Option C. No, because the 100 adults were selected without replacement, the selections are dependent.
The binomial probability formula assumes that the trials are independent, meaning that the probability of success or failure for each trial remains the same regardless of the outcomes of previous trials. However, in this case, the 100 adults were selected without replacement, so the probability of being left-handed for each selection depends on the outcomes of previous selections. Therefore, the binomial probability formula cannot be used to find the probability in this situation. Instead, the hypergeometric distribution can be used to account for the dependence between selections.
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Complete question:
It is assumed that approximately 15% of adults in the U.S. are left-handed. Consider the probability that among 100 adults selected in the U.S., there are at least 30 who are left-handed. Given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? Why or why not?
A. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.
B. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent.
C. No, because the 100 adults were selected without replacement, the selections are dependent.
D. No, because the probability of being right-handed is greater, x must count the number of right-handed adults.
Lecture 4 Problem 28: An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color? (b) of different colors? Repeat under the assumption that whenever a ball is selected, its color is noted and it is then replaced in the urn before the next selection. This is known as sampling with replacemen
The probability of selecting three balls of the same color without replacement is 0.0545, and with replacement is 0.0393. The probability of selecting three balls of different colors without replacement is 0.4591, and with replacement is 0.4968.
(a) To select a set of 3 balls that are all of the same color, we need to choose one of the three colors (red, blue, or green), and then select 3 balls of that color from the urn. There are three ways to choose the color of the balls. For each color, the number of ways to select 3 balls of that color is given by the number of combinations of 3 balls from the set of balls of that color. Thus, the total number of ways to select a set of 3 balls that are all of the same color is:
Number of ways to select 3 red balls + number of ways to select 3 blue balls + number of ways to select 3 green balls
= (5 choose 3) + (6 choose 3) + (8 choose 3)
= 10 + 20 + 56
= 86
The total number of ways to select any set of 3 balls from the urn is given by the number of combinations of 3 balls from the set of 19 balls in the urn:
Total number of ways to select any set of 3 balls = (19 choose 3) = 969
Therefore, the probability that each of the balls will be of the same color is:
P(each ball of the same color) = (number of ways to select 3 balls of the same color) / (total number of ways to select any set of 3 balls)
= 86 / 969
= 0.089
So the probability that each of the balls will be of the same color is approximately 0.089 or 8.9%.
(b) To select a set of 3 balls that are of different colors, we need to choose one ball of each color from the urn. The number of ways to select one ball of each color is given by the product of the number of balls of each color:
Number of ways to select 1 ball of each color = 5 x 6 x 8 = 240
The total number of ways to select any set of 3 balls from the urn is still 969.
Therefore, the probability that each of the balls will be of different colors is:
P(each ball of different color) = (number of ways to select 1 ball of each color) / (total number of ways to select any set of 3 balls)
= 240 / 969
= 0.248
So the probability that each of the balls will be of different colors is approximately 0.248 or 24.8%.
When the balls are selected with replacement, the probabilities remain the same because the probabilities of selecting each ball are unchanged on each draw.
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11. CHALLENGE PROBLEM What percent of the Penders' total monthly net income are the monthly living expenses and fixed expenses? What is the monthly share of annual expenses? Total your three percents and analyze the result
The percent of total monthly net income for the monthly living expenses and fixed expenses is 60%, the monthly share of annual expenses is $3,000 and the total your three percents is 120%.
Explain challenge problem?A challenge problem is a task or question that requires a significant amount of thought, analysis, and problem-solving skills to solve. It often involves complex scenarios, calculations, or decision-making processes, and may require the use of multiple skills or disciplines to arrive at a solution.
To calculate the percentage of the Penders' total monthly net income that goes towards monthly living expenses and fixed expenses, we need to know the actual amounts of their monthly living and fixed expenses, as well as their total monthly net income. Let's assume that the Penders have a total monthly net income of $5,000, and their monthly living expenses and fixed expenses add up to $3,000.
The percentage of their total monthly net income that goes towards monthly living expenses and fixed expenses can be calculated as follows:
$3,000 (monthly living expenses and fixed expenses) ÷ $5,000 (total monthly net income) x 100% = 60%
Therefore, 60% of the Penders' total monthly net income goes towards monthly living expenses and fixed expenses.
