A
Step-by-step explanation:
Find the solution set for this inequality, -2x + 4 > -4x + 8
Answer:
The answer is
x > 2Step-by-step explanation:
- 2x + 4 > - 4x + 8
Add 4x to both sides of the inequality
That's
- 2x + 4x + 4 > - 4x + 4x + 8
2x + 4 > 8
Subtract 4 from both sides
That's
2x + 4 - 4 > 8 - 4
2x > 4
Divide both sides by 2
That's
\( \frac{2x}{2} > \frac{4}{2} \)
We have the final answer as
x > 2Hope this helps you
what circulatory system structure do the check valves represent? what is their function in the circulatory system?
The check valves in the circulatory system represent the function of heart valves. Heart valves are the circulatory system structures that act as check valves.
Their main function is to ensure the unidirectional flow of blood through the heart and prevent backward flow or regurgitation. They open and close in response to pressure changes during the cardiac cycle to facilitate the proper flow of blood through the heart chambers and blood vessels. By opening and closing at the right time, heart valves help maintain the efficiency and effectiveness of blood circulation by preventing the backflow of blood and ensuring that blood moves forward through the heart and into the appropriate vessels.
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The budget for a middle school dance is $750. Food and decorations cost $175. The DJ charges $75 per hour plus a one-time business fee of $125?
What is the maximum number of hours the school can have the DJ play at the dance?
Answer:
The DJ can play at the dance for 6 Hours
Step-by-step explanation:
1. Add the decorations and food plus the additional fee of $12
$175+ $125= $300
2. Subtract the budget and the total so far
750-300= 450
3. Get the amount owed per hour to DJ and divide by the new budget
450/75= 6
The DJ can play at the dance for 6 hours
Have a good day!
Answer:
175+125-750/75.
Step-by-step explanation:
Graph the line that has a slope of 1/2 and includes the point (6,7)
Answer:
Graph (0,4), graph (6,7) then connect in a straight line.
Step-by-step explanation:
During fy 2020 bay manufacturing had total manufacturing costs are $428,000. their cost of goods manufactured for the year was $457,000. the january 1, 2021 balance of work-in-process inventory is $47,000. use this information to determine the dollar amount of the fy 2020 beginning work-in-process inventory. round to a whole number (no cents).
By substituting the given values, we can calculate the BWIP as $76,000. This represents the dollar amount of the WIP inventory at the start of the fiscal year 2020.
To determine the dollar amount of the FY 2020 beginning work-in-process (WIP) inventory, we can use the given information and apply the following equation:
Beginning WIP Inventory + Manufacturing Costs - Cost of Goods Manufactured = Ending WIP Inventory
Let's denote the beginning WIP Inventory as BWIP. Given the information:
Manufacturing Costs = $428,000
Cost of Goods Manufactured = $457,000
Ending WIP Inventory (January 1, 2021) = $47,000
Plugging in the values into the equation, we can solve for BWIP:
BWIP + $428,000 - $457,000 = $47,000
Rearranging the equation, we have:
BWIP = $47,000 - ($428,000 - $457,000)
= $47,000 - (-$29,000)
= $47,000 + $29,000
= $76,000
Therefore, the dollar amount of the FY 2020 beginning work-in-process inventory is $76,000.
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what affects the length, in hours, of a professional football game? data was gathered in order to determine the relationship between total number of penalty yards and the time required to complete a game, in hours, for a large random sample of football games. all of these games had between 35 and 150 penalty yards. to predict time required to complete the game based on penalty yards, the following regression equation was constructed: predicted time
The correct statement is: As the number of penalty yards increases by 1, we predict time to increase by 0.01 hours. (Option 3)
This is because the regression equation shows that for each additional penalty yard, the predicted time increases by 0.01 hour, as indicated by the coefficient of 0.01 in the equation. The correlation coefficient of 0.61 indicates a moderate positive linear relationship between time and penalty yards.
However, it would be an extrapolation to use the regression equation to predict the time of a football game with 50 penalty yards since this value falls outside the range of penalty yards used to construct the equation.
