There are 66 solutions to the inequality x₁ + x₂ + x₃ ≤ 11, where x₁, x₂, and x₃ are nonnegative integers.
To solve this inequality, we must find all the possible combinations of nonnegative integers x₁, x₂, and x₃ that add up to 11 or less. This can be done by breaking down the problem into a series of nested loops. The outermost loop will iterate through all possible values of x₁, while the two inner loops will iterate through all possible values of x₂ and x₃ that add up to the remaining value of 11 minus x₁. We know that the maximum value of x₁ is 11, so the outermost loop will run from 0 to 11. For each value of x₁, the inner loops will run from 0 to (11 - x₁), incrementing by 1 each time. This will ensure that all possible combinations of x₂ and x₃ that add up to 11 minus x₁ are tested. Once we have all the combinations, we can count them to get the total number of solutions. In this case, there are 66 solutions to the inequality.
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Write the equation -4x^2 + 9y^2 + 32x + 36y - 64 = 0 in standard form. SHOW EACH STEP OF THE PROCESS.
Answer:
[tex]\dfrac{(y+2)^2}{4} -\dfrac{(x-4)^2}{9}=1[/tex]
Step-by-step explanation:
Given equation:
[tex]-4x^2 + 9y^2 + 32x + 36y - 64 = 0[/tex]
Collect like terms:
[tex]\implies 9y^2 + 36y -4x^2+ 32x - 64 = 0[/tex]
Move the constant to the right side of the equation:
[tex]\implies 9y^2 + 36y -4x^2+ 32x =64[/tex]
Factor out 9 from the terms in y, and 4 from the terms in x:
[tex]\implies 9(y^2 + 4y) -4(x^2-8x)=64[/tex]
Add the square of half the coefficient of the term in y and x inside the parentheses on the LHS, and the distributed values on the RHS:
[tex]\implies 9\left(y^2 + 4y+\left(\dfrac{4}{2}\right)^2 \right) -4\left(x^2-8x+\left(\dfrac{-8}{2}\right)^2 \right)=64+9\left(\dfrac{4}{2}\right)^2 \right+4\left(\dfrac{-8}{2}\right)^2 \right[/tex]
Simplify:
[tex]\implies 9(y^2 + 4y+4) -4(x^2-8x+16)=64+36-64[/tex]
[tex]\implies 9(y^2 + 4y+4) -4(x^2-8x+16)=36[/tex]
Factor the perfect trinomials:
[tex]\implies 9(y+2)^2 -4(x-4)^2=36[/tex]
Divide both sides by 36:
[tex]\implies \dfrac{9(y+2)^2}{36} -\dfrac{4(x-4)^2}{36}=\dfrac{36}{36}[/tex]
Simplify:
[tex]\implies \dfrac{\diagup\!\!\!\!9(y+2)^2}{\diagup\!\!\!\! 9\cdot 4} -\dfrac{\diagup\!\!\!\!4(x-4)^2}{9 \cdot \diagup\!\!\!\!4}=1[/tex]
[tex]\implies \dfrac{(y+2)^2}{4} -\dfrac{(x-4)^2}{9}=1[/tex]
Therefore, the function is a hyperbola with:
Center: (4, -2)Vertices: (4, -4) and (4, 0)Co-vertices: (1, -2) and (7, -2)Foci: (4, -2±√13)Transverse axis: x = 4Conjugate axis: y = -2[tex]\textsf{Asymptotes}: \quad y =-2 \pm \left(\dfrac{2}{3}\right)(x-4)[/tex]to make one pan of baklava, dorothea needs 400 grams of filo pastry. if dorothea plans to make 6 pans of baklava, how many kilograms of filo pastry will she need?
Dorothea needs 2.4 kilograms of filo pastry to make on pan of baklava.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b.
