find the first four nonzero terms in a power series expansion about x0 for a general solution to the given differential equation. w''-18x^2
Answers
The first four nonzero terms in a power series expansion about x0 for a general solution to the differential equation w''-18x^2=0 are w(x)=C1 + C2(x-x0)^2 + 27/4 C1(x-x0)^4 + 81/40 C2(x-x0)^6.
To find the power series expansion of w(x), we first assume w(x) can be represented by a power series around x0, i.e., w(x)= ∑(n=0)^∞ a_n(x-x0)^n. Then we differentiate w(x) twice to obtain w''(x) = ∑(n=2)^∞ n(n-1) a_n (x-x0)^(n-2).
Substituting w''(x) into the differential equation and setting it to zero, we have ∑(n=2)^∞ n(n-1) a_n (x-x0)^(n-2) - 18(x-x0)^2 ∑(n=0)^∞ a_n(x-x0)^n = 0.
Collecting like powers of (x-x0), we can write the equation as ∑(n=2)^∞ n(n-1) a_n (x-x0)^(n-2) - 18 ∑(n=2)^∞ a_n (x-x0)^n = 0.
To obtain the first few nonzero terms, we equate coefficients of like powers of (x-x0) and solve the resulting system of equations.
At n=0, we get -18a_0=0, which implies a_0=0.
At n=1, we get -18a_1=0, which implies a_1=0.
At n=2, we get 2(2-1)a_2-18a_0=0, which implies a_2=9a_0/2=0.
At n=3, we get 3(3-1)a_3-18a_1=0, which implies a_3=0.
Thus, the first nonzero term is a_4, and we can solve for it to obtain a_4=27/4 C1.
Similarly, we can solve for a_5, a_6, and so on, to obtain higher order terms in the power series expansion.
Substituting these values back into the power series expansion for w(x), we obtain the first four nonzero terms as w(x)=C1 + C2(x-x0)^2 + 27/4 C1(x-x0)^4 + 81/40 C2(x-x0)^6.
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Related Questions
Identify which type of sampling is used: random, stratified, cluster, systematic, or convenience.
_________1. A psychologist selects 12 boys and 12 girls from each of 4 Math classes.
_________2. When he made an important announcement, he based conclusion on 10,000 responses, from 100,000 questionnaires distributed to students.
_________3. A biologist surveys all students from each of 15 randomly selected classes.
_________4. The game show organizer writes the name of each contestant on a separate card, shuffles the cards and draws 5 names.
_________5. Family planning polls 1000 men and 1000 women about their views concerning the use of contraceptives.
_________6. A hospital researcher interviews all diabetic patients in each 10 randomly selected hospitals.
_________7. Smart selects every 100th cell phone from the assembly line and conduct a thorough test of quality.
Answers
The type of sampling used in each scenario is as follows:
Stratified sampling, Convenience sampling, Cluster sampling, Random sampling, Convenience sampling, Cluster sampling, Systematic sampling
The psychologist selects a specific number of boys and girls from each math class, which indicates stratified sampling. The population (students) is divided into strata (math classes) and samples are taken from each stratum.
The conclusion is based on responses from questionnaires that were distributed conveniently to students, indicating convenience sampling. The sample is not randomly selected but consists of those who chose to respond.
The biologist surveys all students from randomly selected classes, indicating cluster sampling. The population (students) is divided into clusters (classes), and all members of the selected clusters are included in the sample.
The game show organizer shuffles and randomly selects contestant names, indicating random sampling. Each name has an equal chance of being selected.
Family planning polls a specific number of men and women, suggesting convenience sampling. The individuals surveyed are conveniently selected and may not represent the entire population.
The hospital researcher interviews all diabetic patients in randomly selected hospitals, indicating cluster sampling. The population (diabetic patients) is divided into clusters (hospitals), and all members of the selected clusters are included in the sample.
Smart selects every 100th cell phone from the assembly line, indicating systematic sampling. A sampling interval is used to select samples at regular intervals, ensuring a systematic and consistent approach.
