Answers
The general solution to the differential equation based on the information is y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)
How to explain the equationBased on the information, dy/dx + 3y = 2x³ e^(-3x)
The integrating factor is e^(∫3 dx) = e^(3x),
e^(3x) dy/dx + 3e^(3x) y = 2x^3 e^(3x - 3x)
d/dx (e^(3x) y) = 2x^3
e^(3x) y = ∫2x^3 dx = (1/2)x^4 + C
C is an arbitrary constant of integration.
y = (1/2) x^4 e^(-3x) + C e^(-3x)
The equation will be y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)
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Related Questions
5/6 having denominator 35
Answers
Answer:( 175/6)
Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35
Which of the points below correctly plots the point (3,7π/6)?
Six plotted points on a coordinate plane.
Select the correct answer below:
A
B
C
D
E
F
Answers
Answer: the answer is D
Step-by-step explanation:
Remember that the coordinates (3,7π6) tell us the radius r=3 and the angle θ=7π6. So the point should be on the circle labeled 3 and form an angle of 7π6 with the positive x-axis. Point D is the correct point.
precalculus problem need help
Answers
1. <C= 90 degree
AC = 13.25 unit
<B= 60 degree
2. <C= 90 degree
AC = 13.
<B= 60 degree
1. Using Sine law
sin C/4 = sin 30/2 = sin B/ AC
so, sin C/4 = 1/4
sin C = 1
C= 90 degree
and, <B= 180 - 30- 90= 60 degree
So, sin 30/2 = sin 60/ AC
1/4 AC = √3/2
AC = 2√3
2. Using Sine law
sin 30/ 7.65 = sin B / 15.3
1/15.3 = sin B/15.3
sin B= 1
B = 90 degree
and, <C= 180 - 90 - 30 = 60
So, 1/15.3 = sin 60/ C
C = 13.25
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Determine if the question is a Statistical Question
Answers
Answer:
satiscal
Step-by-step explanation:
can someone help really fast look at the directions and just do it in a simpler way if you can please hurry somebody
Answers
Answer:
The easiest method to remember when dividing fractions is Keep Change Flip (KCF)
Step-by-step explanation:
I wrote out some examples of KCF. Once you use KCF, you just multiply the fractions normally and then don't forget to write the improper fractions (ex: 12/7) as a mixed number (1 5/7)
If you have any questions about the steps just let me know. I hope this helps ^-^
The profit made by a shop increases each year. The profit made by the shop in year n is £Pn Given that the profit made by the shop in the next year is £Pn + 1 then Pn + 1 = aPn + 800 where a is a constant. The table shows the profit made by the shop in 2018 and in 2019 Year 2018 2019 Profit £24 000 £29 600 Work out the profit predicted to be made by the shop in 2021
Answers
Answer:
£44,384
Step-by-step explanation:
Given the recurrence relation for profit is ...
P[2018] = £24000P[2019] = £29600P[n+1] = a·P[n] +800you want the profit in 2021.
Value of 'a'Using the given relations we have ...
P[2019] = a·P[2018] +800
29600 = a·24000 +800
28800 = a·24000
a = 288/240 = 1.2
Next termsThen the profit for the next two years is ...
P[2020] = 1.2·P[2019] +800 = 1.2·29600 +800 = 36320
P[2021] = 1.2·36320 +800 = 44384
The profit is predicted to be £44,384 in 2021.
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Jon has a rectangular picture that is 54 inches wide and 24 inches tall. He wants to hang it on the wall shown so that it is centered both horizontally and vertically.
Answers
To center the picture both horizontally and vertically on the wall, Jon should hang it 3.75 feet from the left edge of the wall and 3 feet from the top edge of the wall.
First, we need to convert the dimensions of the picture from inches to feet Width: 54 inches = 4.5 feet and Height: 24 inches = 2 feet
To center the picture horizontally, we need to find the distance between the left edge of the wall and the left edge of the picture, and then subtract this distance from the distance between the right edge of the wall and the right edge of the picture.
The difference should be zero if the picture is centered.