To calculate the monthly share of annual expenses, we need to know the total amount of their annual expenses. Let's assume that their annual expenses add up to $36,000. The monthly share of their annual expenses can be calculated as follows:
$36,000 (annual expenses) ÷ 12 (number of months in a year) = $3,000 (monthly share of annual expenses)
To total the three percents, we add the percentage of their total monthly net income that goes towards monthly living expenses and fixed expenses (60%) to the percentage of their monthly share of annual expenses (which is also 60%, since $3,000 is 60% of $5,000). This gives us a total of 120%.
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In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?
x =
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry and in the given parallelogram the required value of x is 3 units.
What is a parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
In a parallelogram, the diagonals are split in half while the opposite sides are equal.
In a rhombus, all four sides are equal and the diagonals intersect at 90 degrees.
So, a parallelogram's diagonals cut each other in half.
Hence, WC = CY.
This is:
2x + 5 = 3x + 2
Take away 2x from each side:
5 = 3x - 2x + 2
5 = x + 2
Take away from both sides:
5 - 2 = x + 2 - 2
3 = x
Therefore, in the given parallelogram the required value of x is 3 units.
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Correct question:
In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?
Find x and y for both questions
The values of x and y are
Figure a: y = 3 and x = 10Figure b: y = 72 and x = 24How to determine the values of x and yFigure (a)
From the question, we have the following parameters that can be used in our computation:
Parallel and congruent lines
This means that
5y - 8 = 2y + 1
So, we have
3y = 9
Divide
y = 3
Also, we have
1/5x + 3 = 4x - 35
So, we have
x + 15 = 20x - 175
This gives
19x = 190
x = 10
Figure (a)
Here, we have
1/3y - 6 = 66 - 2/3y
This gives
y - 18 = 198 - 2y
Evaluate
3y = 216
Divide
y = 72
For x, we have
1/4x + 5 = 1/2x - 7
So, we have
1/2x =+ 12
Evaluate
x = 24
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The total weight of a shipment of boxes is 112 pounds. There are 7 packages in the shipment, and
each package weighs the same amount. The model below can be used to determine w, the weight
of each package.
O 1.6 lbs.
O 78.4 lbs.
O 16 lbs.
O 8 lbs.
Answer: 16 lbs.
Step-by-step explanation:
If there are 7 packages and all of the packages weigh the same, then you would divide the number of packages by the total weight of the packages.
112÷7=16. 16 would be the weight of each package individually.
So, the answer is C;16 lbs.
Could someone help
Me on this?
Answer:
Add parentheses ( ) to make the equation true:
11 x 6 ÷ (8 + 3) = 6
Solve for y
4y + (16 - 7) = 25
y = 4
9 x (8 - 5)
= 27
3. {[3 x (9 + 7)] - 8}
Sorry, can't figure this one out.
5. Mable saved $10 of her lemonade stand money. She then made 7 times as much as the money she had saved. Mable's friend gave her $12. How much money does Mable now have in all?
Mable has $82 all together.
Step-by-step explanation:
You're welcome.
factorization of 120
Answer:
Step-by-step explanation:
120=10*12
120=5*2*4*3
120=5*2*2*2*3
120=(2^3)*3*5
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pie. (No approximations)
Answer: x x x x x x x
Step-by-step explanation:
xxxxxxxxxxxxxxxxxx
-12 = -3/8v
solve for V
Answer:
v = 32
Step-by-step explanation:
-12 = -3/8v
Divided by -3/8, both sides
v = 32
Let's check
-12 = -3/8(32)
-12 = -12
So, v = 32 is the correct answer.
The cost of cultivating a rectangular field at the rate of ₹ 4 per sq. metre is ₹ 2340.
If the breadth of the field is 15 m, find the cost of fencing the field at ₹ 7.5 per
metre.
The cost of fencing the field at ₹ 7.5 per meter is ₹810.
We already know that the area of a rectangle can be calculated using the formula = l*b
We have been told that the rate is ₹ 4 per sq. meter is ₹ 2340 and the breadth is 15 m.
Using these values, we can conclude that -
= l*b * 4 = 2340
= l = 2340 / 60
= l = 39 m
We also know that the perimeter of a rectangle can be calculated using -
= 2(l+b) and the rate of fencing this perimeter is ₹ 7.5 per meter.
Using the values, we get -
= 2(39+15) * 7.5
= ₹ 810
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how to make 7/10 as a decimal
The value of 7/10 as a decimal is 0.7.
