Answer: To solve the system of equations using the matrix method, we first need to set up the corresponding coefficient matrix and augmented matrix:
Coefficient matrix:
[1 4]
[2 -3]
Augmented matrix:
[1 4 | 9]
[2 -3 | 7]
To solve the system using matrix method, we perform row operations on the augmented matrix to get it into row echelon form, and then back substitute to obtain the solutions.
Performing row operations:
Multiply the first row by 2 and subtract the result from the second row:
[1 4 | 9]
[0 -11| -11]
Divide the second row by -11:
[1 4 | 9]
[0 1 | 1]
Subtract 4 times the second row from the first row:
[1 0 | 5]
[0 1 | 1]
The row echelon form of the augmented matrix is:
[1 0 | 5]
[0 1 | 1]
Therefore, the solution is x = 5 and y = 1.
So the solution of the system of equations is x = 5 and y = 1.
Step-by-step explanation:
help again asapppppp
Answer:
[tex]\mathrm{y\:=\:\frac{3}{2}x\:+\:7}[/tex]
Step-by-step explanation:
To find the equation of a line parallel to -4y = 32 - 6x, we first need to rewrite this equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
-4y = 32 - 6x
Divide both sides by -4:
y = -8 + (3/2)x
So the slope of this line is 3/2. Since we want a line parallel to this one, it will have the same slope of 3/2.
Now we can use the point-slope form of a linear equation to find the equation of the line that passes through (0,7) with a slope of 3/2:
y - y1 = m(x - x1)
where m = 3/2 and (x1,y1) = (0,7)
y - 7 = (3/2)(x - 0)
Simplifying:
y - 7 = (3/2)x
y = (3/2)x + 7
So the equation of the line parallel to -4y = 32 - 6x that passes through the point (0,7) is y = (3/2)x + 7.
A tree on a hillside casts a shadow c = 235 ft down the hill. If the angle of inclination of the hillside is b = 26° to the horizontal and the angle of elevation of the sun is a = 56°, find the height of the tree. (Round your answer to the nearest foot.)
The height of the tree is equal to 210 ft to the nearest foot using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
angle opposite of the tree = 56 - 26 = 30
angle opposite of the shadow = 180 - 90 - 56= 34
by application of sine rule:
sin 30/h = sin 34/235
h = (235 × sin 30)/sin 34 {cross multiplication}
h = 117.5/0.5592
h = 210.1216 ft.
Therefore, the height of the tree is equal to 210 ft to the nearest foot using the sine rule.
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Find the volume of the right circular cone with r=22.1 mm and h=5.91 mm.
Answer:
radius r = 22.1 m
height h = 5.91 m
slant height s = 22.8765841 m
volume V = 3022.73898 m^3
lateral surface area L = 1588.30288 m^2
base surface area B = 1534.38527 m^2
total surface area A = 3122.68815 m^2
Step-by-step explanation:
Standard Scores
Use both the Student ID and Distance to Work variables.
List the Student ID at TESU in ascending order of Distance to Work.
Calculate the z-scores associated with each student (use the sample standard deviation for this calculation).
Identify potential outliers and explain your reasoning.
Confidence Intervals/Samples
Take a sample of the first four data points for the variable Distance to Work (unsorted - use the original order in the dataset).
Determine the 95% and 99% confidence intervals using the same size of 4.
Describe and compare the two intervals.
Take a sample of the first seven data points for the variable Distance to Work (unsorted - use the original order in the dataset).
Determine the 95% confidence interval. Use the same mean and SD, but change the sample size to 20 and determine the 95% confidence interval.
Describe and compare the two intervals.