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closest square root of 59.4
Answers
Answer:
8
Step-by-step explanation:
Answer:
the Square root is 7.7 which is rounded up to 8.
Step-by-step explanation:
What are the 3 types of rigid transformations?
Answers
Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.
A rigid transformation, also called isometry, is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:
1. Reflection
→ is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.
The figure is reflected across \(x-\) or \(y-\) axis, and then change \(x-\) or \(y-\) coordinate.
2. Rotation
→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.
The figure is rotated by a degree (ex: 90°), and then change \(x-\) or \(y-\) coordinate. Meanwhile, a point's center rotation stays at the same.
3. Translation
→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right), or vertical reflections (make a figure up or down).
Vertical translation is shifting the graph along \(y-\) axis
Horizontal translation is shifting the graph along \(x-\) axis.
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14. In the following figure, M is the midpoint of
(FA) and (MA) and (MB) are the tangents issued
from M to the circle(C).
F
M
B
(C)
question: Show that ABF is a right triangle.
Answers
Answer:
angle OAM and OBM are right angles because tangents form right angles with radii.
AO=BO and MA=MB
Quadrilateral MAOB =360 degrees
so angles AOB and AMB=90 degrees each
angle MBF=90 degrees
M is the midpoint of FA so MA=MF
MB=MF
Triangle MBF is a right triangle because angle BMF is 90 degrees and MB=MF
(6.8 X103)-(7.2 X 10)
1.1 X 104
X 10
Answers
Answer:
\(5.5\times 10^{-1}\)
Step-by-step explanation:
We need to find the value of the given expression i.e.
\(\dfrac{6.8\times 10^3-7.2\times 10^2}{1.1\times 10^4}\)
We can solve it as follows :
\(=\dfrac{6800-720}{11000}\\\\=\dfrac{6080}{11000}\\\\=0.55\)
or
\(=5.5\times 10^{-1}\)
So, the required answer is equal to \(5.5\times 10^{-1}\).
Blair & Rosen, Inc. (B&R), is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $85,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 9%, whereas the Blue Chip fund has a projected annual return of 8%. The investment advisor requires that at most $55,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be
6(10) + 4(10) = 100.
Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 410.
(a)
Formulate a linear programming model to find the best investment strategy for this client. (Assume N is the amount invested in the internet fund project and B is the amount invested in the Blue Chip fund. Express the amounts invested in thousands of dollars.)
Max _______________ s.t.
Available investment funds
Maximum investment in the internet fund
Maximum risk for a moderate investor
N, B ≥ 0
(b)
Build a spreadsheet model and solve the problem using Excel Solver. What is the recommended investment portfolio (in dollars) for this client?
internet fund$
blue chip fund$
What is the annual return (in dollars) for the portfolio?
$
(b)
Suppose that a second client with $85,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 450. What is the recommended investment portfolio (in dollars) for this aggressive investor?
internet fund$
blue chip fund$
(d)
Suppose that a third client with $85,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 320. Develop the recommended investment portfolio (in dollars) for the conservative investor.
internet fund$
blue chip fund$
Answers
A. N, B ≥ 0 (non-negativity constraint)
B. The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.
C. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
D. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
(a)
The linear programming model to find the best investment strategy for this client can be formulated as follows:
Maximize: 0.09N + 0.08B
Subject to:
N + B ≤ 85 (maximum investment of $85,000)
N ≤ 55 (maximum investment of $55,000 in the internet fund)
6N + 4B ≤ 410 (maximum risk rating of 410 for a moderate investor)
N, B ≥ 0 (non-negativity constraint)
(b)
To solve the problem using Excel Solver, you can set up the following spreadsheet model:
Cell A1: N (amount invested in the internet fund)
Cell B1: B (amount invested in the Blue Chip fund)
Cell C1: =0.09A1 + 0.08B1 (annual return for the portfolio)
Constraints:
Cell A2: ≤ 85
Cell B2: ≤ 85
Cell C2: ≤ 55
Cell D2: ≤ 410
The objective is to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints.
