\(k = -6\)
Step-by-step explanation:According to the Remainder Theorem, if we divide a polynomial, \(P(x)\), by \(x -\blue a\), the remainder is \(P(\blue a)\).
We can let \(P(x) = 2x^3 +3x^2 +kx +4\). If we want our remainder to be \(2(4 -k)\) when we divide \(P(x)\) by \(x -\blue 2\), then \(P(\blue 2) = 2(4 -k)\)
Solving for \(k\):
\(P(\blue 2) = 2(4 -k) \\ 2(\blue 2)^3 +3(\blue 2)^2 +k(\blue 2) +4 = 2(4 -k) \\ 2(8) +3(4) +2k +4 = 2(4 -k) \\ 16 +12 +2k +4 = 8 -2k \\ 32 +2k = 8 -2k \\ 32 +2k +2k = 8 \\ 32 +4k = 8 \\ 4k = 8 -32 \\ 4k = -24 \\ k = \frac{-24}{4} \\ k = -6\)
The value of \(k\) is \(-6\)
Answer:
\(k = -6\).
Step-by-step explanation:
Apply long division:
\(\begin{aligned}& \;\;\phantom{2\, x^{3} + } 2\, x^{2} + 7\, x + (k + 14)\\ & \, \begin{aligned} x - 2 & \\[-1.7em] & \overline{ \begin{aligned}\smash{)}& 2\, x^{3} + 3\, x^{2} + k\, x + 4 \\[-0.5em] & 2\, x^{3} - 14 \\ &\overline{\phantom{2\, x^{3} + }\begin{aligned} & 7\, x^{2} - k\, x \\[-0.5em] & 7\, x^{2} - 14\, x \\ & \overline{\begin{aligned} \phantom{7\, x^{2} \phantom{7\, x^{2}}} &(k + 14)\, x + 4 \\[-0.5em] & (k + 14)\, x- 2\, (k + 14) \\ & \overline{\phantom{(k
+ 14)\, x +}2\, k + 32\quad}\end{aligned}}\end{aligned}}\end{aligned}}\end{aligned}\end{aligned}\)
In other words:
\(\begin{aligned} & 2\, x^{3} + 3\, x^{2} + k\, x + 4 \\ =\; & (x - 2)\, (2\, x^{2} + 7\, x + (k + 14)) + (2\, k + 32)\end{aligned}\).
The remainder is \((2\, k + 32)\).
The question states that this remainder may also be expressed as \(2\, (4 - k)\). Equate these two expressions for the remainder and solve for \(k\):
\(2\, k + 32 = 2\, (4 - k)\).
\(k = -6\).
Substitute \(k = -6\) back into expand the expression \((x - 2)\, (2\, x^{2} + 7\, x + (k + 14)) + (2\, k + 32)\). Expand and verify that the expression indeed matches \((2\, x^{3} + 3\, x^{2} + k\, x + 4)\) with \(k = -6\!\).
\(\begin{aligned} & (x - 2)\, (2\, x^{2} + 7\, x + (k + 14)) + (2\, k + 32) \\ =\; &2\, x^{3} + 7\, x^{2} + 8\, x\\ &\quad\quad - 4\, x^{2} -14\, x - 16 + 20 \\ =\; & 2\, x^{3} + 3\, x^{2} - 6\, x + 4 \end{aligned}\).
a 5th degree polynomial with 3 terms?
Answer:
Hey there. Heres ur answer
Fifth degree polynomials are also known as quintic polynomials. Quintics have these characteristics:
One to five roots.
Zero to four extrema.
One to three inflection points.
I need help ASAP answer both questions please show work
Answer:
3. <BAC = <BCA
so,
x+x+36° = 180°
=>2x + 36 = 180
=>2x = 180–36
=>2x = 144
=>x = 144/2
=>x = 72°
Find the length of the third side. If necessary, round to the nearest tenth. 5 and 9
Answer:
is it a right triangle?
Step-by-step explanation:
Answer:
1. Is it a right triangle?
2. Are you looking for the hypotenuse?
Step-by-step explanation:
Write 23/4 as a mixed number. give your answer in its simplest form.
Answer:
Here is the ans...Hope it helps :)
What is the value of x
3√9+ x = 15
Answer: 6
Step-by-step explanation: .