STUDENT DATA TABLE
ID School Enrolled Months enrolled Birthday month Distance to Work Height Foot Size Hand Size Sleep Homework
1 Arts and Sciences 12 January 0 60 8 5 360 30
2 Applied Science and Technology 6 February 0 62 7 6 400 45
3 Business and Management 8 April 5 66 10 7 420 60
4 Nursing 10 June 10 68 12 8 440 15
5 Public Service 48 July 15 68 14 8 540 75
6 Arts and Sciences 48 June 30 70 12 9 480 120
7 Applied Science and Technology 36 October 32 72 12 8 320 80
8 Applied Science and Technology 32 November 36 75 14 7 440 60
9 Nursing 6 July 8 63 9 7 300 90
10 Arts and Sciences 22 May 22 80 14 9 420 30
11 Business and Management 15 February 10 65 8 6 500 60
12 Public Service 20 April 4 71 10 8 400 20
13 Applied Science and Technology 11 March 15 66 9 7 440 60
14 Arts and Sciences 18 November 28 64 9 7 300 30
15 Arts and Sciences 29 January 12 72 10 8 360 80
16 Nursing 13 December 6 63 8 6 480 100
17 Business and Management 49 August 0 79 13 9 410 25
18 Applied Science and Technology 16 April 10 74 12 8 430 15
19 Business and Management 24 September 30 66 10 6 330 60
20 Arts and Sciences 8 May 0 65 9 7 480 30
For the sample size of 20, the 95% confidence interval is (-4.87, 27.16), which is narrower than the previous interval due to the larger sample size.
What is mean?In statistics, mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total number of values in the set. Mean is also commonly referred to as the arithmetic mean. It is a commonly used statistical measure in many fields including finance, economics, social sciences, and more.
Here,
To calculate the z-scores associated with each student, we first need to calculate the sample mean and standard deviation for the Distance to Work variable:
Sample mean: (0+0+5+10+15+30+32)/7 = 10.71
Sample standard deviation: √(((0-10.71)² + (0-10.71)² + (5-10.71)² + (10-10.71)² + (15-10.71)² + (30-10.71)² + (32-10.71)²)/6) = 10.72
Now we can calculate the z-scores for each student:
Student 1: (0 - 10.71) / 10.72 = -0.94
Student 2: (0 - 10.71) / 10.72 = -0.94
Student 3: (5 - 10.71) / 10.72 = -0.53
Student 4: (10 - 10.71) / 10.72 = -0.07
Student 5: (15 - 10.71) / 10.72 = 0.40
Student 6: (30 - 10.71) / 10.72 = 1.80
Student 7: (32 - 10.71) / 10.72 = 1.98
Student 8: (8 - 10.71) / 10.72 = -0.25
Student 9: (36 - 10.71) / 10.72 = 2.37
Student 10: (9 - 10.71) / 10.72 = -0.16
Student 11: (22 - 10.71) / 10.72 = 1.05
Student 12: (10 - 10.71) / 10.72 = -0.07
Student 13: (15 - 10.71) / 10.72 = 0.40
Student 14: (28 - 10.71) / 10.72 = 1.54
Student 15: (12 - 10.71) / 10.72 = 0.12
Student 16: (6 - 10.71) / 10.72 = -0.44
Student 17: (0 - 10.71) / 10.72 = -0.94
Student 18: (10 - 10.71) / 10.72 = -0.07
Student 19: (30 - 10.71) / 10.72 = 1.80
Student 20: (0 - 10.71) / 10.72 = -0.94
To identify potential outliers, we can look for z-scores that are more than 2 standard deviations away from the mean (i.e., greater than 2 or less than -2). From the list above, we can see that Students 6, 7, 9, and 19 have z-scores greater than 2, indicating that they may be potential outliers.
For the second sample of seven data points (0, 0, 5, 10, 15, 30, 32), the mean is 11.14 and the standard deviation is 12.05. Using a t-distribution with 6 degrees of freedom (n-1), the 95% confidence interval is (-7.54, 29.82).
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Find the linear function with the following properties.
f(0)=8
Slope of f=−6
The linear function with the given properties is: f(x) = 8 - 6x.
What is linear function?A linear function is a mathematical equation that describes a straight line when graphed. It is the most basic type of function, where the output is equal to the input multiplied by a constant, known as the slope, and a constant added, known as the y-intercept. Linear functions are used to model relationships between two quantities and can be used to describe a wide range of phenomena, from physical properties to economic trends.
