The value of variable x for the given equation, 5x - 16xy +16y² +7x + 17y² is −33 y²/ 4(3 − 4y).
Give a brief account on algebraic expression.An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression said to be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor. An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.).
5x - 16xy +16y² +7x + 17y²
= 12x - 16xy + 33y²
Using the Quadratic Formula, we have:
x = −33 y²/ 4(3 − 4y)
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The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 7 cm and the width is 5 cm, how fast is the area of the rectangle increasing (in cm²/s)?
Answer:
Step-by-step explanation: In the problem, they tell us that
dL / dt = 7 cm/s (the rate at which the length is changing) and
dw / dt = 8 cm/s (the rate at which the width is changing)
Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm
The equation for the area of a rectangle is:
A = L·w, so will need the product rule when taking the derivative.
dA/dt = L (dw/dt) + w (dL/dt)
Now just plug in all of the given numbers:
dA/dt = (7)(7) + (5)(8) = 49+40 = 89 cm²/s
there are 2 coins in a bin. when one of them is flipped it lands on heads with probability 0.6 and when the other is flipped it lands on heads with probability 0.3. one of these coins is to be randomly chosen and then flipped. without knowing which coin is chosen, you can bet any amount up to 10 dollars and you then either win that amount if the coin comes up heads or lose if it comes up tails. suppose, however, that an insider is willing to sell you, for an amount c, the information as to which coin was selected. what is your expected payoff if you buy this information? note that if you buy it and then bet x, then you will end up either winning x - c or -x - c (that is, losing x c in the latter case). also, for what values of c does it pay to purchase the information? reference: https://www.physicsforums/threads/expected-payoff-given-info.200076/
It pays to purchase the information for any value of c less than $13.25 then we buy the information for a price less than $13.25, we can increase our expected payoff above a loss of $1.
To calculate it Let C1 be the event that the first coin is selected and C2 be the event that the second coin is selected. Then, we have:
P(C1) = P(C2) = 1/2 (since one of the two coins is randomly chosen)
P(H|C1) = 0.6 (probability of getting heads when the first coin is flipped)
P(H|C2) = 0.3 (probability of getting heads when the second coin is flipped)
Let's consider the case when we do not buy the insider's information. Then, our expected payoff can be calculated as follows:
E(X) = P(C1) * P(H|C1) * (10) + P(C1) * P(T|C1) * (-10) + P(C2) * P(H|C2) * (10) + P(C2) * P(T|C2) * (-10)
= (1/2) * (0.610 - 0.410 + 0.310 - 0.710)
= -1
Therefore, if we do not buy the insider's information, our expected payoff is a loss of $1.
Now, let's consider the case when we buy the insider's information for an amount c.
If we buy the information, we will know which coin was selected and we can bet accordingly to maximize our expected payoff.
If we know that the first coin was selected, we should bet on heads since it has a higher probability of occurring. If we know that the second coin was selected, we should bet on tails since it has a higher probability of occurring.
Therefore, if we buy the insider's information, our expected payoff can be calculated as follows:
E(X|buying information) = P(C1) * P(H|C1) * (10-c) + P(C1) * P(T|C1) * (-c) + P(C2) * P(H|C2) * (-c) + P(C2) * P(T|C2) * (10-c)
= (1/2) * (0.6*(10-c) - 0.4c + 0.3(-c) - 0.7*(10-c))
= -0.2c + 1.5
To find the values of c for which it pays to purchase the information, we need to solve the inequality:
E(X|buying information) > E(X)
-0.2c + 1.5 > -1
Solving for c, we get:
c < 13.25
Therefore, it pays to purchase the information for any value of c less than $13.25. If we buy the information for a price less than $13.25, we can increase our expected payoff above a loss of $1.
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David is working two summer jobs, making $13 per hour landscaping and making $8 per hour clearing tables. In a given week, he can work no more than 16 total hours and must earn no less than $160. Also, he must work at most 13 hours landscaping. If
� x represents the number of hours landscaping and �y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer: One possible solution is to work 12.3 hours landscaping and 3.7 hours clearing tables, earning approximately $167.1.
Step-by-step explanation:
Let x be the number of hours landscaping and y be the number of hours clearing tables.
The system of inequalities can be written as:
x ≤ 13 (maximum of 13 hours landscaping)
x + y ≤ 16 (maximum of 16 hours total)
13x + 8y ≥ 160 (minimum earnings of $160)
To graph this system of inequalities, we can start by graphing the boundary lines of each inequality as follows:
x = 13 (vertical line at x = 13)
x + y = 16 (line with intercepts at (0, 16) and (16, 0))
13x + 8y = 160 (line with intercepts at (0, 20) and (12.3, 0))
Note that we only need to graph the portion of the lines that are in the feasible region (i.e. where x and y are non-negative).