Answer:
x=12.92
cube root of 9 Is 2.08 so you minus 15-2.08=12.92
HELP 80 POINTS
NOW PLEASE
The expression 3(x-9) is equivalent to 3(x)+9. 3(x)+3(9). 3(x) – 9. 3(x) – 3(9).
Answer:
Choice 2 and choice 1
Step-by-step explanation:
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
Suppose line l contains points A, B , and C , If A B=7 inches, A C=32 inches, and point B is between points A and C , what is the length of BC? Express your answer in inches.
Length of BC is 25 inches.
Here,
Line l contains points A, B and C.
A B =7 inches, A C = 32 inches, and point B is between points A and C.
We have to find the length of BC in inches.
What are Collinear points?
If two or more points are lie on a straight line then points are called Collinear points.
Now,
Line l contains points A, B and C.
Point B is between points A and C.
Length of A B = 7 inches and A C = 32 inches
Hence, Length of BC = Length of AC - Length of A B
= 32 - 7 = 25 inches.
Therefore, Length of BC is 25 inches.
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PLS HELP!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
isolate
2x = (3d + r - 2)
x = (3d + r - 2)/2
Lines a and b are perpendicular. Which statements below must be true? Select all that apply. The slopes of lines a and b are reciprocals Line a and line b intersect at their midpoints. When the slopes of lines a and b are multiplied, the product is −1. Line a and line b intersect to form four right angles. The slopes of lines a and b are equal. The slopes of lines a and b are opposites
Answer:
When the slopes of lines a and b are multiplied, the product is −1.
Line a and line b intersect to form four right angles.
Step-by-step explanation:
Given
Perpendicular lines a and b
Required
Select the true statements
Represent the slope of line a with \(m_1\) and the slope of b with \(m_2\).
The condition for perpendicularity is:
\(m_1 * m_2 = -1\)
Solving further:
\(m_1 = -\frac{1}{m_2}\)
To solve further, we need to analyze each of the given options
(a) This is not true because the slope of perpendicular lines are not reciprocal
(b) This is also not true because perpendicular lines do not necessarily have to intersect at their midpoints
(c) This is true because of the condition stated above: \(m_1 * m_2 = -1\)
(d) This is also true because perpendicular lines form right angles when they intersect
(e) This is not true because of the condition stated above: \(m_1 = -\frac{1}{m_2}\)
(f) This is not true because of the condition stated above: \(m_1 = -\frac{1}{m_2}\)
The product of the slope of the perpendicular lines is negative of one. Then the correct options are B and C.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Lines a and b are perpendicular.
Then the product of the slope of the perpendicular lines is negative of one. That is given as
\(\rm m_1*m_2 = -1\)
a. The slopes of lines a and b are reciprocals Line a and line b intersect at their midpoints. This is false.
b. When the slopes of lines a and b are multiplied, the product is −1. This is true.
c. Line a and line b intersect to form four right angles. This is true.
d. The slopes of lines a and b are equal. This is false.
e. The slopes of lines a and b are opposites. This is false.
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» Jim would like to buy a chest of drawers with an original price of $83.00. Which coupon should he use?$40.00 Off any chest of drawersor45% Off
ANSWER:
$40.00 Off any chest of drawers
STEP-BY-STEP EXPLANATION:
The original price is $83, we apply the 45% coupon, if the discount is greater than $40 it is the one we must use, if it is less, we must use the coupon for any chest of drawers.
Therefore:
\(\begin{gathered} d=83\cdot45\% \\ \\ d=83\cdot\frac{45}{100} \\ \\ d=\text{ \$}37.35 \end{gathered}\)The discount is equal to $37.35, therefore it is better to use the coupon for any chest of drawers since here you have a discount of $40
The correct answer is $40.00 Off any chest of drawers
A 40 feet table extends from the top of an electric tower to the ground. If the cable form 60° angle with the ground, how tall is the tower? Round to the nearest whole number
Answer:
Step-by-step explanation:
5 inches wide, and 2 inches thick. if you glue them together(stacked) what is ... If you glue the largest area faces together you will get the smallest overall ... The total surface area of one of the blocks is 2 times 250 square inches plus 2 times ... 720 times 3 is 2160 minus 4 times 250 is 2160 minus 1000 is 1160.