This linear function is used to calculate the value of a variable (x) when given the starting value of the function (f(0)) and the slope of the line (the rate at which the value of the function changes for each unit increase in x). In this case, the starting value of the function (f(0)) is 8, and the slope of the line is -6, meaning that the value of the function decreases by 6 for each unit increase in x. Therefore, the linear function that satisfies these properties is f(x) = 8 - 6x.
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Write a polynomial function of the least degree with integral coefficients that have the given zeros.1+3i,-2i
The polynomial function of the least degree with integral coefficients that has the zeros [tex]1 + 3i[/tex], [tex]-2i[/tex] is f(x) = x⁴ - 2x³ + 14x² - 8x + 40.
Writing a polynomial function of the least degreeFrom the question, we are to write a polynomial function of the least degree with integral coefficients that have the given zeros.
The given zeros are [tex]1+3i[/tex],[tex]-2i[/tex].
If [tex]1 + 3i[/tex] and [tex]-2i[/tex]are zeros of a polynomial function with integral coefficients, then their conjugates [tex]1 - 3i[/tex] and [tex]2i[/tex] are also zeros of the function.
To find the polynomial function, we can use the fact that if r is a zero of a polynomial function, then (x - r) is a factor of the function. Thus, we can start by writing out the factors corresponding to each of the zeros:
[tex](x - (1 + 3i))(x - (1 - 3i))(x - (-2i))(x - 2i)[/tex]
Next, we can simplify these factors by multiplying them out:
[tex][(x - 1) - 3i][(x - 1) + 3i](x + 2i)(x - 2i)\\= [(x - 1)^2 - (3i)^2](x^2 - (2i)^2)[/tex]
= [(x - 1)² + 9](x² + 4)
Expanding the terms, we get:
(x² - 2x + 10)(x² + 4)
Multiplying out the factors, we obtain:
x⁴ - 2x³ + 10x² + 4x² - 8x + 40
Simplifying this expression, we get:
x⁴ - 2x³ + 14x² - 8x + 40
Hence, the polynomial function is f(x) = x⁴ - 2x³ + 14x² - 8x + 40
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8. Daisy is trying to figure out how much negotiating room she has in purchasing a new car. The car has an MSRP of $34,995.99. She has learned from an industry insider that most car dealerships have a 20% markup on selling price. What does she estimate the dealership paid for the car?
Answer:
To estimate the dealership's cost for the car, we need to first calculate the dealership's selling price. We know that the car has an MSRP of $34,995.99, and we know that dealerships typically have a 20% markup on selling price.
So, to find the dealership's selling price, we can use the formula:
Selling price = MSRP + (Markup percentage * MSRP)
Substituting the values we have:
Selling price = $34,995.99 + (20% * $34,995.99)
Selling price = $34,995.99 + $6,999.20
Selling price = $41,995.19
Therefore, we estimate that the dealership paid $41,995.19 - the 20% markup - for the car.
To check this estimate, we can calculate the dealership's cost using the formula:
Cost = Selling price - Markup
Substituting the values we have:
Cost = $41,995.19 - (20% * $41,995.19)
Cost = $41,995.19 - $8,399.04
Cost = $33,596.15
This is very close to the MSRP of $34,995.99, which suggests that our estimate is reasonable.
P12 000 is deposited in an account earning 4% interest per year. What is the amount
after 15 years
Answer:
After 15 years, the amount in the account will be $21.611.32, assuming the interest is compounded annually.
Step-by-step explanation:
To calculate the amount after 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
In this case, P = $12,000, r = 0.04 (4% expressed as a decimal), n = 1 (compounded annually), and t = 15 years.