Given that,
The quantity needed of filo pastry to make one pan of baklava = 400 grams
To find the quantity of pastry to make 6 pans of baklava
Use ratio property,
1 pan of baklava needed = 400 grams
6 pans of baklava needed = 400 x 6 = 2400 grams
Since, 1000 gram = 1 kilogram
2400 gram = 2.4 kilograms
Hence, Dorothea needs 2.4 kilograms of filo pastry.
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if length of a rectangle is (x+7) and breath is (x+5). find the area of the rectangle
Step-by-step explanation:
Area of rectangle is length x breadth.
Area = (x + 7)(x + 5)
= (x² + 5x + 7x + 35)
= (x² + 12x + 35)
events x and y are independent of each other. if the probability of event x occurring is 1 in 4, and the probability of event y occurring is 1 in 5, the probability of both events occurring is ____.
The probability of both events occurring is 1/20.
What are examples and probability?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.
Events X and Y are independent.
The probability of X occurring is 1/4
The probability of Y occurring is 1/5
Since both events are independent, then we have
P(X and Y ) = P(X) * P(Y)
= 1/4 * 1/5
= 1/20
P( X and Y ) = 1/20
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A linear function contains the following points. What are the slope and y-intercept of this function?
The slope and y-intercept of the linear function are -5 and 7 respectively.
What is a linear function?Linear functions are those whose graph is a straight line. In other words, a linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line.
A linear function has one independent variable and one dependent variable.
A linear function has the following form. y = mx + b.
where
m = slopeb = y-interceptTherefore, let's find the slope of the function.
slope = m = Δy / Δx
using (0, 7) and (4, -13)
slope = m = -13 - 7 / 4 - 0
slope = - 20 / 4
slope = -5
Let's find the y-intercept using (0, 7).
y = -5x + b
7 = -5(0) + b
b = y-intercept = 7
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Ruben bought 666 comic books for $ 21 dollar sign, 21. Each comic book was the same price.
What was the cost for 111 comic book?
The cost for 111 books is obtained as $3.5.
What is Unitary method ?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
The given problem can be solved using unitary method as follows,
The cost for 666 books = $21
Then, cost for 1 book = 21/666
Thus, the cost of 111 books = 21/666 × 111
= 21/6
= 3.5
Hence, the cost for 111 comic book is given as $3.5.
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Nelson covered the first 20 miles in 2 1/2 hours, what was his average speed in miles per hour?
Answer:
Nelson's average speed was 8 miles per hour.
Step-by-step explanation:
To find Nelson's average speed, you need to divide the distance he traveled by the time it took him to travel that distance. In this case, Nelson traveled 20 miles in 2 1/2 hours, so his average speed was 20 miles / 2.5 hours = <<20/2.5=8>>8 miles per hour.
Answer:
8 miles per hour
Step-by-step explanation:
In order to find Nelson's average speed, we can set up a proportion. To solve for x, x being miles traveled in one hour.
[tex]\frac{20 miles}{2.5hours} =\frac{x miles }{1 hour}[/tex]
x= 8
in excel, to construct a residual plot, input of a y range and an x range is needed. aimee is examining the relationship between age and square foot range (sqft) of living space. in the scenario provided, what would be the y and what would be the x range data?
For the given case, in the residual plot, the x range is for the age and the y range must be the square foot
A residual plot appears the difference between the observed response and the fitted response values. The ideal remaining plot, called the null residual plot, appears as a random scatter of focuses shaping a roughly constant width band around the identity line. It is vital to check the fit of the model and presumptions – steady change, normality, and freedom of the errors, utilizing the residual plot, alongside normal, sequence, and lag plot.We are given the information that there is a relationship between age and square foot range (sqft) of living space, so for the residual plot the y range must be for the square foot and the x range must the age
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Calculate Habib's average rate of change from 4 to 9 minutes.
average rate of change from 4 to 9 minutes is 2.25 min . division of the y-value change by the x-value change.
what is average rate of change ?It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends.
the difference between the y- and x-values is divided. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity.
