In the constructed GFDT, each class interval represents a range of values, and the frequency column shows how many values fall within each range.
To construct a grouped frequency distribution table (GFDT) for the given dataset, we need to determine the class width, select appropriate class limits, and count the frequency of each class.
Given dataset: 426, 408, 420, 415, 381, 424, 430, 401, 421, 408, 371, 421, 404, 372, 429, 418, 393, 404, 446, 403, 425, 435, 398, 445, 418, 383, 468, 426
To determine the class width, we can find the range of the dataset:
Range = Maximum value - Minimum value
Range = 468 - 371 = 97
Next, we select a nice class width. In this case, let's choose 10 as the class width (a multiple of 5).
Now, we need to determine the number of classes. We can calculate this by dividing the range by the class width:
Number of classes = Range / Class width
Number of classes = 97 / 10 = 9.7
Since we want 10 classes, we can round up to the nearest whole number. Therefore, we will have 10 classes.
To determine the class limits, we can start with the lower class limit. We can choose the first multiple of the class width that is less than or equal to the minimum value in the dataset. In this case, the minimum value is 371, and the class width is 10. The first multiple of 10 less than or equal to 371 is 370. So, the lower class limit of the first class will be 370.
Using the lower class limit and the class width, we can determine the upper class limit for each class by adding the class width to the lower class limit. The upper class limit for each class will be the lower class limit plus the class width, excluding the last class which may have a different width due to rounding.
Here is the constructed grouped frequency distribution table (GFDT) for the given dataset:
vbnet
Copy code
Class Frequency
[370, 380) 3
[380, 390) 2
[390, 400) 3
[400, 410) 6
[410, 420) 5
[420, 430) 6
[430, 440) 3
[440, 450) 3
[450, 460) 1
[460, 470) 1
Note: The notation "[370, 380)" indicates that the lower limit is inclusive and the upper limit is exclusive.
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A pair of fair dice each numbered 1 to 6 i toed. Find the probability of a core of
a. Two odd number
b. A um of 8 or um of 12
C. Both prime or both odd number
The probability of a core of the two odd number be 1/4.
What is meant by probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The outcome of one die has no bearing on the outcome of the other since the two dice are independent.
In this instance, a complex event's probability is calculated by adding its component simple event probabilities.
Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)
The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)
It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are
(1, 1), (1, 3), (1, 5)
(3, 1), (3, 3), (3, 5)
(5, 1), (5, 3), (5, 5)
And in fact, 9 good outcomes over 36 total outcomes means
\($\frac{9}{36}=\frac{1}{4}$$\)
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23x+67= 90
solve
free
Answer:
x=1
Step-by-step explanation:
23x+67=90
23x=23
x=1
Answer:
x=1
hope this helps
have a good day :)
Step-by-step explanation:
Giving brainiest pls help
Answer:
Ivan: 4
Caleb: 4, 4, 4, 4, 4, 4, 4
Step-by-step explanation:
For every 4 Ivan sees, Caleb sees 28. (4 times 7)
Help, Please
I don’t understand
Answer:
(A) ∠1 and ∠3
Step-by-step explanation:
Angles 1 and 3 are vertical angles because they are across from each other in the intersection of two lines.
Hope this helps :)
What is a staticistcal question musa can ask about the club
A statistical question will pose a problem with a potential range of solutions. 'How many hours does an average member of the club at Musa's school spend participating in club events each month?' is a statistical question that Musa might use to help him gather data about the club.
What exactly is a statistical question?Only once varied data have been gathered can a statistical question be addressed. A statistical question is one that may be answered by gathering information, and there will always be variation in the information. Since there is no variability in the data used to answer the question, questions that can be answered by a single data point are not statistical questions. After data has been gathered and examined, the solution can give an interpretation of the data. Although there will be statistics for a non-statistical question, the outcomes won't change. There will be only one solution.
The following qualities should be included in a statistical question:
Indefiniteness
Indeterminism
Answers that are plural
Variability.
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Your friends, Fernando and Amelia, each own a video game designer company. They both want you to join their company. You currently have a part-
time job making $8. 00 per hour. Fernando offers to pay you $15 per hour for the first month and then increase your hourly rate by $1. 00 each month.
