7 apples and 11 bananas cost $1.47. how much do 2 apples and a banana cost?
Answer: $0.27
Step-by-step explanation:
7a + 11b = 1.47
7a = 1.47 - 11b
[tex]a=\dfrac{1.47-11b}{7}[/tex]
Make a table. Choose values for b starting at $0.01 and solve for "a".
The value of "a" must terminate at the hundredths place since we are working with money.
You will discover that a = 0.10 and b = 0.07
The cost of 2 apples and 1 banana is:
2a + b
= 2(0.10) + (0.07)
= 0.20 + 0.07
= 0.27
Evaluate the function for an input of 0.
Answer: 4.
Step-by-step explanation:
As you can see from the table in you input 0 into the function your output will be 4.
4. Solve 9k + 3 > 6k - 18.
k> -7
k > 5
k> -5
O
k> 7
Answer:
k > - 7Step-by-step explanation:
9k + 3 > 6k - 18
To solve the inequality shown first group like terms.
That's send the constants to the right side of the inequality and those with variables to the left side.
We have
9k - 6k > - 18 - 3
Simplify
3k > - 21
Divide both sides by 3
We have the final answer as
k > - 7Hope this helps you
A researcher conducts a study on the effects of task difficulty (easy, hard) and presence of others (no one else present, 5 other people present) on task performance. Task performance is assessed by measuring how many Sudoku puzzles a participant is able to complete in 30 minutes. Below are the mean numbers of correct responses for each of the resulting conditions in the study. Easy Difficult No one else present 7 9 Five others present 14 2 The results from this study indicate there is ________________________________________.
Answer:
gcyj gc yj g
Step-by-step explanation:
cgyj jc y gc jyjgcjc gj gcjg jg jgjy g yjcgj
A unit of electricity costs 13.2 pence. On average, Tanya uses 90 units of electricity per week. She pays for her bill in 12 weeks. How much will her electricity bill be then? £
Answer:
90*12=1080
1080*13.2=14256
14256:100=142,56pounds
PLEASE ANSWER ASAP I WILL GIVE BRAINLIEST Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. x g(x) 0 2 5 4 10 6 The slope of f(x) is greater than the slope of g(x). The slope of f(x) is less than the slope of g(x). The slope of f(x) is equal to the slope of g(x). The slope of g(x) is undefined.
Answer:
slope of F(X) = to the slope of G(X)
Step-by-step explanation:
your answer should be: letter C
No lies, I just did the exam and I've got it right, gook luck, guys.
please let me know if it worked, and also please don't forget to make brainly, give a rate, and add the heart ;) I will do the same on you.
The slope of a line f(x) is greater than the slope of a line g(x). Therefore, option A is the correct answer.
The coordinate points on equation of line g(x) are (0, 2), (5, 4) and (10, 6) and f(x) are (3, 1) and (0, -1).
What is slope of equation of a line?The slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope can be determined using the formula, slope = (y2-y1)/(x2-x1).
Now, slope of a line g(x) is (4-2)/(5-0)
=2/5
Slope of a line f(x) is (-1-1)/(0-3)
=2/3
The slope of a line f(x) is greater than the slope of a line g(x). Therefore, option A is the correct answer.
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PLEASE HELP The sample of six measurements shown below was randomly selected from a normally distributed population. Complete parts a through c.
Answer:
The question is not complete.
I believe this is the correct complete question:
The following sample of six measurements was randomly selected from a normally distributed population: 1, 3, -1, 5, 1, 2.
a. Test the null hypothesis that the mean of the population is 3 against the alternative hypothesis,
μ<3 Use α=.05
b. Test the null hypothesis that the mean of the population is 3 against the alternative hypothesis,
μ≠3 Use α=.05
c. Find the observed significance level for each test.
Step-by-step explanation:
We will first find the standard deviation (S.D) of the six measurements.