Given that
the change in y value occurred in 9 minutes and the change in x value occurred in 4 minutes, the average rate of change was 9 minutes by 4 minutes, or2.25 minutes.
9 min / 4 min
= 2.25 min
average rate of change from 4 to 9 minutes is 2.25 min . division of the y-value change by the x-value change.
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72 = 4s
S=
What does s =?
Answer:
72 = -4s
72 / (-4) = (-4s) / (-4)
-18 = s
Given the equation 8x = 4y + 16, generate a plan to rewrite it in slope-intercept form. Which variable do you solve for?
Answer: Convert the equation to slope-intercept form by solving for the variable y. Use the properties of equality to subtract 16 from both sides, and then divide both sides by 4.
This is for future people who don't want to watch adds or have hit their daily limit, have a nice day!
The slope-intercept form of the equation 8x = 4y + 16 will be y = 2x -4.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation given is 8x = 4y + 16.
We must solve for y as follows;
8x = 4y + 16
4y = 8x -16
By dividing through by 4; we have;
y = 2x -16
Hence the equation for both lines will be y = x +3 and y = x+13
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NEED IT BY TODAY!! PLEASE HELP!!
The tiles that Bruce used were each of a square foot in area. The table shows the area covered by Felicia’s tiles in terms of the number of tiles used.
Number of Tiles Area Covered (sq. ft.)
9 1
18 2
27 3
Bruce and Felicia want to know whose tiles cover the most area per tile.
Q1.) Write an equation representing the area Bruce covered, y, in terms of the number of tiles he used, x.
Q2.) Write an equation representing the area Felicia covered, y, in terms of the number of tiles she used, x.
Q3.) The person whose equation has the greater unit rate is the person whose tiles cover the most area per tile. Whose equation has the greater unit rate?
Q4.) What is the slope and the y-intercept for Bruce’s equation? What is the slope and y-intercept for Felicia’s equation?
Q5.) Which line is steeper, Bruce’s or Felicia’s? Whose slope is greater? Does this match the comparison from Part C?
Answer:
Step-by-step explanation:
Q1. Since each of Bruce's tiles is one square foot in area, his equation is y=x, where y=area and x=#of tiles. The area increases by one square foot for every tile added.
Q2. If it takes 9 of Felicia's tiles to equal 1 square foot, her equation is y=(1/9)x. We can check the table to see if this equation is right. If you put 18 into this equation, you get 2, for 27 you get 3, and so forth
Q3. Bruce has the greater unit rate of 1 and has the tiles that cover the greatest area, as opposed to Felicia, whose unit rate is only 1/9, since each of her tiles covers 1/9 of a square foot
Q4. The slopes are the same as the unit rates. Bruce's is 1, Felicia's is 1/9. Both of their y intercepts are 0, because if they put down 0 tiles, there will be no area covered because the problem does not state that there were tiles placed already before Bruce and Felicia started. You can also see this by graphing their equations
Q5. Bruce's line is steeper, with a slope of 1, versus Felicia's slope, which is 1/9. This matches the comparison from part c where we discovered that Bruce had the greater unit rate
21 divided by 13,280 
Answer: 0.0015813253
Step-by-step explanation:
is you ment to say 14,280 divided by 21 then it would be 632.380952381
What is the value of x? Show your work
Answer: x=16
Step-by-step explanation:
The two angles in the picture is equal to each other.
So the 6x + 4 = 100 degree
6x = 96
x= 16
what is 100 + 9245???????????
HELPPPPPPPPPPPPPPPP
Answer:
The answer is : 9345.
Step-by-step explanation:
N/A
4 students can put together 14 puzzles in 7 mins and 30 seconds. How long will it take them to finish 23 puzzles if another person is added and the time is constant?
10 points please help!,
There are some nickles, dimes, and quarters in a large piggy bank. For every 2 nickles there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins total.
1. How many nickles, dimes, and quarters are in the piggy bank? Explain.
2.How much are the coins worth?
