ABC~ DEF. What sequence of transformations will move ABC onto DEF?
A. A dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
B. A dilation by a scale factor of 1/2, centered at the origin, followed by the translation (x,y)-> (x+7,y)
C. The translation (x,y)->(x+7,y), followed by a dilation by a scale factor of 2 centered at the origin.
D. A dilation by a scale factor of 2, centered at the origin, followed by the translation (x,y)-> (x+7,y)
Answers
Note that the sequence of transformations that will move ABC onto DEF is; "The translation (x,y)->(x+7,y), followed by a dilation by a scale factor of 2 centered at the origin." *Option C)
What is transformation?A transformation is a mathematical function that repositions points in one-, two-, three-, or any other n-dimensional space.
A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.
Note that translation takes B(0,0) to B'(7, 0),
Takes A(0, 4) to A'(7, 0) and C (3, 0) to C' (10, 0)
when you multiply the new points by the scale factor of 2, you'd get the new figure when the coordinates are graphed.
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Answer:
D. Dilation by 2, translation right by 7.
Step-by-step explanation:
You want to know the sequence of transformations that maps ∆ABC to ∆DEF.
Scale factorSegment DE is 8 units long, and located at x=7. Segment AB is 4 units long and located at x=0.
The scale factor is the ratio of segment lengths:
DE/AB = 8/4 = 2
Triangle DEF is dilated by a factor of 2 (eliminates B).
TranslationTriangle DEF is oriented the same way as triangle ABC, so there is no reflection involved (eliminates A). As we noted, segment DE is 7 units to the right of segment AB, so a translation of x ⇒ x+7 is involved.
SequenceThe translation must occur after the dilation about the origin (eliminates C). If it were to occur first, the translation would be multiplied by the scale factor, so that DE would end up at x=14.
The required sequence of transformations is ...
D. A dilation by a scale factor of 2, centered at the origin, followed by the translation (x, y) ⇒ (x+7, y).
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Related Questions
Is y=(1/2)X a linear function
Answers
Answer:
linear
Step-by-step explanation:
have a good day God bless :)
What is the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6)?
Answers
The vector in component form whose tail is the point (−1,5), and whose head is the point (8,−6) is (-9, 11)
What is a vector?A vector is a physical quabntity thet has both magnitude and direction.
To find the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6), we proceed as folows
Since we have the points (-1, 5) and (8, -6) and we want the head to be at (8, -6),
Let A = (8, -6) and B = (-1, 5)
So, AB = B - A
= (-1, 5) - (8, -6)
= (-1 - 8), (5 - (-6))
= (-9, 5 + 6)
= (-9, 11)
So, the vector in component form is (-9, 11)
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Ethan's class is handing out balloon arrangements consisting of 4 balloons each. Each balloon has an equally likely chance of being red, blue, or yellow. Ethan created a spinner to simulate this probability. Here is Ethan's data from 30 trials of 4 spins on the spinner (r = red, b = blue, y = yellow):
ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr
According to this data, what is the experimental probability that an arrangement will consist entirely of balloons that are the same color?
0.012
0.1
0.033
0.33
Answers
The requried, experimental probability is 0.1. Option B is correct.
To find the experimental probability that an arrangement will consist entirely of balloons that are the same color, we need to count the number of times that Ethan got an arrangement where all four balloons were the same color and divide that by the total number of trials.
Looking through the data, we can see that the following trials had all four balloons the same color:
rrrr
bbbb
yyyy
So, out of 30 trials, there were 3 trials where all four balloons were the same color. Therefore, the experimental probability is:
3/30 = 0.1
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Use properties of exponents to verify that 2s − 1 and _1
2 (2)
s
are equivalent.