Amelia says she will start your pay at $8. 00 per hour but she will increase your hourly rate by 10% each month. In order to make the best decision,
you decide to use the mathematics to choose the best offer based on the best hourly wage per month
Write the equations to represent Fernando's job offer and Amelia's job offer. Let x = number of months, y=hourly wage.
Fernando offers to pay $15 per hour for the first month and then increase hourly rate by $1. 00 each month and Amelia says she will start pay at $8. 00 per hour but she will increase hourly rate by 10% each month.
Considering Fernando's offer
Total pay per hour = 15 + (x -1)
= 14 + x
Fernando job pays more than the current part-time job from the very first month.
Considering Amelia's offer
Total pay per hour = 8 × 1.1⁽ˣ⁻¹⁾
Amelia's pay will exceed Fernando's offer when
8 × 1.1⁽ˣ⁻¹⁾ > 14 + x
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
6
�
+
5
�
=
6x+5y=
9
9
−
11
�
−
10
�
=
−11x−10y=
−
20
−20
The system of equations 6x + 5y = 9 and −11x − 10y = −20 has exactly one solution.
Determining the type of solution of the system of equationsGiven that
6x + 5y = 9
−11x − 10y = −20
To determine if the system of equations has no solutions, infinitely many solutions, or exactly one solution, we can use a common method called elimination.
First, we can multiply the first equation by 2 to eliminate y:
12x + 10y = 18
Next, we can add the second equation to the modified first equation to eliminate x:
12x + 10y -11x -10y = 18 - 20
Simplifying both sides:
x = -2
Therefore, the system has exactly one solution
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Which expression is equivalent to 6 (3x + 4)?
9x + 10
9.C +4
18.2 + 4
18.2 + 24
b)simplify the expression
7x2 + 4x – 2 + 8x2 – 9x – 5
Answer:
=25x-7
Step-by-step explanation:
Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.
Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.
Given function is: \(f(x) = -2x^{2}+12x+5\)
\(f(x) = a(x-h)^{2} +k\) , where (h,k) is the vertex
Apply completing the square method to find vertex
\(f(x) = -2x^{2}+12x+5\\\\f(x) = -2(x^{2}-6x)+5\)
Lets take half of coefficient of x is -6
divide by 2 that is -3
square it \((-3)^{2}\) that is 9
Add and subtract 9
\(f(x) = -2(x^{2}-6x+9-9)+5\)
Take out -9 and multiply by -2
\(f(x) = -2(x^{2}-6x+9)+18+5\\\\f(x) = -2(x^{2}-6x+9)+23\)
Now factor the parenthesis part
\(f(x) = -2(x-3)^{2} +23\)
The value of h=3 and k=23
So vertex is (3,23)
The value of 'a' is -2, it means the parabola is upside down. so vertex is maximum
Hence the answer is the vertex is maximum at (3,23)
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5(B + 3) = 4(B - 7) + 2B
Just not entirely sure on my answer please help will vote Brainly
Answer:
The answer is x = 43
Step-by-step explanation:
Solve for B by simplifying both sides of the equation, then isolating the variable.
hoped helped!
Brainly, please?
Answer:
B = 43
Step-by-step explanation:
1. Distribute.
5b + 15 = 4b - 28 + 2b
2. Combine like terms.
5b + 15 = 6b - 28
3. Get B on one side.
5b + 15 = 6b - 28
-5b + 28 = -5b + 28
43 = b
Which one is grader -3.5 or -2.5
Answer:
-2.5 is greater
Step-by-step explanation:
it's greater because it's closer to the whole # 1
Answer:
-2.5
Step-by-step explanation:
When you have negatives , the lowest number would always be the greatest
Find the common ratio r for the geometric sequence and user to find the next three terms.
-6, 18, -54, 162, ...
The common ratio r =
The next three terms are
___,___, and ____
Answer:
the common ratio(r): 3
-486,1458,-4374
-486,1458,-4374Step-by-step explanation:
-6×3=18
18×3=-54
54×3=162
162×3=-486
-486×3=1458
1458×3=-4374
therefore the next three terms are,-486,1458,and -4374
No need for an explanation it is option
Answer:
152
Step-by-step explanation:
Trick question,
4x + 52 + 28 = 180
Then
You subtract 180 and 28 to get 152
A function is graphed on the coordinate plane.