Distance between left edge of wall and left edge of picture = (12 ft - 4.5 ft) / 2 = 3.75 ft
Distance between right edge of wall and right edge of picture = (12 ft - 4.5 ft) / 2 = 3.75 ft
So, the picture is centered horizontally.
To center the picture vertically, we need to find the distance between the top edge of the wall and the top edge of the picture, and then subtract this distance from the distance between the bottom edge of the wall and the bottom edge of the picture.
The difference should be zero if the picture is centered.
Distance between top edge of wall and top edge of picture = (8 ft - 2 ft) / 2 = 3 ft
Distance between bottom edge of wall and bottom edge of picture = (8 ft - 2 ft) / 2 = 3 ft
So, the picture is centered vertically.
Therefore, Jon should hang the picture 3.75 feet from the left edge of the wall and 3 feet from the top edge of the wall to center it both horizontally and vertically.
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una barra de carbono de radio 0'1 mm se utiliza pára construir una resistencia. La resistividad de este material es 3.5 x 10- 5 Ω. m. Que longitud de la barra de carbono se necesita para obtener una resistencia de 10Ω?
Answers
The length of carbon rod is needed to obtain a resistance of 10 ohms is 0.00897 or 8.97 × 10⁻³ meters.
How to determine the length of carbon rod?In Mathematics and Science, the resistance of any conductor (wire) in terms of length can be calculated by using this formula:
Length = RA/ρ
Where:
R is the resistance.A is the area of conductor.ρ is the resistivity.By substituting the parameters, we have:
Length = Rπr²/ρ
Length = [10 × 3.142 × (0.0001)²]/3.5 × 10⁻⁵
Length = 3.142 × 10⁻⁷/3.5 × 10⁻⁵
Length = 0.00897 or 8.97 × 10⁻³ meters.
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Complete Question:
A carbon bar of radius 0.1 mm is used to build a resistor. The resistivity of this material is 3.5 x 10-5 Ω. m. What length of carbon rod is needed to obtain a resistance of 10 ohms?
Out of 50 students taking a midterm psychology exam, 26 answered the first of two bonus questions, 33 answered the second bonus question, and 2 didn't bother with either
Answers
Answer:
This has no answer. Whats the question? Please tell me so I can help you
Is it probability ???
A manager of a factory purchases a large number of sheets of aluminium, all of them longer than 100 cm in length. Each piece is then cut so that it is 100 cm long. The length of a sample of the off-cuts, in cm, resulting from cutting the lengths to size are given below: (Hint: Mean = 6, 5)
5,2 6,6 3,5 8,9 7,5 7,3
Using the data above:
Calculate the coefficient of variation rounded to 1 decimal place
Answers
The coefficient of variation for the off-cuts lengths is 30.0%, which indicates a relatively high degree of variability in the data.
The coefficient of variation (CV) is a measure of relative variability, which is calculated by dividing the standard deviation by the mean, and expressing the result as a percentage. It is used to compare the variability of different datasets, particularly when they have different units or scales.
To calculate the CV for the off-cuts lengths in this problem, we first need to calculate the mean and the standard deviation. The mean is calculated by adding all the values together and dividing by the number of values:
Mean = (5.2 + 6.6 + 3.5 + 8.9 + 7.5 + 7.3) / 6 = 6.5 cm
Next, we need to calculate the standard deviation, which measures the dispersion of the data points from the mean. We can use the formula:
Standard Deviation = √(Σ(xi - x)² / (n - 1))
where xi is the value of each data point, x is the mean, and n is the number of data points.
Standard Deviation = √[(5.2 - 6.5)² + (6.6 - 6.5)² + (3.5 - 6.5)² + (8.9 - 6.5)² + (7.5 - 6.5)² + (7.3 - 6.5)²] / 5
Standard Deviation = 1.951 cm
Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean, and multiplying by 100 to express the result as a percentage:
CV = (1.951 / 6.5) x 100 = 30.0%
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Mary started a bank account with m dollars. The money increased to 6.2 times the sum of the starting amount and $4. Mary then withdrew 3 times there starting amount. The remaining balance was 348.80. Enter the amount of money, in dollars, Mary used to start the account.