Answers
The properties of the exponents are solved and the expression is given by the relation ( 2s )⁻¹ = 1 / 2s
Given data ,
Let the expression be represented as A
Now , the value of A is
( 2s )⁻¹ = 1 / 2s
From the laws of exponents , we get
m⁻ᵃ = ( 1 / mᵃ )
So , on simplifying , we get
( 2s )⁻¹ = 1/ ( 2s )
On further simplification , we get
1/ ( 2s ) = ( 2s )⁻¹
Hence , the expression is ( 2s )⁻¹ = 1/ ( 2s )
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The complete question is attached below :
Use properties of exponents to verify that ( 2s )⁻¹ = 1/ ( 2s ) are equivalent.
The cost of 2 footballs and 3 tennis balls is £21.73.
The cost of 5 footballs and 7 tennis balls is £53.20.
Work out the cost of
a) a football.
b) a tennis ball.
Answers
Answer: A) £7.49
B) £2.25
Step-by-step explanation:
Step 1:
Let the cost of a football be [tex]f[/tex]and the cost of a tennis ball be [tex]t[/tex].
Step 2:
Write the 2 equations we have from the given information:
[tex]2f + 3t = 21.73[/tex] [tex] \textsf{(from the cost of 2 footballs and 3 tennis balls)} [/tex]
[tex]5f + 7t = 53.20[/tex] [tex] \textsf{(from the cost of 5 footballs and 7 tennis balls)} [/tex]
Step 3:
Solve for one variable in one of the equations. For example, we can solve for [tex]f[/tex]in the first equation:
[tex]2f + 3t = 21.73[/tex][tex]2f = 21.73 - 3t[/tex][tex]f = \frac{(21.73 - 3t)}{2}[/tex]Step 4:
Substitute this expression for [tex]f[/tex] into the second equation and solve for [tex]t[/tex]:
[tex]5f + 7t = 53.20[/tex][tex]5[\frac{(21.73 - 3t)}{2}] + 7t = 53.20[/tex][tex]54.325 - 7.5t + 7t = 53.20[/tex][tex]0.5t = 1.125[/tex][tex]t = 2.25[/tex]So, the cost of a tennis ball is £2.25.
Step 5:
Substitute this value of [tex]t[/tex] into the expression for [tex]f[/tex] and solve for [tex]f[/tex]:
[tex]f = \frac{(21.73 - 3t)}{2}[/tex][tex]f = \frac{(21.73 - 3(2.25))}{2}[/tex][tex]f = 7.49[/tex]So, the cost of a football is £7.49
Step 6:
Therefore, the cost of a football is £7.49 and the cost of a tennis ball is £2.25.
Question
Bottles of water come in packages of 5. Cheese sticks come in packages of 12.
What is the least number of packages of each you have to buy to have the same number of bottles of water and cheese sticks?
Drag and drop an answer into each box to complete the statement.
You need to buy____packages of bottles of water and___packages of cheese sticks
Answers
Answer:
12 packages of water
5 packages of cheese sticks
Step-by-step explanation:
The LCM (least common multiple) of 5 and 12 is 60.
w = # of pkgs of water
c = # of pkgs of cheese sticks
5w = 12c = 60
w = 60/5 = 12
c = 60/12 = 5
You would like to estimate the prevalence of a disease. You randomly sample 10 people from the population of interest and 4 of them have the condition. Using a Beta prior with αα and ββ both being 1010, what is the posterior mean prevalence closest to?
Answers
The required posterior mean prevalence is closest to 0.47.
We can use Bayes' theorem to find the posterior distribution of the prevalence parameter, given the data and the Beta prior:
posterior ∝ likelihood x prior
where the likelihood is given by the binomial distribution:
likelihood = P(observing 4 cases out of 10 | prevalence)
and the prior is a Beta distribution with parameters α = β = 10:
prior = Beta(α=10, β=10)
We can calculate the posterior distribution by multiplying the likelihood and prior, and then normalizing:
posterior = Beta(α=14, β=16)
where the posterior Beta distribution has parameters α=14 (10 + 4) and β=16 (10 + 10 - 4).