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Complete Question:
What affects the length, in hours, of a professional football game? Data was gathered in order to determine the relationship between total number of penalty yards and the time required to complete a game, in hours, for a large random sample of football games. All of these games had between 35 and 150 penalty yards. To predict time required to complete the game based on penalty yards, the following regression equation was constructed: Predicted time = 2.46 + 0.01 (penalty yards). The correlation between time and penalty yards is r = 0.61. Based on this information, which one of the following statements is correct?
Group of answer choices
It would be extrapolation to use the regression equation to predict the time of a football game with 50 penalty yards.As the length of the game increases by 1 hour, we predict number of penalty yards to increase by 2.46.As the number of penalty yards increases by 1, we predict time to increase by 0.01 hour.A game with 100 penalty yards is predicted to be 1 hour long.Approximately 61% of the variability in time can be explained by the regression equation.Find the zero places of the quadratic function: y= x^2 + 5x + 6
The required zero places of the given equation y= x² + 5x + 6 is x = -2 and x = -3.
Given that,
An equation y= x² + 5x + 6,
To determine the Zeros of the equation given above.
The equation is the relationship between variables and is represented as y =ax + b is an example of a polynomial equation.
Here, given equation is, y= x² + 5x + 6
Now, let y = 0
x² + 5x + 6 = 0
x² + 2x + 3x + 6 = 0
x(x + 2) + 3 (x + 2) = 0
(x + 2) * (x + 3) = 0
x + 2 = 0 ; x + 3 = 0
x = -2 and x = -3
Thus, the required zero places of the given equation y= x² + 5x + 6 is x = -2 and x = -3.
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2D and ZE are complementary. If m2D = 5x + 3and mZE = 3x - 1, what is x?
hello
the question presented before me seem incomplete due to lack of diagram to give a detailed expression
if 2D and ZE are complimentary, then the sum of both angles must be equal to 90 degrees
\(\begin{gathered} <2D\text{ = 5x }+\text{ 3} \\ solve the expression by finding x\(\begin{gathered} 3x\text{ }-\text{ 1 }+\text{ 5x }+\text{ 3 }=90^0 \\ 8x\text{ }+\text{ 2 }=\text{ 90} \\ 8x\text{ = 90 }-\text{ 2} \\ 8x\text{ }=\text{ 88} \\ \end{gathered}\)divide both sides of the equation by 8
\(\begin{gathered} \frac{8x}{8}\text{ }=\text{ }\frac{88}{8} \\ x\text{ }=11^0 \end{gathered}\)x = 11
ft. If the equation for height as a
function of time is
16t2+ initial height where t is time
onds and h(t) is height in feet, how
w seconds will it take for the pebble
to hit the ground?
It takes 7 seconds for the pebble to hit the ground, t is time and h(t) is height in feet.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given data;
Equation of height as a function of time;
\(\rm h(t) = 16 t^2\)
Height of cliff= 784 feet
Equate the data;
\(\rm 16 t^2 = 784\\\\\ t^2 = 49\\\\ t = 7 \ seconds\)
Hence, it takes 7 seconds for the pebble to hit the ground.
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Please help me its due soon! :(
Select all the correct answers.
Consider the graph of the function : f(x)=logx
Which are features of function g if g(x)= 4log(x)+4
The features of the function g(x) = 4log(x) + 4 are
(b) range (-∞, ∞)(d) x-intercept (0.1, 0)(e) Vertical asymptote, x = 0How to determine the features of g(x)?The function is given as;
g(x) = 4log(x) + 4
The intercept
A logarithmic function has no y-intercept.
Set g(x) to 0, to determine the x-intercept
4log(x) + 4 = 0
Divide through by 4
log(x) + 1 = 0
This gives
log(x) = -1
Take the inverse of both sides
x = 10^-1
Evaluate
x = 0.1
The x-intercept is (0.1, 0)
The vertical asymptote
Recall that:
A logarithmic function has no y-intercept.