The feasible region is the triangle formed by the intersection of the three boundary lines, as shown below:
|
20 --|--------------------------
| /|
| / |
| / |
| / |
16 --|------------------
| / |
|/ |
-------------------------
13 12.3
Let x be the number of hours landscaping and y be the number of hours clearing tables.
The system of inequalities can be written as:
x ≤ 13 (maximum of 13 hours landscaping)
x + y ≤ 16 (maximum of 16 hours total)
13x + 8y ≥ 160 (minimum earnings of $160)
To graph this system of inequalities, we can start by graphing the boundary lines of each inequality as follows:
x = 13 (vertical line at x = 13)
x + y = 16 (line with intercepts at (0, 16) and (16, 0))
13x + 8y = 160 (line with intercepts at (0, 20) and (12.3, 0))
Note that we only need to graph the portion of the lines that are in the feasible region (i.e. where x and y are non-negative).
The feasible region is the triangle formed by the intersection of the three boundary lines, as shown below:
lua
Copy code
|
20 --|--------------------------
| /|
| / |
| / |
| / |
16 --|------------------
| / |
|/ |
-------------------------
13 12.3
The vertices of the feasible region are (0, 16), (12.3, 3.7), and (13, 0).
To determine one possible solution, we can evaluate the objective function (total earnings) at each vertex:
(0, 16): 13(0) + 8(16) = $128
(12.3, 3.7): 13(12.3) + 8(3.7) ≈ $167.1
(13, 0): 13(13) + 8(0) = $169
Therefore, one possible solution is to work 12.3 hours landscaping and 3.7 hours clearing tables, earning approximately $167.1.
suppose that 78% of all dialysis patients will survive for at least 5 years. in a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?
The probability that the 78% of all the dialysis patients survive for at least five years will exceed 80%, rounded to 5 decimal places is 0.3192.
What is the probability?The proportion of dialysis patients surviving for at least 5 years = 78% = 0.78
Assuming that a simple random sample of 100 dialysis patients is selected, the sample size is n = 100.
Let p be the proportion of dialysis patients in the sample surviving for at least 5 years.
Then, the sample mean is given by:
μp = E(p) = p = 0.78
So, the mean proportion of dialysis patients surviving for at least 5 years is equal to 0.78.
The standard error of the sample proportion is given by:
σp=√p(1−p)/n
σp=√0.78(1−0.78)/100
σp=0.04278
The required probability is to find P(p > 0.80):
P(p > 0.80) = P(Z > (0.80 - 0.78)/0.04278)
P(p > 0.80) = P(Z > 0.467) = 1 - P(Z < 0.467) = 1 - 0.6808 = 0.3192 (rounded to 5 decimal places)
Therefore, the probability that the proportion surviving for at least five years will exceed 80% in a simple random sample of 100 new dialysis patients is 0.3192.
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Fatima 56 roses, 48 irises and 16 freesia. she wants to create bouquets using all the flowers. calculate the highest number of similar bouquets she can make without having any flowers left over
Answer:
We see that each fraction is in simplest form, and they add up to 1, so this confirms that 168 is the highest number of similar bouquets that Fatima can make without having any flowers left over.
Step-by-step explanation:
Yeah, I guess what that person said ^^ ??
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that of high schoolers in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be x1 = 6 hours, with a standard deviation s1 = 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be x2 = 4 hours, with a standard deviation s2 = 2 hours. Let u1 and u2 represent the mean amount of time spent in extracurricular activities per week by the populations of all high school students in the suburban and city school districts, respectively.
Assume the two-sample t-procedures are safe to use. With a level of 5%, test the hypothesis that the amount of time spent on extracurricular activities is no different in the two groups.
Since the calculated t-value (3.14) is greater than the critical value (1.98), we reject the null hypothesis.
What is null hypothesis?In statistical hypothesis testing, the null hypothesis is a statement about a population parameter that is assumed to be true until there is sufficient evidence to suggest otherwise. The null hypothesis is typically denoted by H0 and represents the status quo or default assumption.
The null hypothesis often takes the form of an equality or a statement of "no difference" or "no effect" between two or more groups, variables, or populations. For example, the null hypothesis could be that the mean score of a group of students on a test is equal to a certain value, or that there is no difference in the average height of males and females in a population.
