Ellie uses approximately 0.5625 yards or 9/16 of a yard of fabric for one doll dress, which can be useful in calculating the total cost of fabric required for a certain number of doll dresses.
Given that Ellie uses 27 lengths of fabric for 48 doll dresses, we can calculate the amount of fabric she uses for one dress by dividing the total yards of fabric by the number of dresses.
Dividing 27 by 48, we get 0.5625 yards, or approximately 9/16 of a yard, for one doll dress. This means that each dress requires a little more than half a yard of fabric.
This information can be useful in calculating the cost of fabric required to make a certain number of doll dresses. If we know the cost of fabric per yard, we can multiply it by the number of yards required to determine the total cost of fabric. In this case, if the cost of fabric is $5 per yard, the cost of fabric for one doll dress would be approximately $2.81.
In conclusion, Ellie uses approximately 0.5625 yards or 9/16 of a yard of fabric for one doll dress.
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nikolas is suspected of a crime and is asked to take a polygraph test. although he is innocent, what are the chances that he will be falsely accused?
The chances that Nikolas will be falsely accused in a polygraph test are dependent on the accuracy of the test and the criteria used to determine guilt or innocence.
Polygraph tests, also known as lie detector tests, are controversial and have varying degrees of accuracy. The accuracy of a polygraph test depends on many factors, including the expertise of the administrator, the type of test administered, and the physiological response of the individual being tested.
Furthermore, the criteria used to determine guilt or innocence based on the results of a polygraph test can vary. In some cases, a single inconclusive result may be enough to exonerate an individual, while in other cases, a single positive result may be enough to accuse an individual.
It is not possible to provide a specific numerical probability for the chances of Nikolas being falsely accused in a polygraph test.
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Question 5 (20 points)
The midpoint M and one endpoint of AB are given. Find the coordinates of the other endpoint.
A(-8,4) and M(5,-9).
a
(10,-22)
b
(18,-8)
c
(18,-22)
d
(6,-22)
Answer:
Let B be the other endpoint of AB.
We know that the midpoint M of AB has coordinates (5, -9), which means that the average of the x-coordinates of A and B is 5, and the average of the y-coordinates of A and B is -9:
( x_A + x_B ) / 2 = 5( y_A + y_B ) / 2 = -9Substituting the coordinates of point A (-8, 4), we can solve for the x-coordinate of point B:
( -8 + x_B ) / 2 = 5Simplifying the equation, we get:
-8 + x_B = 10x_B = 18Now, substituting the same coordinates of point A and the y-coordinate of midpoint M (-9), we can solve for the y-coordinate of point B:
( 4 + y_B ) / 2 = -9Simplifying the equation, we get:
4 + y_B = -18y_B = -22Therefore, the coordinates of point B are (18, -22).integers $a$, $b$, $c$, and $d$, not necessarily distinct, are chosen independently and at random from $0$ to $2007$, inclusive. what is the probability that $ad-bc$ is even?
If integers a, b, c, and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, the probability that ad-bc is even is 10/16.
To solve the problem, we need to consider the parity of the product ad and bc separately. If both ad and bc are even, then their difference (ad-bc) is even. If both ad and bc are odd, then their difference is even as well. However, if one of ad and bc is odd and the other is even, then their difference is odd.
For ad to be even, either a or d (or both) must be even. Similarly, for bc to be even, either b or c (or both) must be even. Therefore, the probability that ad and bc are both even is the product of the probabilities that a, b, c, and d are even:
P(ad even) = P(a even)P(d even) = (1004/2008)^2 = 1/4
P(bc even) = P(b even)P(c even) = (1004/2008)^2 = 1/4
The probability that ad-bc is even is the sum of the probabilities that both ad and bc are even and that both ad and bc are odd:
P(ad-bc even) = P(ad even and bc even) + P(ad odd and bc odd)
= P(ad even)P(bc even) + P(ad odd)P(bc odd)
= 1/4 * 1/4 + 3/4 * 3/4
= 1/16 + 9/16
= 10/16
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Graph the following features:
Y-intercept = −3
Slope = negative 2/5
The equation of equation according to the given unknown is [tex]y=-3x-\frac{2}{5}[/tex]
The edges that connect the graph's vertices (also known as nodes) are its vertices (lines). The use of the linear graph extends beyond mathematics into a variety of disciplines, including computer science, linguistics, biology, physics, and chemistry. The best example of a graph structure in real life is GPS, which allows you to follow a route or determine a road's direction.
