True - the statement says that a basic variable corresponds to a pivot column in the coefficient matrix. From the definition of basic variables, basic variables correspond to the columns that have a leading 1's (pivot columns).
A mathematical system model based on the use of a linear operator is known as a "linear system" in systems theory. In contrast to nonlinear cases, linear systems often display considerably simpler traits and attributes.
In linear systems, the variables are really only multiplied with constants and then added together; they are never multiplied by each other. In order to express both static and dynamic relationships between variables, linear systems are used.
Something relating to a line is linear. To build a line, all of the linear equations are used. Any equation that doesn't result in a straight line is considered as non. It has a variable slope value and appears as a curve on a graph.
A linear system is one in which both the superposition and homogeneity principles hold true.
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the value of the expression\[(2^{1004} 5^{1005})^2-(2^{1004}-5^{1005})^2\]is $k\cdot10^{1004}$ for some positive integer $k$. what is $k$?
The value of K is 20
The LHS (Left Hand Side) reduces to 2 x 10^1005
2 x 10^1005 =k x 10^1004
k =[2 x10^1005] / [10^1004] = 2 x 10
k =20
A positive integer is defined as a whole number greater than zero. All counting numbers are included in the set of positive integers.
Positive numbers include: 1, 2, 88, 800, 9000, and so on. Positive numbers are whole numbers with the symbol (+) in front of the numerical value. Most of the time, the plus sign is simply represented without the symbol. Positive numbers outnumber negative numbers and zero. On the number line, positive numbers are represented to the right of zero
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Simplify each expression
2x+8x+4x.
7(3x)
8y+4x+6y
4(7x+5y)
Answer:
1. 12x
2. 21x
3. 14y+6x
4. 28x+20y
Step-by-step explanation:
Find the total amount and total interest after forty years if the interest is compounded every twenty years.
Principal = ₹50{,}000=₹50,000equals, ₹, 50, comma, 000
Rate of interest = 0. 5 \%=0. 5%equals, 0, point, 5, percent per annum
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\mathbb{R}50000\\ r=rate\to 0.5\%\to \frac{0.5}{100}\dotfill &0.005\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &20 \end{cases}[/tex]
[tex]A = 50000\left(1+\frac{0.005}{1}\right)^{1\cdot 20}\implies A=50000(1.005)^{20} \implies \boxed{A \approx 55244.78} \\\\\\ 55244.78~~ - ~~50000 ~~ \approx ~~ \stackrel{earned~interest}{\boxed{5244.78}}[/tex]
A closet in the shape of a rectangular prism has the measurements shown. What is the height of the closet, in feet, if its volume is 220 ft3?
What are all real and complex roots of the following functions?
The volume can be calculated by simply multiplying the base's area by its height. The prism's two sides should be measured using the same units. To get cubic feet, it is ideal to measure in feet.
The cubic feet of a rectangular prism can be calculated in what way?The volume can be calculated by simply multiplying the base's area by its height. The prism's two sides should be measured using the same units. To get cubic feet, it is ideal to measure in feet.The base's area multiplied by the height gives the rectangular prism its volume. Using cubic units, the volume of a rectangular prism is equal to Length x Width x Height.The volume can be calculated by simply multiplying the base's area by its height. The prism's two sides should be measured using the same units. To get cubic feet, it is ideal to measure in feet.To learn more about rectangular prism refer to:
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The height of the rectangular prism is 8 ft.
What formula can be used to determine the cubic feet of a rectangular prism?The base's area and height alone can be used to determine the volume. The two sides of the prism should be measured in the same units. It's best to measure in feet to get cubic feet.
The rectangular prism's volume is equal to the base's area times the height. Length x Width x Height, in cubic units, equals the volume of a rectangular prism.
The base's area and height alone can be used to determine the volume. The two sides of the prism should be measured in the same units. It's best to measure in feet to get cubic feet.