To convert 7/10 to a decimal, we need to divide the numerator (7) by the denominator (10). This can be done by long division or using a calculator.
When we divide 7 by 10, we get 0.7. Therefore, 7/10 as a decimal is 0.7.
In decimal form, 0.7 can be interpreted as 7 tenths, or 70 hundredths, or 700 thousandths, etc. It is a way of expressing a fraction as a decimal, which is a more convenient and commonly used way of writing numbers.
It's worth noting that 7/10 can also be written as a percentage, which would be 70%. This means that 7 out of 10 is equivalent to 70 out of 100, which is the same as 0.7 in decimal form.
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Help me please it is math
−13w−7
Explanation:
−6w+(−8)+1+(−7w)
Add −8 and 1 to get −7.
−6w−7−7w
Combine −6w and −7w to get −13w.
−13w−7
Answer: -13w-7
-6w - 8 + 1 -7w
-6w + - 8 + 1 + -7w
Question 11 help ! Urgently
Answer:
Can u pls type the question in??
What are the answers to 15,16,17 and 18 ????
The missing sides of each pair of similar triangles are listed below:
Case 15: w = 5, x = 25 / 12, y = 65 / 12, z = 169 / 12
Case 16: x = 12, y = 6√3, z = 3√5
Case 17: x = 40 / 3, y = 32 / 3
Case 18: x = 5, y = 20, z = 10√3
How to find the values associated to system of similar triangles
In this problem we find four cases of pairs of similar triangles, whose missing sides can be found by means of proportion formulas and Pythagorean theorem. Now we proceed to determine the missing lengths for each length:
Case 15
w = √(13² - 12²)
w = 5
12 / w = w / x
w² = 12 · x
x = w² / 12
x = 5² / 12
x = 25 / 12
y = √[(25 / 12)² + 5²]
y = 65 / 12
z = 12 + x
z = 169 / 12
Case 16
6 / 3 = x / 6
x = 36 / 3
x = 12
y = √(x² - 6²)
y = √(12² - 6²)
y = 6√3
z = √(3² + 6²)
z = 3√5
Case 17
y / 8 = 8 / 6
y = 8² / 6
y = 64 / 6
y = 32 / 3
x = √(8² + y²)
x = √[8² + (32 / 3)²]
x = 40 / 3
Case 18
x = √[10² - (5√3)²]
x = 5
y = x + 15
y = 20
z = √[15² + (5√3)²]
z = 10√3
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Its in the form of a picture
The slope of UN is solved to be
= -4 / 3How to find the slope of UNThe slope of UN is solved using the points denoting U and N and the points are
U (4, -2) and N (1, 2)
Formula for slope is
= change in y direction / change in x direction
= (-2 - 2) / (4 - 1)
= -4 / 3
The slope of UN is -1 1/3
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what is the percent of change from 75 to 24?
Select all equations that are true. A. 3/4 − 1/2 = 1/4 B. 9/16 − 4/8 = 5/8 C. 7/8 − 3/4 = 1/8 D. 7/15 − 1/3 = 6/15 E. 1/2 − 1/20 = 10/20
The correct expression after subtraction is,
⇒ 7/8 - 3/4 = 1/8
Option C is true.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Now, We can all the expressions as,
A). 3/4 - 1/2 = 1/4
LHS;
⇒ 3/4 - 1/2
⇒ (6 - 4) / 8
⇒ 4/8
⇒ 1/2 ≠ 1/4
Hence, It is not true.
B. 9/16 - 4/8 = 5/8
LHS;
⇒ 9/16 - 4/8
⇒ (9 - 8)/16
⇒ 1/16 ≠ 5/8
Hence, It is not true.
C. 7/8 − 3/4 = 1/8
LHS;
⇒ 7/8 - 3/4
⇒ (7 - 6)/8
⇒ 1/8
Hence, It is true.
D. 7/15 − 1/3 = 6/15
LHS;
⇒ 7/15 - 1/3
⇒ (7 - 5)/15
⇒ 2/15 ≠ 6/15
Hence, It is not true.
E. 1/2 − 1/20 = 10/20
LHS;
⇒ 1/2 - 1/20
⇒ (10 - 1)/20
⇒ 9/20 ≠ 10/20
Hence, It is not true.
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How to convert 185cm to feet?