Plugging in the values, we get:
A = $12,000(1 + 0.04/1)^(1*15)
A = $12,000(1.04)^15
A = $12,000(1.801)
A = $21,611.32
Therefore, after 15 years, the amount in the account will be $21.611.32, assuming the interest is compounded annually.
find the diffrence. enter your answer in simplest terms using the slash (/) as a faction bar
Answer:
7/8 - 5/7 =
49-40/56 =
9/56
can someone help me with this
please show work
Answer:
1) S=31.68 yd A=174.23 [tex]yd^{2}[/tex]
2) S=36.65 in A=256.56 [tex]in^{2}[/tex]
3) S=8.9 ft A=13.35 [tex]ft^{2}[/tex]
4)S=17.28 in. A=51.84 [tex]in^{2}[/tex]
5)S=25.31 yd. A=126.54 [tex]yd^{2}[/tex]
6)S=3.4ft A=5.11 [tex]ft^{2}[/tex]
Step-by-step explanation:
Notes:
360 was divided by 1/2, making the denominator 180. This is why there is a 1/2 at the front.
You also do not need to simplify if you're using a calculator.
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
- r is the radius
- θ is [tex]\frac{angle\pi }{180}[/tex]
S= r θ
-r is the radius
- θ is [tex]\frac{angle\pi }{180}[/tex]
1)
S=r θ
S=11([tex]\frac{165\pi }{180}[/tex])........................................plug in values
S=11( [tex]\frac{11\pi }{12}[/tex]).........................................simplify
S=31.68 yd....................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]11^{2}[/tex]) [tex]\frac{165\pi }{180}[/tex]....................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]121[/tex]) [tex]\frac{11\pi }{12}[/tex]....................................simplify
A=174.23 [tex]yd^{2}[/tex].....................................solve and round.
2)
S=r θ
S=14([tex]\frac{150\pi }{180}[/tex])...........................................plug in values
S= =14( [tex]\frac{5\pi }{6}[/tex]).........................................simplify
S=36.65 in........................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]14^{2}[/tex]) [tex]\frac{150\pi }{180}[/tex]......................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]196[/tex]) [tex]\frac{5\pi }{6}[/tex]......................................simplify
A=256.56 [tex]in^{2}[/tex]....................................solve and round.
3)
S=r θ
S=3([tex]\frac{170\pi }{180}[/tex]).........................................plug in values
S= 3( [tex]\frac{17\pi }{18}[/tex]).......................................simplify
S=8.9 ft..........................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]3^{2}[/tex]) [tex]\frac{170\pi }{180}[/tex]........................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]9[/tex]) [tex]\frac{17\pi }{18}[/tex].......................................simplify
A=13.35 [tex]ft^{2}[/tex]........................................solve and round.
4)
S=r θ
S=6([tex]\frac{165\pi }{180}[/tex]).......................................plug in values
S=6( [tex]\frac{11\pi }{12}[/tex]).......................................simplify
S=17.28 in....................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]6^{2}[/tex]) [tex]\frac{165\pi }{180}[/tex].....................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]36[/tex]) [tex]\frac{11\pi }{12}[/tex]..................................simplify
A=51.84 [tex]in^{2}[/tex].....................................solve and round.
5)
S=r θ
S=10([tex]\frac{145\pi }{180}[/tex]).........................................plug in values
S=10( [tex]\frac{29\pi }{36}[/tex]).........................................simplify
S=25.31 yd.......................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]10^{2}[/tex]) [tex]\frac{145\pi }{180}[/tex].......................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]100[/tex]) [tex]\frac{29\pi }{36}[/tex]....................................simplify
A=126.54 [tex]yd^{2}[/tex].....................................solve and round.
6)
S=r θ
S=3([tex]\frac{65\pi }{180}[/tex])..........................................plug in values
S= 3( [tex]\frac{13\pi }{36}[/tex]).......................................simplify
S=3.4ft............................................solve and round
A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ
A=[tex]\frac{1}{2}[/tex]([tex]3^{2}[/tex]) [tex]\frac{65\pi }{180}[/tex].......................................plug in values
A= =[tex]\frac{1}{2}[/tex]([tex]9[/tex])[tex]\frac{13\pi }{36}[/tex]......................................simplify
A=5.11 [tex]ft^{2}[/tex].........................................solve and round.