The y-intercept is the point at which the graph crosses the y-axis. The most important step in graphing any function with the formula y = f(x) is finding the intercepts. For a function, an intercept can take one of two forms. What they are is what the x-intercept and y-intercept are. A function's "intercept" is the location where the axis is cut by the function's graph.
we have the equation y=mx+b
m is the slope and b is the y-intercept
[tex]y=-3x-\frac{2}{5}[/tex]
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Does anyone have the Unit: Functions homework 3 WRITING EQUATIONS OF LINEAR FUNCTIONS ???
The Equation of the linear function is y = 2x + 1.
Here's a step-by-step explanation using the terms you've provided:
1. Identify the slope (m) and y-intercept (b): In a linear function, the equation is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept.
2. Find the slope: If you're given two points on the line (x1, y1) and (x2, y2), you can find the slope by using the formula: m = (y2 - y1) / (x2 - x1).
3. Determine the y-intercept: If you know the slope and one point on the line (x, y), you can find the y-intercept by rearranging the equation: b = y - mx.
4. Write the equation: Once you have the slope and y-intercept, you can write the equation in the form y = mx + b.
For example, suppose you are given two points on a line: (1, 3) and (3, 7). To write the equation of the linear function:
Step 1: Find the slope (m):
m = (7 - 3) / (3 - 1) = 4 / 2 = 2
Step 2: Determine the y-intercept (b) using one of the points, say (1, 3):
b = 3 - (2 * 1) = 1
Step 3: Write the equation:
y = 2x + 1
So, the equation of the linear function is y = 2x + 1.
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un trabajador de la construccion empuja una carga de 60kg sobre el piso a lo largo de una distancia de 14 m aplicando una fuerza de 260 N, luego levanta la carga verticalmente hasta una plataforma que se encuentra a 1.2 m del piso. este trabajo lo realizo en un total de 3 minutos . ¿cual es el trabajo y la potencia total desarrollada por el trabajador?
The total work done by the worker is approximately 4346.32 J, and the power developed by the worker is approximately 24.14 W.
How to solve
To calculate the total work done by the worker, we need to consider both the horizontal pushing work and the vertical lifting work.
Horizontal pushing work:
Work (W) = Force (F) × Distance (d) × cos(θ)
where θ is the angle between the force and the displacement.
Since the force is applied horizontally and the displacement is also horizontal, the angle between them is 0 degrees, and cos(0) = 1.
W_horizontal = F × d × cos(0)W_horizontal = 260 N × 14 m × 1W_horizontal = 3640 J (joules)Vertical lifting work:
To calculate the work done in lifting the load vertically, we first need to find the force required to lift the load. The force required to lift the load is equal to the weight of the load:
Weight (Wt) = Mass (m) × Acceleration due to gravity (g)
where g ≈ 9.81 m/s² (approximately, on Earth's surface).
Wt = 60 kg × 9.81 m/s²
Wt ≈ 588.6 N
Now, we can calculate the work done in lifting the load:
W_vertical = Wt × h × cos(0)
where h is the vertical height.
W_vertical = 588.6 N × 1.2 m × 1
W_vertical ≈ 706.32 J
Now, we can find the total work done:
W_total = W_horizontal + W_verticalW_total = 3640 J + 706.32 JW_total ≈ 4346.32 J
Next, we'll calculate the power developed by the worker. Power is the rate of doing work, and it can be calculated as:
Power (P) = Work (W) / Time (t)
The worker does the work in 3 minutes, so we need to convert this time to seconds:
t = 3 min × 60 s/min = 180 s
Now, we can calculate the power:
P = W_total / t
P ≈ 4346.32 J / 180 s
P ≈ 24.14 W (watts)
So, the total work done by the worker is approximately 4346.32 J, and the power developed by the worker is approximately 24.14 W.
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The question in English is:
A construction worker pushes a 60-kg load across the floor a distance of 14 m by applying a force of 260 N, then lifts the load vertically to a platform that is 1.2 m above the floor. I do this work in a total of 3 minutes. What is the total work and power developed by the worker?
How many yards are there if there are 5 1/2 feet?
Answer:
1.83 yards
Step-by-step explanation:
which of the following statements about pearson's correlation coefficient is true? group of answer choices it cannot be used with a binary variable (those taking on a value of 0 or 1). it can be used as an effect size measure. it varies between 0 and 1. it can be used on ranked data.