185 centimeter is approximately equal to 6.0696 feet
To convert 185cm to feet, we can use the following formula:
1 cm = 0.0328 feet
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The distance in feet = conversion factor × The distance in centimeter
Substitute the values in the equation
185 cm = 185 x 0.0328
Multiply the numbers
= 6.0696 feet ( rounded to four decimal places )
Therefore, 185cm is 6.0696 feet.
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A cheetah can run 105 miles in hours. At that rate, how far can the cheetah run in 6 hours?
A cheetah could run 630 miles in 6 hours
Answer:
It can run 630 miles in 6 hours.
Step-by-step explanation:
If the cheetah can run 105 miles per hour
then,
in 6 hours, it can run 105*6 miles.
105*6= 630
Hope this helps.
Chris is 6 feet tall and he casts a shadow that is 5 feet longHe measures that the shadow cast by the school building is 30 feet longHow tall is the school building?
The school building is 36ft tall.
What is Pythagoras theorem?The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Chris is 6 feet tall and he casts a shadow that is 5 feet long
He measures that the shadow cast by the school building is 30 feet long
We can say the ratios will be same 6/h = 5/30
h =6 × 6 = 36 ft
Hence the school building is 36ft tall.
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function w gives the weight of a cat, in kilograms, when it is m months old, which statement represents the meaning of the equation w(7) = 4 in this situation?
Using the given equation, The weight of a cat when it is 7 months old is 4 kilograms.
Which equation is this?Equations describe physical processes and the relationship between different physical quantities. Equations are mathematical and physical statements. Physical quantities are presented using simple variables, and after that, a personal variable, such as your energy, may be indicated.
An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14. Algebraic equations in mathematics frequently have one or more variables.
In this situation, the statement "w(7) = 4" represents that a cat that is 7 months old weighs 4 kilograms.
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Fabrizio's curtain company is making curtains for a local hotel. He wants each curtain to be 48
inches long. At the fabric store, fabric is sold by the foot. If Fabrizio's curtain company wants to
make 62 curtains, how many feet of fabric will he need?
1 inch
foot
1
==
12
Answer:
248 feet
Step-by-step explanation:
Since each curtain is 48 inches long, or 4 feet long, Fabrizio will need:
62 curtains × 4 feet per curtain = 248 feet of fabric
Therefore, Fabrizio's curtain company will need 248 feet of fabric to make 62 curtains.
Answer:
248 feet...
Step-by-step explanation:
Each curtain is 48 inches long, which is 4 feet (since there are 12 inches in a foot). Therefore, 62 curtains will require:
62 curtains x 4 feet per curtain = 248 feet of fabric.
So Fabrizio's curtain company will need to purchase 248 feet of fabric from the store...
find the ordered pairs in f(x)=x^2-2x+3 and f(x)=-2x+19
The ordered pairs in f(x)=x^2-2x+3 and f(x)=-2x+19 are (√21, 24 - 2√21) and (-√21, 24 + 2√21)
How to find the ordered pairTo find the ordered pairs of the two functions, we need to solve the system of equations:
f(x) = x^2 - 2x + 3
f(x) = -2x + 19
We can set the two expressions for f(x) equal to each other:
x^2 - 2x + 3 = -2x + 19
Simplifying and rearranging, we get:
x^2 = 21
Taking the square root of both sides, we get:
x = ± √21
Therefore, there are two ordered pairs that satisfy both equations:
(√21, f(√21)) and (-√21, f(-√21))
To find the values of f(√21) and f(-√21), we can substitute the values of x into either equation. Let's use the first equation:
f(√21) = (√21)^2 - 2(√21) + 3 = 21 - 2√21 + 3 = 24 - 2√21
f(-√21) = (-√21)^2 - 2(-√21) + 3 = 21 + 2√21 + 3 = 24 + 2√21
Therefore, the two ordered pairs are:
(√21, 24 - 2√21) and (-√21, 24 + 2√21)
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randy went to terriffic tacos and purchased 5 tacos and 3 drinks for his friends. Randy spent $16.60. Jeff went to terrific tacos abd purchased 7 tacos and 4 drinks for his friends. Jeff spent $22.85. What is the cost of one taco at terrific tacos.
The cost of one taco at Terrific Tacos is $3.45. To calculate this, we can start by finding the total cost for all tacos purchased.