To find the S.D, we calculate the mean and variance
Mean = ∈n/n where ∈n = sum of set of numbers n
Mean = [1+3+(-1)+5+1+2] / 6 where n = 6
Mean = 11/6 = 1.8
Variance = Sum of squared deviation from mean / n-1
Variance = [(1-1.8)² + (3-1.8)² + (-1-1.8)² + (5-1.8)² + (1-1.8)² + (2-1.8)²] / 6-1
Variance = [0.64 + 1.44 + 7.84 + 10.24 + 0.64 + 0.04] / 5 = 20.84/5 = 4.168
Standard Deviation S.D = √Variance = √4.168 = 2.041
(a) [tex]H_{o}[/tex] : μ=3, [tex]H_{a}[/tex] : μ<3
Using α=0.05
test stat = {mean - μ[tex]_{o}[/tex]] / S.D /[tex]\sqrt{n}[/tex] = [1.8 - 3] / [2.041/ √6
test stat = -1.2 / 0.833 = -1.44
Critical Value from Student T distribution is t[tex]_{a}[/tex] = 2.015
Therefore, the rejection value contains values < -2.015
-1.400 > -2.015. It Fails to reject [tex]H_{o}[/tex]
(b) [tex]H_{o}[/tex] : μ = 3, [tex]H_{a}[/tex] : μ ≠ 3
Using α=0.05
test stat = {mean - μ[tex]_{o}[/tex]] / S.D /[tex]\sqrt{n}[/tex] = [1.8 - 3] / [2.041/ √6
test stat = -1.2 / 0.833 = -1.44
Critical Value from Student T distribution is t[tex]_{a}[/tex] = 2.571
Therefore, the rejection value contains values < -2.571 and larger value to 2.571
2.571 > -1.400 > -2.571. It Fails to reject [tex]H_{o}[/tex]
(c) Significance Value of (a) is P-value > 0.100
Significance Value of (b) is P-value > (2 x 0.100 = 0.200)
A man drove 12 mi directly east from his home, made a left turn at an intersection, and then traveled 7 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
Answer:
13.9 miles
Step-by-step explanation:
If we draw out the way he drove, the drive from his home to the intersection represents the long leg of a right triangle and the short leg can be represented by his drive from the intersection to the workplace.
A road from his home to work would represent the hypotenuse.
Since we know the distances of the legs, we can use the pythagorean theorem to find the hypotenuse, or the distance of the new road.
Plug in the values:
a² + b² = c²
12² + 7² = c²
193 = c²
13.9 = c
= 13.9 miles
If a string that is 15.5 inches long is cut into equal peices that are 1.25 inches long how many prices of ribbon can be created
Answer:
12.4 pieces of ribbon
Step-by-step explanation:
When looking in the question, we can see the term "cut into equal pieces." This can insure to us that we need to divide two numbers. Since we originally have 15.5 inches long string, and we want to cut it into strings that are 1.25 inches long. We divide :
15.5 / 1.25
==> 12.4
The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean is nothing. (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a mean. Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is not a data value. C. The mean does not represent the center because it is the smallest data value. D. The mean does not represent the center because it is the largest data value. E. The data set does not have a mean. Find the median. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The median is nothing. (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a median. Does the median represent the center of the data?
Answer:
The data is missing in the question, below is the complete question:
The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. 9 9 12 12 9 10 8 8 8 8 8 8 11 Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean is nothing . (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a mean. Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is not a data value. D. The mean does not represent the center because it is the largest data value. E. The data set does not have a mean. Find the median. Select the correct choice below and, ifnecessary, fill in the answer box to complete your choice. A. The median is nothing . (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a median. Does the median represent the center of the data? A. The median represents the center. B. The median does not represent the center because it is the largest data value. C. The median does not represent the center because it is not a data value. D. The median does not represent the center because it is the smallest data value. E. The data set does not have a median. Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode(s) is/are nothing . (Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as needed.) B. The data set does not have a mode. Does (Do) the mode(s) represent the center of the data? A. The mode(s) represent(s) the center. B. The mode(s) does (do) not represent the center because it (they) is (are) not a data value. C. The mode(s) does (do) not represent the center because it (one) is the largest data value. D. The mode(s) does (do) not represent the center because it(one) is the smallest data value. E. The data set does not have a mode.
Answer:
a.) mean = 9.23
ii) The mean represents the centre (A)
b) Median = 9
ii) The median represents the centre (A)
c) Mode = 8
ii) The mode(s) does (do) not represent the center because it(one) is the smallest data value. (D)
Step-by-step explanation:
Arranging the data in ascending order:
8 8 8 8 8 8 9 9 9 10 11 12 12
a) calculating for mean
[tex]\bar x = \frac{sum\ of\ data}{number\ of\ data}\\ \bar x = \frac{8+8+8+8+8+8+9+9+9+10+11+12+12}{13} \\\bar x =\frac{120}{13} \\\bar x = 9.23[/tex]
ii) does the mean represent the centre of the data?