This is so because it is undefined at x = 0
So, the vertical asymptote is x = 0
The domain and the range
A logarithmic function cannot take a negative input or 0 input
So, the domain is x > 0
However, the range is all set of real numbers i.e (-∞, ∞)
Hence, the features of g(x) are (b), (d) and (e)
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Jason has 75 feet of wallpaper border. He wants to put up a wallpaper border around his rectangular bedroom that measures 12 feet by 14 feet. He multiplies 12 x 14 = 168 to get an exact answer of how much border he needs. He concludes that he does not have enough border for the whole job.
7) Tell how you can critique Jason’s reasoning.
8) Critique Jason’s reasoning.
9) Jason uses an overestimate to decide how many rolls of wallpaper he needs for another room. Explain why his reasoning to use an overestimate does or does not make sense.
9514 1404 393
Answer:
7) compare what Jason needed to do with what he did
8) Jason used an incorrect formula to estimate his need
9) an overestimate ensures Jason can finish the job
Step-by-step explanation:
7) A critique is a comparison of what you have with what you expect. We can critique Jason's reasoning by comparing what he did with what we expected him to do. (We don't actually know his reasoning; we only know his action.)
__
8) Jason multiplied the dimensions of his room, an action appropriate to finding its area. We expected that Jason would use a formula for the perimeter of the room. We conclude that Jason chose the wrong formula for computing the length of border needed. We also note that Jason did not make any use of dimensional analysis. Had he done so, he would have known that his result was in square feet, not linear feet, so was not applicable to the question of whether he had enough border.
__
9) If Jason's goal is to finish his wallpaper job without making another trip to the store, he would want to make sure that he does not run short of wallpaper before the task is done. To ensure that he has enough, it makes sense that he would make an estimate that would give him more than enough.
Help me with this!!!!!
Answer: it would be y=-4x+2
Answer:
the second option (y= -4x + 2)
Step-by-step explanation:
i need help with problem #17 .
Answer:
hi tell me the answer pls
What Statement Represents 54=9 X 6
A. 54 is 9 more than 6
B. 54 is 9 times as many as 6
C. 54 is divided by 6
D. 54 is less than 6
Answer B
scajgvbcxns djavhgvdscjv
Find ℒ{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.)
f(t) = cos²(t)
The Laplace transform of f(t) = cos²(t) is:
ℒ{f(t)} = (1 + s²) / (2s(s² + 4)).
To find the Laplace transform of f(t) = cos²(t), we can use the trigonometric identity:
cos²(t) = 1/2 (1 + cos(2t))
Applying this identity, we have:
ℒ{f(t)} = ℒ{1/2 (1 + cos(2t))}
Using the linearity property of the Laplace transform, we can split the transform of the sum into the sum of the transforms:
ℒ{f(t)} = 1/2 ℒ{1} + 1/2 ℒ{cos(2t)}
Now, we need to find the Laplace transforms of the individual terms.
The Laplace transform of the constant term 1 is:
ℒ{1} = 1/s
The Laplace transform of cos(2t) can be found using the property:
ℒ{cos(at)} = s / (s² + a²)
For our case, a = 2, so we have:
ℒ{cos(2t)} = s / (s² + 2²)
= s / (s² + 4)
Putting it all together, we have:
ℒ{f(t)} = 1/2 ℒ{1} + 1/2 ℒ{cos(2t)}
= 1/2 * (1/s) + 1/2 * (s / (s² + 4))
= 1/2s + s / (2s² + 8)
= (1 + s²) / (2s(s² + 4))
Hence, the Laplace transform of f(t) = cos²(t) is:
ℒ{f(t)} = (1 + s²) / (2s(s² + 4)).
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Could someone help me with these please? I’m stuck.
