It is not possible for every student to receive postcards from exactly the same three students to whom they sent postcards.
Let's assume it is possible that every student receives postcards from exactly the same three students to whom he/she sent postcards.
Each student sends postcards to 3 other students. So the total number of postcards sent is 7 x 3 = 21.
If we count the number of postcards received by all 7 students, it should be equal to 21. However, this is not the case if each student receives postcards from exactly the same three students to whom he/she sent postcards.
If a student A sends postcards to B, C, and D, then B, C, and D should send postcards back to A. This means that each of B, C, and D will send postcards to two other students, and each of those two students will send postcards to two others as well.
So if we draw a diagram, it will look like this:
A
/ | \
B C D
/ \ | / \
E F G H
In the above diagram, A sends postcards to B, C, and D, and receives postcards back from them. B sends postcards to A, E, and F. C sends postcards to A, G, and H. D sends postcards to A, E, and H. E sends postcards to B, D, and G. F sends postcards to B, C, and H. G sends postcards to C, E, and F. H sends postcards to D, C, and F.
If we count the number of postcards received by each student, we get:
A: 3
B: 3
C: 3
D: 3
E: 3
F: 3
G: 3
H: 3
Therefore, it is possible that every student receives postcards from exactly the same three students to whom he/she sent postcards.
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please help me and I will give a branlist.
The vertices of the image of QRTW for a dilation with center (0, 0) and a scale factor of 1/4 include the following:
Q' (-0.5, 0.75).
R' (-0.75, 0.25).
T' (0.5, -0.25).
W' (0.25, 1).
What is dilation?In Mathematics and Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin (0, 0) as follows:
Ordered pair Q (-2, 3) → Ordered pair Q' (-2 × 1/4, 3 × 1/4) = (-0.5, 0.75).
Ordered pair R (-3, 1) → Ordered pair R' (-3 × 1/4, 1 × 1/4) = (-0.75, 0.25).
Ordered pair T (2, -1) → Ordered pair T' (2 × 1/4, -1 × 1/4) = (0.5, -0.25).
Ordered pair W (2, 4) → Ordered pair W' (2 × 1/4, 4 × 1/4) = (0.25, 1).
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Determine the surface area of a square pyramid that has a perimeter of 32 cm
and a slant height of 15 cm
Given that the perimeter of the square base is 32 cm, The surface area of the square pyramid is 304 cm².
The surface area of a square pyramid can be calculated using the formula: SA = B + (1/2)Pl, where B is the area of the base, P is the perimeter of the base, l is the slant height, and SA is the total surface area.
Given that the perimeter of the square base is 32 cm, we can divide it by 4 to find the length of each side: 32 cm / 4 = 8 cm.
Now, we can calculate the area of the base by squaring the length of a side: B = (8 cm)² = 64 cm²
Using the given slant height of 15 cm, we can plug in the values into the formula for SA: SA = 64 cm² + (1/2)(32 cm)(15 cm) = 64 cm² + 240 cm² = 304 cm².
Therefore, the surface area of the square pyramid is 304 cm².
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A tortoise is walking in the desert. It walks for 6.4 meters at a speed of 4 meters per minute. For how many minutes does it walk?
Answer:
1.6 minutes
Step-by-step explanation:
6.4 meters/4 speed
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Khloe sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
95 visitors purchased no costume.
288 visitors purchased exactly one costume.
13 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth.
In linear equation, 0.76 will purchase one or more costumes as a decimal to the nearest hundredth.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
from the given information
the probability that the next person will purchase one or more costumes
= 288 + 13/288 + 13 + 95
≈ 0.76
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i need this paper finished within 2 hours to stay in honors math. help? (2 attachments for 50 points)
Answers:
Q.1 B. 6.88.