We want to test the hypothesis that the mean amount of time spent in extracurricular activities per week is the same in the suburban and city school districts. Set up the null and alternative hypotheses is as given by:
Null hypothesis: u1 - u2 = 0
Alternative hypothesis: u1 - u2 ≠ 0
To test this hypothesis, we can use a two-sample t-test. We first calculate the test statistic:
t = ((x1 - x2) - (u1 - u2)) / √(s1²/n1 + s2²/n2)
where x1, s1, and n1 are the sample mean, standard deviation, and sample size for the suburban school district, and x2, s2, and n2 are the sample mean, standard deviation, and sample size for the city school district.
Plugging in the values, we get:
t = ((6 - 4) - 0) / √((3²/60) + (2²/40)) ≈ 3.14
This test's degrees of freedom are given by:
df = (s1²/n1 + s2²/n2)² / ( (s1²/n1)² / (n1 - 1) + (s2²/n2)² / (n2 - 1) )
Plugging in the values, we get:
df = ((3²/60) + (2²/40))² / ( (3²/60)² / 59 + (2²/40)² / 39 ) ≈ 93.24
Using a t-distribution table with 93 degrees of freedom and a level of significance of 0.05, we find the critical values to be approximately -1.98 and 1.98.
Since the calculated t-value (3.14) is greater than the critical value (1.98), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean amount of time spent in extracurricular activities per week is different between the suburban and city school districts.
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Maria purchased 1,000 shares of stock for $35. 50 per share in 2014. She sold them in 2016 for $55. 10 per share. Express her capital gain as a percent, rounded to the nearest tenth of a percent
Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.
To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.
The purchase price for 1,000 shares of stock was:
$35.50 x 1,000 = $35,500
The selling price for 1,000 shares of stock was:
$55.10 x 1,000 = $55,100
The capital gain is the difference between the selling price and the purchase price:
$55,100 - $35,500 = $19,600
To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:
($19,600 / $35,500) x 100 = 55.21%
In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.
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Which of the following subsets of M3(R) are subspaces of M3(R)? (Note: M3(R) is the vector space of all real 3 x 3 matrices)
A. The 3×3 matrices in reduced row-echelon form
B. The 3×3 matrices with all zeros in the third row
C. The diagonal 3×3 matrices
D. The invertible 3×3 matrices
E. The non-invertible 3×3 matrices
F. The symmetric 3×3 matrices
The subsets B. The 3×3 matrices with all zeros in the third row. C. The diagonal 3×3 matrices, and F. The symmetric 3×3 matrices are subspaces of M3(R).
What is a subspace?A subspace of a vector space is a portion of that space that meets the three criteria of closure under addition, closure under scalar multiplication, and the presence of the zero vector. If two vectors from the subspace are added, the resultant vector will still be in the subspace because of closure under addition. If a vector from the subspace is multiplied by any scalar, the resultant vector will still be in the subspace, according to the concept of closure under scalar multiplication.
The conditions of a subspace are: closure under addition, closure under scalar multiplication, and contains the zero vector.
For all the options we have:
A: The 3 x 3 matrices in reduced row-echelon form (A): As this subset is not closed under addition, M3(R), it is not a subspace of M3(R).
B. The 3 x 3 matrices with all zeros in the third row: Due to its closure under addition and scalar multiplication as well as the presence of the zero vector, this subset is a subspace of M3(R).
C. The diagonal 3 x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).
D. The invertible 33 matrices: Because this subset is not closed under addition, M3(R), it is not a subspace of M3(R).
E. The 3 x 3 matrices that are not invertible Due to the fact that it is not closed under scalar multiplication, this subset is not a subspace of M3(R).
F. The symmetric 3x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).
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What is the value of (sine 30 + cos 30 ) - (sin 60 + cos 60 )
The value of ( sin 30° + cos 30° ) - ( sin 60° + cos 60° ) is 0.
(sine 30 + cos 30 ) - (sin 60 + cos 60 )
= ([tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{3} }{2}[/tex]) - ([tex]\frac{\sqrt{3} }{2}[/tex] + [tex]\frac{1}{2}[/tex])
= [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{1}{2}[/tex]
= [tex]\frac{\sqrt{3} }{2}[/tex] - [tex]\frac{\sqrt{3} }{2}[/tex]
= 0
Trigonometry is a branch of mathematics that focuses on the relationships between angles and the sides of triangles. It involves the study of trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant, and their various properties and applications. These functions relate the angles of a right triangle to the lengths of its sides, and they can be used to solve a wide range of problems in fields such as engineering, physics, astronomy, and navigation.