What is the value of the function when x = -2?
Answer:
1/2x-2
Step-by-step explanation:
if this is set up as y=mx+b then we already know the slope of the line to be 1/2 all that we are changing is where it intersects the y axis with is now -2
If triangle ABC is first reflected across the x-axis, and then rotated 90 degrees couter-clockwise, where will Point A' and Point A'' be located if Point A is located at (3,-5)?
PLEASE ANSWERRRR PLEASEEE!!! I WOULD GREATLY APPRECIATE ITTTTT.
Answer:
the answer is 3,5 for A' and 5,3 A''
Step-by-step explanation:
when you reflect across the x axis the formula becomes x, -y its already negative and 2 negatives equals a positive then when you rotate it 90 degrees you make the formula y, x and that's how you get 5, 3
also kind of weird I had this exact same question like even the same typo you from cisd
Factor the following quadratic:
y=3x^2-13x-10
Answer:
(3x+2)(x−5)
Step-by-step explanation:
Factor 3x2−13x−10
3x2−13x−10
=(3x+2)(x−5)
The length of a copper wire is 1.6 centimeters (cm). what is the length of this wire in meters (m)? 1.6 times. 10–3 m 1.6 times. 10–2 m 1.6 times. 102 m 1.6 times. 103 m
The length of the copper in meters is 1.6 times 10^-2 meters.
According to the given question.
The length of a copper is 1.6 centimeters.
As we all know that
1 meter = 100 centimeter
⇒ 1 centimeter = 1/100 meters or 10^-2 meters
So, to find the length of the copper wire in meters. We have to convert 1.6 centimeters to meters.
Therefore,
The length of the copper wire in meters
= 1.6/100 meters
= 1.6 × 10^-2
= 1.6 times 10^-2 meters
Hence, the length of the copper in meters is 1.6 times 10^-2 meters.
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Answer:
Its B: 1.6X10-2m
what happens to the ols intecept and slope estimates when all observations on the independent variable are identical
When all observations on the independent variable are identical in a linear regression model, it leads to a situation known as perfect multicollinearity.
How to explain the informationPerfect multicollinearity occurs when there is an exact linear relationship between the independent variables, making it impossible to estimate unique intercept and slope coefficients using ordinary least squares (OLS) regression.
In the presence of perfect multicollinearity, the OLS estimation method fails because it relies on inverting the matrix of the independent variables, which becomes singular or non-invertible when there is a perfect linear relationship. Consequently, it becomes impossible to obtain unique estimates for the intercept and slope coefficients.
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assume that a grade of a, b, c, d, f, i, or nc is assigned to each of 10 students. in how many different ways can grades be assigned?
There are numerous ways to grade a class of ten students. There are seven possible grades that could be given (A, B, C, D, F, I, or NC), depending on the grading scheme employed.
This indicates that there are mathematically 7 to the power of 10 (710) distinct methods to give the kids grades. There are approximately 8.3 billion ways to grade the ten pupils, or 8,300,000,000 ways in total.
Because there are seven different grades for each student, this number is extremely high. The number of possible options increases exponentially because there are 10 pupils. As a result, there are countless alternatives for how to assess the 10 kids.
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Pls help with my math problem!!!!
Answer:
Step-by-step explanation:
A
Is 10 12 15 a Pythagorean triple?
No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.
To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.
In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.
10^2 + 12^2 = 100 + 144 = 244
244 ≠ 15^2
Therefore, 10 12 15 is not a Pythagorean triple.
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What number should be added to both sides of the equation to complete the square? x2 + 8x = 4
Answer:
2 x 2+ 8 x 0= 4
Step-by-step explanation:
Answer:
c.16
hope this helps some one, have a nice day :)
Step-by-step explanation:
i just took the quiz and got it correct
You must decide whether to buy new machinery to produce product X or to modify existing machinery. You believe the probability of a prosperous economy next year is 0.7. Prepare a decision tree and use it to calculate the expected value of the buy new option. The payoff table is provided below (+ for profits and - for losses).
When entering the answer, do not use the $ symbol. Do not enter the thousand separator. Enter up to 2 decimal places after the decimal point. For example, $6,525.35 must be entered as 6525.35
N1: Prosperity ($) N2: Recession ($)
A1 (Buy New) $1,035,332 $-150,000
A2(Modify) $823,625 $293,648
The expected value of the "Buy New" option is 724732.60.