The true statement regarding Pearson's correlation coefficient is that it can be used as an effect size measure.What is Pearson's correlation coefficient?Pearson's correlation coefficient is a statistic that measures the strength and direction of the linear relationship between two quantitative variables.
It is a measure of the linear correlation between two variables, which ranges from -1 to 1. Pearson's correlation coefficient can be used to examine the degree of relationship between two continuous variables.
When it comes to Pearson's correlation coefficient, the following statements are correct:It can be used as an effect size measure.It can be used on ranked data.It cannot be used with a binary variable (those taking on a value of 0 or 1).It varies between -1 and +1.
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What is the value of (7x)⁰
Answer:
the value of (7x)° is one because any thing power 0 is one
The answer of this question bc it showing me the answer is 4-9
Answer:
Your answer of 4¹⁸ is correct.
Step-by-step explanation:
In (4⁶)³ the exponents would be multiplied. 6 multiplied by 3 is 18 and therefore the correct answer would be 4¹⁸
Answer:
B. 4^18
Step-by-step explanation:
(4^6)= 4096
(4096)^3= 68,719,476,736
So, (4^6)^3= 68,719,476,736
AND
4^18= 68,719,476,736
Hope it helped! :)
Brainliest? Please.
what is the value of x?
Answer:
42
Step-by-step explanation:
evaluate each expressions when a=2and b=6. 7a-ab+b
if a regular polygon of 12 side with radius 4 units long is given, then its area is equal to
The area of the polygon with 12 sides is 48 square units.
Calculating the area of the polygonTo find the area of a regular polygon with 12 sides and a radius of 4 units, we can use the formula:
A = 12 * Area of 1 triangle
Where
Area of 1 triangle = 1/2 * radius * sin(360/n)
So, we have
Area of 1 triangle = 1/2 * 4^2 * sin(360/12)
Area of 1 triangle = 1/2 * 4^2 * sin(30)
Evaluate
Area of 1 triangle = 4
Substituting the given values, we get:
A = 12 * 4
Evaluate
Area = 48
So the area is 48 square units.
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of center for the data, and what is its value?
The median is the best measure of center, and it equals 3.5.
The median is the best measure of center, and it equals 3.
The mean is the best measure of center, and it equals 3.
The mean is the best measure of center, and it equals 3.5
The best measure of center for this data would be the median, as it is less affected by outliers and works well for skewed data. To find the median, we arrange the data in order: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5. There are 16 data points, so the median would be the average of the 8th and 9th values, which is 3.5. Therefore, the best measure of center for this data is the median, and its value is 3.5.
So the correct answer is: The median is the best measure of center, and it equals 3.5.
tank contains 80 kg of salt and 2000 l of water. a solution of a concentration 0.02 kg of salt per liter enters a tank at the rate 6 l/min. the solution is mixed and drains from the tank at the same rate. (a) what is the concentration of our solution in the tank initially? concentration
the initial concentration of the solution in the tank is 0.04 kg/L.
Tank contains 80 kg of salt and 2000 L of water. A solution of a concentration 0.02 kg of salt per liter enters a tank at the rate 6 L/min. The solution is mixed and drains from the tank at the same rate.
What is the concentration of our solution in the tank initially?
Initially, the tank contains 80 kg of salt and 2000 L of water. To determine the initial concentration of the solution in the tank, we need to use the following formula:
concentration = mass of solute / volume of solution
In this case, the mass of solute (salt) is 80 kg and the volume of solution is 2000 L. Therefore, the initial concentration of the solution in the tank is:concentration = 80 kg / 2000 L = 0.04 kg/L
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Ron said that he would spend $400 of his paycheck on nine items that costs $50 each. Why is this not reasonable? A. This is not reasonable because nine items at $50 each would cost $450. B. This is not reasonable because nine items at $50 each would cost $360. C. This is not reasonable because the nine items only cost $50. D. This is not reasonable because he would have too much money left over.
As Ron said he would spend $400 of his paycheck on these items, it is not reasonable because the total cost of the items is $450, which is $50 more than the amount he planned to spend. So, option A is correct.
As per given information,
Ron want to spend $400.
Ron wants to buy nine items that each cost $50.
To find the total cost of these items, we need to multiply the number of items by the cost of each item .