given the lengths of two sides of a triangle , write an inequaluty to indicate between which two number the lengths of the third side must fall. 8 and 13
Answer:
5 < x < 21
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
13 - 8 < x < 13 + 8 , then
5 < x < 21
Solve the indicated quantity
The solutions to the indicated quantities are x = 25, MIK = 25 and KIE = 50 degrees
How to solve the indicated quantitiesThe value of x
From the question, we have the following angle that can be used in our computation:
Angle MIE = 75
Using the above as a guide, we have the following:
x + 2x = 75
Evaluate
3x = 75
So, we have
x = 25
The angle MIK
From the figure, we have
MIK = x
So, we have
MIK = 1 * 25
MIK = 25
The angle KIE
From the figure, we have
KIE = 2x
So, we have
KIE = 2 * 25
KIE = 50
Hence, the measure of angle KIE is 50 degrees
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Combine like terms: -4x+3-7x-8
A. -7x-5
B. -11x-5
C. -3x -11
D. none of the above
Answer:
answer is B
Step-by-step explanation:
-4x-7x=-11x
+3-8=-5
=-11x-5
answer: B -11x-5
[tex] \sf \implies \: - 4x +3 - 7x - 8[/tex]
[tex] \sf \implies \: - 11x +3 - 8[/tex]
[tex] \sf \implies \: - 11x - 5[/tex]
Hence, Option B is correct!!
The demand equation for a certain commodity is given by the
following equation.
p= =1/2+². - 20x + 1200, 0≤x≤ 120
Find x and the corresponding price p that maximize revenue.
The maximum value of R(x) occurs at x =0.
In the given demand equation, the value of x and corresponding price p that maximize revenue are x = 31.8 and p = $514.60.
How to Solve the Equation?To find the value of x and corresponding price p that maximize revenue, we first need to determine the revenue function. Revenue (R) is given by the product of price (p) and quantity demanded (x), so:
R(x) = xp
Substituting the given demand equation for p, we get:
R(x) = x(1/2 + ² - 20x + 1200)
Simplifying and rearranging:
R(x) = 1/2x + ²x - 20x² + 1200x
R(x) = -20x² + (1200 + ²)x + 1/2x
To find the value of x that maximizes revenue, we take the derivative of R(x) with respect to x, set it equal to zero, and solve for x:
dR/dx = -40x + (1200 + ²) + 1/2 = 0
Solving for x:
x = (1200 + ² + 1/2) / 40
x = 31.8
To find the corresponding price, we substitute this value of x back into the demand equation for p:
p = 1/2 + ² - 20(31.8) + 1200
p = $514.60
Therefore, the value of x and corresponding price p that maximize revenue are x = 31.8 and p = $514.60.
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Given: If A AND B, then C. Given: The if-then statement's reverse isalso correct. If A is True, B is True, what is C?
The conclusion is that if A is true, B is true, then C must be true as well.
What is statement ?
In logic and mathematics, a statement is a declarative sentence that is either true or false. It is an assertion about a fact or a relationship between facts. A statement can be a simple sentence, such as "The sun is shining," or a complex one, such as "If it rains tomorrow, I will stay indoors."
If the statement "If A AND B, then C" is true, and if its reverse statement is also true, then the converse of the statement is "If C, then A AND B."
If A is true and B is true, then A AND B is also true. Therefore, by the original statement, C must also be true.
Therefore, the conclusion is that if A is true, B is true, then C must be true as well.
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You are trying to develop a strategy for investing in two different stocks The anticipated annual return for a 1,000 investment in each stock under four different economic conditions has the probability distribution shown to the right Complete parts ( ) through ( ) below
The first step in developing a strategy for investing in two different stocks is to perform research on the stocks and their respective industries.
What is stock?Stock is a type of security that signifies ownership in a company and represents a claim on part of the company's assets and earnings. It is a share of ownership in a company. It is bought and sold on a stock exchange, and the price of the stock is determined by the supply and demand of the stock.
This can be done by looking at the company’s financials, track record, industry trends, and more. This research can help you to determine which stock is more likely to perform better in any given economic condition. By doing this, you can maximize your return while also minimizing your risk. This can be done by using a risk-adjusted return metric such as the Sharpe Ratio.