1. There are 80 Nickels, 120 dimes, and 300 quarters in the piggy bank.
2. The coins worth is $91
How many types of coins are there?
There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.
1 Quarter = 25 cent
1 dime = 10 cents
1 Nickel = 5 cents
1 penny = 1 cent
Assume that, the number of Nickel coins is x.
Given that, 2 nickles there are 3 dimes.
1 nickle there are 3/2 dimes.
x nickles there are 3x/2 dimes.
Also given that,
2 dimes there are 5 quarters.
1 dimes there are 5/2 quarters.
3x/2 dimes there are (5/2) × (3x/2) quarters = 15x/4.
There is 500 coins in the piggy.
Therefore, x + (3x/2) + (15x/4) = 500
(4x + 6x + 15x) /4 = 500
25x/ 4 = 500
x = 80.
The number of dimes is (3 × 80)/2 = 120
The number of quarters is (15 × 80)/4 = 300.
The total cost of 80 nickles, 120 dimes, and 300 quarters is
= [(80 × 5) + (120 × 10) + (300 × 25)] cents
= 400 + 1200 + 7500 cents
= 9100 cents
= $(9100/100)
= $ 91
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The blue segment below is the diameter of O. what is the length of the radius of the circle?
Answer: D) 2.95 units
Step-by-step explanation:
I just took this
What i the ratio between the number of edge and the number of vertice of a cube? Find few olid having ame ratio and why?
The ratio between the number of edges and the number of vertice of a cube is 2:3. All Prisms have a ratio of edges and vertices will be the same as that of the cube.
Edge – The outlines where two cube sides touch one another.
Vertices – The indicates the point where a cube's three sides meet.
Number of edges of a cube = 12
Number of vertices in a cube = 8
The ratio of edges in vertices = 12 : 8
= 3 : 2
Hence, the ratio between the number the edges and the number of vertices of a cube is 3 : 2
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Find the measure of each missing angle
The measure of the angles ∠1, ∠2, and ∠3 will be 38°, 65°, and 52°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Angle ∠1 is given by the property of complementary. Then we have
∠1 + 38° = 90°
∠1 = 52°
Angle ∠1 and angle ∠3 are complementary angles. Then we have
∠1 + ∠3 = 90°
52° + ∠3 = 90°
∠3 = 52°
Angle ∠2 is given by the property of supplementary. Then we have
∠2 + 52° + 63° = 180°
∠2 = 65°
The measure of the angles ∠1, ∠2, and ∠3 will be 38°, 65°, and 52°, respectively.
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How do you simplify 25^(3/2)?
Answer:
I'm sure the answer is 125
Step-by-step explanation:
Hope it helps ; )
Shaundra went to 4 stores and found these prices for cases of water.
Super Buy: 12 bottles for $3.96
Fresh Grocers: 8 bottles for $2.08
Saveway: 24 bottles for $5.52
Shop and Go: 36 bottles for $7.56
Lod
Which store charges the least amount per bottle?
Answer:
Step-by-step explanation:To determine which store charges the least amount per bottle, you need to calculate the price per bottle for each store. You can do this by dividing the total price of the cases by the number of bottles in each case.
For Super Buy, the price per bottle is $3.96 / 12 bottles = $0.33 per bottle.
For Fresh Grocers, the price per bottle is $2.08 / 8 bottles = $0.26 per bottle.
For Saveway, the price per bottle is $5.52 / 24 bottles = $0.23 per bottle.
For Shop and Go, the price per bottle is $7.56 / 36 bottles = $0.21 per bottle.
Based on these calculations, it looks like Shop and Go charges the least amount per bottle at $0.21.
what is the probability that a five-digit integer chosen at random is divisible by 5? (enter your probability as a percent.) %
The probability that a five-digit integer chosen at random is divisible by 5 is 13.1 %.
Given :
what is the probability that a five-digit integer chosen at random is divisible by 5 .
Probability :
Probability is a branch of mathematics that deals with the occurrence of a random event.