Given the volume rectangular prism = 220 ft²
(x - 5.5)(x + 3)(x) = 220 ft²
(x - 5.5)(x + 3)(x) = 220 ft²
x³ −2.5x² −16.5x = 220
x = 8
Thus, the height of the rectangular prism is 8 ft.
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The least-squares regression model y =−3. 4+5. 2x and correlation coefficient r=−0. 66 were calculated for a set of bivariate data with variables x and y. What is closest to the proportion of the variation in y that cannot be explained by the explanatory variable?
The proportion of variation that the regression line can account for is indicated by the coefficient of determination.
56.44% of the variation cannot be explained by the provided regression line. The correlation coefficient for the question is R = - 0.66.
From the provided R value, the Coefficient of determination, R2, can be calculated.
R2 = - 0.662 = 0.4356.
This implies that, the percentage of variation that can be explained is equal to (0.4356) x 100%, or 43.56%.
100% - 43.566% = 56.446% is the percentage of variation that cannot be explained.
As a result, 56.44% of the variation in y cannot be explained.
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One morning Sam cycles 5 km in 20 minutes and Dwight cycles 6 km in 30 minutes. Determine who cycles faster?
Speed is calculated by dividing distance by time. Here Sam is cycling at a speed of 15 km/h and Dwight at a speed of 12km/h. So Sam cycles faster.
Speed is the rate of change in distance. so it is calculated using distance/time. Here the distance is in km and time is in minutes. The unit of distance is either m/s or km/h. So we have to do conversions first.
Lets convert the minutes to hours.
Sam cycles for 20 minutes. So 20 min = 20/60 h = 0.33 h
Dwight cycles 30 minutes. So 30 min = 30/60 h = 0.5 h
Now lets calculate the speed.
Speed Sam cycles = 5 km/ 0.33 h = 15 km/h
Speed Dwight cycles = 6 km/0.5 h = 12 km/h.
So Sam is faster than Dwight.
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The average annual income for five alepeople lat year wa $35,516Four of the alepeople earned thee annual amount: $36,230, 34,500 38,250, and $33,000What wa the annual income of the fifth aleperon?
The answer to the question can be calculated by using the average formula.
The average of a set of numbers is calculated by adding all of the numbers together and dividing the sum by the number of numbers in the set. In this case, the five alepeople earned a total of $176,506, and when divided by 5, the average annual income comes to $35,516.
To calculate the fifth aleperson's income, we subtract the income of the first four alepeople from the total income earned, $176,506. Subtracting the income of the first four alepeople, $36,230 + $34,500 + $38,250 + $33,000, gives us a remaining total of $24,026. When we divide this remaining total by 1, the average annual income for the fifth aleperson comes to $24,026.
Therefore, the fifth aleperson earned an annual income of $24,026. This can be expressed using the formula (total income – (income of aleperson 1 + income of aleperson 2 + income of aleperson 3 + income of aleperson 4)) / number of alepeople = income of fifth aleperson. In this case, (176,506 – (36,230 + 34,500 + 38,250 + 33,000)) / 1 = 24,026.
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Kylie invested $2,800 in an account paying an interest rate of 5 1/2% compounded annually. Ariana invested $2,800 in an account paying an interest rate of 5 3/4% compounded continuously. After 12 years, how much more money would Ariana have in her account than Kylie, to the nearest dollar?
If Kylie invested $2800 for interest rate of 5(1/2)% compounded annually and Ariana invested $2800 at rate of 5(3/4)% compounded continuously , then after 12 yrs Ariana would have $259.023 more than Kylie.
We have to find the difference in amount of money in the Kylie and Ariana's accounts after 12 years, we need to calculate the value of each investment after 12 years .
For Kylie's investment:
The formula for calculating the future value of a sum invested at a interest rate compounded annually is:
Value = Principle × (1 + r)ⁿ
Where:
Amount invested (P) = 2800 ;
r = interest rate = 5(1/2)% = 11/2% = 5.5% = 0.055 ;
n (time) = 12 years
⇒ Value = $2800 × (1 + 0.055)¹²
= $2800 ×(1.055)¹²
= $5323.38 .