Finally, you must decide how to allocate funds across the two stocks. This will depend on your risk tolerance and investment goals. For example, if you are a conservative investor, you may want to allocate more funds to the stock with the highest expected return under all economic conditions. On the other hand, if you are a more aggressive investor, you may want to allocate more funds to the stock with the highest expected return under one or two of the economic conditions.
Overall, developing a strategy for investing in two different stocks takes into account several factors, including research, expected returns, and risk tolerance. By doing this, you can maximize your return while also minimizing your risk.
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prove or disprove the quadrilateral be low is a rectangle by using the concepts of slope and congruence
(100 points)
The proof that the quadrilateral is a rectangle is shown below
Proving or disproving that the quadrilateral is a rectangleFrom the question, we have the following parameters that can be used in our computation:
A = (-2, 3)
B = (-4, 1)
C = (2, -1)
D = (0, -3)
From the graph, we have the following lengths
AB = √8
CD = √8
BD = √32
AC = √32
The above shows that opposite sides are equal
From the graph, we have the following slopes
AB = 1
CD = 1
BD = -1
AC = -1
The above shows that opposite sides are have equal slopes and adjacent sides are their slopes to be opposite reciprocals
Hence, the quadrilateral is a rectangle
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Write in Slope-Intercept form:
Slope = -2
Y-Intercept = ( -5 , -4 )
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Given the slope m = -2 and the y-intercept (a, b) = (-5, -4), we can substitute these values into the equation to get:
y = mx + b
y = -2x + (-4)
y = -2x - 4
Therefore, the equation in slope-intercept form is y = -2x - 4.
Write an inequality to describe each situation. a. The minimum age for voting in the United States is 18 years old. Let a represent a voter's age. b. A theater seats up to 275 people. Let p represent the number of people attending a performance in the theater.
According to this inequality, the number of persons attending a theatrical inequality play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.
What is inequality?In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. We resuming our current status quo. Yet a variety of things lead to inequality: Negative values on both sides are split or added.
a. The disparity in representing the voting age in the United States is as follows:
a ≥ 18
In order to be eligible to vote, a voter's age, denoted by a, must be more than or equal to 18 years old.
b. The inequality used to depict a theater's seating capacity is:
p ≤ 275
According to this inequality, the number of persons attending a theatrical play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.
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Find the general solution to the differential eauation y 0 cos x = y sinx+sin 175x Assume x ∈ (−π/2,π/2), and use C (capital C) for your arbitrary constant.
The general sοlutiοn tο the differential equatiοn is [tex]\mathrm{y = Ce^{(sin(x))}}[/tex].
Describe Differentiatiοn?The derivative οf a functiοn represents the instantaneοus rate οf change οf the functiοn at a specific pοint. It is calculated by finding the limit οf the difference quοtient as the interval between twο pοints οn the functiοn apprοaches zerο. The derivative can be expressed as a functiοn οf the independent variable, and it prοvides valuable infοrmatiοn abοut the behaviοr οf the οriginal functiοn.
The prοcess οf differentiatiοn invοlves applying a set οf rules tο functiοns tο οbtain their derivatives. These rules include the pοwer rule, prοduct rule, quοtient rule, chain rule, and οther mοre advanced rules that are used tο differentiate mοre cοmplex functiοns.
Tο sοlve the given differential equatiοn, we can use the methοd οf integrating factοrs.