Using Excel Solver, set the objective to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints in cells A2, B2, C2, and D2.
The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.
(b)
For the aggressive investor with a maximum portfolio risk rating of 450, the linear programming model remains the same, except for the constraint on the maximum risk rating.
The new constraint would be: 6N + 4B ≤ 450
Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
(d)
For the conservative investor with a maximum portfolio risk rating of 320, the linear programming model remains the same, except for the constraint on the maximum risk rating.
The new constraint would be: 6N + 4B ≤ 320
Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
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if the average correlation among the items on an anxiety scale is r = .95, we can say that the scale has
Answers
Answer:
a strong and almost perfect positive linear correlation.
Carly and Stella have learned that their building can have no more than 195
offices.
Write an inequality to describe the relationship between the number of floors,
, and the maximum number of offices for the floor plan assigned to your team.
Answers
The inequality to describe the relationship between the number of floors (f) and the maximum number of offices (o) is:
f * o ≤ 195.
Let's assume that the number of floors in the building is represented by the variable "f" and the maximum number of offices on each floor is represented by the variable "o". To write an inequality describing the relationship between the number of floors and the maximum number of offices, we can use the following inequality:
f * o ≤ 195
In this inequality, the product of "f" and "o" represents the total number of offices in the building. We multiply the number of floors by the maximum number of offices per floor to obtain the total number of offices. The inequality states that the total number of offices must be less than or equal to 195.
This inequality ensures that the building does not exceed the maximum limit of 195 offices. It allows for flexibility in the distribution of offices across the floors, as long as the total number of offices does not exceed the given limit.
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A bee flies at 6 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 14 minutes, and then flies directly back to the hive at 4 feet per second. It is away from the hive for a total of 17 minutes. What equation can you use to find the distance of the flowerbed from the hive?
Answers
The equation that can be used to find the distance of the flowerbed from the hive is as follows:
10d/24 = 180
How to find distance?Distance is the total movement of an object without any regard to direction.
Therefore, distance can be represented mathematically as follows;
speed = distance / time
distance = speed × time
time = distance / speed
Hence, the first journey from the flowerbed to the hive is 6 ft per seconds.
t₁ = d / 6
The second journey.
t₂ = d / 4
The total time the bees use to fly = 17 - 14 = 3 minutes = 180 seconds
Therefore,
t₁ + t₂ = d / 6 + d / 4
t₁ + t₂ = 4d + 6d / 24
t₁ + t₂ = 10d / 24
The equation that can be used to find the distance of the flowerbed from the hive is as follows:
10d/24 = 180
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A store pays $697 for a snow board and marks the price up by 42%. What is the amount of the mark-up? please help
Answers
Answer:
$292.74 :)
Step-by-step explenation
i searchd it
Precipitation for the month of March was 6 ½ inches less than average. In April, the precipitation was 2 ⅜ inches less than average. How many inches below average was the precipitation for both March and April?
Answers
Answer:
The precipitation for both March and April was 8 7/8 inches below average
Step-by step explanation;
For the month of march, precipitation was 6 1/2 inches less than average
For the month of April, precipitation was 2 3/8 inches left.
Now we want to calculate how many inches less than average was precipitation in both wants
What we simply do here is to add the inches with which they were both left than average in both months
That would be;
6 1/2 + 2 3/8
= 13/2 + 19/8 = (52 + 19)/8 = 71/8 = 8 7/8 inches
mmon Core Algebra I - MA3109 B-IC
Activity
Vertical Stretches and Shrinks of Exponential Functions
Assignment Active
Identifying a Function
Which is a stretch of an exponential decay function?