Decision Tree:
To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:
Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:
Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)
Substituting the given values in the above formula, we get:
Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60
Therefore, the expected value of the "Buy New" option is 724,732.60.
Conclusion:
To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.
The expected value of the "Buy New" option is 724,732.60.
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List the sets of numbers from smallest to largest. (Real, integers, whole, counting,
rational, irrational) *
Answer:
See below.
Step-by-step explanation:
counting: 1, 2, 3, 4, ...
whole: 0, 1, 2, 3, 4, ...
integers: ... , -3, -2, -1, 0, 1, 2, 3, ...
rational: all numbers that can be written as a ratio of integers
irrational: all numbers that cannot be written as a ratio of integers
real: all the numbers listed above
A local restaurant charges $15 for a jumbo cheese pizza and $1.35 for each additional topping. Write an equation, in slope-intercept form, to represent the total cost, y, for x toppings on a jumbo pizza.
A local restaurant charges $15 for a jumbo cheese pizza and $1.35 for each additional topping.
the total cost, y, for x toppings on a jumbo pizza is represented in slope-intercept form, by the equation y = $1.35x + $15
The slope-intercept equation for the total cost, y, for x toppings on a large cheese pizza is y = mx + b, where m is the slope and b is the y-intercept.
First, we must determine the slope (m). The slope shows the $1.35 cost of each subsequent topping. So, m = $1.35.
The y-intercept must then be determined (b). The y-intercept shows the large cheese pizza's starting cost of $15. So, b = $15.
When we plug these values into the equation, we get:
y = $1.35x + $15
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Maya and Edward cut lawns in the summer to earn spending money. Maya has a newer lawnmower, so Edward takes 15 minutes longer to cut a lawn than Maya. Working together they can both cut a lawn in 18 minutes. How long would it take Edward to cut a lawn alone?
Answer:
The answer would be 45 minutes.
Step-by-step explanation:
Just skipped to the answer on Edementum.
A fraction is a way to describe a part of a whole. The time it takes Edward to cut the lawn alone is 45 minutes.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Let the time taken by Maya to lawn the garden be x.
The rate at which Maya lawn = 1/x
Maya has a newer lawnmower, so Edward takes 15 minutes longer to cut a lawn than Maya. Therefore,
The rate at which Edward lawn = 1/(x+15)
Working together they can both cut a lawn in 18 minutes.
The rate at which they both work = 1/18
Now, the rate of working can be compared as,
1/x + 1/(x+15) = 1/18
(x+ x + 5)/x(x+15) = 1/18
(2x + 15)18 = x(x+15)
36x + 270=x² + 15x
x²-21x-270=0
x = 30, -9
Since time can not be negative. Therefore, the time it takes Edward to cut the lawn alone is,
x + 15
= 30 + 15
= 45 minutes
Hence, the time it takes Edward to cut the lawn alone is 45 minutes.
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*PLS HELP MEE* There are 80 servings in a box of cereal. Each serving size is 1/8 of a cup of cereal. If one person eats 1 cup and another eats 3 cups, how many cups are left in the box of cereal?
Answer:
2 cups left in the ceral box!
Step-by-step explanation:
please just trust me i worked it out and got the answer and you just have to trust me please! MAY I HAVE BRAINLIEST IF ITS RIGHT? HAVE A GREAT DAY!!!
Find the height of an equilateral triangle with sides 12 cm long.
Answer:
12cm
Step-by-step explanation:
Since it is an equilateral triangle, meaning that all sides are equal the height is 12 cm.
Find the value of c that completes the square
x^2-16x+c
Please help me with how to do this, and show me. Thank you.
Answer:
The value that completes the square is: c=8
Step-by-step explanation:
Find the value of c that completes the square \(x^2-16x+c\)
The formula used is: \(a^2-2ab+b^2=(a-b)^2\)
In the question given the value c can be found by breaking the middle term. we are given -16x while the general formula is 2ab for middle term so,
2(x)(8) = 16x
so, c= 8
Solving:
\(x^2-16x+c\\=x^2-2(x)(8)+(8)^2-(8)^2\\=(x-8)^2-64\)
So, the value that completes the square is: c=8