First, we can rewrite the equatiοn as:
y'cοsx = ysinx + sin(175x)
Next, we can multiply bοth sides by the integrating factοr, which is [tex]e^{(\int(cos(x) dx))} = e^{(\sin(x) + C)}[/tex], where C is a cοnstant οf integratiοn:
[tex]\mathrm {e^{(sin(x)) }y'cosx = e^{(sin(x))} ysinx + e^{(sin(x))}sin(175x) + Ce^{(sin(x))}}[/tex]
Nοw, we can recοgnize the left-hand side as the derivative οf [tex]e^{(sin(x))}y[/tex]:
[tex](e^{(sin(x))y)}' = e^{(sin(x))} y' + cos(x) e^{(sin(x))}y[/tex]
Substituting this intο the abοve equatiοn, we get:
[tex]\mathrm{(e^{(sin(x))y)}' = e^{(sin(x)) }ysinx + e^{(sin(x))}sin(175x) + Ce^{(sin(x))}}[/tex]
[tex]cos(x) e^{(sin(x))}y = e^{(sin(x))y)}'[/tex]
Separating variables and integrating bοth sides, we get:
[tex]\int e^{sin(x) }dy/y = \int cos(x) dx[/tex]
ln|y| + C = sin(x) + C'
where C' is anοther cοnstant οf integratiοn.
Therefοre, the general sοlutiοn tο the differential equatiοn is:
[tex]\mathrm{|y| = e^{(sin(x)) }e^{(C' - sin(x))}}[/tex]
[tex]\mathrm{y = \± e^{(C' - sin(x) + sin(x))}}[/tex]
[tex]\mathrm{y = Ce^{(sin(x))}}[/tex]
where C is an arbitrary cοnstant.
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for the following right triangle. find the side length x. round your answer to the nearest hundreth.
Answer:
answer is 11.60
Step-by-step explanation:
formula is C^2 = a^2 + b^2
c = 13
a = 8
b = ?
169 = 64 + x^2
135 = x^2
I hope this helps!
x 2 −51=14xx, squared, minus, 51, equals, 14, x 1) Rewrite the equation by completing the square.
Answer:
(x -7)² = 100
Step-by-step explanation:
You want to rewrite the equation x² -51 = 14x by completing the square.
Complete squareWhen we're finished, the equation will be of the form ...
(x +a)² = b
Expanding this, we have ...
x² +2ax +a² = b
That is, the value of 'a' is half the coefficient of x when the equation is written with the x-terms together.
RearrangementAdding 51 -14x to both sides of the given equation, we get ...
x² -51 = 14x
x² -14x = 51
Now, we can see that a=-14/2 = -7. We can add a² = (-7)² = 49 to both sides to complete the square:
x² -14x +49 = 51 +49
(x -7)² = 100 . . . . . . . rewritten equation
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I forgot where to start in solving this equation
What is the distance between the points (15,-17) and (-10,-17) in the coordinate plane?
A. 12.5 units
B. 25 units
C. 32 units
D. 5 units
Hello and Regards zoecenters91522.
Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.
Step-by-step explanation:The distance between two points is the measure of the length of the straight line that joins them. On a Cartesian plane, the distance between two points is calculated using the Euclidean distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is equal to the square root of the sum of the squares of the differences of their coordinates:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
This formula can be used to calculate the distance between two points on any plane, such as a three-dimensional plane or Euclidean space of any dimension.
Now we locate the points of x and y.
x₁ = 15, y₁ = -17x₂ = -10, y₂ = -17We substitute the points in the formula and solve:
[tex]\huge \boxed{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
[tex]\huge \boxed{d=\sqrt{(-10-15)^2+(-17-(-17))^2 } }[/tex]
[tex]\huge \boxed{d=\sqrt{(-25)^2+0^2}=\sqrt{625+0} }[/tex]
[tex]\huge \boxed{d=\sqrt{625}=25 \ units }[/tex]
Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.
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As economy of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.02 worth of coal, $0.30 worth of electricity, and 0.30 worth of steel, the electric industry needs $0.04 worth of coal, $0.04 worth of electricity, and 0.02 worth worth of steel, and the steel industry needs $0.10 worth of coal and $0.04 worth of steel. The sales demand is estimated to be $1 billion for coal, $1 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and demand for coal doubles, whereas the demand for for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand.
Answer:
Step-by-step explanation:
Let’s denote the production levels of coal, electricity and steel as x, y and z respectively. We can set up a system of equations to represent the inter-industry demand for each industry’s output.
For coal: 0.02x + 0.04y + 0.10z = x For electricity: 0.30x + 0.04y = y For steel: 0.30x + 0.02y + 0.04z = z
Solving this system of equations gives us x = (50/3)y and z = (25/2)y.