Probability = 9^3 * 8 * 2 / 9 * 10^4
= 729 * 8 * 2 / 9 * 10000
= 5832 * 2 / 9 * 10000
= 11809 / 90000
= 0.131
converting into percentage :
= 0.131 * 100 %
= 13.1 %
Therefore The probability that a five-digit integer chosen at random is divisible by 5 is 13.1 %
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Principal = 6,000, rate of interest = 10% p.a., time = 3 years
please solve
Answer:
$7800
Step-by-step explanation:
1 year = 10%
3 years = 30%
30% = 0.3
6000 times 0.3 = $1800
6000 + 1800 = $7800
So, they will pay $7800
How do you solve 3^x = 500 ?
by using log notation, the value of x =㏒₃500 or x = 5.657
what is log notation?Log notation is a mathematical expression used to represent any exponential relationship in its inverse form.
How to solve the index?we use log notation to solve an equation in where an unknown variable is in index form. By applying logarithm laws, we write an exponential equation in the inverse form and finally we get the unknown values.
in the above equation 3ˣ = 500
using log notation, we get ㏒₃500 = x
x= 5.657
hence, the solution is x = 5.657
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the results of a mathematics placement exam at two different campuses of mercy college follow: campus sample size sample mean population standard deviation 1 330 33 8 2 310 31 7 the college wants to test the hypothesis that the mean score on campus 1 is higher than on campus 2. if we test the null hypothesis at the 5% level of significance, what is the decision?
If we test the null hypothesis at the 5% level of significance, then the decision is (c)reject null hypothesis and conclude the means are different .
In the question ,
it is given that ,
the results of a mathematics placement exam for two different campuses of college ,
we have to test the hypothesis that the mean score on campus 1 is higher than on campus 2 .
sample size (n₁) is = 330
the sample size (n₂) is = 310
the sample mean (μ₁) = 33
the sample mean (μ₂) = 31
the standard deviation , σ₁ = 8
the standard deviation , σ₂ = 7
the test statistic test z can be calculated using the formula ,
z = (μ₁ - μ₂)/√(σ₁²/n₁ + σ₂²/n₂)
Substituting the values of the sample size , sample mean and standard deviation ,
we get ,
z = (33 - 31)/√(8²/330 + 7²/310)
Simplifying further ,
we get ,
Z = 3.37
the test is for the null hypothesis at the 5% level of significance .
that means ,
Z₀.₉₅ = 1.645 ;
So , the p value = P(Z > 3.37)
= 1 - P(Z < 3.37)
= 1 - 0.9996
= 0.0004
since the p-value is (0.0004) < the level of significance (0.05) .
we can reject the null hypothesis .
There is significant evidence to conclude that the mean score on campus 1 is higher than campus 2 .
Therefore , the correct option is (c) .
The given question is incomplete the complete question is
The results of a mathematics placement exam at two different campuses of mercy college follow: ( the table is given below)
The college wants to test the hypothesis that the mean score on campus 1 is higher than on campus 2. if we test the null hypothesis at the 5% level of significance, what is the decision ?
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would using standard deviations be a good way to detect fraud? explain your answer. yes, because the standard deviations of these two distributions are very close in value. no, because the standard deviations of these two distributions are not equal. no, because the standard deviations of these two distributions are not too different from one another. yes, because a standard deviation of 2.58 will indicate fraud. any other value will indicate legitimate expense amounts. yes, fraudulent reports will always have a standard deviation that is greater than 2.46.
(a) The standard deviation is 2.582
(b) No, because the standard deviations of these two distributions are not too different from one another.
a) In this question we have been given
The given information is:
First Digit 1 2 3 4 5 6 7 8 9
Probability 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9
Now we find the standard deviation.
