The fraction of the numbers in the distribution that are between 50 and 70 is; 95/100
How to use the empirical rule in statistics?
We are given;
Mean = 60
Standard deviation = 5
To find the numbers in the distribution that are between 50 and 70, it means that the numbers are going to be 2 standard deviations from the mean because 2σ = 2 * 5 = 10 which is the difference of both pairs from the mean.
According to empirical rule, 2 standard deviations from the mean is approximately 95/100 or 95%.
Complete question is;
In a certain distribution, the mean is 60 with a standard deviation of 2. At least what traction of the numbers are between the following pair of numbers? At least of the numbers in the distribution are between 50 and 70
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1.2 Generate a three-column table where you evaluate how learning takes place according to: • Piaget • Vygotsky • Bruner (15)
While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.
Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:
Theorist Approach to Learning Key Concepts
Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.
Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.
Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.
While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.
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Find an equation of the line that goes through the points (7,8) and (4,-8). Write your answer in the form y=mx+b .y= x+ Preview m : ; Preview b : Write your answers as integers or as reduced fractions in the form A/B.Submit QuestionQuestion 2
For this question we will use the two points formula for the equation of a line:
\(y-8_{}=\frac{-8-8}{4-7}(x-7)\text{.}\)Solving for y we get:
\(\begin{gathered} y-8=\frac{-16}{-3}(x-7), \\ y-8=\frac{16}{3}x-\frac{112}{3}, \\ y=\frac{16}{3}x-\frac{112}{3}+8, \\ y=\frac{16}{3}x-\frac{88}{3}. \end{gathered}\)Answer:
\(y=\frac{16}{3}x-\frac{88}{3}.\)Solve for all possible values of x.
√60 8x = x - 9
The possible values of x are 3 and 7
Solving rational expressionsGiven the rational expression below;
√60-8x = x - 9
Square both sides to have:
(60-8x)² = (x-9)²
60-8x = x²-18x+81
Equate to zero to have;
x²-18x+81 - 60 + 8x = 0
x² - 10x + 21 = 0
x² -3x-7x +21 = 0
x(x-3)-7(x-3) = 0
x = 3 and 7
Hence the possible values of x are 3 and 7
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The length of a rectangle is 4 units greater than its width, and the area of the rectangle can be
expressed by the equation y = x + 4x. What is a reasonable domain for this function?
O
O
O
O
A y>0
By> 4
C X>0
D X> 2
The reasonable domain for this function is \((x > 0)\) .
The collection of all feasible values for the independent variable is referred to as a function's domain.
When we substitute different values for the independent variable from the domain, the dependent variable's range refers to the set of all conceivable values for that variable.
Let the width of the rectangle be x units.
Thus as per given information length becomes x+4 units.
It is given, the area of rectangle can be expressed by the equation
\(y=x^{2} +4x\)
Now let's find domain of this function.
clearly x cannot be zero and x cannot be negative because x represents the width of the rectangle and the width of a rectangle cannot be zero or negative.
Therefore the domain of the function is
\((0,\infty)\) or x>0 .
Therefore the domain is given by the thirds option (c) x>0 .
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In Mr. Romano‘s class, 40% of the students like baseball. If 14 of his students
like baseball, how many students are in Mr.Romano’s Class?
Answer:
35
Step-by-step explanation:
The number of students in Mr.Romano’s class is 35.
Given that, in Mr. Romano‘s class, 40% of the students like baseball.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of students in Mr.Romano’s class be x.
Here, 40% of x = 14
⇒ 40/100 × x = 14
⇒ 0.4x = 14
⇒ x = 14/0.4
⇒ x = 35
Therefore, the number of students in Mr.Romano’s class is 35.
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4. A Space Z engineer is testing the design of a new heat shield for its Komodo spacecraft. The design is meant to prevent
the interior of the shield from reaching a temperature of 200◦C. Over the course of 24 trials, the average temperature
of the shield was 194.37◦C with a standard deviation of 4.29◦C. Assume all temperature measurements follow a normal
distribution.