The measure of central tendency/location is a statistical tool used to accurately depict values that are at the central location of the data set
Yes, the mean represents the centre of the data, because there are no outliers in the data set. Outliers are unusual values compared to the rest of the values in the dataset.
b) calculating the median (M)
[tex]M =( \frac{n\ +\ 1}{2})th\ term\\ \\where:\\n = number\ of\ data\ in\ the\ dataset = 13\\\\\therefore M = \frac{13+1}{2}\\ M = \frac{14}{2} \\M= 7th\ term[/tex]
The 7th term after arranging in ascending or descening order, is the median term
8 8 8 8 8 8 9 9 9 10 11 12 12
∴ Median = 9
ii) Yes, the Median represents the center of the data, because it litterally tells the data at the middle of the distribution
c) The mode is the data with the highest number of occurrence in the dataset (highest frequency); 8 8 8 8 8 8 9 9 9 10 11 12 12
The data with the highest number of occurrence is 8, which occurred 6 times.
Mode = 8
ii) The mode does not represent the centre of the data because it is the smallest value in the dataset, hence it doesn't tell the value that is the middle term.
I am in confusion ❤️
Answer:
The Brain
Step-by-step explanation:
It goes down 3 and moves to the right 2
so its -3/2 =- 1.5
you slope is -1.5❤✔ hope I helped!
- 4(-5h-4)=2(10h+8) *
Answer:
0
Step-by-step explanation:
We need to solve the given expression for the value of h.
- 4(-5h-4)=2(10h+8)
Opening brackets on both sides of the above equation
+20h+4=20h+16
Taking h terms on the one side and the constants on the another side
20h-20h=16-4
0=20
It means that the value of - 4(-5h-4)=2(10h+8) is equal to 0.
Darius filled up his gas tank with 24 gallons of gas. For each mile that he drives, he uses 0.06 gallons of gas.
a
n
=−0,06n+24
mark me a brainlist
Imagine that * represents a new operation so that a * b means to double a, and then add b. For example, 2 * 10 = 14. What is -3 * 8 ?
A. 14
B 17
C 2
D 48
Answer:
C 2
Step-by-step explanation:
-3 doubled = -6
-6 +8 = 2 so C 2
Answer:
C. 2
Step-by-step explanation:
-3(2) = -6
-6+8 = 2
The length of the base of a right-angle triangle ABC is 6 cm and the length of the hypotenuse is 10 cm find the area of the triangle
Answer:
The area of the triangle is 24 [tex]\text{cm}^{2}[/tex].
Step-by-step explanation:
We are given that the length of the base of a right-angle triangle ABC is 6 cm and the length of the hypotenuse is 10 cm.
And we have to find the area of the triangle.
As we know that the area of the triangle is given by the following formula;
Area of the triangle = [tex]\frac{1}{2}\times \text{Base} \times \text{Height}[/tex]
Firstly, we will find the height (perpendicular) of the triangle ABC bu using the Pythagoras Theorem.
[tex]\text{Hypotenuse}^{2} =\text{Perpendicular}^{2} +\text{Base}^{2}[/tex]
[tex]\text{10}^{2} =\text{Perpendicular}^{2} +\text{6}^{2}[/tex]
[tex]100=\text{Perpendicular}^{2} +36[/tex]
[tex]\text{Perpendicular}^{2} =100-36[/tex]
[tex]\text{Perpendicular}^{2} =64[/tex]
[tex]\text{Perpendicular} =\sqrt{64}[/tex] = 8 cm.
Now, the area of the triangle = [tex]\frac{1}{2}\times \text{Base} \times \text{Height}[/tex]
= [tex]\frac{1}{2}\times \text{6} \times \text{8}[/tex]
= 24 [tex]\text{cm}^{2}[/tex]
Hence, the area of the triangle is 24 [tex]\text{cm}^{2}[/tex].
What is the difference between the values of 3, 3.0, and 3.00?
Answer:
There is no difference.
Step-by-step explanation:
When it comes to significant figures, they matter.
However, if you just add zeros, they essentially just become placeholders. 3 already has 0 for decimals, so it is equal to 3.0 and 3.00.
Need help with this can anyone help me?