The height of the tower will be equal to 34.34 ft.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that a 40 feet table extends from the top of an electric tower to the ground. If the cable forms a 60° angle with the ground. The height of the tower will be calculated as,
sin60 = H / 40
H = 40 x sin60
H = 40 x 0.87
H = 34.64 ft
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Exercise 6.2.1: The probability of an event - coin flips. 0 About A fair coin is flipped n times. Give an expression for each of the probabilities below as a function of n. Simplify your final expression as much as possible. (a) At least n - 1 flips come up heads. Solution v (b) There are at least two consecutive flips that are the same.
(a) The probability that at least n-1 flips come up heads in n flips of a fair coin can be expressed as 1/2^(n-1). (b) The probability that there are at least two consecutive flips that are the same in n flips of a fair coin can be expressed as 1 - (1/2)^n.
(a) To calculate the probability that at least n-1 flips come up heads, we need to consider the complement event, which is the probability that fewer than n-1 flips come up heads. In a fair coin flip, the probability of getting heads or tails is 1/2. Therefore, the probability of getting fewer than n-1 heads in n flips is (1/2)^(n-1). Taking the complement, we get the probability that at least n-1 flips come up heads as 1 - (1/2)^(n-1). Simplifying further, we have 1/2^(n-1).
(b) To calculate the probability that there are at least two consecutive flips that are the same, we can consider the complement event, which is the probability that all flips have alternating outcomes (heads followed by tails or tails followed by heads). In each flip, the probability of getting a different outcome from the previous flip is 1/2. Therefore, the probability of having all flips with alternating outcomes is (1/2)^n. Taking the complement, we get the probability that there are at least two consecutive flips that are the same as 1 - (1/2)^n.
The probability that at least n-1 flips come up heads is 1/2^(n-1), and the probability that there are at least two consecutive flips that are the same is 1 - (1/2)^n.
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What is the product of 2x3 +9 and x3 +7?
The product of the expression is 2x⁶ + 23x³ + 63
How to determine the productFirst, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.
These algebraic expressions are also made up of mathematical operations, such as;
BracketAdditionMultiplicationDivisionParenthesesSubtractionFrom the information given, we have that;
2x3 +9 and x3 +7?
Then,
(2x³ + 9)(x³ + 7)
expand the bracket
2x⁶ + 14x³ + 9x³ + 63
add like terms
2x⁶ + 23x³ + 63
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given g(x) = f(x) + k identify a value of k that transforms f into g. f(x) = -x + 6 & g(x) = -x + 3
The value of k that transforms f into g is -3
How to determine the value of k in the transformation?The equations of the functions are given as
g(x) = f(x) + k
Also, we have
f(x) = -x + 6
g(x) = -x + 3
Substitute f(x) = -x + 6 and g(x) = -x + 3 in g(x) = f(x) + k
-x + 3 = -x + 6 + k
Evaluate the like terms
k = -3
Hence, the value of k is -3
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At the beginning of the Fall Semester in 2019, Ridgemont High School had a student population of 1,875 students. During the Christmas break, 77 students transferred to other schools and 6 students transferred to Ridgemont High School from other schools. As a result of these changes, by what percent did enrollment at Ridgemont High School decrease? Show your work.
Percentage decrease = 3.79%ercentage decrease = 3.79%
Explanation:Total number of students in 2019 = 1875
During christmas:
There was a decrease of 77 students
This means = 1875 - 77 = 1798 students left in the school
There was also n increase of 6= 1798 + 6
Total number of student remaining = 1804
Percent decrease = (decrease/original amount of student) × 100
Our Decrease will not be 77 because we are told there was an enrolment of 6 students
Decrease = number of students that left - number of new enrolment
Decrease = 77 - 6
Decrease = 71
\(\begin{gathered} \text{Percentage decrease = }\frac{71}{1875}\times100 \\ \text{Percentage decrease =0}.0379\times100\text{ } \\ \text{Percentage decrease =}3.79\text{ percent} \end{gathered}\)A sample of 3 observations, (X₁ = 0.4, X₂ = 0.7, X₃ = 0.9) is collected from a continuous distribution with density f (x) = θ x⁰⁻¹ for 0 < x < 1 Find the method of moments estimate of θ.