Please be quick I only have an hour to submit. Thank you
Answers
* Mary started the account with m dollars
* The balance increased to 6.2 times the sum of m dollars and $4
* So the balance became: 6.2 * (m + 4)
* Mary then withdrew 3 times the starting amount (3 * m)
* The remaining balance is 348.80
To find m, the starting amount, we can set this up as an equation:
6.2 * (m + 4) - 3m = 348.80
Simplify:
6.2m + 24 - 3m = 348.80
3.2m + 24 = 348.80
3.2m = 324.80
m = 101
So the amount of money Mary used to start the account was $101.
Here are the key steps:
1) Identify the starting amount as m dollars
2) Calculate the increased balance: 6.2 * (m + 4)
3) Calculate the withdrawal amount: 3 * m
4) Set up an equation to solve for m:
6.2m + 24 - 3m = 348.80
5) Simplify and solve the equation for m
6) The solution is m = 101 therefore the starting amount was $101
Does this help explain the steps and logic to solve the word problem? Let me know if any part of the solution is unclear or if you have any other questions!
I can also re-explain the steps in another way or provide an additional example if needed. The core concept is setting up the necessary calculations and equations to work backwards and determine the unknown starting value (m) based on the provided information about deposits, withdrawals, and ending balances.
Please feel free to ask for clarification or provide another example you would like help solving. I'm happy to discuss word problems and strategy further!
Hello random community i have a question to ask what is 7/8 - 3/4
Answers
Answer: 1/8
Step-by-step explanation:
First make the bottom half the same:
3/4*2/2=6/8
We don’t need to change the first portion since they have a common factor
7/8-6/8=1/8
Prove Vin 20 + los 20 = 1
Answers
The prove of the trig identity gives sin²θ + cos²θ = 1.
What is the proof of the trig identity?The proof of the trig identity is determined as follows;
Let's consider a right triangle with one acute angle θ.
Let the hypotenuse have length 1
Let the length of the adjacent side = cosθ
then, the opposite side length = sinθ
Apply Pythagorean theorem, to determine the hypotenuse side;
(sinθ)² + (cosθ)² = 1²
sin²θ + cos²θ = 1
Thus, we have proved the identity.
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Simplify \sqrt[3]{576000 \cdot 4 \cdot 48}
Answers
The simplification of the cube root of the given expression ∛ ( 576000 × 4 × 48 ) is equal to 480.
The expression is equal to ,
∛ ( 576000 × 4 × 48 )
Write all the factors of the given numbers,
576000 = 576 × 1000
⇒ 576000 = 24 × 24 × 10³
Now,
48 = 24 × 2
And 4 = 2 × 2
Simplify this expression,
Use the fact that the cube root of a product is equal to the product of the cube roots of the factors.
∛ (a × b × c) = ∛a × ∛b × ∛c
Using this property, simplify ∛(576000 × 4 × 48) as follows,
∛(576000 × 4 × 48) = ∛(576000) × ∛(4) × ∛(48)
Rewrite the given expression in the factor form,
∛ ( 576000 × 4 × 48 )
= ∛ 24 × 24 × 10³ × 2 × 2 × 2 × 24
= ∛ 24³ × 10³ × 2³
= ∛(24)³ × ∛(10)³ × ∛(2)³
= 24 × 10 × 2
= 480
Therefore, the simplification of the given expression is equal to 480.
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The above question is incomplete, the complete question is:
Simplify ∛ ( 576000 × 4 × 48 )
Can someone help me out these in order please
Answers
To find the circumscribed side of a triangle, the steps to follow are:
1. Construct the perpendicular bisector of one of the sides of the triangle.
2. Construct the perpendicular bisector of the second side of the triangle.
3. Identify the point of intersection for the two perpendicular bisectors. This is the circumcenter of the triangle and the center of the circumscribed triangle.