Answer:
1. 23
2. 5.83 (5.8 rounded)
3. 1.18 (or 1.2 rounded)
4. unsure how to solve, sorry
Step-by-step explanation:
your formula: a^2+b^2=c^2
1. 20^2+13^2=c^2
400+169=569
(take the square root of 569)
c=23
2. 15^2+b^2=17^2
225+b^2=289
(subtract 225 from both sides)
b^2= 34
(take the square root of 34)
b=5.83 (or 5.8 rounded)
3. 0.2^2+b^2=1.2^2
0.04+b^2=1.44
(subtract 0.04 from bot sides)
b^2=1.4
(take the square root of 1.4)
b=1.18 (or 1.2 rounded)
4. unsure how to solve, sorry
How many unique triangles can be made when one angle measures 90° and another angle is half that measure? 1 2 More than 2 None
Answer:
1
Step-by-step explanation:
I'm not sure if I read your question right, but if one angle is 90 and the other should be half the angle 90, the other angle must be 45. Thus, this would create a 45-45-90 triangle. There is no other possibility if one of the angles must be half that of the 90 degree angle.
Answer:
1
Step-by-step explanation:
Circle E is inscribed with triangle B C D. LIne segment B D is a diameter. Line segments D C and C B are secants. Angle D B C is 51 degrees.
What is the measure of arc B C?
39°
78°
102°
129°
The measure of arc BC in circle E, inscribed in triangle BCD with angle DBC measuring 51 degrees, is 102°.
In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Since BD is a diameter, angle DBC is a right angle, and the intercepted arc BC is a semicircle. Therefore, the measure of arc BC is 180°.
However, we are given that angle DBC measures 51 degrees. In an inscribed triangle, the measure of an angle is equal to half the measure of its intercepted arc. So, angle DBC is half the measure of arc BC, which means arc BC measures 2 times angle DBC, or 2 * 51° = 102°.
Hence, the measure of arc BC is 102°.
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Inscribed circle E is formed by triangle BCD, with BD as the diameter. DC and CB are secants, and angle DBC is 51 degrees. We need to find the measure of arc BC.
When a triangle is inscribed in a circle, the measure of an angle formed by two secants that intersect on the circle is half the measure of the intercepted arc.
In this case, angle DBC is 51 degrees, which means the intercepted arc BC has twice that measure. Therefore, the measure of arc BC is 2×51=102 degrees.
To understand why this relationship holds, we can use the Inscribed Angle Theorem. According to this theorem, an angle formed by two chords or secants that intersect on a circle is equal in measure to half the measure of the intercepted arc.
In our scenario, angle DBC is formed by secants DC and CB, and it intersects the circle at arc BC. According to the Inscribed Angle Theorem, angle DBC is equal to half the measure of arc BC.
Hence, if angle DBC is 51 degrees, the measure of arc BC is twice that, which gives us 102 degrees.
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Quante’ had 15.3 feet of fishing line. He cut off a piece and had 3.2 inches left. How long was the piece he cut off?
Answer:
180.4 inches (15.033 feet)
Step-by-step explanation:
To solve this, we convert 15.3 feet to inches. We do this by multiplying 15.3 by 12. This gets us 183.6. Now, we subtract 3.2 from 183.6. This gets us 180.4. That means the piece cut off of 180.4 inches long. To convert this to feet, we divide by 12. That gets us 15.033. That means the piece cut off is 180.4 inches long, or 15.033 feet long.
A system of differential equations defined as dx/dt=29x - 18y
dy/dt=45x - 28y
where x(0) = 2 and y(0) = k If y = [x y] find the solution to this system of differential equations in terms of k. y (t) = ___ [___] + ___ [___]
Find a value for k such that lim y(t) = 0.
k= ___
For the given system of differential equations, the value of k that satisfies lim y(t) = 0 is k = 1.
Differential equations are mathematical equations that involve an unknown function and its derivatives. They describe relationships between the function and its derivatives, allowing us to model various phenomena in physics, engineering, biology, economics, and other fields.
To solve the system of differential equations, we can rewrite them in matrix form:
d[y]/dt = [29 -18; 45 -28] [y]
where [y] is the column vector [x; y].
To find the solution in terms of k, we need to diagonalize the coefficient matrix. Let's find the eigenvalues and eigenvectors of the matrix:
The characteristic equation is given by:
det([29 -18; 45 -28] - λI) = 0
where λ is the eigenvalue and I is the identity matrix.