The posterior mean of a Beta distribution with parameters α and β is:
posterior mean = α / (α + β)
Plugging in the values of α and β from the posterior distribution, we get:
posterior mean = 14 / (14 + 16) = 0.467
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Determine that the value x=9 of the following expiration given x2+3x-5
Answers
Step-by-step explanation:
To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:
9^2 + 3(9) - 5 = 81 + 27 - 5 = 103
Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.
rate my answer, please.
Select the correct answer from each drop-down menu.
Veronica wants to cut a sheet of paper into squares with an area of 12 square inches. For the best approximation, the length of each side of the square pieces of paper must be approximately equal to
inches. If each side were exactly this length, the area of each square would be
square inches.
Answers
The area of each square would be 36 square inch.
We have,
Area of sheet = 12 square inches
So, the area of square to be cut
= 12in × 12in
= 144 square in
Now, number of squares=4
So, area of each square =144÷4
=36 square inches
Thus, the side of each square is
= 36/4
= 6 inch
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Faster please!! thanks!! 30 points + brainliest!!
Which is an example of simple random sampling created from each given population?
Answers
An example of simple random sampling is given as follows:
C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.Hence the samples for this problem are classified as follows:
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139(x-28)
Please help would save a girls lifeee fr fr
Answers
Answer:
69
Step-by-step explanation:
(139) + (x-28) = 180 (adjacent angles on straight line add up to 180)
x - 28 = 41
x = 69
Find a quadratic equation which has solutions x=4/9 and x=9/2. Write the quadratic form in the simplest standard form x^2+bx+c
Answers
Answer:
[tex](x - \frac{4}{9} )(x - \frac{9}{2} ) = 0[/tex]
[tex] {x}^{2} - \frac{89}{18} x + 2 = 0[/tex]
Find that the radius of curvature of ^2y=x^3-a^3
at the point where the
curves cut the X-axis.
Answers
The radius of curvature of the curve [tex]a^{2y[/tex]=x³-a³ at the point where the curve intersects the x-axis is 27[tex]a^{\frac{3}{2}[/tex].
To find the radius of curvature of the curve [tex]a^{2y[/tex]=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.
When the curve intersects the x-axis, y=0. Therefore, we have:
a⁰ = x³ - a³
x³ = a³
x = a
Next, we need to find the derivative of y with respect to x:
dy/dx = -2x/(3a²√(x³-a³))
At the point where x=a and y=0, we have:
dy/dx = -2a/(3a²√(a³-a³)) = 0
Therefore, the radius of curvature is given by:
R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)
To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:
d/dx(dy/dx) = -2/(3a²(x³-a³[tex])^{\frac{3}{2}[/tex]) + 4x²/(9a⁴(x³-a³[tex])^{\frac{1}{2}[/tex])
At x=a, we have:
d/dx(dy/dx) = -2/(3a²(a³-a³[tex])^{\frac{3}{2}[/tex]) + 4a²/(9a⁴(a³-a³[tex])^{\frac{1}{2}[/tex]) = -2/27a³
Therefore, the radius of curvature is:
R = (1/|-2/27a³|) = 27[tex]a^{\frac{3}{2}[/tex]
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A playground 88 ft long and 58 ft wide is to be resurfaced at a cost of $2.75 per sq ft. What will the resurfacing cost?
The resurfacing will cost $.
(Simplify your answer. Type an integer or a decimal.)
Answers
Answer: $1856
Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856
Lawrence is increasing the rectangular patio in his backyard. His patio is currently 12
feet by 10 feet. He wants to increase the patio by adding a decorative tile the same width (x) all the way around creating a total area of 180 square feet. Select all the quadratic equations that represent Lawrence’s new patio area.
Answers
The quadratic equation representing the new patio area after adding a decorative tile of width x all the way around is: 0 = 4x^2 + 44x - 60
Options A and E are correct.
What is a Quadratic Function?In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Since the area of the new patio is given as 180 square feet, we can create a quadratic equation to represent the new patio area:
Area = length × width
180 = (12 + 2x) × (10 + 2x)
After we expand, the answer is given as 0 = 4x^2 + 44x - 60
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Express sin
�
L as a fraction in simplest terms.