Q2. Sorry Not clearly visible its blurred
Q3. The closest answer choice is C. 4.9
Q4. 2.94
Q5. Set B
Q6. C
Step-by-step explanation:
Q1.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 32, 43, 38, 28, 51
Mean = (32 + 43 + 38 + 28 + 51) / 5 = 38.4
Next, we need to find the absolute deviations of each number from the mean
|32 - 38.4| = 6.4
|43 - 38.4| = 4.6
|38 - 38.4| = 0.4
|28 - 38.4| = 10.4
|51 - 38.4| = 12.6
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5 = 6.88
Therefore, the answer is B. 6.88.
Q3.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 12.7, 22, 23.5, 24, 11, 22
Mean = (12.7 + 22 + 23.5 + 24 + 11 + 22) / 6= 18.2
Next, we need to find the absolute deviations of each number from the mean
|12.7 - 18.2| = 5.5
|22 - 18.2| = 3.8
|23.5 - 18.2| = 5.3
|24 - 18.2| = 5.8
|11 - 18.2| = 7.2
|22 - 18.2| = 3.8
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (5.5 + 3.8 + 5.3 + 5.8 + 7.2 + 3.8) / 6 = 5.9
Therefore, the closest answer choice is C. 4.9. However, this answer is not correct as the calculated value is 5.9.
Q4.
To find the average distance of these points from the mean of the data, we need to first find the mean of the data.
The mean of the data can be found by adding up all the values and dividing by the total number of values:
Mean = (-8 + 6.2 + 2.5 + 12 - 2 - 1.3 + 15 - 2 + 0 + 7) / 10
= 29.4 / 10
= 2.94
The average distance from the mean is found by taking the absolute value of the difference between each value and the mean, adding them up, and dividing by the total number of values:
Average Distance from Mean = (|(-8) - 2.94| + |6.2 - 2.94| + |2.5 - 2.94| + |12 - 2.94| + |-2 - 2.94| + |-1.3 - 2.94| + |15 - 2.94| + |-2 - 2.94| + |0 - 2.94| + |7 - 2.94|) / 10
= (10.94 + 3.26 + 0.44 + 9.06 + 4.94 + 4.24 + 12.06 + 4.94 + 2.94 + 4.06) / 10
= 5.688
Therefore, the average distance of these points from the mean of the data is 5.688, which is option D.
Q5.
o find out if the mean and median are equal in a set of data, we need to calculate both the mean and median and compare them.
Mean is calculated by adding up all the values and dividing by the total number of values.
Median is the middle value of the data when it is arranged in order.
Let's calculate the mean and median of both data sets:
A. (5, 3, 5, 8, 2, 5)
Mean = (5 + 3 + 5 + 8 + 2 + 5) / 6
= 4.6667
To calculate the median, we first need to arrange the data in order:
2, 3, 5, 5, 5, 8
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set A are not equal (4.6667 ≠ 5), set A is not the correct answer.
B. (7, 3, 5, 11, 5, 3)
Mean = (7 + 3 + 5 + 11 + 5 + 3) / 6
= 5.8333
To calculate the median, we first need to arrange the data in order:
3, 3, 5, 5, 7, 11
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set B are equal (5.8333 ≈ 5), set B is the correct answer.
Therefore, the set of data in which the mean and median are equal is set B: (7, 3, 5, 11, 5, 3). Answer: B.
Q6.
To answer this question, we need to first find the mean, median, and range of the data:
Data: 10, 23, 52, 18, 5, 60, 35
Mean = (10 + 23 + 52 + 18 + 5 + 60 + 35) / 7
= 28.57
Median = 23
To find the range, we need to subtract the smallest value from the largest value:
Range = 60 - 5
= 55
Now, let's evaluate each statement:
A. The mean is greater than the range.
- 28.57 > 55
- This statement is false.
B. The range is 50.
- The range is 55, not 50.
- This statement is false.
C. The median is less than the mean.
- The median is 23 and the mean is 28.57
- This statement is true.
D. The median is greater than the range.
- 23 > 55
- This statement is false.
Therefore, the statement that is true is C. The median is less than the mean.
suppose that the number of log-ons to a computer network follow a poisson process with an average of three counts per minute, a. what is the mean time between counts? b. what is the standard deviation of the time between counts?
a) Mean time between counts is 0.3333 minutes.
b) Standard deviation of time between counts is 0.5774 minutes.
a. Mean time between counts: The mean time between counts can be computed as the inverse of the Poisson rate parameter (λ): Mean time between counts = 1/λ.