4. Construct a circle that has a radius that is the length from the circumcenter to one of the vertices of the triangle.
What is the circumscription of a triangle?A circumscribed triangle is one in which a circle is drawn in the center of the triangle and the circle goes round while touching only three vertices of the triangle.
To draw the circumscribed side of a triangle, you can start by constructing the perpendicular bisector of one of the sides and then the second side. Next, identify the point of intersection, and finally construct the circle.
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Explain how to simplify this expression: 4a + 19 - 3a - 7
Answers
Answer:
1a+12
Step-by-step explanation:
Set up and find the meaure of the arc or angle indicated.
Answers
Applying the inscribed angle theorem, the measure of the angle is calculated: 35°.
How to Find the Measure of the indicated angle using the Inscribed Angle Theorem?Recall the following based on the inscribed angle theorem:
Measure of an arc = 2(measure of inscribed angle)
Also not that half of a circle is equal to 180 degrees. Therefore, we have:
Measure of arc QR = 180 - 110 = 70 degrees.
Measure of angle QRS = 1/2(measure of arc QR)
Plug in the values:
Measure of angle QRS = 1/2(70)
Measure of angle QRS = 35°
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Determine the type of probability:
A spinner has 4 equal-sized spaces labeled A, B, C, and D.
The chance of landing in any of the spaces is 1/4, or 25%.
Answers
Answer:
Theoretical Probability
Step-by-step explanation:
Total number of possible outcomes
awarding 84 points!!! Before playing a game that uses a spinner, you decide to examine the fairness of the spinner. The spinner is divided into 5 equally-sized sectors that are numbered 1, 2, 3, 4 and 5.
You spin the spinner 1000 times and notice that 5 is spun 203 times.
Which statement best describes the fairness of the spinner?
There is not enough information to determine if the spinner is probably fair.
The spinner is probably fair because 5 was spun approximately 200 times.
The spinner is probably not fair because 5 was spun 203 times which is more than expected.
Answers
Answer: The spinner is probably because 5 was spun approximately 200 times
Step-by-step explanation:
What are the polar coordinates of the point A shown below?
Select the correct answer below:
(−2,5π6)
(2,π3)
(2,−5π6)
(3,π3)
(−3,−π6)
(3,−5π6)
Answers
Answer:
(−3,−π/6)
Step-by-step explanation:
Note that the point is on the circle whose radius is labeled 3, so r=3 or r=−3. Of the choices available, only an angle of −π6, drawn from the negative x axis plots at the point A. So θ=−π6, and r must be negative, as the angle is measured from the negative x axis. Thus, the polar coordinates are (−3,−π6).
This query is about identifying the polar coordinates of a specific point on a graph. However, without an accompanying graphical representation, a definitive answer cannot be provided based on the options given. Polar coordinates represent a point using the distance from a reference point and an angle from a reference direction.
Explanation:The question is about polar coordinates, a way of expressing the location of a point in two-dimensional space. Without seeing the actual point A on a graph, it is not possible to definitively determine its polar coordinates from the provided choices. However, it is very crucial to know that polar coordinates represent a point in the plane using the distance from a reference point and an angle from a reference direction. The distance, represented as r, should always be non-negative whereas the angle θ can range from 0 to 2π, or in negative, -π to π. An understanding of these may help you determine the coordinates of the point A in your problem.
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Use the stem-and-leaf plot of Monthly Sales Goals to answer the question that follows.
Monthly Sales Goals (in thousands)
Stem Leaf
1 2 5 5 8
2 4 4 6
3 4 6
4 7 8 9
What is the range of the monthly sales goals? Round to the nearest thousand.
$12,000
$24,000
$37,000
$49,000
Answers
The range of the monthly sales goals is; 37,000.
We are given the stem plot :
Stem Leaf
1 2, 5, 5, 8
2 4, 4, 6
3 4, 6
4 7, 8, 9
The largest number is 49 and the smallest is 12. Since is in thousands, the numbers become 49,000 and 12,000.