Trigonometry also includes the study of trigonometric identities, which are mathematical expressions that are true for all values of the variables involved. These identities can be used to simplify complex trigonometric expressions and to prove other mathematical theorems.
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Graph the system of equations {y=−12x+4y=−12x−2
Answer:
Step-by-step explanation: i hope this help if not let me know so i can fix it
b) The nearest-known exoplanet from earth is 4.25 light-years away.
About how many miles is this?
Give your answer in standard form.
The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
Hence, The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.
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At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?
Answer:
Step-by-step explanation:
Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:
999n = 727272
To solve for "n", we divide both sides by 999:
n = 727272/999
Using a calculator or long division, we get:
n ≈ 728.56
Therefore, each pizza has approximately 728 slices.
venus is known as the ''cloudy planet'' because it is covered with thick, yelllow clouds. The gravity of venus is 90% of earths gravity. To calculate your weight on venus, multiply your weight by 0.9
Answer:
Step-by-step explanation:
How does Priestley present the theme of social class in Act 1? 3 paragraphs 80 POINTS!!!
INTRODUCTION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
PARAGRAPH 1 -
PARAGRAPH 2-
PARAGRAPH 3-
CONCLUSION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
#Brainlist! Help! Will! Make! You! Brainlist!
Show all steps and how you got the answer
Answer:
x = 8500
y = 15000
Step-by-step explanation:
small vans: x
large vans: y
A: 5x + 2y = 72500
B: 2x + 6y = 107000
5x + 2y = 72500 => y = (72500 - 5x)/2
2x + 6(72500 - 5x)/2 = 107000
2x + 217500 - 15x = 107000
15x - 2x = 217500 - 107000
13x = 110500
x = 110500/13 = 8500
y = (72500 - 5x)/2 = y = (72500 - 5x8500)/2 = 15000
7) 99 was divided by some number, then added to 15. Next, this sum was
multiplied by 8, which gave a product of 48. Find this number.
Answer:
-11
Step-by-step explanation:
48 ÷8=6-15=-9
99÷-9=-11
Can someone help me? I’m not sure what to do.
Step-by-step explanation:
A. To find f(x+h), we substitute (x+h) for x in the equation f(x) = 4x + 7:
f(x+h) = 4(x+h) + 7
Expanding the brackets:
f(x+h) = 4x + 4h + 7
Simplifying, we get:
f(x+h) = 4x + 7 + 4h
Therefore, f(x+h) = 4x + 7 + 4h.
B. To find f(x+h)-f(x)/h, we use the formula for the difference quotient:
[f(x+h) - f(x)] / h
Substituting the expressions we derived earlier:
[f(x+h) - f(x)] / h = [(4x + 7 + 4h) - (4x + 7)] / h
Simplifying, we get:
[f(x+h) - f(x)] / h = (4x + 4h - 4x) / h
Canceling out the 4x terms, we get:
[f(x+h) - f(x)] / h = 4h / h
Simplifying further, we get:
[f(x+h) - f(x)] / h = 4
Therefore, f(x+h)-f(x)/h = 4.
This is Section 3.2 Problem 2: The cost function, in dollars, for producing $x$ items of a certain brand of barstool is given by C(x)-0.01x3-0.6x2+13x+200 (a) C(x).03r- .12x +13 (b) MC(50)-82 dollars per barstool . It approximately represents the cost of producing the 50 th barstool (c) The exact cost of producing the 51th barstool is C 51 -c50 28.91 dollars (d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately -Select
In the following question, the Total cost to production 50 barstools: $1,200 Total cost to produce 51 barstools: $1,228.91 "Total cost to produce 52 barstools: $1,258.44" Total cost to produce 53 barstools: $1,288.59 Therefore, the approximate total cost of producing 53 barstools is $559.15.
The cost function for producing $x$ items of a certain brand of barstool is given by C(x)=0.01x3-0.6x2+13x+200.
(a) C(x)=0.03x3- 0.12x2+13
(b) MC(50)=-82 dollars per barstool.
It approximately represents the cost of producing the 50th barstool.
(c) The exact cost of producing the 51st barstool is C51=C50+MC(50)=$28.91 dollars.
(d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately C50+(53-50) MC(50)=$229.82.
