=2
The fraction of students ages 10 to 17 who favor math or science is
Answer:
So if 17/25 of the students like math, science, and art and 3/20 of the students like art only. We first need to find common demoninator. 68/100 and for the second one 15/100. Subtract them both
68-15 = 53/100 of the students factor math, and science or 53%
The result of which expression will best estimate the actual product of (-4/5)(3/5)(-6/7)(5/6)
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
[tex]\frac{-4}{5} * \frac{3}{5} * (\frac{-6}{7} ) * \frac{5}{6}[/tex]
[tex]\frac{(-4) * 3}{5 * 1} * \frac{(-1)}{7} \\\\\frac{12}{35}[/tex]
The article "A Shovel with a perforated blade reduces energy expenditure required for digging wet clay" (Human Factors, 2010:492-502) reported on an experiment in which each of 13 workers was provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on stable energy expenditure (measured in kilocalories per kg of subject per pounds of clay):
1 2 3 4 5 6 7 8 9 10 11 12 13 Worker Conventional 0.0011 0.0014 0.0018 0.0022 0.001 0.0016 0.0028 0.002 0.0015 0.0023 0.0017 0.002 0.0014 Perforated 0.0011 0.001 0.0019 0.0013 0.0011 0.0017 0.0024 0.002 0.0013 0.0017 0.002 0.0013 0.0013 Carry out a test of hypotheses at significance level 0.05 to see whether the true average energy expenditure using the conventional shovel exceeds that using the perforated shovel. (hint: this is a paired-design!). Make sure to calculate a p-value!
Answer:
Step-by-step explanation:
Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.
The data for the test are the differences between the true average energy expenditures of the shovels.
μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.
Conventional perforated diff
0.0011 0.0011 0
0.0014 0.0010 0.0004
0.0018 0.0019 -0.0001
0.0022 0.0013 0.0009
0.0010 0.0011 -0.0001
0.0016 0.0017 -0.0001
0.0028 0.0024 0.0004
0.0020 0.002 0
0.0015 0.0013 0.0002
0.0023 0.0017 0.0006
0.0017 0.002 -0.0003
0.0020 0.0013 0.0007
0.0014 0.0013 0.0001
Sample mean, xd
= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077
xd = 0.0002077
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923
Standard deviation = √(0.00000158923/13
sd = 0.00035
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (0.0002077 - 0)/(0.00035/√13)
t = 2.14
We would determine the probability value by using the t test calculator.
p = 0.027
Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.
Simplify the answer pls
Answer:
Step-by-step explanation:
24/3 - 4
8 - 4 = 4
|x+12| =-9
Pls help!!!!
Answer:
x=-21
Step-by-step explanation:
x+12=-9
minus twelve on both sides
-9-12 equals -21
x=-21
The value of m compared to the standard is
1/1000
1000
1/100
10
what are the answers to the following quadratic equation:
x^2-4x-12
Answer:
6 and -2
Step-by-step explanation:
x^2-4x-12
set up equal to zero
x^2-4x-12=0
lets factor:
(x-6)(x+2)=0
x-6=0
x=6
or
x+2=0
x=-2
Answer:
x=6 x=-2
Step-by-step explanation:
x^2-4x-12 = 0
Factor
What two numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6)(x+2) =0
Using the zero product property
(x-6) =0 x+2 = 0
x=6 x=-2
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
its b I belive
Step-by-step explanation:
Answer:
The answer is B.
Step-by-step explanation:
In order to find (f-g)(x), you have to subtract g(x) from f(x) :
[tex]f(x) = {3}^{x} + 10[/tex]
[tex]g(x) = 2x - 4[/tex]
[tex](f - g)(x) = {3}^{x} + 10 - 2x - ( - 4)[/tex]
[tex](f - g)(x) = {3}^{x} + 10 - 2x + 4[/tex]
[tex](f - g)(x) = {3}^{x} - 2x + 14[/tex]
The length of a rectangular driveway is five feet more than three times the width. The area is 350ft2. Find the width and length of the driveway.
Answer:
width -- 10 ftlength -- 35 ftStep-by-step explanation:
We can let x represent the width. Then the length will be represented by (3x+5), a value 5 more than 3 times the width.
The area is the product of length and width, so is ...
A = (3x +5)(x) = 3x^2 +5x
To make the area 350, we can find the value of x from ...