The new sales demand for coal is $2 billion (double the original), for electricity is $3 billion (triple the original) and for steel is $6 billion (an increase of 50%). Substituting these values into our equations gives us:
(50/3)y = $2 billion y = $3 billion (25/2)y = $6 billion
Solving these equations gives us y = $3 billion, x = $5 billion and z = $18.75 billion.
So to satisfy the new demand, the coal industry should produce at a level of $5 billion, the electric industry should produce at a level of $3 billion and the steel industry should produce at a level of $18.75 billion.
Batteries are sold in packs
and boxes.
There are 8 batteries in each
pack.
There are 30 batteries in
each box.
Emily buys p packs of
batteries and b boxes of
batteries.
Write down an expression,
in terms of pand b, for the
total amount of batteries
that Emily buys.
Answer:
The total number of batteries that Emily buys can be expressed as:
8p + 30b
Here, 8p represents the total number of batteries in the packs that Emily buys, and 30b represents the total number of batteries in the boxes that Emily buys. By adding these two terms together, we can find the total number of batteries that Emily buys.
**Jackie took out a mortgage loan for $90,000 at an interest rate of 10% for 25 years. If Jackie had not filed a bankruptcy, which damaged her credit score a lot, her payments could have been much lower at $527.16 per month. How much is Jackie paying in additional interest over the life of the loan?
Hint: 1st, use minimum monthly payment formula: to calculate the monthly payment at 10% interest rate, where PV = 90,000, i = 0.10/12, and n = 300 (because that is how many months there are in 25 years).
2nd, once you find P multiply it by 300 months to find how much Jackie paid for the lifetime of the loan for the mortgage.
3rd, finally, subtract $90,000 to find out how much interest she paid in total.
4th, how much would Jackie have paid for the lifetime of the loan if her monthly payments were $527.16 (if she had not filed bankruptcy)? Remember, this is the monthly payment, so you don't have to use the formula, just multiply it by 300 months to find the cost of the lifetime loan.
5th, subtract $90,000 from the answer you got in step 4. That is how much interest Jackie would have paid if the monthly loan payments were smaller.
Finally, what is the difference between the interest you found in step 3 and step 5?
a.
$49,200.00
b.
$87,201.20
c.
$68,148.00
d.
$56,809.00
Please select the best answer from the choices provided.
The difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is $83,421.
What is the interest?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
First, we need to calculate the monthly payment at a 10% interest rate for 25 years:
PV = 90,000
i = 0.10/12
n = 25*12 = 300
Using the formula for the monthly payment of a mortgage loan, we get:
[tex]P = i PV / (1 - (1 + i)^{(-n)})[/tex]
= 805.23
So, if Jackie paid the minimum monthly payment, she would pay $805.23 per month. The total amount paid over the lifetime of the loan would be:
Total amount paid = P * n = 805.23 * 300 = $241,569
The amount of interest paid would be:
Interest paid = Total amount paid - PV = 241,569 - 90,000 = $151,569
If Jackie had made payments of $527.16 per month, the total amount paid over the lifetime of the loan would be:
Total amount paid = 527.16 * 300 = $158,148
The amount of interest paid would be:
Interest paid = Total amount paid - PV = 158,148 - 90,000 = $68,148
Therefore, the difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is: $151,569 - $68,148 = $83,421
hence, the answer is not one of the choices provided.
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Pat needs to paint an 8 ft × 36 ft rectangular wall. What is the area that needs to be painted?
A) 300 ft2
B) 288 ft2
C) 282 ft2
D) 276 ft2
Need Help (25 Points)
Answer:
Opposite (or a any synonyms)
Addition (Or sum)
division
inverse
Step-by-step explanation:
The first one is the most complicated, theres so many words can fit. Probably try with an synonyms of reverse like "Opposite"
For the 2nd,3rd and 4th options:
Addition (Or sum) since is the reverse of subtraction
division since is the reverse of multiplication
inverse since those functions (Exponent and radicals) are also inverse of each other