The average of 3 counts per minute is the same as the rate parameter λ in a Poisson process. Thus, the mean time between counts is: Mean time between counts = 1/λ = 1/3 = 0.3333 minutes (20 seconds approximately).
b. Standard deviation of the time between counts: The standard deviation of a Poisson process is equal to the square root of the mean.
Therefore, the standard deviation of the time between counts can be calculated as follows: Standard deviation of time between counts = sqrt(mean) = sqrt(1/λ) = sqrt(1/3) = 0.5774 minutes (approximately 35 seconds).
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the high school dropout rate in the united states is greater than 25 percent. c. wright mills would classify this situation as
The high school dropout rate in the United States is greater than 25 percent. C. Wright Mills would classify this situation as a societal issue.
This is because societal issues are matters of public concern that affect large numbers of people and require collective action to resolve. The high school dropout rate in the United States is an example of a societal issue because it has widespread implications for both individuals and society as a whole.
According to Mills, a societal issue is one that cannot be attributed solely to the actions of individuals. Instead, it is the result of social structures and processes that operate at a broader level.
For example, the high school dropout rate in the United States is influenced by a variety of factors such as poverty, race, and family background. These factors are not solely determined by the actions of individual students but are instead shaped by broader social forces such as economic inequality and institutional racism.
To address the high school dropout rate, therefore, requires collective action at the societal level. This may involve policy changes, community-based initiatives, or other forms of collective action aimed at addressing the underlying social factors that contribute to the problem.
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A system of linear equations and a reduced matrix for the system are given. 1 0 Nm 1 x - y + z = 3 3x + 2z = 7 (x - 4y + 2z = 5 0 1 0 1 Use the reduced matrix to find the general solution of the system, if one exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (x, y, z) = ( (x, y, z) = *) (b) If multiple solutions exist, find two specific solutions. (Enter your answers as a comma-separated list of ordered triples. If there is no solution, enter NO SOLUTION.) (x, y, z) =
a) General solution of the system is (x, y, z) = (2, 0, 1).
b) There are no multiple solutions, and we cannot find two specific solutions.
How to evaluate each part of the question?The given system of linear equations is:
1) x - y + z = 3
2) 3x + 2z = 7
3) x - 4y + 2z = 5
The reduced matrix for this system is:
1 0 1
0 1 0
0 0 1
Using the reduced matrix, we can rewrite the system of linear equations as:
1) x + z = 3
2) y = 0
3) z = 1
Now we can solve the system step by step:
From equation (3), we know that z = 1.
Next, we can use the value of z in equation (1) to find x:
x + 1 = 3
x = 3 - 1
x = 2
Finally, from equation (2), we know that y = 0.
So, the general solution of the system is (x, y, z) = (2, 0, 1).
(b) Since there is only one solution to this system, there are no multiple solutions, and we cannot find two specific solutions.
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Suppose the demand d, in units sold, for a company's jeans at price x, in dollars, is d(x) = 400 - 4x.
a. If revenue = price x demand, write the rule for the
function r(x), which represents the company's
expected revenue in jean sales. Then state the
domain of this function.
b. If the price is $40, how much revenue will the
company earn?
Revenue
Price
a. The revenue function, r(x), is given by the product of the price x and the demand function d(x):
[tex] \sf r(x) = x \times d(x) = x \times (400 - 4x) = 400x - 4x^2[/tex]
The domain of this function is the set of possible prices that can be charged for the jeans, which is typically a positive real number, or in interval notation: (0, infinity).
b. If the price is $40, we can find the revenue by plugging in x = 40 into the revenue function:
[tex] \sf r(40) = 400(40) - 4(40)^2 = 16,000 - 6,400 = 9,600[/tex]
Therefore, the company will earn $9,600 in revenue if they sell their jeans at a price of 40
Complete the table and graph the corresponding ordered pairs. Draw the line defined by the points to
represent all solutions to the equation: 4x + 2y = 8
Plot the x-intercept of (-0.5,0) Plot the y-intercept of (0,-2) Draw a line passing through both intercepts.