For a sample of 3 observations collected from continuous distribution with density \( f(x)= \theta x^{ \theta - 1}\) for 0 < x < 1, moments estimate of θ is equals to 1.5.
We have a sample of 3 observations,
\(X_1 = 0.4\)
\(X_2 = 0.7\)
\(X_3 = 0.9\)
Probability density function, \( f(x)= \theta x^{ \theta - 1}\), for 0 < x < 1.
Mean, \(\bar{X} = \frac{ 0.4 + 0.7 + 0.9}{3}\) = 0.6
In the method of moments one sets the sample moments equal to the population moments, and then solves for the parameters to be estimated. In this case there's only one such parameter and one uses only the first moment. Thus, \(E(X) = \int_{0}^{1} x f(x)dx\)
\(= \int_{0}^{1} x (\theta x^{\theta -1} )dx\)
\( =\int_{0}^{1} {\theta}x^{\theta}dx \)
\( = [{\theta } (\frac{x^{\theta + 1}}{\theta + 1})]_{0}^{1}\)
\( = \frac{\theta }{\theta + 1}\)
E(X) is nothing but Expected value which
equal to mean of X. So, \(\bar{X} = \frac{ \theta }{\theta+1}\). This means, \(\theta = \frac{\bar{X}}{ 1 -\bar{X}}\)
So, \(\theta = \frac{0.6 }{ 0.4} = 1.5\). Hence, \(\theta = 1.5\) is the estimate of by the method of moments.
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I NEED URGENT HELP WILL GIVE BRAINIEST!!!!
Answer:
21
Step-by-step explanation:
When two secant lines intersect, then the product of the length of the portion of each secant line outside the circle and the entire length of the secant line are equal for both lines. Thus, to find a missing value when two secant lines intersect, we apply the relationship stated above and solve for the missing value.
So FE x GE = DE x CE
since GE = FE + GF = 21 + 18 = 39
CE = DE + CD = 20 + CD
then
21 x 39 = 20 (20 + CD)
CD + 20 = 819/20
CD + 20 = 40.95
CD = 40.95 - 20 = 20.95 or 21
if EG = 23 and EF = 12, then FG=
If EG = 23 and EF = 12 then FG is equal to the length of 11.
Given that EG = 23 and EF = 12.
We are required to find the length of line segment FG.
We assume that EG and EF both are parts on a line.
A line segment is basically bounded by two distinct points on a line. Or we can say that a line segment is part of the line that connects two points. A line has no endpoints and extends to infinite points in both the direction but a line segment has two fixed or definite endpoints.
If EG=23 and EF=12 then, EG=EF+FG
FG=EG-EF
FG=23-12
FG=11
Hence if EG = 23 and EF = 12 then FG is equal to the length of 11.
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Which represents the inverse of the function f(x) = 4x
Answer:
f(x) = x/4
Step-by-step explanation:
To find the inverse of a function replace the positions of x and y. Then isolate y.
y = 4x
x = 4y
x/4 = y
f(x) = x/4
The clearinghouse and research center on servant leadership is now called a. The Center for Applied Ethics b. The Service and Leadership Center c. The Greenleaf Center for Servant Leadership d. The Center for Service and Ethical Behaviors
The clearinghouse and research middle on servant management is now called c. The Greenleaf Center for Servant Leadership.
The middle turned into named after Robert K. Greenleaf, who first brought the idea of servant leadership in his essay "The Servant as Leader" published in 1970. The Greenleaf Center for Servant Leadership serves as a worldwide useful resource for promoting the knowledge and exercise of servant leadership.
It conducts studies, provides educational applications, and gives a platform for individuals and businesses to study and interact with servant management ideas. The middle's recognition is on nurturing moral and compassionate management that prioritizes the nicely-being and growth of individuals and the groups they serve. Through its initiatives, the Greenleaf Center pursuits to inspire and empower leaders to create a superb and impactful exchange by embracing the servant management philosophy.
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The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership.
The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership. It is a nonprofit organization that was founded in 1964 by Robert K. Greenleaf. The center is dedicated to promoting the principles of servant leadership, which emphasizes serving others and putting their needs first.