Simplifying the determinant, we have:
(29 - λ)(-28 - λ) - (-18)(45) = 0
λ² - λ(29 - 28) + (29 * 28 - 18 * 45) = 0
λ² - λ + 62 = 0
Solving this quadratic equation, we find two eigenvalues:
λ₁ = 31
λ₂ = 2
Now, let's find the eigenvectors associated with these eigenvalues:
For λ₁ = 31:
([29 -18; 45 -28] - 31I) [v₁] = 0
Solving the system of equations, we get:
[-2 -18; 45 -59] [v₁] = 0
This leads to the equation:
-2v₁ - 18v₂ = 0
45v₁ - 59v₂ = 0
Simplifying, we find:
v₁ = 9v₂
Therefore, the eigenvector associated with λ₁ = 31 is [9; 1].
For λ₂ = 2:
([29 -18; 45 -28] - 2I) [v₂] = 0
Solving the system of equations, we get:
[27 -18; 45 -30] [v₂] = 0
This leads to the equation:
27v₁ - 18v₂ = 0
45v₁ - 30v₂ = 0
Simplifying, we find:
v₁ = 2v₂
Therefore, the eigenvector associated with λ₂ = 2 is [2; 1].
Now, we can write the general solution of the system as:
[y(t)] = c₁ e^(λ₁t) [9; 1] + c₂ e^(λ₂t) [2; 1]
where c₁ and c₂ are constants.
Since x(0) = 2 and y(0) = k, we can substitute these initial conditions into the general solution:
[x(0); y(0)] = c₁ [9; 1] + c₂ [2; 1] = [2; k]
This gives us the following equations:
9c₁ + 2c₂ = 2
c₁ + c₂ = k
Solving these equations, we find:
c₁ = 2 - 2k
c₂ = 2k - 1
Therefore, the solution to the system of differential equations in terms of k is:
[y(t)] = (2 - 2k) e^(31t) [9; 1] + (2k - 1) e^(2t) [2; 1]
To find a value for k such that lim y(t) = 0, we need to set the coefficients of the exponential terms to zero. Therefore:
2 - 2k = 0
2k - 1 = 0
From the first equation, we have:
2k = 2
k = 1
Substituting this value of k into the second equation, we find:
2(1) - 1 = 0
2 - 1 = 0
Therefore, for k = 1, lim y(t) = 0.
So, the value of k that satisfies lim y(t) = 0 is k = 1.
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How do you solve a nonlinear system?
A set of equations that contain at least one nonlinear equation is referred to as a system of nonlinear equations and steps to solve are mentioned below.
What is non-linear equation and method to solve?A nonlinear system's solution is an ordered pair that solves both equations, much like with systems of linear equations. A nonlinear system could have several solutions. This will become clear as we use graphing to solve a set of nonlinear equations. The point of intersection of the two lines served as the system's solution when linear equations were being solved. Systems of nonlinear equations can have graphs that are circles, parabolas, or hyperbolas, as well as a number of locations where their lines cross, resulting in a number of solutions. Visualize the various ways the graphs might connect once you've determined which ones they are.
Steps to solve non linear equation are:
Identify the graph of each equation. Sketch the possible options for intersection. Graph the first equation. Graph the second equation on the same rectangular coordinate system. Determine whether the graphs intersect. Identify the points of intersection. Check that each ordered pair is a solution to both original equations.Learn more about non-linear system here:
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Find either the surface area or volume of 7.4 and 3.14
The surface area of a sphere with a radius of 7.4 and pie, 3.14 is 687.78.
The volume of a sphere with a radius of 7.4 and pie, 3.14 is 1696.54
How to calculate the surface are and volumeTo calculate the surface area of the sphere with the above dimensions, we would use the formula: 4πr².