So,
Total cost of items = 9 x 50
Total cost of items = 450
This results in a total cost of $450.
This is not reasonable because nine items at $50 each would cost $450
Therefore, option A is correct.
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in 2015 there were about 22 million teenagers (ages 13-17) in the united states. they each sent an average of 900 text messages per month. About how many text messages did all of the teenagers in the united states send each month
express your answer in scientific notation
To express the ans in scientific notation is 1.98 x [tex]10^{10}[/tex] text messages per month.
How to calculate Average?You must add up all of the numbers in a set and divide the result by the total amount of numbers in order to determine the average of the set of numbers. The mean is another name for this.
The steps to calculating the average are as follows:
Sum up each of the set's numbers.
Count how many numbers there are in all.
subtract the total number of numbers from the sum of the numbers.
The average (mean) is calculated using the following formula:
Average equals ((Sum of Numbers)/ (Total Number of Numbers)
To calculate the total number of text messages sent by all teenagers in the United States in a month, we can multiply the number of teenagers by the average number of text messages sent by each teenager:
Total text messages = (number of teenagers) x (average number of text messages per teenager)
Total text messages = 22,000,000 x 900
Multiplying these numbers gives us:
Total text messages = √19,800,000,000
Total text messages = 140712.473 text messages per month.
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the number of fatal accidents that happen at a specific street crossing per year is represented by random variable x. f(x) is the probability mass function while f(x) is the cumulative distribution function. the correct calculation for the probability that there are more than 2 but less than 5 accidents is group of answer choices f(3) f(4) f(5) - f(2) f(5) - f(3) f(4) - f(3)
The correct answer is f(5) - f(2).
The probability of having more than 2 but less than 5 accidents can be calculated by subtracting the cumulative probability of having 2 or fewer accidents (represented by f(2)) from the cumulative probability of having 5 or fewer accidents (represented by f(5)).
We can calculate the probability of having exactly 3 accidents (represented by f(3)), the probability of having exactly 4 accidents (represented by f(4)), and then sum them up. Another valid answer is f(3) + f(4) - f(2).
Both approaches should yield the same result since they represent the same probability of having more than 2 but less than 5 accidents. It's important to note that the probability mass function (f(x)) represents the probability of a specific value of x occurring.
While the cumulative distribution function (F(x)) represents the probability of x being less than or equal to a specific value.
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A hyperbola centered at the origin has a vertex at (−6, 0) and a focus at (10, 0). which are the equations of the directrices? x = ± y = ± x = ± y = ±
The equations of the directrices are x = -3.6 and x = 3.6.
To find the equations of the directrices for a hyperbola, we need to first identify its major components.
Since the hyperbola is centered at the origin, its center is (0, 0). We are given a vertex at (-6, 0) and a focus at (10, 0).
1. Determine the value of a and c:
Since the vertex is at (-6, 0), the distance from the center to the vertex is |a| = 6.
Since the focus is at (10, 0), the distance from the center to the focus is c = 10.
2. Calculate the value of b using the relationship[tex]c^2 = a^2 + b^2:[/tex]
[tex]c^2 - a^2 = b^2[/tex]
[tex]10^2 - 6^2 = b^2[/tex]
[tex]10^2 - 6^2 = b^2[/tex]
[tex]100 - 36 = b^2[/tex]
[tex]64 = b^2[/tex]
b = 8
3. Find the distance from the center to the directrices (d) using the relationship [tex]d = a^2 / c[/tex]:
[tex]d = a^2 / c[/tex]
[tex]d = 6^2 / 10[/tex]
d = 36 / 10
d = 3.6
4. Determine the equations of the directrices:
Since the hyperbola is horizontal, the directrices will be vertical lines.
The directrices are located at a distance of d from the center, so their equations are x = ±d.
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Select all that are not polynomials.
Multiple select question.
cross out
A)
49x2 – 64
cross out
B)
−7xy+2y
cross out
C)
45y2+y – y3+8+x3
cross out
D)
-16
cross out
E)
3x−2+6x2
Answer:
B) −7xy+2y
E) 3x−2+6x^2
A local restaurant recently began to offer an eat-in pizza promotion for their famous double-decker pizza. When priced at $17.99/person, the promotion attracted 112 customers per day on average. When they raised the price to $19.99/person they attracted an average of only 96 customers per day.
What price should the promotion be set at to generate the maximum daily profit?
Answer:
the price that generates maximum profit is $152.94, rounded to the nearest cent.