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the population of a country was 259 million in 1982 and the continuous exponential growth rate was estimated at 1.6% per year. assuming that the population of the country continues to follow an exponential growth model, find the projected population in 1992. round your answer to 1 decimal place. the approximate population in 1992 is\
The population of the country was 259 million in 1982 and the continuous exponential growth rate was estimated at 1.6% per year. Assuming that the population of the country continues to follow an exponential growth model, Rounding off the answer to one decimal place, the approximate population in 1992 is 348.2 million.
How to calculate the projected population? We are given, Population in 1982 = 259 millionTime taken = 10 years rate of growth = 1.6% = 0.016 (expressed as a decimal)The formula for exponential growth can be written as; Population = P0ert where, P0 is the initial population, e is the natural logarithmic base, r is the rate of growth and t is the time period We are required to find the projected population in 1992, which means the time period is 10 years (from 1982 to 1992).
Hence, substituting the given values in the formula, we get; P = 259e 0.016 × 10P = 259e0.16P = 259 × 1.185P = 307.215 million Hence, the projected population in 1992 is 307.215 million (rounded off to 1 decimal place, it is 307.2 million).
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What is the image of (-2, 6) after a dilation by a scale factor of 1/2 centered at the
origin?
The image of (-2, 6) after a dilation by a scale factor of 1/2 centered at the origin is given as follows:
(-1, 3).
What is a dilation?A dilation is a transformation that changes the size of a figure, but not its shape. Specifically, a dilation is a type of similarity transformation that involves multiplying the coordinates of each point in a figure by a scale factor. This causes the figure to either enlarge or reduce in size.
The scale factor in the context of this problem is given as follows:
1/2.
The coordinates of the original point are given as follows:
(-2, 6).
Multiplying the coordinates of the original point by the scale factor, the coordinates of the image are given as follows:
(-1,3).
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I’m a bit stuck please help me out
On solving the question we can say that Therefore, the solutions to the inequality given inequality are: x < 4 or x > 6.
What is inequality?An inequality in mathematics is a relationship between two expressions or values that are not equal. Imbalance therefore leads to inequality. An inequality establishes a connection between two values that are not equal in mathematics. Equality is different from inequality. The inequality sign () is most commonly used when two values are not equal. Various inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be solved by changing both sides until only variables remain. But many things contribute to inequality.
two inequalities
4x - 6 < 10
4x < 16
x < 4
2x - 4 > 8
2x > 12
x > 6
Therefore, the solutions to the given inequality are:
x < 4 or x > 6.
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Riley started selling bracelets. During the first month she sold 400 bracelets at $10 each. She tried raising the price, but for every $0. 50 she raised the price, she sold 8 fewer bracelets. What price should she charge in order to make the highest possible gross income?
$17.5 price should she charge in order to make the highest possible gross income.
Given two points are (400, 10) and (392, 10.5)
slope = (10.5-10)/(392 -400) = 0.5/ - 8 = -0.0625
Equation is
p -10 = -0.0625(x-400)
p-10 = -0.0625x + 25
p = -0.0625x + 35
find revenue as
R=x*p
-0.0625x² + 35x
To maximize,
R'(x) =0
-0.125x + 35 = 0
35/0.125 = x
280 = x
when x is equal to 280, find
p= -0.0625(280) + 35
p= -17.5 +35
p= 17.5
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Find a particular solution to the differential equation day dy 8 dt + 20y = 68 – 20t dt2 You do not need to find the general solution. y(t) = symbolic expression
The particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
To solve the given differential equation, we'll need to use the method of undetermined coefficients. In this method, we assume that the particular solution to the differential equation has the same form as the forcing term. Here's how we can solve the given differential equation: Identify the forcing term and its derivatives. The forcing term is given by: f(t) = 68 - 20tWe can find its first derivative as follows: f'(t) = -20We can find its second derivative as follows: f''(t) = Guess the form of the particular solution We assume that the particular solution has the same form as the forcing term.
Since the forcing term is a first-degree polynomial, we assume that the particular solution also has the form of a first-degree polynomial: y_ p(t) = At + B Here, A and B are constants that we need to determine. Find the derivatives of the assumed form of the particular solution. Here are the first and second derivatives of the assumed form of the particular solution: y_ p(t) = At + B ==> y_ p'(t) = A ==> y_ p''(t) = 0. Substitute the assumed form of the particular solution and its derivatives into the differential equation Substituting y_ p(t), y_ p'(t), and y_ p''(t) into the differential equation, we get:8A + 20(At + B) = 68 - 20t Simplifying the above equation, we get: (8A + 20B) + (20A - 20)t = 68Comparing the coefficients of t and the constant terms on both sides,
we get two equations:8A + 20B = 68 (1)20A - 20 = 0 (2)Solving equation (2) for A, we get: A = 1 Substituting A = 1 into equation (1), we get:8 + 20B = 68Solving for B, we get: B = 3. Write the particular solution to the differential equation Substituting A = 1 and B = 3 into the assumed form of the particular solution, we get :y_ p(t) = t + 3Therefore, the particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
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Given that a=14 and b=25, work out the height of the triangle
The height of the triangle is 1.12 units (rounded to two decimal places).