Answers
Answer:
3/5
Step-by-step explanation:
opposite/hypotenuse
21/35
Simplify by dividing by 7 on the numerator and denominator
3/5
Need Help!!!! A pre-image has coordinates J(3, -6) and K(-1, -2). The image has coordinates J'(6, 3) and K'(2, -1). Describe the clockwise rotational path of the line segment.
Answers
After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.
So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)
The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.
The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:
Midpoint of JK: (1, -4)
Midpoint of J'K': (4, 1)
The slope of the vector: 3/5
(x₁ + x₂)/2, (y₁ + y₂) /2
Point-slope formula: y - y₁ = m(x - x₁)
Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)
Applying simplification , we get: y = (- 3/5)x - 1.2
To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:
y - 1 = (7/3)( x - 4)
Apply simplification , we get: y = (7/3)x - 17/3
To evaluate the intersection point, we can solve the system of equations:
y =(- 3/5)x - 1.2 = (7/3)x - 17/3
Evaluating for x and y, we get x = -6 and y = -1.
Therefore, the center of rotation is (-6, -1).
√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)
Distance between image points and center of rotation
√( ( 6 - (-6))² + ( 3 - (-1))² = 13
The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).
The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':
Angle of vector: arctan(5/3) = 59.04 degrees
Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
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Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below:
Population 1: 69, 68, 62, 68, 68, 62, 69
Population 2: 76, 68, 68, 72, 76, 70, 70, 70
Is there evidence, at an α=0.025
level of significance, to conclude that those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested.
A. The value of the standardized test statistic:
B. The rejection region for the standardized test statistic:
C. Your decision for the hypothesis test:
Answers
A. The value of the standardized test statistic is -2.391.
B. The rejection region for the standardized test statistic is t <-2.160.
C. The decision for the hypothesis test is to reject the null hypothesis.
How to explain the hypothesisEmploying a t-distribution table or calculator along with 13 degrees of freedom (n1 + n2 - 2) enables us to ascertain the rejection region for the t-statistic at an α=0.025 level of significance (two-tailed test):
Rejection Region: t < -2.160 or t > 2.160
Given that -2.391 falls in the rejection region, we repudiate the null hypothesis. At the α=0.025 level of significance, we are provided sufficient evidence to support that those who consistently partake in exercise generally have a lower resting heart rate than those who do not.
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TONS OF POINTS - please help
The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will
travel follows a parabolic arch that can be described by this polynomial.
f(x) = -0.05(x2-26x-120)
He is supposed to land on a safety net 30 feet away. Does the function give you
enough information to tell you where he will land? If so, how far from the cannon will he land?
Make Sense of the Problem
3 points: 1 point for each answer.
-What do you know?
-What do you want to find out?
-What kind of answer do you expect?
1. The function f(x)=-0.05(x2-26x-120)
Represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent
2.what do the zeros of this function represent? Remember the zeros are where f(x)=0
3. Will the zeros tell you where the net should be placed? Why or why not?
4.to find zeros, set the function equal to 0, and then factor the polynomial start by setting the function equal to 0
5. Next factor the polynomial x2-26x-120. To identify the factors, complete the table: note this does not contain all the factors of -120, but it has enough to let you factor the polynomial
(I tried to type out the table )
pqp+q
P. q. p. |
————————— |
10. | 12 | blank. |
—————————.|
-10 | 12 |. Blank. |
—————————.|
30. |. -4. |. Blank. |
—————————-|
4. |. 30. | blank. |
—————————.|
6. Which values of p and w give the correct factors
7. Factor the polynomial completely
0=-0.05(x2 - 26x -120)
8. Find the roots of equation by setting each factor equal to 0 and solving for x.
Hint: there are three factors, but the constant factor, -0.05, does not equal zero
Solve for x with the other two factors
9. Identify the roots
Answers
Answer:
Step-by-step explanation:
2344
an experienced bungee jumper leaps from a tall bridge and falls towards the water. The bridge is 241 feet above the water and the bungee cord is 149 feet long unstretched. When will the cord begin to strech? The gravity formula is as follows: h(t)= -16t + [tex]v_{0}[/tex]t + [tex]h_{0}[/tex]
Answers
The cord will begin to stretch after approximately 1.46 seconds.