(a) Test at the 1% level of significance if the shield’s average temperature is less than 200◦C.
(b) Explain a Type I error in the context of the data.
At the 1% level of significance, the heat shield for the Komodo spacecraft have average temperature of 191.811° C < x-bar < 196.73° C which is less 200◦C
Type I error is explained below
How to know of the shield's average temperature is less than 200 degree Celsius1% level of significance means that the p value or the probability of the temperature of the new heat shield for Komodo spacecraft being less than 200° C is less than 1%
The range of average temperatures of the shield is given by the formula
= x-bar ± t(s/√n)
Definition of variables
mean, x-bar = 194.37° C
standard deviation, s = 4.29° C
sample size, n = 24
significance level = 1%
confidence level = 1 - significance level = 1 - 0.01 = 0.99 = 99%
z score, z
For sample size less than 30, n < 30. t scores are used
degree of freedom, df = n - 1 = 24 - 1 =23
t score for 99% confidence level and df of 23 = 2.808
substituting into the formula
= x-bar ± t(s/√n)
= 194.37 ± 2.808 (4.29/ √24)
= 194.27 ± 2.4589
= 191.811 ° C < x-bar < 196.73° C
Type I error in the context
Type I error is when the engineer's test shows that the interior of the Konodo spacecraft is below 200° C when the interior is actually above 200° C
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The winner of a 100 mile race drove his car to victory at a rate of 120.1229 mph. What was his time to the nearest thousandth of an hour)?
His time was hours.
(Round to the nearest thousandth.)
Answer:
\(t=1.201\ \text{hour}\)
Step-by-step explanation:
Given that,
Distance, d = 100 mile
Velocity of the winner, v = 120.1229 mph
We know that velocity of an object is equal to distance per unit time. Let t is the time. So,
\(v=\dfrac{d}{t}\\\\t=\dfrac{d}{v}\\\\t=\dfrac{120.1229}{100 }\\\\t=1.201229\ \text{hour}\\\\\text{Round to the nearest thousandth}\\\\t=1.201\ \text{hour}\)
Hence, 1.201 hour is taken by the winner.
An AP has first term as 3 and Common difference of 2 how many terms are needed to make the sum to 99
Answer:
9
Step-by-step explanation:
The \(n\)term is \(2n+1\).
\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)
The number of terms that needed to make the sum to 99 is 9
The first term of the arithmetic progression = 3
The common difference = 2
The sum of n term is = (n/2) [2a+(n-1)d]
Where a is the initial term
d is the common difference
Substitute the values in the equation
(n/2) [2(3)+(n-1)2] = 99
(n/2) [6 + 2n - 2] = 99
(n/2)[4+2n] = 99
n(2 + n) = 99
2n + \(n^2\) = 99
\(n^2\) + 2n - 99 = 0
Split the terms
\(n^2\) - 9n +11n - 99 =0
n(n -9) + 11(n - 9) = 0
(n + 11)(n - 9) = 0
n = -11 or 9
Since n cannot be a negative number, therefore n = 9
Hence, the number of terms that needed to make the sum to 99 is 9
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A woman 5 feet tall stands next to her daughter who is 4 feet tall on a sunny day. If the worstan's shadow has length 3 feet, what is the length, in feet, of her daughter's
shadow
Answer:
2 ft
Step-by-step explanation:
The fraction of PKR 1 is 50 paisas
The fraction that represents the rate between PKR and Paisas is given as follows:
1/50.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:
1/50.
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In class, we developed the formula
(a) Use the formula (using appropriate substitutions) to find the closed form for ∑2
= 2
(b) Use the formula in the notes for ∑
= 13 to find the closed form expression form for
∑
= 3 (assume a ≥ 1 and a ≤ b)
(c) In class, we developed the formula
Use this formula and some algebra to derive a closed form for the sum ∑
= 0( ― 1)2 ― 1
(d) Test your closed form solution in (c) to find the value of ∑3
= 0( ― 1)2 ― 1 and see if
it matches the manual computation of the 4 terms of the sum.