The mean for given data is:
μ = ∑xP(X = x)
μ = (1*1/9) +(2*1/9)+(3*1/9)+(4*1/9)+(5*1/9)+(6*1/9)+(7*1/9)+(8*1/9)+(9*1/9)
μ = 5
The standard deviation is:
σ² = ∑(x - μ)²P(X)
σ² = (1 - 5)² *1/9 +(2 - 5)²*1/9+(3 - 5)²*1/9+(4 - 5)²*1/9 + (5 - 5)²*1/9+(6 - 5)²*1/9+(7-5)²*1/9+(8-5)²*1/9)+(9-5)²*1/9
σ² = 2.582
(b) The uniform distribution's standard deviation is 2.582, while Benford's law's standard deviation is 2.46
Using the standard deviation to detect fraud is not a good idea because the two distributions have about the same standard deviation
Therefore, (a) The standard deviation is 2.582
(b) using standard deviations would not be a good way to detect fraud.
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The complete question is:
Benford’s law and fraud
(a) Using the graph from Exercise 21, calculate the standard deviation σY. This gives us an idea of how much variation we’d expect in the employee’s expense records if he assumed that first digits from 1 to 9 were equally likely.
(b) The standard deviation of the first digits of randomly selected expense amounts that follow Benford’s law is . Would using standard deviations be a good way to detect fraud? Explain your answer.
Find the x-intercepts.
2x²-3x + 1
y = 2x² + 8x + 6
(0.5, [?]), ([ ]. [D
What are some benefits of representing data sets using frequency distributions What are some benefits of using graphs of frequency distributions? What are some benefits of representing data sets using frequency distributions?
a. Organizing the data into frequency distribution can make patterns within the data more evident:
b. Organizing the data into frequency distribution makes it possible to graph quantitative data
c. It is easier t0 determine the minimum and maximum values of a data set when has been arranged into a frequency distribution.
What are some benefits of using graphs of frequency distributions?
a. It can be easier to determine the class boundaries by looking at a graph of the frequency distribution_
b. Graphing a frequency distribution makes possible to determine the relative frequencies of each of the classes_
c. It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution_
d. Graphing frequency distribution makes it possible to find the total number of observations.
Representing data sets using frequency distributions and using graphs of frequency distributions can have several benefits. Here are some of the benefits of representing data sets using frequency distributions:
a) Organizing the data into afrequency distribution can make patterns within the data more evident. By organizing the data into classes or bins and counting the number of observations within each class, you can see how the data is distributed and identify patterns or trends that may not be immediately apparent when looking at the raw data.
b) Organizing the data into a frequency distribution makes it possible to graph quantitative data. Many types of graphs, such as bar graphs and histograms, are based on frequency distributions and can be used to visualize the distribution of data.
c) It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution. By organizing the data into classes, you can easily see the range of values within each class and determine the overall range of the data set.
Here are some of the benefits of using graphs of frequency distributions:
a) It can be easier to determine the class boundaries by looking at a graph of the frequency distribution. When you create a graph of a frequency distribution, the class boundaries are often marked along the x-axis, which makes it easy to see where one class ends and the next begins.
b) Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes. By looking at the heights of the bars on a bar graph or the heights of the columns on a histogram, you can see how each class compares to the others and determine the overall shape of the distribution.
c) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. Graphs are a visual representation of data, and they can help you see patterns or trends that may not be immediately apparent when looking at the data in tabular form.
d) Graphing frequency distributions makes it possible to find the total number of observations. By adding up the frequencies of all the classes, you can determine the total number of observations in the data set.
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(g) Water is flowing through a circular channel at 8 m/s. Find the number of m*2
discharged per minute if the channel, always full, has a radius of 8 cm.
Answer:
Below
Step-by-step explanation:
( Your question asks for m^2 discharge......I think you need m^3 discharge per minute)
Find the volume of a cylinder that is 8 meters long with radius of 8cm ( .08 m)
area = pi r^2 = pi (.08)^2 = .0201 m^2
area * 8 m = volume PER SECOND
volume PER SECOND * 60 = volume per minute
.0201 * 8 * 60 = 9.65 m^3 / min discharge