To graph 4x + 2y = 8, we'll first look at the x-intercept and y-intercept.
The x-intercept occurs when y is zero, and the y-intercept occurs when x is zero.
0 = 4x + 2y => x = -0.5y = 4x + 2(0) => y = -2
From the two equations, we get the ordered pairs(-2,0), and (-0.5,0) as our intercepts.
The line defined by these two points and that represent all solutions to the equation is:
y = -2x + 4
The table would show different values of x for different values of y, but since there are no specific values to solve, you
just have to use the slope-intercept formula to determine the points on the graph.
Here's how to plot the ordered pairs on a graph:
Plot the x-intercept of (-0.5,0)
Plot the y-intercept of (0,-2)
Draw a line passing through both intercepts.
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Put the items below into order of length, from shortest to longest. Car Mobile phone Football pitch Tennis racket Paper clip S
Answer:
Paper clip, Mobile phone, S, Tennis racket, Car, Football pitch.
helppppppppp plsssssssssssssssssss
if the dental director wanted to analyze the data collected from the cpi, which type of descriptive statistics should be used to measure central tendencies?
To measure central tendencies in the data collected from the Consumer Price Index (CPI), the dental director should use measures of central tendency, such as the mean, median, and mode.
The mean is the average of a set of numbers and is calculated by adding all the numbers together and then dividing by the total number of numbers. The median is the middle number when the numbers are placed in order from least to greatest. The mode is the number that appears most often in a set of numbers.
Using these measures of central tendency will allow the dental director to gain a better understanding of the CPI data, as they will be able to identify the center point of the data and also see how frequently particular values appear. This can help in making informed decisions about policies and other changes.
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to begin a bacteria study, a petri dish had 2800 bacteria cells. each hour since, the number of cells has increased by 3.3%. let t be the number of hours since the start of the study. let y be the number of bacteria cells. write an exponential function showing the relationship between y and t.
[tex]y = 2800(1.033)^t[/tex] is the exponential function for starting population of 2800 bacterium cells that is shown to multiply exponentially over time using this function, increasing by a factor of 1.033 every hour.
We can use an exponential function of the type y = abt to simulate the development of bacteria cells over time, where y stands for the number of cells, t for the number of hours, and a and b for constants that we must establish.
Since we now know there are 2800 bacterium cells, we can enter this number into the equation to obtain:
[tex]2800 = ab^0[/tex]
By simplifying this equation, we obtain a = 2800, which informs us that there are 2800 bacterium cells in the initial population.
We must use the knowledge that the number of cells rises by 3.3% every hour to get the value of b. By dividing this percentage growth by 100, we can convert it to a decimal, yielding a growth rate of 0.033. The value of b can then be obtained by multiplying this growth rate by 1:
b = 1 + 0.033 = 1.033
These values of a and b are what we obtain when we enter them into our exponential function:
[tex]y = 2800(1.033)^t[/tex]
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The associative property works with expressions that use
A
division and subtraction. B
addition and subtraction. C
multiplication and division. D
multiplication and addition
The associative property works with expressions that use multiplication and addition. The correct option is (D).
The associative property is a rule in mathematics that allows us to change the grouping of the numbers or variables in an expression without changing the result. This property only applies to addition and multiplication, and not to subtraction and division.
The associative property of addition tells us that we can add a group of numbers in any order, and the result will be the same. For example, (2 + 3) + 4 is the same as 2 + (3 + 4). The associative property of multiplication tells us that we can multiply a group of numbers in any order, and the result will be the same. For example, (2 × 3) × 4 is the same as 2 × (3 × 4).
However, the associative property does not work with subtraction and division. For example, (10 - 3) - 2 is not the same as 10 - (3 - 2). Similarly, (12 ÷ 2) ÷ 3 is not the same as 12 ÷ (2 ÷ 3). Therefore, the correct answer to the question is D - the associative property works with expressions that use multiplication and addition.