For Ariana's Investment , the rate is compounded continuously ;
the future value can be calculated by using exponential function ;
Value = 2800 × e^(rt) ;
Where: initial investment = 2800 ;
r = interest rate = 5(3/4)% = 23/4% = 5.75% = 0.0575 and
n (time) = 12 ;
⇒ Value = $2800 × e^(0.0575×12)
= $5582.403 .
Therefore , After 12 years Ariana would have $5582.403 and Kylie would have $5323.38, Ariana would have $259.023 more than Kylie.
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Find the x-intercept of each line defined below and compare their values.
Equation of Line A:
x+y = 3
Select values from Line B:
X
0
1
2
3
Y
3
2
1
0
and the x-intercept of Line B is
The x-intercept of Line A is
Therefore the x-intercept of Line A is
the x-intercept of Line B.
If an equation isn't in the y is mx + b form, we can still find the intercepts by substituting 0 where necessary and solving for the remaining variable.
Using an equation, how do you determine a line's x-intercept?When y = 0, we solve the equation for x to determine the x-intercept. The line crosses the x-axis at y=0, explaining this. If an equation isn't in the y = mx + b form, we can still find the intercepts by substituting 0 where necessary and solving for the remaining variable.
With x = 0, solve for y to determine the y-intercept.
Utilizing the given points, determine the slope.
In the expression for the line, y = mx + c, include the slope's value.
Now solve the equation y = mx + c to determine the value of c using the values of any of the supplied locations.
Place y = 0 in y = mx + c to determine the x-intercept.
Place x = 0 in y = mx + c to determine the y-intercept.
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The main beam to a circus tent is 75 feet tall and is supported by 120 foot wires that extend to the ground. To the nearest degree, what is the angle that is created from the wire and the ground?
The angle that is created from the wire and the ground is 39°
Now, According to the question:
The main beam to a circus tent is 75 feet tall and is supported by 120 foot wires that extend to the ground.
We have to find the angle that is created from the wire and the ground.
Based on the given condition:
Using the definition of the sine function, we have that
[tex]sin(a) = \frac{75}{120}[/tex]
then, we can take inverse sine in both sides of the equality to clear a
a = [tex]sin^-^1\frac{75}{120}[/tex]
a = 38.68218745
and rounding to the nearest degree, the answer will be 39 degrees.
a = 39°
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Learn with an example
or Watch a video
Write a system of equations to describe the situation below, solve using substitution, and fill
in the blanks.
Peter works in the shipping department of a toy factory that makes radio-controlled
helicopters. Small helicopters weigh 3 pounds each, and are shipped in a container that
weighs 14 pounds. Large ones, on the other hand, weigh 4 pounds apiece, and are shipped in
a container that weighs 13 pounds. If these boxes can hold a certain number of helicopters
each, all of the packed containers will have the same shipping weight. What would the total
weight be? How many helicopters would fit in either container?
Helicopters would fit in either container is 1 and total weight is 4 pound.
What is Linear system of inequality?
At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.
With the exception of the inequality symbol, a linear inequality is nearly identical to a linear equation.
Three basic categories of economic disparity exist:
Income disparity the degree to which income is distributed unequally among a group of people is known as income inequality.Pay Inequality. Income. The pay of an individual differs from their income. Pay simply relates to money received from employment inequality of wealth.Let 'x' represent the number of helicopters per box.
3x+14=4x+13
We move all terms to the left:
3x+14-(4x+13)=0
We get rid of parentheses
3x-4x-13+14=0
We add all the numbers together, and all the variables
-1x+1=0
We move all terms containing x to the left, all other terms to the right
-x=-1
x=-1/-1
x=1
Hence, Helicopters would fit in either container is 1 and total weight is 4 pound.