How to solve for when the stretch startsh(t) = -16t^2 + V0t + h0
149 = h0 - h(t)
Substituting h0 = 241 and h(t) = -16t^2 + V0t into this equation, we get:
149 = 241 - (-16t^2 + V0t)
we get:
16t^2 - V0t - 92 = 0
4(16)(-92) / (2(16)
t = sqrt(1856) / 32
Using a calculator, we get:
t ≈ 1.46 seconds
Therefore, the cord will begin to stretch after approximately 1.46 seconds.
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Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed.
Answers
The 95% confidence interval is (22.8876, 49.1124)..
To find the 95% confidence interval for the difference in means between two populations, we can use the formula:
CI = (x1 - x2) ± z*(SE)
where x1 and x2 are the sample means of the two populations, SE is the standard error, z is the critical value from the standard normal distribution corresponding to the level of confidence.
Substituting the given values into the formula, we have:
CI = (264 - 228) ± 1.96*(6.69)
Simplifying this expression, we have:
CI = 36 ± 13.1124
Therefore, the 95% confidence interval for the difference in means between the two populations is (22.8876, 49.1124).
This means that we are 95% confident that the true population difference in means falls between 22.8876 and 49.1124. We can interpret this interval as a range of plausible values for the population difference in means, based on the sample data.
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A first-year teacher wants to retire in 40 years. The teacher plans to invest in an account with a 6.95% annual interest rate compounded continuously. If the teacher wants to retire with at
least $125,000 in the account, how much money must be initially invested? Round your answer to the nearest dollar.
O$10,234
O$10,755
O $7,902
O $7,755
Answers
The money invested by the teacher to have at least 125,000 in her account after 40 years of a 6.95% annual interest rate compounded continuously is 7755. Hence, the right solution to the question is option D
Compound interest is given by
A = P[tex](1+r)^t[/tex]
where A is the amount
P is the principal
r is the rate of interest
t is the time
Given in the question,
A = $125,000
r = 6.95% or 0.0695
t = 40 years
P is to be found
A = P[tex](1+r)^t[/tex]
125000 = P [tex](1 + 0.0695)^{40[/tex]
125000 = P * [tex]1.0695^{40[/tex]
125000 = 16.118P
P = 7755
The teacher should invest $7755 initially.
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A circle has an area of 45 square meters. What is the area of a sector with an arc measure of 70 degree?
______m^2
Answers
The area of a sector is 8.75 [tex]m^{2}[/tex].
What is a sector?A sector is a part of a given circle which is bounded by two radii and an arc. The area of a sector can be determined by;
area of a sector = (θ/ 360)π[tex]r^{2}[/tex]
where r is the radius, and θ is the central angle.
Given a circle whose area is 45 sq. m.; then;
area of a circle = π[tex]r^{2}[/tex]
45 = π[tex]r^{2}[/tex]
r = [tex]\sqrt{\frac{45}{\pi } }[/tex]
Then,
area of a sector = (θ/ 360)π[tex]r^{2}[/tex]
= ([tex]\frac{70}{360}[/tex])*π*[tex][\sqrt{\frac{45}{\pi } }] ^{2}[/tex]
= [tex]\frac{7}{36}[/tex]*π*45/π
= [tex]\frac{7}{36}[/tex]*45
= 8.75 sq. m.
The area of the sector is 8.75 [tex]m^{2}[/tex].
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Write a recursive formula for
Answers
Answer:
[tex]a(1) = 144[/tex]
[tex]a(n) = 144{( - \frac{1}{6} )}^{n - 1} [/tex]
[tex]a(n) = - \frac{1}{6} a(n - 1)[/tex]
This is for the following two questions.