◎m=²[
Of(x) = -(5)
Of(x) = 5(²)
O fix) = 5(5)*
Answers
The stretch of an exponential decay function is y = 2(1/5)ˣ
Which is a stretch of an exponential decay function?From the question, we have the following parameters that can be used in our computation:
The list of exponential functions
An exponential function is represented as
y = abˣ
Where
a = initial valueb = growth/decay factorIn this case, the exponential function is a decay function
This means that
The value of b is less than 1
An example of this is, from the list of option is
y = 2(1/5)ˣ
Hence, the exponential decay function is y = 2(1/5)ˣ
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Complete question
Which is a stretch of an exponential decay function?
Of(x) = -(5)ˣ
Of(x) = 5(2)ˣ
O fix) = 2(1/5)ˣ
what is two and four nineths plus two thirds
Answers
Answer:
3 1/9
Change 2/3 to 6/9. Add 6/9 + 4/9 to get 10/9. Make a mixed number, 1 1/9. Add 2, 3 1/9.
An analogue signal received at a detector, measured in microvolts, is normally distributed with mean of 185 and variance of 244. What is the IQR for analogue signal received
Answers
The answer is \(0.5544135^{\circ}$\)
given data
\({mean}(\mu)=185^{}$ \\Variance $\left(\sigma^{2}\right)=244$\)
\(\begin{aligned}&\sigma=\sqrt{244} \\&\sigma=15.6205\end{aligned}\)
\(\frac{P(x < 184)}{p(x < 203)}\)
\(\Rightarrow \frac{p\left(\frac{x-\mu}{\sigma} < \frac{184-185}{15.6205}\right)}{P\left(\frac{x-\mu}{\sigma} < \frac{203-185}{15.6205}\right)}\)
\(\Rightarrow \frac{P(z < -0.064)}{P(z < 1,1523)}\) (From z table)
\($\Rightarrow \frac{p(z < -0.06)}{p(z < 1.15)}$\)
\($\Rightarrow \quad \frac{0.47608}{0.87493}$\)
\($\Rightarrow 0.5544135^{\circ}$\)
\(=0.5544135^{\circ}$\)
What is analogue signal ?
Analog signals are continuous signals that represent other time-varying quantities with their time-varying features, commonly referred to as their variables or variable features. To put it another way, analog signals are comparable to other time-varying signals. An analog audio signal is an illustration of an analog signal. In this case, the pressure connected with the sound waves continually affects the instantaneous voltage associated with the analog data. Digital signals vary from analog signals in that the continuous amount in digital signals is a representation of a series of discrete values. An electric signal is typically referred to as a "analog signal." Human speech, pneumatic signals, and mechanical signals are other signal forms that can be categorized as analog signals.So the more about analogue signal visit.
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quick math question i got stuck on this please help for a mark on brainliest:)
Answers
Answer:
you have to change the sign from - to +
Step-by-step explanation:
-1.8 + k = 8.2
k = 8.2 + 1.8
k = 10
Answer:
sorry this is the way that I usually solve these kinds of problems but, She forgot to make -1.5 into a positive. if that makes sense
Help, i dont understand this!
Answers
The function is increasing in the interval -1<x<3 (Letter D).
FunctionA function can be represented by a graph or an equation. When you have a linear function the graphic representation is a straight line. If you have a curve, the graph can be represented by a quadratic function, cubic function, and others.
All functions can be classified as:
increasing - when the values of y increase with the increasing of x-values decreasing - when the values of y decrease with the increasing of x-valuesThe question asks for the interval where the function increases. Thus, from the graph is possible to see that the function increases when x is between –1 and 3 because the values of y increase with the increase of x-values.
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first to help gets marked brainliest… pls explain how u got the answer plsss
Answers
..............................
Answer:
177 ft below sea level
Step-by-step explanation:
282
10 x 12 = 120. This represents how man ft the hot air balloon rose.
282 - 120 = 162. Keep in mind your still below sea level.
162 + 15 = 177
You add 15 because the hot air balloon is going down 15 feet which adds to being below sea level. ( Your going deeper/lower)
identify the number and type of solutions for the equation 9x2 − 12x 4 = 0.
Answers
Answer:
9x^2-12x+4=0
Step-by-step explanation:
you can use factorization method or Quadratic method (Almighty formular).