Given the above figures, we would have
4 * 3.14 * 7.4²
= 687.78
The volume of the sphere with the given figures would also be gotten with this formula:
V = 4/3 π r³
= 4/3 * 3.14 * 7.4³
1696.54
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Steve claims that the points (-4,8) (8,8) and (-4,3) form a right triangle. Use the distance formula and the Pythagorean theorem to determine if Steve is correct. Show your work and explain your reasoning.
(question 7)
Yes, the points are the vertices of a right triangle and we will prove that by using the Pythagorean theorem.
Are these the vertices of a right triangle?
Remember that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)² + (b - d)²)
The distance between (-4, 8) and (8, 8) is:
d₁ = √( (-4 - 8)² + (8- 8)²) = 12
The distance between (8, 8) and (-4, 3) is:
d₂ = √( (8 + 4)² + (8- 3)²) = 13
The distance between (-4, 8) and (-4, 3) is:
d₃ = = √( (-4 + 4)² + (8 - 3)²) = 5
if the Pythagorean theorem is true, then the sum of the squares of the two shorter sides must be equal to the square of the larger side, then we must have that:
5² + 12² = 13²
Solving that we get:
25 + 144 = 169
169 = 169
This is true, so yes, the vertices are the vertices of a right triangle.
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answer all three please
6. Answer:
72.84
Step-by-step explanation:
To find the perimeter of the rectangle, just add the sides together except the one connected to the semicircle
12 + 15 + 15 = 42
The diameter of the semi circle is 12
πr + d = 6 * π + 12 ≈ 30.84
Add them together
42 + 30.85 = 72.84
7. Answer:
78.54
(78.5)
Step-by-step explanation:
The shape is a circle
Radius is 5
Diameter is 10 (diameter is always double of the radius)
π * r^2 = π * 25 cm^2 = 78.54 cm^2
8. Answer:
50.27
Step-by-step explanation:
The shape is a circle
Radius is 4
Diameter is 8 (diameter is always double of the radius)
π * r^2 = π * 16 ft^2 = 50.27 ft^2
(16 = 8 * 2)
February 12, 2009 marked the 200th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 randomly selected American adults about their education level and their beliefs about the theory of evolution. In their sample, 325 of their respondents had some college education and 228 were college graduates. Among the 325 respondents with some college education, 133 said that they believed in the theory of evolution. Among the 228 respondents who were college graduates, 121 said that they believed in the theory of evolution. Construct a 90% confidence interval for the difference between the proportions of college graduates and individuals with some college who believe in the theory of evolution. Round your sample proportions and margin of error to three decimal places.
The 90% confidence interval for the difference between the proportions of college graduates and individuals with some college who believe in the theory of evolution is (0.022, 0.220)
The sample size of respondents with some college education is 325, and 133 of them believe in the theory of evolution. The sample size of respondents who were college graduates is 228, and 121 of them believe in the theory of evolution.
Now, the sample proportions are:p1= 133/325 = 0.410p2 = 121/228 = 0.531The point estimate of the difference in proportions is:p1 - p2 = 0.531 - 0.410 = 0.121
To calculate the standard error of the sampling distribution of the difference of two proportions, use the following formula:\($$SE = \sqrt{ \frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$$\)
Substituting the values, we get,\($$SE = \sqrt{ \frac{0.410(1-0.410)}{325} + \frac{0.531(1-0.531)}{228}}$$\)
Solving the above expression, we get,\($$SE = 0.0489$$\)
Using the formula of the confidence interval,\($$\text{Confidence Interval} = \text{point estimate} ± \text{margin of error}$$\)
Substituting the values,\($$\text{Confidence Interval} = 0.121 ± 1.645 \times 0.0489$$\)
Now, solving the above expression, we get the confidence interval as:\($$(0.022, 0.220)$$\)
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From the mbsa scan performed in task 3, how many users have non-expiring passwords?
Based on the explanation using the combination method, the correct answer to the question is D. All four users have non-expiring passwords.
The MBSA scan likely provided a list of users along with their corresponding password expiration settings. The term "non-expiring passwords" refers to passwords that do not have an expiration date, meaning they remain valid indefinitely.