(a) The closed form for ∑2 is 2.
(b) The closed form expression for ∑3 is 24.
(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.
(d) The value of -3 matches the manual computation of the four terms.
Our closed form solution is correct.
To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:
∑2 = n(a + l) / 2
In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.
We also know that there is only one term, so n = 1.
Substituting these values into the formula, we have:
∑2 = 1(2 + 2) / 2
= 4 / 2
= 2
The formula for the sum of the first n terms of an arithmetic series is:
∑n = n(a + l) / 2
In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).
Substituting these values into the formula, we get:
∑3 = 3(3 + 13) / 2
= 3(16) / 2
= 48 / 2
= 24
The formula we developed in class is:
∑n = n(a + a + (n - 1)d) / 2
In this case, we have a = 0 (the first term) and d = -1 (the common difference).
Substituting these values into the formula, we get:
∑n = n(0 + 0 + (n - 1)(-1)) / 2
= n(0 - n + 1) / 2
= n(1 - n) / 2
To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):
∑3 = 3(1 - 3) / 2
= 3(-2) / 2
= -6 / 2
= -3
Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:
0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1
= 0 - 1 - 2 - 3
= -6
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suppose that the length of a certain rectangle is 7 meters less than four times its width. The perimeter of the rectangle is 46 meters. find the length and width of the rectangle.
The answer to the given question is length is 17m and width is 6m
Given that a rectangle's length is 7 meters less than its width.
And also given the perimeter of the rectangle is 46 meters.
We know that the rectangle's perimeter is twice the sum of its length and width.
l - length of the rectangle
w - width of the rectangle
P - perimeter of the rectangle
Then we have P = 2 × (l + w)
Given that a rectangle's length is 7 meters less than its width.
⇒ l = 4 × w - 7
Given the perimeter of the rectangle is 46 centimeters.
⇒ 2 × ( l + w) = 46
⇒ 2 × (4w - 7 + w) = 46 (using the value of length given in terms of width)
⇒ 4w - 7 + w = 23 (dividing by 2 on both the sides)
⇒ 5w - 7 = 23
⇒ 5w = 23 + 7
⇒ 5w = 30
⇒ w = 6 (dividing both sides by 5)
Using the width value in the length equation, we get
l = 4 × 6 - 7
⇒ l = 24 - 7
⇒ l = 17
Therefore, The rectangle is 17 meters in length and 6 meters in width.
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Sunshine Preschool has a teeter totter that spins in a circle. The distance from the center to the outside edge of the teeter totter is 37 inches (in.).
What is the circumference of the circle that the teeter totter makes as it spins? Round your answer to the nearest hundredth of an inch.
The formula for circumference is used to determine the diameter of the circle that the teeter totter creates as it spins, which is 232.12 inches.
The circumference of the circle that the teeter totter makes as it spins is given by the formula:
Circumference = 2 * pi * radius
where "pi" is the mathematical constant approximately equal to 3.14, and "radius" is the distance from the center of the circle to its outside edge.
In this problem, we are given that the distance from the center to the outside edge of the teeter totter is 37 inches, which means that the radius of the circle is also 37 inches. Therefore, we can use the formula for circumference to calculate the distance around the circle that the teeter totter makes as it spins.
In this case, the radius is 37 inches, so we can plug in these values to get:
Circumference = 2 * 3.14 * 37
Simplifying this expression gives:
Circumference = 232.12
Therefore, the circumference of the circle that the teeter totter makes as it spins is approximately 232.12 inches, rounded to the nearest hundredth of an inch.
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HELP HELP HELP
Write the inequality in interval notation and graph.