The number of the solution of the equation is 2 and the solution is equal and real which is 2/3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.The equation is given below.
9x² - 12x + 4 = 0
The discriminant is given as,
D = (-12)² - 4 x 9 x 4
D = 144 - 144
D = 0
Then the roots of the equation is given as,
9x² - 12x + 4 = 0
(3x)² - 2 · 3x · 2 + (2)² = 0
(3x - 2)² = 0
x = 2/3
The number of the solution of the equation is 2 and the solution is equal and real which is 2/3.
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Triangle A
Triangle B
Which of the following sequences of transformations will carry triangle A onto triangle B?
O A. Rotate triangle A 90° clockwise about (-1,-4), reflect it over the x-axis, and translate it 3 units to the left.
ОВ.
Translate triangle A 1 unit up and 1 unit to the left, rotate it 90° clockwise about the origin, and reflect it over the y-axis.
Answers
Answer:
A
Step-by-step explanation
A
Answer:
Do not trust his answer!! its B
Step-by-step explanation:
I did this question and i picked A because the other person said too but it was wrong
Can you guys help me please bc I tried this and I got it wrong .
Answers
Answer:
\(\frac{1}{3}\)
Step-by-step explanation:
you multiply the denominator with the denominator and the numerator with the numerator
\(\frac{5}{6}x\frac{2}{5}\)
\(\frac{5x2}{6x5}\)
\(\frac{10}{30}\)
\(\frac{1}{3}\)
Hopes this helps please mark brainliest
The joint probability density function of X and Y is given by f(x, y) = ce^(−x−2y) , 0 ≤ x < [infinity], 0 ≤ y < [infinity].
a. Find c.
b. Find P(X < 1, Y < 1).
c. Find P(X > Y ).
d. Find the distribution function of the random variable X − Y .
e. Are X and Y independent?
f. Compute the conditional density of X given that Y = y, where 0 ≤ y < [infinity].
Answers
a. the value of c is 2. b. the probability P(X < 1, Y < 1) is given by 1 - e^-1 - e^-2 + e^-3. c. P(X > Y ) is (-e^(-x-2y) + e^(-2y)y) + e^(-2y) - e^(-2y)y.
a. Finding the value of c:
To find the value of c, we need to integrate the joint probability density function (PDF) over the entire range of x and y and set it equal to 1, since the PDF must satisfy the normalization condition.
The joint PDF is given by f(x, y) = ce^(-x-2y)
∫∫f(x, y) dx dy = 1
∫∫ce^(-x-2y) dx dy = 1
Integrating with respect to x first:
∫[0,∞] ce^(-x-2y) dx = [-ce^(-x-2y)] [0,∞] = ce^(-2y)
Integrating the result with respect to y:
∫[0,∞] ce^(-2y) dy = [-1/2 * ce^(-2y)] [0,∞] = 1/2
Setting this equal to 1:
1/2 = 1/c
Solving for c:
c = 2
Therefore, the value of c is 2.
b. Calculating P(X < 1, Y < 1):
To find the probability P(X < 1, Y < 1), we need to integrate the joint PDF over the given region.
P(X < 1, Y < 1) = ∫[0,1] ∫[0,1] 2e^(-x-2y) dx dy
Integrating this expression, we get:
P(X < 1, Y < 1) = ∫[0,1] [-2e^(-x-2y)] [0,1] dy
= ∫[0,1] -2e^(-1-2y) + 2e^(-2y) dy
= [-e^(-1-2y) + e^(-2y)] [0,1]
= (-e^(-1-2) + e^(-2)) - (-e^(-1) + e^0)
= (-e^-3 + e^-2) - (-e^-1 + 1)
= 1 - e^-1 - e^-2 + e^-3
Therefore, the probability P(X < 1, Y < 1) is given by 1 - e^-1 - e^-2 + e^-3.
c. Finding P(X > Y):
To find the probability P(X > Y), we need to integrate the joint PDF over the region where X > Y.