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Factor 6y–42z
Write your answer as a product with a whole number greater than 1.
6(y - 7z) This is a product with a whole number greater than 1 (6), since we factored out a 6 from the original expression.
What is a factor?A factor is an expression or number that evenly divides another expression or number without leaving a remainder.
According to question:To factor the expression 6y - 42z, we need to find the greatest common factor (GCF) of the two terms.
The GCF of 6y and 42z is 6, since both terms are divisible by 6. We can factor out the 6 from both terms, leaving:
6(y - 7z)
Notice that the term inside the parentheses (y - 7z) cannot be factored any further, since there is no common factor other than 1. Therefore, the fully factored form of 6y - 42z is:
6(y - 7z)
This is a product with a whole number greater than 1 (6), since we factored out a 6 from the original expression.
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GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Answer:
x>7
Step-by-step explanation:
The circle is open so seven is not included which eliminates the second and fourth choice.
x<7 means x is less than seven which is wrong.
x> means x is greater than seven.
Answer:
x > 7
Step-by-step explanation:
We see that the arrow is going to the right, signaling greater than.
We know that it is not greater than or equal to, since the dot is not shaded.
So, the answer is x > 7.
what is the probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket? local authorities report that tickets usually are given to 23% of cars stopped
The probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket is 2.37.
Given Probability of giving tickets to cars that are stopped = 0.23
Probability of not giving tickets to cars that are stopped = 1 - 0.23 = 0.77
the probability that at least 67 out of 100 cars stopped at a roadblock will not be given a ticket
Here n = 100, p = 0.77, q = 0.23
mean = np = 100*0.77 = 77
standard deviation = [tex](sigma = \sqrt{(100)*(0.77)*(0.23) } = 4.208[/tex]
[tex]P(X\geq 67) = \frac{67 - 77}{4.208}[/tex] = 2.37
P-VALUE is 0.99126 from z-table
Probability is a fundamental concept in mathematics that helps us quantify the likelihood of events occurring and is applicable to a wide range of fields. It is a measure of the uncertainty of an event, expressed as a number between 0 and 1. An event with probability 0 is impossible, while an event with probability 1 is certain.For example, the probability of rolling a six on a fair six-sided die is 1/6, since there is only one favorable outcome out of six possible outcomes.
Probability theory has wide applications in fields such as statistics, finance, engineering, and physics, among others. It is used to model and analyze various phenomena, including weather patterns, stock prices, quantum mechanics, and more.
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exponents and powers
express the number 729 in exponential form
Step-by-step explanation:
729 = 9³ = (3²)³ = 3⁶
I hour that is what you needed.
the feasible corner points are (48,84), (0,120), (0,0), and (90,0). what is the maximum possible value for the objective function?
In linear programming, the feasible region is the set of all feasible solutions that satisfy the constraints of the problem. The feasible corner points are the extreme points of the feasible region, which represent the optimal solutions to the problem. In this case, we have four feasible corner points: (48,84), (0,120), (0,0), and (90,0).
To find the maximum possible value for the objective function, we need to evaluate the objective function at each of the feasible corner points and select the one that gives the highest value. The objective function is a linear combination of the decision variables and represents the quantity that we are trying to maximize or minimize.
Assuming that the objective function is in the form of z = ax + by, where x and y are the decision variables and a and b are constants, we can evaluate the objective function at each of the feasible corner points:
At (48,84): z = a(48) + b(84)
At (0,120): z = a(0) + b(120)
At (0,0): z = a(0) + b(0)
At (90,0): z = a(90) + b(0)
Since we don't have the values of a and b, we cannot calculate the maximum possible value of the objective function. However, we can compare the values of the objective function at each of the feasible corner points and select the one that gives the highest value.
Therefore, we can conclude that the maximum possible value for the objective function will be obtained at one of the feasible corner points: (48,84), (0,120), (0,0), or (90,0).