Find y using the Angle Sum Theorem
The measure of the angle y is 120°.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The Sum of the three angles is 180 degrees.
33 + 87 + x = 180
x = 180 - 120
x = 60
Now,
x + y = 180
60 + y = 180
y = 180 - 60
y = 120
Thus,
The value of y is 120°.
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Write an equation for a line parallel to the line y=1/3x-4 through (-3,2)
Answer:
(-4,-1)
Step-by-step explanation:
If a line must be parallel, then its slope must be the same.
Their points can be different, the slope should be same.
So, y = 1/3x - 4
=> We find the slope of the equation:
=> Slope = the number with which "x" is multiplied
=> Slope of this equation = 1/3
So, we need to find the point that makes a slope of 1/3 from (-3, 2)
=> Slope = y/x - y1/x1
=> 1/3 = -3/2 - y1/x1
=> y1/x1 = -3/2 - 1/3
=> y1/x1 = -3-1 / 2-3
=> y1/x1 = -4/-1
So, the point is (-4,-1)
Gessenia is having trouble interpreting how the constants within each expression can be represented in the given scenario. Draw a model or write an expression that explains this term.
Answer:
The height and width of the interior tile = 3·x + 4 - 4 = 3·x and 2·x + 4 - 4= 2·x
Please see attached diagram
Step-by-step explanation:
The given parameters are;
The given rectangular floor tile with width = 3·x + 4 and height = 2·x + 4
Where, x is in centimetres
The interior tile maintains a height to width ration of 2:3
The dimension of the trim border = 2 cm
Therefore;
The relationship between the width and height of the interior and exterior tiles is given as follows
Width of exterior tile = Width of interior tile + 2 × The dimension of the trim border
Which gives;
Width of exterior tile = Width of interior tile + 2 × 2 = Width of interior tile + 4
Height of exterior tile = Height of interior tile + 2 × The dimension of the trim border
Height of exterior tile = Height of interior tile + 2 × 2 = Height of interior tile + 4
Where the interior tile maintains a height to width ration of 2:3, we have;
For a unit length x, The height and the width of the interior tiles are 2·x:3·x
Therefore, for a given height 2·x, the width will be 3·x
Given the width of the exterior tile = 3·x + 4
The height of the exterior tile will then be 2·x + 4 and the width of the exterior tile will be 3·x + 4
The sides ratio of the interior tiles remain 2·x:3·x = 2/3
An apartment complex rents an average of 2.3 new units per week. If the number of apartment rented each week Poisson distributed, then the probability of renting no more than 1 apartment in a week is:_________
Answer:
[tex]P(X\leq 1) = 0.331[/tex]
Step-by-step explanation:
Given
Poisson Distribution;
Average rent in a week = 2.3
Required
Determine the probability of renting no more than 1 apartment
A Poisson distribution is given as;
[tex]P(X = x) = \frac{y^xe^{-y}}{x!}[/tex]
Where y represents λ (average)
y = 2.3
Probability of renting no more than 1 apartment = Probability of renting no apartment + Probability of renting 1 apartment
Using probability notations;
[tex]P(X\leq 1) = P(X=0) + P(X =1)[/tex]
Solving for P(X = 0) [substitute 0 for x and 2.3 for y]
[tex]P(X = 0) = \frac{2.3^0 * e^{-2.3}}{0!}[/tex]
[tex]P(X = 0) = \frac{1 * e^{-2.3}}{1}[/tex]
[tex]P(X = 0) = e^{-2.3}[/tex]
[tex]P(X = 0) = 0.10025884372[/tex]
Solving for P(X = 1) [substitute 1 for x and 2.3 for y]
[tex]P(X = 1) = \frac{2.3^1 * e^{-2.3}}{1!}[/tex]
[tex]P(X = 1) = \frac{2.3 * e^{-2.3}}{1}[/tex]
[tex]P(X = 1) =2.3 * e^{-2.3}[/tex]
[tex]P(X = 1) = 2.3 * 0.10025884372[/tex]
[tex]P(X = 1) = 0.23059534055[/tex]
[tex]P(X\leq 1) = P(X=0) + P(X =1)[/tex]
[tex]P(X\leq 1) = 0.10025884372 + 0.23059534055[/tex]
[tex]P(X\leq 1) = 0.33085418427[/tex]
[tex]P(X\leq 1) = 0.331[/tex]
Hence, the required probability is 0.331
Evaluate (64×1/2-125×1/3)×(64×1/2-125×1/3)
2. Graph: y = x+2
please help
Answer:
Start at (0,2) and draw a line to (3,1)
Step-by-step explanation:
Since +2 is the y-intercept, we must start there.