P(X > Y) = ∫[0,∞] ∫[y,∞] 2e^(-x-2y) dx dy
Integrating this expression, we get:
P(X > Y) = ∫[0,∞] [-e^(-x-2y)] [y,∞] dy
= ∫[0,∞] -e^(-x-2y) + e^(-2y)y dy
= [-e^(-x-2y) + e^(-2y)y] [y,∞]
= (-e^(-x-2y) + e^(-2y)y) - (-e^(-2y) + e^(-2y)y)
= (-e^(-x-2y) + e^(-2y)y) + e^(-2y) - e^(-2y)y
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How do you find 3/4 of 20
Fast response please!!
Answers
Answer:
15
Step-by-step explanation:
3/4(20/1) = (3*20)/(4*1)
60/4
15
.... ≤))≥
.... _| \_
................................
Answers
Answer:
x = 63°
it is an isosceles triangle, so K and M are equal
Step-by-step explanation:
let K be x, since K=M means both equals x
x + x + 54° = 180°
2x + 54° = 180°
2x = 180° minus 54°
2x = 126°
x = 63°
to prove
63° + 63° + 54° = 180°
peace
(1+2)+6=1+(2+6) which property is this
Answers
Answer:
Associative.
Step-by-step explanation:
The associative property is the property that means an equation's result will be the same regardless of grouping the factors together or reversing the equation.
e.g
\((a - b) \times c = c \times (b-a)\)
In an orchard, there are 6 apple trees for every 4 pear trees. Create a ratio table to determine the number of apple trees in the orchard if there are 42 pear trees.
Answers
Answer:
Step-by-step explanation:42 divided by 6= 7 and then times 7 by 4 to get 28 which leaves you with the ratio 2:8
Let a = 24, b = 12, and c = 4. Evaluate ac+bc .
Answers
Answer:
144
Step-by-step explanation:
If u multiply 24 x4 it is 96 and when I multiply 12x4 is 48 and u add 96 plus 48 u get 144.
Please help me solve this
Answers
Answer:
C
Step-by-step explanation:
range 0 to 1 0 is no chance 1 is 100% chance x will be in this range
Find the area
2 cm
17 cm
Help me please
Answers
Step-by-step explanation:
you question isn't clear enough
find the area of what actually?
Answer:
square = 34
triangle = 17
Step-by-step explanation:
How do you graph -3x+4y<4
Answers
The graph is a dashed line, shaded area below the boundary line since y is less than (3/4)x + 1).
What is the graph of -3x + 4y < 4?Given the inequality in the question;
-3x + 4y < 4
First, rearrange the inequality in slope-intercept form ( y = mx + b )by solving for y.
-3x + 4y < 4
4y < 3x + 4
Divide each term by 4
4y/4 < 3x/4 + 4/4
y < (3/4)x + 1
Now, compare to the slope-intercept form ( y = mx + b )
y < (3/4)x + 1
Slope m = 3/4
b = 1 which gives the y-intercept: ( 0,1 ).
Now, graph a dashed line, then shade the area below the boundary line since y is less than (3/4)x + 1 ( y < (3/4)x + 1 ).
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what is the cost of installing a fence around a rectangular shaped lot if the cost of the fence is $3.25 per linear foot and the lot is 80 ft. wide and 120 ft. deep?
Answers
The cost of installing a fence around an 80 ft. wide and 120 ft. deep rectangular lot, with the fence priced at $3.25 per linear foot, will be $1,300.
To determine the cost of installing a fence around a rectangular lot, you need to calculate the total length of the fence required and then multiply that by the cost per linear foot. The given dimensions of the lot are 80 feet wide and 120 feet deep.
First, calculate the perimeter of the rectangular lot. The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length (or depth) and W is the width. In this case, the perimeter is P = 2(120) + 2(80) = 240 + 160 = 400 feet.
Next, multiply the total length of the fence by the cost per linear foot, which is $3.25. So, the cost of installing the fence is 400 feet × $3.25 per linear foot = $1,300.
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