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9,
The volume of a sphere can be calculated using the formula V=²³, where r is the radius of the sphere.
43
Given that a sphere has a radius of 2 cm, calculate its volume correct to two decimal places.
V= Enter your next step here
cm³
Answer: v = 33.51 cm^3
Step-by-step explanation:
Plug in radius to equation
V = 4/3 * π * 2^3
V = 4/3 * 8 * π
v = 33.51
pls solve this question for me
The exponential function that represents the table that is given will be A. f(x) = 6(2)^x.
When when x is 6, the value of the function will be A. 384.
How to calculate the function?It should be noted that in Mathematics, the function simply shows the relationship between the variables that are given.
Based on the table, the exponential function that represents the table that is given will be A. f(x) = 6(2)^x.
In this case, when x is 6, the value of the function will be:
= 6 × 2^x
= 6 × 2^6
= 6 × 64
= 384
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which value of X is the solution of the equation 2X = X +5 
Answer: To solve the equation 2X = X + 5, we can start by isolating X on one side of the equation by subtracting X from both sides:
2X - X = X + 5 - X
X = 5
Therefore, X = 5 is the solution of the equation 2X = X + 5.
Step-by-step explanation:
The solution for x in the equation 2x = x + 5 is obtained by isolating the variable x, leading to the answer x = 5.
Explanation:To solve for x in the equation 2x = x + 5, you need to isolate x. Start by subtracting x from both sides of the equation to get 2x - x = x + 5 - x which simplifies to x = 5.
The procedure used here is a standard method in algebra known as isolating the variable. This means the objective is to get the variable (x in this case) alone on one side of the equation.
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Complete the following probability distribution table:
Probability Distribution Table
X P(X)
−
19
0. 3
−
17
0. 2
−
16
55
0. 2
0.3 is the value of Probability Distribution Table X P(X)
Now, According to the question:
The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.
Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.
So here to find the value of the probability of X corresponding to the value 16 we should use the following steps:
Sum of given probabilities = (0.3+ 0.2 + 0.2) = 0.7
Required probability = 1 - sum of given probabilities = 1 - 0.7 = 0.3
Hence the complete probability table is:
X P(X)
19 0.3
17 0.2
16 0.3
55 0.2
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Write a system of equations.. Taxi company #1 charges a fee of $10 plus $2,50 per mile, Taxi company #2 charges $4.00 per mile with no fee.
HELP
Using Linear equations, the two equations of the given data are $10 + $250x and $4x
A linear equation example is what?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Using linear Equations,
Let x be the miles covered,
Taxi company 1 charges = $10 + $250x
Taxi company 2 changes = $4x
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Please help It's due today....There are two questions
The area of figures 1 and 2 will be 438 square yards and 110 square inches, respectively
What is the area?The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
1. The area of figure 1 is given as,
A = Sum of area of (Trapezoid + Rectangle + Rectangle)
A = 1/2 x (6 + 8) x 10 + 8 x 36 + 10 x 8
A = 70 + 288 + 80
A = 438 square yd
2. The area of figure 2 is given as,
A = Area of a triangle - Area of a rectangle
A = 1/2 x (8 + 7) x (10 + 14) - 7 x 10
A = 180 - 70
A = 110 square inches
The area of figures 1 and 2 will be 438 square yards and 110 square inches, respectively
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A jar contains 22 yellow, 26 green, 17 red, and 20 purple marbles. A marble is drawn at random. Find P(not purple)
The probability of not finding purple jar is 0.8.
Firstly we will find the probability of drawing purple marble. The formula to be used for this is -
Probability = number of favourable outcomes ÷ total number of outcomes
Number of favourable outcomes = number of purple marbles
Total number of outcomes = sum of the number of marbles
Total number of outcomes = 22 + 26 + 17 + 20
Performing addition
Total number of outcomes = 85
Probability = 20/85
Performing division
Probability = 0.2
Probability of not finding purple = 1 - probability of finding purple
Probability of not finding purple = 1 - 0.2
Performing subtraction
Probability of not finding purple = 0.8
Thus, the probability is 0.8.