3x^2 +5x = 350
This can be solved a number of ways. One of them is "completing the square".
3(x^2 +5/3x) = 350
We choose to divide by 3 and add the square of half the x-coefficient.
x^2 +5/3x +(5/6)^2 = (350/3) + (5/6)^2
(x +5/6)^2 = 4225/36 . . . . simplify
x +5/6 = ±√(4225/36) = ±10 5/6 . . . . take the square root
x = 10 or -11 2/3 . . . . subtract 5/6
The positive solution is the one of interest: x = 10.
The driveway is 10 ft wide and 35 ft long.
Determine whether the sampling method is independent or dependent. A stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks. He randomly selects 13 energy stocks and computes the rate of return for the past year.
Answer:
The sampling method is independent.
Step-by-step explanation:
Samples are said to be dependent when the data chosen in one sample has an effect on the data to be chosen in the other sample, while samples are said to be independent if the data chosen in one sample has no effect on the data to be chosen on the other sample.
Here, the stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks, so, he randomly selects 13 energy stocks. Since the energy stocks he chose were randomly selected, it means the data he selected from the energy stock will not dictate the type of data to be selected from the financial stock. Thus, the sampling method is said to be independent.
I need help! Someone help me please
Answer:
4. 27
Step-by-step explanation:
11-10=1 which is <=16
15-10=5 which is <=16
26-10=16 which is <=16
27-10=17 which isn't <=16
Therefore 27 doesn't satisfy the inequality
Answer:
4. 27
Step-by-step explanation:
w - 10 ≤ 16
w≤16 + 10
w ≤ 26
11 ≤ 26
15≤26
26≤26
26≤ 27 False
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Since they are similar, hence taking proportionality,
CA/CB = d1/d2
Cross Multiplying
We get
CA × d2 = CB × d1
OR
d1×CB = d2 × CA
The bottom of a ladder must be placed 3 ft. from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall? Round your answer to the nearest tenth.
Use the Pythagorean theorem to solve.
Height = sqrt(12^2 -3^2)
Height = sqrt(144-9)
Height = sqrt(135)
Height = 11.6189 = 11.6 feet
What is the next pattern ?
Please answer this correctly
Answer:
14.28 mm
Step-by-step explanation:
Find the circumference if it were a normal circle, then divide it by 4.
C = 2[tex]\pi[/tex]r
C = 2[tex]\pi[/tex](4)
C = 8[tex]\pi[/tex]
Divide it by 4
2[tex]\pi[/tex] + 4 + 4 = 14.28
Answer:
25.13 mm is the circumfrence, I believe.. Been a while since I've worked with this
Step-by-step explanation:
Borachio eats at the same fast food restaurant every day. Suppose the time X between the moment Borachio enters the restaurant and the moment he is served his food is normally distributed with mean 4.2 minutes and standard deviation 1.3 minutes. Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
Answer:
26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 4.2, \sigma = 1.3[/tex]
Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
This is 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 4.2}{1.3}[/tex]
[tex]Z = 0.615[/tex]
[tex]Z = 0.615[/tex] has a pvalue of 0.7308.
1 - 0.7308 = 0.2694
26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
Researchers want to compare the effectiveness of an extract of St. John's Wort with placebo in outpatients with major depression. They recruited 200 adult outpatients diagnosed as having major depression and having a baseline Hamilton Rating Scale for Depression (HAM-D) score of at least 20. Participants were randomly assigned to receive either St. John's Wort extrat, 900 milligrams per day (mg/day) for 4 weeks, increased to 1200 mg/day in the absence of an adequate response thereafter, or a placebo for 8 weeks. The response variable was the change on the HAM-D over the treatment period. After analysis of data, it was concluded that St. John's Wort was not effective for treatment of major depression.
Required:
a. What type of experimental design this is?
b. What is the population that is being studied?
c. What is the response variable in this study?
d. What are the treatments?
e. Identify the experimental units.
f. What is the control group in this study?