Step-by-step explanation:
Let's begin by finding the profit generated by the promotion at each price point.
At $17.99/person:
Profit = Revenue - Cost
Profit = $17.99 x 112 - (10 + 5 + 3) x 112
Profit = $2016.64
At $19.99/person:
Profit = Revenue - Cost
Profit = $19.99 x 96 - (10 + 5 + 3) x 96
Profit = $1497.12
To find the price that generates maximum profit, we need to use the formula:
Price = (Fixed Cost + Variable Cost) / Number of Customers + Profit per Customer
We can assume that the fixed cost for the restaurant is $10,000 per day, and the variable cost per person is $5 for ingredients and $3 for labor.
For $17.99/person:
Price = ($10,000 + (5 + 3) x 112) / 112 + ($2016.64 - $17.99)
Price = $152.94
For $19.99/person:
Price = ($10,000 + (5 + 3) x 96) / 96 + ($1497.12 - $19.99)
Price = $156.24
Therefore, the price that generates maximum profit is $152.94, rounded to the nearest cent.
I need some help please
Joe D. Curios is exploring a river with a strong curent. He paddles upstream by day taking measurements and readings of water quality going 5 miles a day. He drops an anchor at night, but the current is so strong is still pushes his boat 3 miles downstream each night. His destination is the dam, which is 10 miles upstream from his starting point . If he starts his journey on june 1, when will he reach the dam?
CAN U PLEASE WRITE THE WHOLE EQUATION OUT ON A PIECE OF PAPER PLEASE>>>>>>>>
Joe will reach the dam on June 6, which is 5 days after he starts his journey on June 1.
What is distance?
Distance is the measure of how far apart two objects or locations are from each other.
Let's first calculate the net distance Joe travels each day:
Net distance = Distance paddled upstream - Distance pushed downstream by the current
Net distance = 5 miles - 3 miles
Net distance = 2 miles
This means that Joe moves 2 miles closer to the dam each day.
To reach the dam, Joe needs to cover a distance of 10 miles upstream from his starting point. Since he covers 2 miles per day, he will take:
Days taken to reach the dam = Distance to cover ÷ Distance covered each day
Days taken to reach the dam = 10 miles ÷ 2 miles per day
Days taken to reach the dam = 5 days
Therefore, Joe will reach the dam on June 6, which is 5 days after he starts his journey on June 1.
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HELP MEEEE PLEASE THANK UUU
The modal class of time spent exercising from the table that shows the time spent exercising, is 40 < x ≤ 50.
The class that the median lies is 30 < x ≤ 40.
How to find the modal and median class ?The modal class would be the one that has the highest frequency which is the class that has the most time spent exercising. That class is the 40 < x ≤ 50 class with 21 people.
The class in which the median lies is the middle class and we need to find the total first:
= 18 + 14 + 3 + 16 + 21 + 7
= 79 people
The median frequency is therefore:
= ( 79 + 1 ) / 2
= 40 th position
This is located in the 30 < x ≤ 40 class.
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The mass of a red blood cell is about 2.7 X 10−112.7 X 10 −11 grams. There are about 2.5 X 10132.5 X 10 13 red blood cell in a human body. What is the total mass, in grams, of the red blood cells in a human body? Express your answer in standard form
Answer:
6.75 x 10^2 g
Step-by-step explanation:
Mass of Red Blood Cells
The mass of a red blood cell is about 2.7 X 10−112.7 X 10 −11 grams. There are about 2.5 X 10132.5 X 10 13 red blood cell in a human body. What is the total mass, in grams, of the red blood cells in a human body? Express your answer in standard form
To find the total mass of red blood cells in a human body, we need to multiply the mass of one red blood cell by the total number of red blood cells in the body:
Total mass = (mass of one red blood cell) x (total number of red blood cells)
Total mass = (2.7 x 10^-11 grams) x (2.5 x 10^13 red blood cells)
Multiplying these two numbers gives:
Total mass = 6.75 x 10^2 grams
In standard form, this is:
Total mass = 6.75 x 10^2 g
does this situation represent a markov chain? explain. (b) set up the transition probability matrix and diagram. (c) determine the number of classes and classify them. (d) the first light is green. compute and interpret all probabilities after three more lights. (e) if kymere has many street lights between home and the university, what proportion of these lights are green, yellow, and red? [no technology estimations permitted. solve this problem with a system of equations showing every step and fraction answers only.]