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Jean wrote two correct variable expressions to represent the phrase "the quotient of a number and 3. "
Which variable expressions could Jean have written?
Select each correct answer.
3n
n ÷ 3
n3
13n
Option B is correct :- n ÷ 3
The given verbal expression is " the quotient of a number and 3."
We have to convert this verbal expression to algebraic expression.
The quotient of a number and 3, represents the division between an unknown number and the number 3.so the possible answer is n ÷ 3.
Here "Quotient" means "Division"
Let "n" be a number and it is divided by 3.
So,
we can write "the quotient of n and 3" as n÷3.
Algebraic expression
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations . Expressions are made up of terms.
Expression
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
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To find a two-digit number such that if the places of its digits are interchanged, a number will be obtained that is four and a half times greater than the given
1. Tom has a standard set of pool balls. If he were to draw one ball at random, what is the probability that it will be red or yellow? Give your answer in its simplest form. A 1/7 ???
2. If you throw a single die twice, what's the probability of first getting a 3 and then getting another odd number? A 4/6 simplified 2/3 ??
1. The probability of drawing a red or yellow ball from a standard set of pool balls is 4/7.
2. The probability of first getting a 3 and then getting another odd number is 1/12.
1. Tom has a standard set of pool balls, which includes 7 different colored balls: red, yellow, blue, purple, orange, green, and black. There are 2 red balls and 2 yellow balls out of 7 total balls.
To find the probability of drawing a red or yellow ball, we will add the probabilities of drawing each color separately.
Probability of drawing a red ball = 2/7
Probability of drawing a yellow ball = 2/7
Probability of drawing a red or yellow ball = (2/7) + (2/7) = 4/7
Hence, the probability of drawing a red or yellow ball is 4/7.
2. If a single die twice, the total possible outcomes are = 6x6 = 36.
To find the probability of getting a 3 on the first throw and then getting another odd number on the second throw, we have to find the number of outcomes that meet these conditions and then divide it by the total number of outcomes.
First throw: 3 (1 outcome)
Second throw: odd number (3, 5) (3 outcomes)
So there are a total of 1x3 = 3 outcomes that meet the given conditions.
Thus, Probability = 3/36 = 1/12
So, the probability of first getting a 3 and then getting another odd number is 1/12.
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PLS HELP 30 POINTS AND BRAINLIEST.......
ABC → A’B’C’ is a reflection. Use this to answer the questions below.
Triangle ABC is the preimage and triangle A'B'C' is the image. The equation for the line of reflection is x = 4.
What is Reflection?Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
(A) Pre image is the figure before reflection is done.
So the pre image is triangle ABC.
(B) Image is the reflected figure.
So the image is triangle A'B'C'.
(C) Coordinates of the output are :
A'(8, 9), B'(12, 4) and C'(8, 4)
(D) The line of the reflection is the parallel line to Y axis passing through 4 on the X axis.
So the equation is x = 4.
Hence triangles ABC and A'B'C' are preimage and image respectively. The coordinates for the output are A'(8, 9), B'(12, 4) and C'(8, 4).
The equation of the line of reflection is x = 4.
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HELPP PLEASE WILL GIVE BRAINLY
The American flag has 50 stars, 7 red stripes, and 6 white stripes. Write a ratio to represent the ratio of stars to red stripes.
7 to 50
6:50
50 to 7
50 over 63
Answer:
50 to 7
Step-by-step explanation:
number of stars to number of red stripes
all acceptable ways to represent ratios:
50 to 7
50 : 7
50 over 7
Which of the following inequalities matches the graph?
graph of an inequality with a dashed line through the points 0, 3 and 1, 9 with shading above the line
−6x + y < 3
6x + y < 3
6x − y < −3
The correct inequality is not listed
Answer: The correct inequality that matches the graph is 6x + y < 3.