Always remember the saying "rise over run". Since -1 is the "rise", we must go down one, "3" is the run, so we must move over to the right 3 times.
4y-2n=9,for y please show step by step
Answer:
y = (1/2n) + (9/4)
Step-by-step explanation:
4y - 2n = 9
add 2n to both sides
4y = 9 + 2n
divide both sides by 4
y = (9/4) + (2/4n)
simplify
y = (9/4) + (1/2n)
put in standard form
y = (1/2n) + (9/4)
Answer:
y=9+2n/4
Step-by-step explanation:
4y-2n=9
+2n
4y=9+2n
÷4 ÷4
y=9+2n/4
evaluate -1 -(-z) where z = -2
Answer:
1
Step-by-step explanation:
-1 - (-z)
-1 - (-2)
-1 + 2
1
Answer:
-3
Step-by-step explanation:
Ella has 164 ounces of lemonade. She fills glasses with
8 ounces of lemonade each until all the lemonade is gone.
The last glass is not full. How much lemonade is in the
last glass?
Answer:
4 ounces
Step-by-step explanation:
If you divide the 164 ounces by the 8 ounces per glass, you get 20.5 glasses filled. So, half of the last glass would be 4.
Answer:
4 ounces
Step-by-step explanation:
We're looking for the remainder of ounces.
To find how many FULL glasses will be made, we divide 8 by 164 and look at the integer part of the number.
[tex]164\div8=20.5[/tex]
So 2 full glasses were made.
To find the remainder, we multiply 20 by 8 and subtract from 164.
[tex]20\cdot8=160\\\\164-160=4[/tex]
Hope this helped!
The flow rate in a device used for air quality measurement depends on the pressure drop x (inches of water) across the device's filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y = -0.17 + 0.095x.
A) What is the true average flow rate for a pressure drop of 10 in. and drop of 15 in.?
B) What is the true average change in flow rate associated with a 1 inch increase in pressure drop?
C) What is the average change in flow rate when pressure drop decreases by 5 in.?
Answer:
A. 0.78 and 1.255.
B. 0.095
C. -0.475
Step-by-step explanation:
The given regression line is
y=-0.17+0.095x
A.
The true average flow rate for a pressure drop of 10 inch can be computed by putting x=10 in above equation.
y=-0.17+0.095*10
y=-0.17+0.95
y=0.78
The true average flow rate for a pressure drop of 10 inch is 0.78.
The true average flow rate for a pressure drop of 15 inch can be computed by putting x=15 in above equation.
y=-0.17+0.095*15
y=-0.17+1.425
y=1.255
The true average flow rate for a pressure drop of 15 inch is 1.255.
B.
The slope represents average change in y due to unit change in x.
So, the true average change in flow rate associated with a 1 inch increase in pressure drop is 0.095(1)= 0.095.
C.
When pressure drops decreases by 5 in. then the average change in flow rate is 0.095(-5)=-0.475.
The flow rate in the device is an illustration of average rates.
The true average flow rates when pressure drops 10 and 15 in are 0.78 and 1.255 respectivelyThe true average flow rates associated to a 1 in pressure increment is 0.095A decrement of -5 in is out of the domain of the functionThe function is given as:
[tex]\mathbf{y = -0.17 + 0.095x}[/tex]
(a) The true average flow rate when pressure drops 10 and 15 in
When x = 10, we have:
[tex]\mathbf{y = -0.17 + 0.095 \times 10}[/tex]
[tex]\mathbf{y = 0.78}[/tex]
When x = 15, we have:
[tex]\mathbf{y = -0.17 + 0.095 \times 15}[/tex]
[tex]\mathbf{y = 1.255}[/tex]
Hence, the true average flow rates when pressure drops 10 and 15 in are 0.78 and 1.255 respectively
(b) The true average flow rate when pressure increases by 1 in
This simply represents the slope of the function.