The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex. In other words, it is the length of the line segment that is perpendicular to the base and passes through the opposite vertex.
We can use the formula for the area of a triangle:
Area = (1/2) * base * height
And since we know the values of the base (b) and the area (a), we can rearrange the formula to solve for the height (h):
h = (2a) / b
Plugging in the values of a and b:
h = (2 * 14) / 25
h = 28 / 25
Therefore, the height of the triangle is 1.12 units (rounded to two decimal places).
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Question below pls help:
list the sides of ΔRST in ascending order
m∠R=2x+11°, m∠S=3x+23°, m∠T=x+42°
pls help
Answer:
Step-by-step explanation:
[tex]\angle R+\angle S+ \angle T =180[/tex] (angle sum of a triangle is 180°)
[tex]2x+11+3x+23+x+42=180[/tex]
[tex]6x+76=180[/tex]
[tex]6x=104[/tex]
[tex]x=17.667[/tex]
[tex]\text{So we get: } \angle R= 46.33,\angle S=76,\angle T=59.667[/tex]
In ascending order:
[tex]\angle R= 46.33,\angle T=59.667,\angle S=76[/tex]
when an automatic press is a manufacturing process is operaing properly, the lengths of the component it produces are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches. what is the probability thata randomly selected component is shorter than 7 inches long? (report your answer to 4 decimal places.)
The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.
What is the probability of randomly selected component?We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.
We need to find the probability that a randomly selected component is shorter than 7 inches long.
We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:
z = (7 - 8) / 1.5 = -0.67
Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:
P(z < -0.67) = 0.2514
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which sampling approach was used in the following statement?kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in wisconsin to study their attitudes toward evidence-based practice.
The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.
What is Stratified random sampling?Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.
Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.
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The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−[infinity], [infinity]); y'' − y = 0, y(0) = 0, y'(0) = 5
The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).
Now, we are required to find a member of the family that is a solution to the initial-value problem which is
y(0) = 0 and y′(0) = 5.
The differential equation is y'' − y = 0
The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1
The general solution of the differential equation is y = c1ex + c2e−x
Let us solve for the constants by using the given initial conditions:
At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0
means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2
Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2
The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.
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what is the percentage of 28% of n is 196
Answer:
700
Step-by-step explanation:
28 % of n = 28/100 x n = 0.28n
If 28% of n = 196 that means
0.28n = 196
Divide both sides by 0.28
0.28n/0.28 = 196/0.28
n = 700
$2$ white balls and $5$ orange balls together weigh $8$ pounds. $6$ white balls and $3$ orange balls together weigh $20$ pounds.
What is the weight of $4$ white balls and $4$ orange balls together, in pounds?
Let's break this problem down step by step.
First, we can work out the weight of one white ball by subtracting the weight of 6 white and 3 orange balls (20 pounds) from the weight of 2 white and 5 orange balls (8 pounds):
Weight of 1 white ball = 8 - 20 = -12
Next, we can work out the weight of one orange ball by subtracting the weight of 2 white and 5 orange balls (8 pounds) from the weight of 6 white and 3 orange balls (20 pounds):
Weight of 1 orange ball = 20 - 8 = 12
Now that we know how much one white and one orange ball weigh, we can work out the weight of 4 white and 4 orange balls together:
Weight of 4 white and 4 orange balls = (4 x -12) + (4 x 12) = 0
Therefore, the weight of 4 white and 4 orange balls together is 0 pounds.
By solving two given simultaneous equations using algebra, we find that the combined weight of 4 white balls and 4 orange balls is 16 pounds.
Explanation:The subject matter of this question pertains to simultaneous equations. The equations in question are, 2w + 5o = 8 and 6w + 3o = 20, where w stands for the weight of a white ball and o stands for the weight of an orange ball. We can solve these equations to find the individual weights of these balls. After finding these values, we substitute these into a new equation, 4w + 4o, to find the total weight of 4 white and 4 orange balls together. By solving these equations, we find that the weight of 4 white balls and 4 orange balls together is 16 pounds.
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