This inequality can be graphed by plotting the points (0,3) and (1,9) as the boundary of the solution set, and shading the area above the line. The graph will be a line with a negative slope that pass through the points (0,3) and (1,9) and the shaded area will be above the line, which match the graph you have described.
We can check this by plugging the points (0,3) and (1,9) into the inequality to see if they satisfy it:
6(0) + 3 < 3 => 3 < 3 which is true
6(1) + 9 < 3 => 6 + 9 < 3 which is false
This confirms that the inequality 6x + y < 3 matches the graph.
Step-by-step explanation:
Write the cubic functions in factored form and standard form. Zeros: x = -3, x = 0, x = 1
The cubic function with the zeros x = -3, x = 0 and x = 1 is given as follows:
y = x³ + 2x² - 3x.
How to define the function?We are given the zeros of the function, hence the function is defined using the Factor Theorem, as a product of the linear factors of the function.
The zeros of the function are given as follows:
x = -3.x = 0.x = 1.Then the linear factors are given as follows:
(x + 3).x.(x - 1).Considering a leading coefficient of 1, the function is defined as follows:
y = x(x + 3)(x - 1)
y = x(x² + 2x - 3)
y = x³ + 2x² - 3x.
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how many radians does the minute hand of a clock move in 45 minutes please i need help asap i will give brainliest.
Answer:
B 3pi/2
Step-by-step explanation:
So half of a circle is pi therefore a quarter is pi/2.
So 15 mins is pi/2.
3 * pi/2 =45 mins
3pi/2 = 45 mins
Compare 689,323,148 and 689,423,148 using 100,000 more than or 100,000 less than
689,323,148 is 100,000 less than 689,423,148 in the given comparison.
How can I compare complete numbers the best way possible?Comparing the digit count is important. Indicating a larger number is the presence of additional digits. We should compare the highest place values, or the digit that is farthest to the left of the numbers, if the number of digits in both numbers is the same.
Compare the amount of digits. A higher number is indicated by more digits. The higher place values should be compared if the number of digits is the same. The next place value to the right should be compared if the digits at the highest place value are the same.
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The worked example showed how to solve an inequality of the form, y = ax + b. How does your method change when the inequality is in a different form?
if i was talking to a friend on a cell phone and i suddenly couldn't hear them because my phone ran out of battery power, what part of the mathematical model of communication would best explain this problem? scom 2050
The mathematical model of communication would classify this issue as channel capacity.
The greatest quantity of data that can be transferred error-free across a communication channel, such as a mobile phone network, is represented by the channel capacity. In this instance, the phone's battery power determines the channel capacity. As the battery depletes, the phone's ability to send and receive information declines, making it impossible to hear the person on the other end of the line.
Communication models are streamlined depictions of the communication process. Most models attempt to explain both verbal and nonverbal communication, and frequently regard it as a message-exchange. Their purpose is to provide a concise picture of the intricate communication process.
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What is the greatest possible length of a side of a triangle whose perimeter is 1000 and all of whose sides have integral lengths?
The greatest possible length of a side of a triangle whose perimeter is 1000 and all of whose sides have integral lengths is 400.
We have to determine the greatest possible length of a side of a triangle whose perimeter is 1000 and all of whose sides have integral lengths.
The sides of a triangle have lengths ratio 5:7:8.
The perimeter of triangle is the sum of all sides. So
5x + 7x + 8x = 1000
20x = 1000
Divide by 20 on side we get
x = 50
The length of all sides:
5x = 5 × 50 = 250
7x = 7 × 50 = 350
8x = 8 × 50 = 400
Hence, the greatest possible length of triangle is 400.
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The complete question is:
The sides of a triangle have lengths ratio 5:7:8. What is the greatest possible length of a side of a triangle whose perimeter is 1000 and all of whose sides have integral lengths?