The answer to the questions are as follows - a) Yes this situation represents a Markov chain. b)The matrix and diagram are shown below. c)There are two classes.d) the probabilities of the Markov chain being in the states "Green", "Yellow", and "Red" after three more lights are approximately 0.37, 0.33, and 0.3, respectively. e)The proportion of green lights is approximately 0.43, the proportion of yellow lights is approximately 0.19, and the proportion of red lights is approximately 0.29.
(a) Yes, this situation represents a Markov chain since it has the property of memorylessness, meaning that the probability of moving to a certain state in the future depends only on the current state and not on the past.
(b) The transition probability matrix for the Markov chain can be set up as follows:
P =
| 0.4 0.3 0.3 |
| 0.5 0.2 0.3 |
| 0.2 0.5 0.3 |
where the rows and columns correspond to the states "Green", "Yellow", and "Red", respectively, the diagram of the Markov chain is shown below:
(0.4) (0.3) (0.3)
Green -----> Yellow -----> Red
<----- (0.5) <----- (0.2) <----- (0.3)
(0.1) (0.3) (0.4)
(c) There are two classes in the Markov chain: {Green, Yellow} and {Red}. The first class is recurrent, while the second class is transient.
(d) The probability vector after three more lights can be computed by multiplying the initial probability vector [1 0 0] (since the first light is green) by the transition probability matrix three times. That is, we need to compute:
[1 0 0] * P * P * P
= [0.37 0.33 0.3]
Therefore, the probabilities of the Markov chain being in the states "Green", "Yellow", and "Red" after three more lights are approximately 0.37, 0.33, and 0.3, respectively.
(e) Let g, y, and r denote the proportions of green, yellow, and red lights. Then we have the following system of equations based on the transition probability matrix:
0.4g + 0.5y + 0.2r = g
0.3g + 0.2y + 0.5r = y
0.3g + 0.3y + 0.3r = r
Simplifying each equation, we get;
0.3g - 0.5y + 0.2r = 0
0.3g + 0.3y - 0.5r = 0
-0.3g + 0.2y + 0.3r = 0
Solving this system of equations using Gaussian elimination, we get:
g = (3/7)
y = (4/21)
r = (9/35)
Therefore, the proportion of green lights is approximately 0.43, the proportion of yellow lights is approximately 0.19, and the proportion of red lights is approximately 0.29.
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The complete question is given below-
There are three possible states for a traffic light: Green (G), Yellow (Y), and Red (R) and they simultaneously give the signal. a)Does this situation represent a Markov chain? explain. (b) set up the transition probability matrix and diagram. (c) determine the number of classes and classify them. (d) the first light is green. compute and interpret all probabilities after three more lights. (e) if kymere has many street lights between the home and the university, what proportion of these lights are green, yellow, and red? [no technology estimations permitted. solve this problem with a system of equations showing every step and fraction answers only.]
Which technique is most appropriate to use to solve each equation? Drag the name of the technique into the box to match each equation. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. x² + 4x = 15 2x(x−3)=0
We use factoring to solve the first Equation, x² + 4x = 15, and use the zero product property to solve the second equation, 2x(x−3)=0.
For the first equation, x² + 4x = 15, we can use the quadratic formula or completing the square technique to solve it. However, since the equation is already in standard form, we can use factoring to solve it. By rearranging the equation, we get x² + 4x - 15 = 0. This can be factored as (x + 5)(x - 3) = 0. Therefore, the solutions are x = -5 and x = 3.
For the second equation, 2x(x−3)=0, we can use the zero product property to solve it. This property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. Therefore, we have 2x = 0 or x - 3 = 0. Solving for x, we get x = 0 or x = 3. These are the solutions to the equation.
In summary, we use factoring to solve the first equation, x² + 4x = 15, and use the zero product property to solve the second equation, 2x(x−3)=0.
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Which is the correct order of the polynomial 7x3y3-3xy5+2x2y4-x4y2 in descending powers of x?
A.-x4y2+7x3y3+2x2y4-3xy5
B.-3xy5+2x2y4+7x3y3-x4y2
C.7x3y3-3xy5+2x2y4-x4y2
D.-x4y2+2x2y4-3xy5+7x3y3
The correct order of the polynomial [tex]7x^3y^3 - 3xy^5 + 2x^2y^4 - x^4y^2[/tex] in descending powers of x is:
[tex]-x^4y^2 + 7x^3y^3 + 2x^2y^4 - 3xy^5[/tex]
Therefore, the answer is option A.