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the purchasing agent at a local hardware store noticed a sale on hammers. the original price of the hammers was $12 each. with the discount, he could get each hammer for $9.50. what percentage was the discount (rounded to nearest whole percentage)?
The percentage discount on the hammers is about 21%.
The discount is the difference between the original price and the discounted price.
Discount = $12 - $9.50
subtract the numbers
= $2.50
To find the percentage discount, we divide the discount by the original price and multiply by 100
Percentage discount = ( Discount / Original price ) x 100
Substitute the values in the equation and find the percentage discount
Percentage discount = ( $2.50 / $12 ) x 100
Do the arithmetic operation
Percentage discount = 20.83%
Rounding to the nearest whole percentage, the discount is approximately equal to 21%.
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An empty shipping box has a mass of 2. 75 kilograms. An electronics store is packing 5 identical laptops in the shipping box. Each laptop has a mass of 1. 65 kg. The cost to ship the box was $40. 00 for the first 5 kg and $3. 15 for each kilogram over 5 kg. What was the cost to ship the packed box?
The cost to ship a box containing 5 laptops, weighing a total of 11 kg (including the empty box), is $58.90, with a cost of $40.00 for the first 5 kg and $3.15 for each additional kilogram.
The total mass of the packed shipping box can be found by adding the mass of the laptops (5 * 1.65 kg = 8.25 kg) to the mass of the empty box (2.75 kg) for a total mass of 11 kg.
Since the cost to ship the box is $40.00 for the first 5 kg and $3.15 for each additional kilogram over 5 kg, we can split the total mass into two parts: the first 5 kg and the additional weight above 5 kg.
The cost to ship the first 5 kg is $40.00, and the remaining weight is 11 kg - 5 kg = 6 kg.
The cost to ship the additional 6 kg is $3.15 per kilogram, so the total cost to ship the packed box is:
$40.00 + $3.15 * 6 kg = $58.90
Therefore, the cost to ship the packed box is $58.90.
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What most likely happened in the game below when analyzing the win probability chart?
Group of answer choices
TB started as the favorite, then fell behind most of the game, and then had a last minute comeback
TB led the entire game and ended up winning
NO started as the favorite and then had a comeback at the end of the game
This shows that TB did not have a game-long advantage but rather needed to recover from a deficit to triumph.
what is probability ?A subfield of mathematics known as probability studies random events and the possibility that they will occur. It entails calculating the probability of an event happening and expressing it as a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. The possibility of a coin landing heads-up, the chances of winning a game, or the likelihood of a disease spreading throughout a population are just a few examples of real-world occurrences that may be studied and understood using probability.
given
It is most likely that option 1 happened, according to the victory probability chart in the illustration provided: TB came out as the favourite, trailed for the majority of the game, then made a late comeback.
The graph demonstrates that the victory probability for TB initially increased before sharply declining as NO seized the lead and kept it for the most of the game.
The dramatic increase in the win probability for TB towards the end of the chart, however, shows that TB came back and won in the final few minutes of the game.
This shows that TB did not have a game-long advantage but rather needed to recover from a deficit to triumph.
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find the measure in degrees of the angle
Answer:
120°
Step-by-step explanation:
We know that the exterior angle of a triangle is equal to the sum of the interior opposite angles.
Let the unknown angle be x.
Accordingly,
70° + 50° = x
120° = x
scores on an iq test are normally distributed with a mean of 100 and a standard deviation of 15. what is the z-score for an iq score of 122?
The z-score for an IQ score of 122 is 2.
This is calculated by subtracting the mean (100) from the score (122) and dividing by the standard deviation (15). So, 122-100=22, 22/15=2.
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what extraneous solution arises when solving for the point of intersection of the line f(x)=-1/2x+6 and the square root function f(x)= √x-4
The extraneous solution which arises when solving for the point of intersection of the line and the square root function is 20.
What is an extraneous solution?
An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
We are given two equations as f(x) = [tex]\frac{-1}{2}[/tex]x + 6 and f(x) = √x - 4.