Range = highest value - the lowest value
Range = 49,000 - 12,000 = 37,000
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.HELPPPPPPPPPPPPPPPPP
Answers
Answer:
[tex]\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1[/tex]
Step-by-step explanation:
Slope intercept form of a line equation is
y = mx + b
where
m = slope
b = y-intercept
A perpendicular line to y = mx + b will have a slope of -1/m
Let's first find the equation for line z in slope-intercept form
Slope m for a line = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line
Slope of line z is
[tex]m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}[/tex]
So line z will have an equation of the form
[tex]y = -\dfrac{3}{5}x + b[/tex]
We know that a line perpendicular to this line will have a slope of
[tex]- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}[/tex]
So the equation of the perpendicular line is
[tex]y = \dfrac{5}{3}x + b[/tex]
Only one of the 4 choices, name choice A has this slope of 5/3
Therefore the correct answer choice is A
There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:
The perpendicular line passes through (3, 6). This means when x = 3, y =6
Substitute these values of x, y into the equation for the perpendicular line and solve for b
[tex]y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1[/tex]
This corresponds to Choice A
8y^2+6xy
evaluate the given polynomial at:
x=3, y=1
. Replace the variable(s) in the polynomial with the specific value(s) given and determine the value of the polynomial by performing the indicated operations.
Answers
Answer:
Putting the values of x and y in the given polynomial
[tex] = 8({1})^{2} + 6(3)(1)[/tex]
[tex] = 8(1) + 18[/tex]
[tex] = 8 + 18[/tex]
[tex] = 26[/tex]
Hence the value of polynomial is 26
Solve the following differential equations
Answers
Which sequences are geometric? Select three options.
O-2.7, -9, -30, -100, ...
0-1, 2.5, -6.25, 15.625,...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4,-4, -12, -20, ...
Answers
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
8, 0.8, 0.08, 0.008, ...
Answer:
A. -2.7, -9, -30, -100, ...
B. -1, 2.5, -6.25, 15.625, ...
C. 9.1, 9.2, 9.3, 9.4, ...✔️
D. 8, 0.8, 0.08, 0.008, ...✔️
E. 4, -4, -12, -20, ... ✔️
Hope you understand
Let me know if you need further explaination
A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $27. For 9 pounds of jelly beans and
7 pounds of almonds, the total cost is $51. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans:
Cost for each pound of almonds:
Answers
Answer:
Cost for each pound of jelly beans: $2.75
Cost for each pound of almonds: $3.75
Step-by-step explanation:
Let J be the cost of one pound of jelly beans.
Let A be the cost of one pound of almonds.
Using the given information, we can create a system of equations.
Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:
[tex]\implies 3J + 5A = 27[/tex]
Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:
[tex]\implies 9J + 7A = 51[/tex]
Therefore, the system of equations is:
[tex]\begin{cases}3J+5A=27\\9J+7A=51\end{cases}[/tex]
To solve the system of equations, multiply the first equation by 3 to create a third equation:
[tex]3J \cdot 3+5A \cdot 3=27 \cdot 3[/tex]
[tex]9J+15A=81[/tex]
Subtract the second equation from the third equation to eliminate the J term.
[tex]\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}[/tex]
Solve the equation for A by dividing both sides by 8:
[tex]\dfrac{8A}{8}=\dfrac{30}{8}[/tex]
[tex]A=3.75[/tex]
Therefore, the cost of one pound of almonds is $3.75.
Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.
Using the first equation:
[tex]3J+5(3.75)=27[/tex]
[tex]3J+18.75=27[/tex]
[tex]3J+18.75-18/75=27-18.75[/tex]
[tex]3J=8.25[/tex]
[tex]\dfrac{3J}{3}=\dfrac{8.25}{3}[/tex]
[tex]J=2.75[/tex]
Therefore, the cost of one pound of jelly beans is $2.75.