The inequality in interval notation is [ -1, ∞ ) from the given equation x ≥ - 3
What is interval notation ?Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways. They do not, however, intend to indicate any particular location. Instead, they serve as a concise approach to express an inequality or a set of inequalities.A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.a collection of all real numbers. The interval notation (,) can be used to denote a function's domain as only real values.Given data :
x ≥ - 3
x is greater than or equal to - 3, so - 3 is our smallest value of the interval so it goes on the left. Since there is no upper endpoint (it is ALL values greater than or equal to 3),
we put the infinity symbol on the right side. The boxed end on 3 indicates a closed interval.
In interval notation it is [ -1, ∞ )
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Expand (2+√3) (1+√3) Give your answer in the the form c+d√3 where c and d are integers.
Step-by-step explanation:
Using FOIL,
(2 + √3)(1 + √3)
= (2)(1) + (2)(√3) + (√3)(1) + (√3)(√3)
= 2 + 2√3 + √3 + 3
= 5 + 3√3.
Find the cost of excavating a space 81 ft long, 42 ft wide, 9 ft deep at a cost of $36/yd.
The cost of excavating a space 81 ft long, 42 ft wide, 9 ft deep at a cost of $36/yd. is $367, 416
How to find the area?The area of the object or space is the space it occupies
The area is denoted by
Area= Lenght * Breadth * Height
Area = 81 * 42 * 9 feet
Area = 30,618 ²
Feet to Yards Converter
From
Foot (ft)
To
Yard (yd)
Feet
ft
Yards
yd
Calculation
Yards to feet ►
How to convert feet to yards
1 yard is equal to 3 feet:
1yd = 3ft
The distance d in yards (yd) is equal to the distance d in feet (ft) divided by 3:
d(yd) = d(ft) / 3
Example
Convert 20 ft to yards:
d(yd) = 20ft / 3 = 6.6667yd
How many yards in a foot
One foot is equal to 0.33333 yards:
1ft = 1ft / 3 = 0.33333yd
How many feet in a yard
One yard is equal to 3 feet:
Remember that 1yd = 3×1yd = 3ft
How to convert 10ft to yards
Divide 10 feet by 3 to get yards:
10ft = 10ft / 3 = 3.33333yd
Feet to yards conversion table
Feet (ft) Yards (yd)
0.01 ft 0.0033333 yd
0.1 ft 0.033333 yd
1 ft 0.33333 yd
2 ft 0.66667 yd
3 ft 1.00000 yd
4 ft 1.33333 yd
5 ft 1.66667 yd
6 ft 2.00000 yd
7 ft 2.33333 yd
8 ft 2.66667 yd
9 ft 3.00000 yd
10 ft 3.33333 yd
20 ft 6.66667 yd
30 ft 10.00000 yd
40 ft 13.33333 yd
50 ft 16.66667 yd
60 ft 20.00000 yd
70 ft 23.33333 yd
80 ft 26.66667 yd
90 ft 30.00000 yd
100 ft 33.33333 yd
Then covert the feet into yards
This shows that 30618 feet = 10206 yards
The cost of each yard is $36/yd.
Then the cost of excavating the space $36*10206 = $367,416
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Which statement is true about the function f(x) = 6x7?
The function is even because f(–x) = f(x).
The function is odd because f(–x) = –f(x).
The function is odd because f(–x) = f(x).
The function is even because f(–x) = –f(x).
Answer: The function is odd because f(–x) = –f(x).
Step-by-step explanation:
\(f(x)=6x^7\\\\f(-x)=6(-x)^7 = -6x^7\\\\\therefore f(x)=-f(-x)\)
The function is odd because f(–x) = –f(x).
How to determine the true statement?The function is given as:
f(x) = 6x^7
A function is odd if the following is true
f(-x) = -f(x)
Calculate f(-x)
f(-x) = 6(-x)^7
f(-x) = -6x^7
Calculate -f(x)
-f(x) = -6x^7
By comparison;
f(-x) = -f(x) = -6x^7
Hence, the function is odd because f(–x) = –f(x).
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(a) A yoga instructor collected student data. She found that students who had less sleep did not tend to burn more or fewer calories
during class. What can she conclude?
There is no correlation between amount of sleep and number of calories burned.