Answer:
a) Experimental Design: Randomised Experimental Design
b) Population : All Adult outpatients diagnosed with major depression
c) Responsive Variable : Effectiveness of extracts on depression patients' HAM-D rating
d) Treatments : John Wart extracts or Placebo
e) Experimental units : 200 adult outpatients diagnosed with major depression having HAM-D score > 20
Step-by-step explanation:
a) Randomised Experimental Design is being used : As experimental units are randomly assigned to any of the experimental groups, each receiving different treatments
b) Population refers to the entire group of objects or individuals, to whom the experiment research can be applied. So, all adult outpatients diagnosed with major depression as per HAM-D depression score are population
c) Responsive variable is the dependent variable being affected by independent variables. It is effectiveness of extracts on depression patients, ie change in change on the HAM-D depression rating
d) Treatments are the ways or objects with which experimental units are treated. These are John wart extracts or Placebo
e) Experimental units are the selected sample people or objects for experiment conduct. These are '200' adult outpatients diagnosed with major depression, having a baseline Hamilton Rating Scale for Depression (HAM-D) score > 20
If Romeo earns 8% more than Juliet, Romeo’s salary is how many times Juliets salary?
A) 1.08
B) 0.92
C) 80
D) 108
Answer:
1.08
Step-by-step explanation:
If Romeo earns 8% more than Juliet,
Example?
If Juliet earns $80
80x8% = 6.40 So his pay would be 80 + 6.40
If you times 80 by 1.08 (this would also be 108%) you would get $86.40
What’s the correct answer for this question?
Answer:
B:
Step-by-step explanation:
Measure of ARC AFB is 180°
Why?
This is because AB is a diameter.
ASAPPPP
I HAVE AND IMAGE BELOW
Answer:
#1
Step-by-step explanation:
The associative property of addition states that we can "flip" two expressions that are being added. Therefore, our answer is the first one because it can be rewritten as 3x + (-7y) which then is equivalent to -7y + 3x.
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
Answer:
Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg = 78.5%
The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.
Step-by-step explanation:
Complete Question
According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
Solution
The Central limit theorem allows us to say
The mean of sampling distribution is approximately equal to the population mean.
μₓ = μ = 1.20 kg
And the standard deviation of the sampling distribution is given as
σₓ = (σ/√N)
σ = population standard deviation = 0.14 kg
N = sample size = 3
σₓ = (0.14/√3) = 0.08083
Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, that is, percentage of all samples of three men with mean brain weights within 1.10 kg and 1.30 kg.
P(1.10 ≤ x ≤ 1.30)
We first normalize or standardize 1.10 and 1.30
The standardized score for any value is the value minus the mean then divided by the standard deviation.
For 1.10 kg
z = (x - μₓ)/σₓ = (1.10 - 1.20)/0.08083 = -1.24
For 1.30 kg
z = (x - μₓ)/σₓ = (1.30 - 1.20)/0.08083 = 1.24
To determine the required probability
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)
We'll use data from the normal distribution table for these probabilities
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)
= P(z ≤ 1.24) - P(z ≤ -1.24)
= 0.89251 - 0.10749
= 0.78502 = 78.502%
The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.
Hope this Helps!!!
Please answer this correctly
Answer:
10-19 ⇒ 3
50-59 ⇒ 4
Answer:
# of ties # of racks
10-19 3
50-59 4
Step-by-step explanation:
Using the Stem and Leaf plot, our data is:
11, 12, 16
21
32, 34, 36, 37, 39
41, 45
51, 52, 53, 56
# of ties # of racks
10-19 3 (11, 12, 16)
50-59 4 (51, 52, 53, 56)
A study of the effect of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to fall asleep. These data are obtained:
Smokers: 69.3 56.0 22.1 47.6 53.2 48.1 52.7 34.4 60.2 43.8 23.2 13.8
Non-Smokers: 28.6 25.1 26.4 34.9 28.8 28.4 38.5 30.2 30.6 31.8 41.6 21.1 36.0 37.9 13.9
Which group having greater value of relative dispersion and why?
Answer:
The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.
CV smokers: 0.387
CV non-smokers: 0.234
Step-by-step explanation:
We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).
Then, first we calculate the mean and standard deviation for the smokers data:
Mean: 43.7
Standard deviation: 286.5
[tex]M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\[/tex]
The mean and standard deviation for the non-smokers is:
Mean: 30.3
Standard deviation: 50.9
[tex]M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\[/tex]
Now, we can calculate the coefficient of variation:
CV smokers:
[tex]CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387[/tex]
CV non-smokers:
[tex]CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234[/tex]