Now, on equating both the equations, we get
⇒ [tex]\frac{-1}{2}[/tex]x + 6 = √x - 4
On squaring both sides, we get,
⇒ [tex](\frac{-1}{2}x + 6)^{2}[/tex]= x - 4
⇒ [tex]\frac{1}{4}x^{2}[/tex] + 36 - 6x = x - 4
⇒ [tex]\frac{1}{4}x^{2}[/tex] + 40 = 7x
⇒ [tex]\frac{1}{4}x^{2}[/tex] -7x + 40 = 0
⇒ [tex]x^{2}[/tex] -28x + 160 = 0
⇒ x = 20 , 8
For point of intersection, we will substitute x = 20 in both the equations.
So, we get
⇒ f(x) = [tex]\frac{-1}{2}[/tex] (20) + 6
⇒ f(x) = -10 + 6
⇒ f(x) = -4
Similarly,
⇒ f(x) = √20 - 4
⇒ f(x) = √16
⇒ f(x) = 4
Since both the solutions are not same so this is an extraneous solution.
Hence, the extraneous solution which arises is 10.
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How do you put fractions in order from least to greatest?
To put fractions in order from least to greatest, you need to compare their values by finding the common denominator.
Here are the steps to follow:Step 1: Find a common denominator for all the fractions.
Step 2: Convert each fraction to an equivalent fraction with the common denominator.
Step 3: Compare the numerators of the equivalent fractions. The fraction with the smallest numerator is the smallest fraction, and the fraction with the largest numerator is the largest fraction.
Step 4: If two or more fractions have the same numerator, compare their denominators. The fraction with the smallest denominator is the smallest fraction, and the fraction with the largest denominator is the largest fraction.
Step 5: Write the fractions in order from least to greatest.
For example, let's say you need to put the fractions 1/3, 2/5, and 3/8 in order from least to greatest.
Step 1: The common denominator for 3, 5, and 8 is 120.
Step 2: Convert each fraction to an equivalent fraction with a denominator of 120.
1/3 = 40/120
2/5 = 48/120
3/8 = 45/120
Step 3: Compare the numerators of the equivalent fractions: 40 < 45 < 48
Step 4: Since 40 is not equal to 45 or 48, we don't need to compare the denominators.
Step 5: Write the fractions in order from least to greatest: 1/3 < 3/8 < 2/5.
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My bed is 3 inches by 2 2/3 by 1/3 what is the volume of my bed.
Answer:
2 [tex]\frac{2}{3}[/tex] [tex]in^{2}[/tex]
Step-by-step explanation:
the area of one lateral face of a right pyramid with an equilateral triangular base is 75 square meters. if the slant height is 30 meters, what is the length of the side of its base, in meters?
A right pyramid with an equilateral triangular base has a lateral face with a surface area of 75 square meters. The side of the base of a slant with a height of 30 meters is 5 meters long.
Let’s call the side length of the equilateral triangular base “s”. We know that the area of one lateral face is 75 square meters, and that face is a triangle with base s and height 30 meters (the slant height). We can use the formula for the area of a triangle to solve for s:
Area = (1/2) * base * height
75 = (1/2) * s * 30
Simplifying the equation, we get:
75 = 15s
s = 75/15
s = 5
Therefore, the length of the side of the equilateral triangular base is 5 meters.
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A triangle has two sides 4 and 15 what value could the length of the third side be
The answers
are 12, 15, 13
__________________________________________________________
The sum of two sides must be equal to or greater than the third side.
4+15 = 19; 4 + 19 = 23; 15 + 19 = 34.
19 is a possible answer.
4 + 15 = 19; 15 + 15 = 30
15 is a possible answer.
4 + 15 = 19; 4 + 13 = 17; 15 + 13 = 28
13 is a possible answer.
4 + 12 = 16; 4 + 15 = 19; 15 + 12 = 27
12 is a possible answer.
4 + 11 = 15; 4 + 15 = 19; 11 + 15 = 26
11 is a possible answer.
15 + 4 = 19; 4 + 4 = 8
4 is NOT a possible answer because 4 + 4 is less than 15.
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