5 tacos purchased by Randy cost $17.25, and 7 tacos purchased by Jeff cost $24.15. This brings the total cost for all tacos to $41.40. Then, we can divide this total cost by the total number of tacos purchased (12) to get the cost of one taco:
$41.40 / 12 = $3.45.To calculate this, it is important to remember that the total cost of both orders is the sum of Randy's cost and Jeff's cost. This is because both orders were placed at the same restaurant. Then, the total cost needs to be divided by the total number of tacos purchased by both customers. This gives the cost of one taco at Terrific Tacos.
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assume you have applied for two jobs a and b. the probability that you get an offer for job a is 0.25. the probability of being offered job b is 0.20. the probability of getting at least one of the jobs is 0.40. what is the probability that you will be offered both jobs? enter your answer as a decimal rounded to two places.
Answer: the probability of being offered both jobs is 0.05, or 5%
Step-by-step explanation:
To solve this problem, we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where P(A or B) is the probability of getting at least one job offer, P(A) is the probability of getting an offer for job A, P(B) is the probability of getting an offer for job B, and P(A and B) is the probability of getting an offer for both jobs.
Substituting the given values, we get:
0.40 = 0.25 + 0.20 - P(A and B)
Solving for P(A and B), we get:
P(A and B) = 0.25 + 0.20 - 0.40 = 0.05
Therefore, the probability of being offered both jobs is 0.05, or 5% (rounded to two decimal places).
what is a capacity of a large bottle of lemonade
about 2.1134 us quarts
Complete the square by finding the missing values.
The missing values are 81/4 and 9/2, the complete square is x² - 9x + 81/4 = ( x - 9/2 )².
What are the missing values of the square?Given square in the question;
x² - 9x + [ ] = ( x - [ ] )²
To complete the square, we use the form ax² + bx + c.
Compare the form to the square;
a = 1b = -9c = 0Now, consider the vertex form of a parabola.
a( x + d )² + e
We find d, using the formula
d = b/2a
Plug in the values
d = -9/(2×1 )
d = -9/2
Next, find the value of e, using the formula
e = c - b²/4a
Plud in the values
e = 0 - (-9)²/(4×1)
e = -81/4
Hence, the complete square will be;
x² - 9x + 81/4 = ( x - 9/2 )²
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Which equation represents the graph?
a graph of a line that passes through the points 0 commas negative 3 and 4 commas negative 1
y equals negative one-half times x plus 6
y equals one-half times x minus 3
y = 2x − 3
y = −2x + 6
The equation of line passes through the points (0, -3) and (4, -1) will be;
⇒ y = 1/2x - 3
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (0, -3) and (4, -1)
Now,
Since, The equation of line passes through the points (0, -3) and (4, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (-3)) / (4 - 0)
m = 2 / 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - (-3) = 1/2 (x - 0)
⇒ y + 3 = 1/2x
⇒ y = 1/2x - 3
Therefore, The equation of line passes through the points ((0, -3) and
(4, -1) will be;
⇒ y = 1/2x - 3
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what is the area of a rhombus with an angle measuring 30 degrees and sides measuring 9 inches?
The area of a rhombus with an angle measuring 30 degrees and sides measuring 9 inches, the answer will be 40.5 inches.
By using trigonometry,
Here, it is given that:
Side which is 's' is equal to 9 inches
Angle which is denoted as 'A' is equal to 30 degrees
Square of side s is equal to 9 × 9 = 81 inches
Area of rhombus, A = s² × sin (30°)
A = 81 × 1/2
A = 40.5 inches
A rhombus is a particular kind of parallelogram in geometry where two pairs of opposite sides are congruent. Accordingly, a rhombus has equal length on each side. Square and rhombus are frequently confused in students. The main distinction between a square and a rhombus is that a square has all internal angles that are right angles, whereas a rhombus does not.
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PLEASE HELP
Roberta grows pea plants, some in shade and some in sun. She picks 8 plants of each type at random and records the heights.
Shade plant heights (in.) 7 12 10 12 9 12 10 8
Sun plant heights (in.) 19 24 19 19 23 24 20 20
Express the difference in the means as a multiple of their ranges.
The difference in the means is
times the ranges.
The difference in the means is times the ranges. (19-9)/(24-7)=10/17 = 0.588235294, or slightly more than half a time the ranges of the two samples.
What is height?Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).
This means that the mean of the sun plants is more than half a time the range of the two samples larger than the mean of the shade plants.
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