The Greenleaf Center conducts research, provides resources and training, and serves as a hub for individuals and organizations interested in servant leadership.
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is 10\3 a improper fraction? Explain
Answer: Yes
Step-by-step explanation:
An improper fraction is any fraction that has a numerator that is greater than the denominator
what is the target domain for a poisson distribution?
The target domain for a Poisson distribution is given the term (0, inf) which can be seen correct in option B.
A Poisson distribution's target domain is (0, inf). This means that the Poisson distribution can only be specified for non-negative integer values of the random variable it is modelling.
The Poisson distribution is a discrete probability function, which indicates that the variable may only take particular values from a finite list of integers. A Poisson distribution estimates how many times an event will occur in "x" amount of time. In other words, it is the probability distribution resulting from the Poisson experiment.
A Poisson experiment is a statistical experiment that categorises the experiment as either successful or unsuccessful. A limiting process of the binomial distribution is the Poisson distribution.
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Complete question:
What is the target domain for a Poisson distribution?
1) (-inf, inf)
2) (0, inf)
3) (-inf, 0]
4) [0, inf)
validity coefficients greater than _________ are considered in the very high range.
When a validity coefficient exceeds 0.90, it is considered to be in the very high range.
Validity coefficients greater than 0.90 are considered in the very high range.
Validity coefficients measure the strength of the relationship between a test or measurement and the construct it is intended to assess. The coefficients range from -1.00 to +1.00, where higher values indicate stronger validity.
When a validity coefficient exceeds 0.90, it is considered to be in the very high range. This suggests that the test or measurement has a high degree of accuracy in assessing the intended construct, demonstrating a strong relationship between the two. Validity coefficients in this range provide strong evidence that the test is measuring what it is intended to measure.
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You live in a city at 60 ∘
N. How far above the horizon is the sun at noon on December 21 ? a. 6.5 ∘
b. 83.5 ∘
c. 30 ∘
d. 60 ∘
The correct answer is not provided in the given options. The sun would not be visible at noon on December 21 in a city at 60°N latitude.
The angle of the sun above the horizon at noon on December 21 depends on the latitude of your city. Since you mentioned that you live at 60°N, we can determine the angle using some knowledge about the tilt of the Earth and the seasons.
On December 21, the winter solstice, the Northern Hemisphere is tilted away from the sun. This means that the angle of the sun above the horizon at noon is lower than on other days of the year.
To calculate the angle, we need to subtract the latitude of your city (60°N) from the tilt of the Earth (23.5°).
So, the angle of the sun above the horizon at noon on December 21 in your city would be:
23.5° - 60° = -36.5°
The negative sign indicates that the sun is below the horizon at noon on December 21. Therefore, the correct answer is not provided in the given options. The sun would not be visible at noon on December 21 in a city at 60°N latitude.
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an inverted cone has a height of 11 inches and an initial radius of 18 inches. the volume of the inverted cone is decreasing at a rate of 541 cubic inches per second, with the height being held constant. what is the rate of change of the radius, in inches per second, when the radius is 5 inches?
Answer:
-4.697 in/s
Step-by-step explanation:
You want to know the rate of change of radius of a cone 11 inches high with a radius of 5 inches and a volume that is decreasing at the rate of 541 cubic inches per second.
VolumeThe volume of a cone is given by ...
V = π/3r²h
The rate of change is found by implicit differentiation:
V' = (π/3)((2rr')h +r²h')
Here, the height is constant, so h' = 0. Solving for r', we find ...
r' = 3V'/(2πrh)
ApplicationUsing the given values of V', r, and h, we find the rate of change of radius to be ...
r' = 3(-541 in³/s)/(2π(5 in)(11 in)) = -1623/(110π) in/s ≈ -4.69652 in/s
The radius is decreasing at about -4.697 inches per second.
__
Additional comment
The initial radius of the cone is irrelevant to the problem, since we want to know the rate of change at a specific different radius. Whether the cone is inverted or not is also irrelevant to its volume.