Find the parallelogram
Answers
Answer: -14
Step-by-step explanation:
I hope this helps
find the equation of the following lines:
parallel to the line joining (1;2) and (-2;-2) and passing through (4;1)
passing through the point (2; -3) and perpendicular to the line joining (2;-3) to (-1;-1)
Answers
Answer:
[tex]\textsf{1)}\quad y = \dfrac{4}{3}x-\dfrac{13}{3}[/tex]
[tex]\textsf{2)} \quad y = \dfrac{3}{2}x-6[/tex]
Step-by-step explanation:
To find the equation of a line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1), we first need to find the slope of the line joining (1, 2) and (-2, -2).
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{-2-1}=\dfrac{-4}{-3}=\dfrac{4}{3}[/tex]
Parallel lines have the same slope, so the slope of the parallel line is m = 4/3.
Substitute the found slope and point (4, 1) into the point-slope formula:
[tex]\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - 1 &= \dfrac{4}{3}(x - 4)\\\\y - 1 &= \dfrac{4}{3}x-\dfrac{16}{3}\\\\y &= \dfrac{4}{3}x-\dfrac{13}{3}\end{aligned}[/tex]
Therefore, the equation of the line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1) is:
[tex]\boxed{y = \dfrac{4}{3}x-\dfrac{13}{3}}[/tex]
[tex]\hrulefill[/tex]
To find the equation of a line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3), we first need to find the slope of the line joining (2, -3) and (-1, -1).
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-(-3)}{-1-2}=\dfrac{2}{-3}=-\dfrac{2}{3}[/tex]
The slopes of perpendicular lines are negative reciprocals, so the slope of the parallel line is m = 3/2.
Substitute the found slope and point (2, -3) into the point-slope formula:
[tex]\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - (-3) &= \dfrac{3}{2}(x - 2)\\\\y+3&= \dfrac{3}{2}x-3\\\\y &= \dfrac{3}{2}x-6\end{aligned}[/tex]
Therefore, the equation of the line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3):
[tex]\boxed{y = \dfrac{3}{2}x-6}[/tex]
A standard deck of
52
5252 cards contains
4
44 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered
2
22 through
10
1010, a jack, a queen, a king, and an ace.
Bashir decides to pick one card at random from a standard deck of
52
5252 cards. Let
�
FF be the event that he chooses a face card (a jack, queen, or king of any suit) and
�
SS be the event that he chooses a spade.
What is
�
(
�
or
�
)
P(F or S)P, left parenthesis, F, start text, space, o, r, space, end text, S, right parenthesis, the probability that the card Bashir chooses is either a face card or a spade?
Answers
The probability that Bashir chooses a card that is either a face card or a spade is 11/26.
To find the probability that the card Bashir chooses is either a face card or a spade, we need to add the probabilities of the two events occurring and then subtract the probability of their intersection (choosing a face card that is also a spade).
First, we need to find the probability of choosing a face card. There are 12 face cards in a deck (4 jacks, 4 queens, and 4 kings), and a total of 52 cards, so the probability of choosing a face card is
P(F) = 12/52 = 3/13
Next, we need to find the probability of choosing a spade. There are 13 spades in a deck (from 2 to ace), and a total of 52 cards, so the probability of choosing a spade is
P(S) = 13/52 = 1/4
To find the probability of choosing either a face card or a spade, we can use the formula
P(F or S) = P(F) + P(S) - P(F and S)
We need to find the probability of choosing a face card that is also a spade (their intersection). There are only 3 face cards that are spades (jack of spades, queen of spades, king of spades), so the probability of choosing a face card that is also a spade is
P(F and S) = 3/52
Now we can plug in the values to get
P(F or S) = P(F) + P(S) - P(F and S)
P(F or S) = 3/13 + 1/4 - 3/52
P(F or S) = 12/52 + 13/52 - 3/52
P(F or S) = 22/52
P(F or S) = 11/26
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Find the Constant of proportionality of Henderson Toll Road Cost
Answers
The constant of proportionality is equal to 3/10.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the miles traveled.x represents the cost ($).k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/10 = 6/20 = 9/30
Constant of proportionality, k = 3/10.
Therefore, the required linear equation is given by;
y = kx
y = 3/10(x)
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