A couple plans to retire in 35 years. At that time, they would like to have enough money in an account so that they can receive a $6,000 every month end for the next 25 years. The account earns 8% APR compounded monthly and will continue to do so until there is a zero balance in the account.
To achieve this goal, how much money does the couple need to have in this account by the time they retire?
If they have not saved any money yet, how much does the couple need to deposit each month end until they retire?
Answers
The couple needs to deposit about $554.49 each month end until they retire to reach their goal.
How to solveTo find the monthly deposit needed, we'll use the future value of an ordinary annuity formula:
FV = PMT * [((1 + r)^n - 1) / r]
We already know the future value (FV) as $953,776.53, and we want to solve for PMT, the monthly deposit:
PMT = FV / [((1 + r)^n - 1) / r]
We'll use the same r (0.08/12) and a new n (35 * 12) for the 35 years until retirement:
PMT = 953776.53 / [((1 + 0.08/12)^(35*12) - 1) / (0.08/12)]
PMT ≈ 554.49
Thus, the couple needs to deposit about $554.49 each month end until they retire to reach their goal.
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A software developer's current annual gross wage is $93,400. For retirement, the developer wants to have enough saved to live off 80% of the current annual gross wage and draw 4% the
first year. What is the total amount the developer will need in retirement savings to meet their retirement income goal?
O$1,868,000
O$1,688,000
O$1,088,600
O $1,068,800
Answers
Answer:
c
Step-by-step explanation:
what is the maths formula for area
Answers
Answer:
Quick internet search:
18. AB =
A
8
Los
D
B
1
Answers
Answer: the area of the triangle is 150 cm².
Step-by-step explanation:
To solve this problem, we need to use the formula for the area of a triangle:
Area = (1/2) x base x height
From the diagram, we can see that the base of the triangle is 20 cm and the height is 15 cm. Plugging these values into the formula, we get:
Area = (1/2) x 20 cm x 15 cm
Area = 150 cm²
Therefore, the area of the triangle is 150 cm².
A construction company will be penalized each day of delay in construction for bridge. The penalty will be $4000 for the first day and will increase by $10000 for each following day. Based on its budget, the company can afford to pay a maximum of $ 165000 toward penalty. Find the maximum number of days by which the completion of work can be delayed.
Answers
Answer:
The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.
Step-by-step explanation:
We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is
[tex]S_{n}[/tex] = 165000.
Let us find the amount as arithmetic series as follows:
4000 + 5000 + 6000
The arithmetic series being, first term is [tex]a_{1}[/tex] = 4000, second term is [tex]a_{2}[/tex] = 5000.
We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:
[tex]d = a_{2} - a_{1} = 5000 - 4000 = 1000[/tex]
The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] ( ‘ d ‘ being the difference. )
Next we can substitute a = 4000, d = 1000 and [tex]S_{n}[/tex] = 165000 in “ [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] “ which can be represented as:
Determining, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex]
⇒ 165000 = [tex]\frac{n}{2}[/tex] [( 2 x 4000 ) + ( n - 1 ) 1000 ]
⇒ 2 x 165000 = n(8000 + 1000n - 1000 )
⇒ 330000 = n(7000 + 1000n)
⇒ 330000 = 7000n + [tex]1000n^2[/tex]
⇒ [tex]1000n^2[/tex] + 7000n - 330000 = 0
⇒ [tex]1000n^2[/tex] ( [tex]n^2[/tex] + 7n - 330 ) = 0
⇒ [tex]n^2[/tex] + 7n - 330 = 0
⇒ [tex]n^2[/tex] + 22n - 15n - 330 = 0
⇒ n( n + 22 ) - 15 ( n + 22 ) = 0
⇒ ( n + 22 )( n - 15 ) = 0
⇒ n = -22, n = 15
We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.
Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.
Needing help finding this answer!
Answers
Answer:
78.947%
Step-by-step explanation:
It says A OR B, so:
5/19 + 6/19 + 4/19
11/19 + 4/19
15/19 = approx. 0.78947 = 78.947%