There is a correlation between amount of sleep and number of calories burned. There may or may not be causation. Further studies would
have to be done to determine this.
There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely
an increase in the number of calories burned with an increase in the amount of sleep.
Answer:
The answer is ( A) -There is no correlation between amount of sleep and number of calories burned
Step-by-step explanation:
I don’t know if that’s the correct answer and not sure if I did the table right helppp please :( !
To check if the given line is exponential, we can starting by making a table for a set of values. Let's do like in the picture, for x = 0, x = 1, x = 2:
\(\begin{gathered} (5\cdot0)^3=0^3=0 \\ (5\cdot1)^3=5^3=125 \\ (5\cdot2)^3=10^3=1000 \end{gathered}\)Here is the table then:
x | y
0 | 0
1 | 125
2 | 1000
For an exponential line, we can divide two y values of consecutive x values, and all consecutive values mus t be equal.
We would start by doing:
\(\frac{125}{0}\)And comparing it to
\(\frac{1000}{125}\)To see if they are equal. However, we can't divide by zero. Because of this, (5x)³ can't be exponential.
To be a linear line or straight line, the difference between consecutive values must be equal, so we should compare:
\(125-0=125\)With:
\(1000-125=875\)Because they are not equal, (5x)³ is not linear nor straight.
So it can't be alternatives A, B or C. So It has to be alternative D.
Given the following coordinates complete the glide reflection transformation.
A(−1,−3)
B(−4,−1)
C(−6,−4)
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
Given:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
To find:
The image after glide reflection transformation.
Solution:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
If a figure is reflected over the x-axis, then
\((x,y)\to (x,-y)\)
Using this, we get
\(A(-1,-3)\to A'(-1,3)\)
\(B(-4,-1)\to B'(-4,1)\)
\(C(-6,-4)\to C'(-6,4)\)
If a figure is shifting 10 units right, then
\((x,y)\to (x+10,y)\)
Using this we get
\(A'(-1,3)\to A''(-1+10,3)\)
\(A'(-1,3)\to A''(9,3)\)
Similarly,
\(B'(-4,1)\to B''(-4+10,1)\)
\(B'-4,1)\to B''(6,1)\)
And,
\(C'(-6,-4)\to C''(-6+10,4)\)
\(C'(-6,-4)\to C''(4,4)\)
Therefore, the vertices of the image are A''(9,3), B''(6,1) and C''(4,4).
Mandy borrows $10,000 for 3 years at a 6% interest. What is the cost of the loan, or total interest?
Answer:
Interest Earned ₹ 1,800
Principal Amount ₹ 10,000
Total Value ₹ 11,800
The cost of the loan for Mandy will be $11800 and the total interest for 3 years will be $1800.
What is simple interest?Simple interest is a predetermined proportion of the principal amount borrowed or lent that is paid or received over a set period of time.
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
In another word, if the principle amount is the same in each time period then the interest will also same for every time period.
Given that
Principle amount = $ 10000
Time period = 3 years
Rate of interest = 6%
Rate of interest at the end of 1st year
10000 × 6/100 ⇒ $600
Since in simple interest rate of interest remain same so
Rate of interest for 3 years
3 × 600 = $ 1800 hence rate of interest will be $1800.
Cost of the loan = principle amount + total interest
Cost of the loan = 10000 + 1800 ⇒ $11800 will be the cost of the loan.
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what is 2 ( 6x +1 ) equal to
What is the value of the equation
Answer:
304
Start with parenthesis then do multiplication, then do addition and subtraction. Just remember PEMDAS
P arenthesis
E xponents
M ultiplication
D ivsion
A ddition
S ubtraction
Hope this helps :)
As a promotional feature, a store conducts a weekly raffle. During any week, 40% of the customers who turn in one or more tickets do not bother to turn in tickets the following week. On the other hand, 30% of the customers who do not turn in tickets will turn in one or more tickets the following week. Find and interpret the steady matrix for this situation.