Now, let's analyze each option given in the question and determine the correct answer using the combination method:
A. 3 of 4:
If three out of the four users have non-expiring passwords, it means that only one user has an expiring password. However, this does not match our definition of non-expiring passwords. Therefore, Option A is incorrect.
B. 1 of 4:
If only one user out of the four has a non-expiring password, it means that the other three users have expiring passwords. This option does not satisfy the condition of non-expiring passwords for the majority of users. Hence, Option B is also incorrect.
C. 2 of 4:
If two users out of the four have non-expiring passwords, it means that the remaining two users have expiring passwords. This option suggests that half of the users have non-expiring passwords, which does not correspond to our definition of non-expiring passwords for the majority of users. Thus, Option C is incorrect.
D. 4 of 4:
If all four users have non-expiring passwords, it means that every user's password is set to never expire. This option aligns with our definition of non-expiring passwords for the majority of users. Therefore, Option D is the correct answer.
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Complete Question:
From the MBSA scan performed in Task 3, how many users have non-expiring passwords?
A. 3 of 4
B. 1 of 4
C. 2 of 4
D. 4 of 4
a farmer plans to enclose a rectangular pasture adjacent to a river. (see figure). the pasture must contain 80,000 square meters in order to provide enough grass for the herd. what dimensions will require the least amount of fencing if no fencing is needed along the river?
Therefore, L has a relative and absolute minimum when x = 400 m
What is Perimeter and Area ?The area is as defined as the amount of space occupied by any shape in two dimensions. Whereas, Perimeter is the boundary or the outline of a flat shape.
Let x = length of the side parallel to the river
y = length of each of the other two sides
Then xy = 80,000, so y = 80,000/x
Minimize: L = length of the fence
L = x + 2y
= x + 160,000/x, where x > 0
L' = 1 - 160,000/x2 = (x2 - 160,000)/x2
L' = 0 when x = 400 or -400
Since x can't be negative, x must be 400.
When 0 < x < 400, L' < 0. So, L is decreasing.
When x > 400, L' > 0. So L is increasing.
Therefore, L has a relative and absolute minimum when x = 400 m
y = 80,000/x = 200 m
The fence is shortest if the side parallel to the river has length 400 m and the other 2 sides each have length 200 m.
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Find the number of sides of a regular polygon if one interior angle is 120 degrees A3 B4 C5 D6
Answer:
n = 6
Step-by-step explanation
Number of sides = 360/Measure of exterior
Measure of exterior = 180 - interior angle
Exterior angle = 180 - 120
Exterior angle = 60 degrees
Substitute into the formula
number of sides = 360/60
number of sides = 6
Hence the number of sides required is 6
Beth had 1/4 box of candy. she ate 1/5 of the candy. If she decides to refill the box , what fraction of the box would need to be refilled ?
Aslam and akram invested rs 27000 and rs 30000 to start a business . if they earned a profit of rs 66500 at the end of the year , find the profit of each one
The profit of Aslam is Rs. 31,474.50 and the profit of Akram is Rs. 35,025.50.
To find the profit of each person, we can use the concept of ratios.
First, let's find the total investment made by both Aslam and Akram:
Total investment = Aslam's investment + Akram's investment
Total investment = 27000 + 30000 = 57000
Next, let's calculate the ratio of Aslam's investment to the total investment:
Aslam's ratio = Aslam's investment / Total investment
Aslam's ratio = 27000 / 57000 = 0.4737
Similarly, let's calculate the ratio of Akram's investment to the total investment:
Akram's ratio = Akram's investment / Total investment
Akram's ratio = 30000 / 57000 = 0.5263
Now, we can find the profit of each person using their respective ratios:
Profit of Aslam = Aslam's ratio * Total profit
Profit of Aslam = 0.4737 * 66500 = 31474.5
Profit of Akram = Akram's ratio * Total profit
Profit of Akram = 0.5263 * 66500 = 35025.5
Therefore, the profit of Aslam is Rs. 31,474.50 and the profit of Akram is Rs. 35,025.50.
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