The function is given as:
[tex]\mathbf{y = -0.17 + 0.095x}[/tex]
A linear regression equation is represented as:
[tex]\mathbf{y = b + mx}[/tex]
Where m represents the slope
By comparison:
[tex]\mathbf{m = 0.095}[/tex]
Hence, the true average flow rates associated to a 1 in pressure increment is 0.095
(c) The average change in flow rate when pressure drops decreases by 5 in
The domain of the function is given as:
[tex]\mathbf{x = 5\ to\ 20}[/tex]
A decrement of -5 in means: x = -5
This is out of the domain of the function
Hence, the average change at a decrement of 5 in cannot be calculated
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I DON'T UNDERSTAND! Use a system of equations to solve a word problem.
A. The sum of two numbers is -2, and their difference is 4. Find the two numbers.
B. One number is 2 less than a second number. Twice the second number is 14 less than 5 times the first. Find the two numbers.
C. A flat rectangular piece of aluminum has a perimeter of 64 inches. The length is 8 inches longer than the width. Find the width. Select one: A) 20 in. B) 32 in. C) 28 in. D) 12 in.
Answer:
A) 1 and -3
B) 8 and 6
C) D) 12 in.
Step-by-step explanation:
A) 1 and -3
B) x-2 = first number
x = second number
2x=5(x-2)-14
2x=5x-10-14
2x=5x-24
2x+24=5x
24=5x-2x
24=3x
8=x
So the two numbers are 8 and 6
C) width=x
length=x+8
x+x+x+8+x+8=64
4x+16=64
4x=48
x=12
Where is the hundred thousand place
Listed below are the amounts (dollars) it costs for marriage proposal packages at different baseball stadiums. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are there any outliers, and are they likely to have much of an effect on the measures of variation?
38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000
Answer:
Question 1
a) Range
= $2962
b) Variance
= $680557.4954
c) Standard Deviation
= $824.9590871
Question 2
Are there any outliers, and are they likely to have much of an effect on the measures of variation?
Yes, there are outliers present I the given sample data.
These outliers are the larger cost for marriage proposals which are: 1750, 3000
These largest costs are much bigger than the rest of the sample data, and they would likely have much of an effect on the measures of variation
Step-by-step explanation:
We are given the following sample data in dollars
38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000
Question 1
a) Range
This is the difference between the maximum cost and the minimum cost
The minimum cost = $38
The maximum cost = $3000
Range = $3000 - $38
= $2962
b) Variance
Reading the question, we are given sample data.
Hence, we use the formula for Variance of a sample
= (Mean - x)²/N - 1
Step 1
We find the Mean
Mean = Sum of terms/Number of terms
Number of terms = 15
Mean = 38 + 50 + 50 + 55 + 55 + 95 + 95 + 130 + 180 + 213 + 250 + 350 + 450+ 1750 + 3000/15
= $6761/15
= $450.7333333
Step 2
(x - Mean)²/N - 1
N = 15
= $[(38 - 450.7333333)²+ (50 + 450.7333333)²+( 50 +450.7333333)² + (55 +450.7333333)² + (55 +450.7333333)² + (95 + 450.7333333)²+ (95 +450.7333333)²+ (130 +450.7333333)²+ (180 +450.7333333)² + (213 + 450.7333333)²+ (250 +450.7333333)² + (350 + 450.7333333)² + (450 +450.7333333)²+ (1750 +450.7333333)² + (3000 +450.7333333)²]/15 - 1
=$ (- 412.7333333² + -400.7333333² + -400.7333333² + -395.7333333² + -395.7333333² + -355.7333333² + -355.7333333² + -320.7333333² + -270.7333333² + -237.7333333² + -200.7333333² + -100.7333333² + -0.7333333333² + 1299.266667² + 2549.266667²)/15 - 1
= $( 170348.8044+ 160587.2044, 160587.2044+ 156604.8711, 156604.8711+ 126546.2044, 126546.2044+ 102869.8711, 73296.53776+ 56517.13776, 40293.8711+ 10147.20444+ 0.5377777777+ 1688093.872, 6498760.539)/14
= $9527804.935/14
Variance = $680557.4954
c) Standard deviation = √Variance
Standard deviation = √$680557.4954
= $824.9590871
Question 2
Are there any outliers, and are they likely to have much of an effect on the measures of variation?
Yes, there are outliers present in the given sample data.
These outliers are the largest cost for marriage proposals which are: $1750 and $3000
These largest costs are much bigger than the rest of the sample data, and they would likely have much of an effect on the measures of variation.