What is polynomial function?
A polynomial function is a mathematical function that consists of a sum of terms, where each term is a constant multiplied by one or more variables raised to a non-negative integer power.
When we arrange a polynomial in descending order of powers of one of its variables, it means we are writing the terms with the highest power first, followed by terms with the next highest power, and so on until we reach the constant term (which has no variable).
In this case, the polynomial is [tex]7x^3y^3-3xy^5+2x^2y^4-x^4y^2[/tex]. To write this in descending order of powers of x, we need to start with the term that has the highest power of x, which is [tex]-x^4y^2[/tex].
Then we write the term with the next highest power of x, which is [tex]7x^3y^3[/tex]. After that, we write the term with the next highest power of x, which is [tex]2x^2y^4[/tex]. Finally, we write the term with the lowest power of x, which is [tex]-3xy^5[/tex].
So the correct order of the polynomial in descending powers of x is option A: [tex]-x^4y^2+7x^3y^3+2x^2y^4-3xy^5[/tex].
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what is the probability of rolling a value higher than eight with a pair of fair dice? question 15 options: 6/36 18/36 10/36 8/36 12/36
Explanation:
We want a dice sum larger than 8. Meaning we want the sum to be either: 9, 10, 11, or 12
Here are the four ways to add to 9
3 + 6 = 9
4 + 5 = 9
5 + 4 = 9
6 + 3 = 9
Here are the three ways to add to 10
4 + 6 = 10
5 + 5 = 10
6 + 4 = 10
and here are the two ways to add to 11
5 + 6 = 11
6 + 5 = 11
and finally there's only one way to get a sum of 12
6 + 6 = 12
There are 4+3+2+1 = 10 different sums we want out of 6*6 = 36 dice rolls possible.
That's how we get to 10/36 as the final answer.
10/36 reduces to 5/18, but it appears your teacher decided not to reduce.
The correct option is D.
The probability of rolling a value higher than eight with a pair of fair dice is 4/36 or 1/9.What is the probability of rolling a value higher than eight with a pair of fair dice?To find the probability of rolling a value higher than eight with a pair of fair dice, you have to find the number of ways to get a sum greater than 8 and divide it by the total number of possible outcomes when rolling two dice.The maximum sum that can be obtained by rolling two dice is 12 (6 + 6). So, we need to find the number of ways that we can obtain 9, 10, 11, or 12. The possible combinations are:(3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), and (6,6).Therefore, there are 10 possible outcomes in which the sum of the two dice is greater than 8. The total number of possible outcomes when rolling two dice is 6 × 6 = 36.So, the probability of rolling a value higher than eight with a pair of fair dice is:10/36 = 5/18 or approximately 0.277 or 27.7%.
Therefore the correct answer is option D ) 8/36.
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Find the area of the Trapezoid
6.7 km
13.6 km
5.2 km
6.4 km
6 km
please explain I'll mark brainlisest
I hope the solution helps you.
Factorise using identities
Having factorized using identities, the result is [(a^2c + b^2a + c^2b)/(abc)][(a^2 + b^2 + c^2 - a^2b^2c^2)/(a^2b^2c^2)]
What is the explanation for the above response?One possible approach to factorizing the expression is to use the identity:
a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc)
If we let a = b/c, b = c/a, and c = a/b, then we can substitute these expressions into the identity and simplify:
(a/b)^3 + (b/c)^3 + (c/a)^3 - 3abc/a^3b^3c^3
= [(a/b) + (b/c) + (c/a)][(a/b)^2 + (b/c)^2 + (c/a)^2 - (a/b)(b/c) - (a/b)(c/a) - (b/c)(c/a)]
= [(a^2c + b^2a + c^2b)/(abc)][(a^2 + b^2 + c^2)/(a^2b^2c^2) - 1]
= [(a^2c + b^2a + c^2b)/(abc)][(a^2 + b^2 + c^2 - a^2b^2c^2)/(a^2b^2c^2)]
Therefore, the factorization of the given expression is:
(a/b)^3 + (b/c)^3 + (c/a)^3 - 3 = [(a^2c + b^2a + c^2b)/(abc)][(a^2 + b^2 + c^2 - a^2b^2c^2)/(a^2b^2c^2)]
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