Given statement solution is :- Interpreting the steady matrix:
The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.
The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.
The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.
To analyze the steady matrix for this situation, let's consider the two groups of customers: those who turn in tickets and those who do not turn in tickets.
Let's denote the proportion of customers who turn in tickets as X and the proportion of customers who do not turn in tickets as Y.
According to the given information:
40% of the customers who turn in tickets do not turn in tickets the following week. This means that 60% of the customers who turn in tickets will turn in tickets again the following week.
30% of the customers who do not turn in tickets will turn in tickets the following week. This means that 70% of the customers who do not turn in tickets will continue not turning in tickets the following week.
Based on these percentages, we can construct the steady matrix:
java
Copy code
| Customers turning in tickets (X) | Customers not turning in tickets (Y) |
----------|----------------------------------|--------------------------------------|
Next week 0.6 0.3
This week 0.4 0.7
Interpreting the steady matrix:
The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.
The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.
The value 0.4 in the bottom left cell represents the proportion of customers who do not turn in tickets this week but will turn in tickets next week.
The value 0.7 in the bottom right cell represents the proportion of customers who do not turn in tickets this week and will continue not turning in tickets next week.
These values describe the transition probabilities between the two customer groups. For example, if there are 100 customers in total, 60 of them will turn in tickets next week, and 40 of them will not. Similarly, 30 customers who turn in tickets this week will not do so next week, while 70 customers who do not turn in tickets this week will continue to not turn them in next week.
The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.
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Help pleasee!!!!!!!!
Answer:
35
Step-by-step explanation:
Since two lines are parallel ,
By Thales Theorem ,
=> 3x - 5/10 = (28-8)/8
=> 3x -5/10 = 20/8
=> 24x - 40 = 200
=> 24x = 240
=> x = 10
And ,
=> JK = 3x - 5 + 10 = 3x + 5
=> JK = 3 × 10 + 5 = 35
EXPONENTIAL FUNCTIONS HELP Write the function for each graph described below. the graph of f(x) = 2x reflected across the x-axis. The graph of f(x)= 1/3x translated up 5 units. The graph of f(x) = 3x left 2 units, and down 3. The graph of f(x) = 1/2x translated down 2 units. The graph of f(x) = 4x stretched horizontally by a factor of 3. The graph of f(x) = 2x up 4 units, right 3.
Answer:
-2^x(1/3)^x +53^(x +2) -3(1/2)^x -24^(x/3)2^(x -3) +4Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
Answer:
-2^x
(1/3)^x +5
3^(x +2) -3
(1/2)^x -2
4^(x/3)
2^(x -3) +4
Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
find the area of circle plz help will be much appreciated thanks
Answer:
Is there an option for 201.06 cm2
Answer:
201 cm
Step-by-step explanation:
rogress: The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer A motor oil retailer needs to fill 50 one quart bottles, and he has two tanks: one that contains 12 gallons of oil and one that contains 2 gallons of oil. Which will he need to fill the bottles? The 2 gallon tank is enough. He will need both tanks. The 2 gallon tank is not enough, but the 12 gallon tank is enough. Question ID: 53297 Even both tanks will not be enough.
The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.
Find the solution ?The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.
A motor oil store has two tanks: one holds 12 gallons of oil, and the other holds 2 gallons of oil. In order to determine which tank will require to fill the bottles, the following computation must be done:
Quarts to gallons is 4 to 1.
1/4 x 60 = X
60/4 = X
15 = X
Since the motor oil vendor requires 15 gallons of oil, he must use both tanks but will still be short by 1 gallons
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The percentage of people accessing the internet increased from 61% in 2000 to 83% in 2012 whats the absolute change in percentage points
Answer: i think the answer is 22% im not sure though
Step-by-step explanation:
but the absolute value means the whole value so just subtract 61% from 83% and that would be 22%. i hope this helps
Find m2ABC.
Ad
37°
21°
B
m/ABC =
C
Answer:
it might be 58 , just look it up I don't really know