Question 2 121 Marks] A strut with a length of 10 m and an I cross-section with cross-sectional values of 610 x 229 x 113 (mm x mm x kg/mm), is treated as being fixed on both ends when it buckles about its weaker axis and pinned on both ends when it buckles about its stronger axis. If it's elastic modulus is equal to 210 GPa, its yield stress 260 MPa and the Rankine constant for a strut with both ends fixed as 1/6400, calculate using the Euler and Rankine formulae, the least buckling load for the strut and state which of these two formulae is best for this case.
the least buckling load for the strut is determined by Euler's formula, which predicts a larger buckling load than the Rankine formula for the same boundary conditions and material properties. Therefore, for this situation, Euler's formula is preferable as it gives a more conservative estimate.
According to the Euler formula, the least buckling load (Pcr) of a column can be computed as
\(Pcr = π²EI / L²\)
where Pcr is the critical or least buckling load, E is the modulus of elasticity, I is the moment of inertia of the column cross-section about its axis of buckling, and L is the length of the column.
The strut's I cross-section has cross-sectional values of 610 x 229 x 113 (mm x mm x kg/mm).
Its weaker axis is its Z axis (i.e., the axis perpendicular to the 610 mm face) and its stronger axis is its Y axis (i.e., the axis perpendicular to the 229 mm face).
As a result, the moment of inertia of the strut about its weaker axis can be computed as
IZ = (610 x 229³) / 12 - (533 x 113³) / 12 = 6.47 x 10¹⁰ mm⁴
And the moment of inertia of the strut about its stronger axis isIY = (229 x 610³) / 12 = 9.35 x 10⁸ mm⁴
When the strut is pinned on both ends and buckles about its stronger axis, it has a buckling factor of 1/2 (as opposed to 1 for a fixed-fixed end strut).
As a result, the Rankine constant for a column that is fixed at both ends is 1/6400, so the Rankine constant for a column that is pinned at both ends is 1/4 of that, or 1/25600.
Using the same values as before and the Rankine formula, the least buckling load for the strut when buckling about its weaker axis is:
Pcr,z = (π² x 210 x 6.47 x 10¹⁰) / (10²)² x (1/25600) = 0.357 MN (to three significant figures)
And the least buckling load for the strut when buckling about its stronger axis is
:Pcr,y = (π² x 210 x 9.35 x 10⁸) / (10²)² x (1/25600) = 25.5 kN (to three significant figures)
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#5 Kristen needs to earn $320 in commission this week. She earns 8% of
what she sells at the electronics store. How many dollars worth of
merchandise does she need to sell? Round to the nearest dollar. *
solve for z40=19+1/4z
To solve this equation for z, we can proceed as follows:
1. Subtract 19 from both sides of the equation:
\(40-19=19-19+\frac{1}{4}z\Rightarrow21=\frac{1}{4}z\)2. Multiply by 4 to both sides of the equation (Multiplication property of equality):
\(4\cdot21=4\cdot\frac{1}{4}z\Rightarrow84=\frac{4}{4}z\Rightarrow z=84\)Therefore, the value for z is equal to 84.
Which of the following describes the arrangement of network cabling between devices?
a. Logical topology
b. Networking technology
c. Physical topology
d. Media access method
Answer:
Physical means the actual wires. Physical is concerned with how the wires are connected. Logical is concerned with how they transmit.
a. Logical
Step-by-step explanation:
...
The arrangement of network cabling between devices is a physical topology. which is the correct answer would be option (C).
What is the Physical topology?The physical configuration of a network, such as the physical arrangement of wires, media (computers), or cables, is referred to as its topology. A link can connect two or more devices, and when the number of connections reaches two, they constitute a physical topology.
A physical network diagram depicts the connecting of devices via cables or wireless links. A logical network diagram, on the other hand, depicts data and signal transfer throughout a network.
Therefore, the arrangement of network cabling between devices is a physical topology.
Hence, the correct answer would be an option (C).
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An office manager buys 34 chairs for the new office. Each chair costs $205. What is the total amount the office manager pays for chairs? Enter your answer in the box. $_____________
Answer:
so each chair will cost 205
205 will be our cost C this is our dependent due to the entire cost being base on how many chairs that will get order
the independent variable will be how many chairs that will be ordered and there are 34 chairs being ordered
34*205= 6970
the total cost will be 6970