Complete question :
A builder has an 6-acre plot divided into 1/4 -acre home sites. How many 1/4 -acre home sites are there?
Answer:
24 home sites
Step-by-step explanation:
Given :
Total size of land = 6 - acre
Size of each home site = 1/4 acre
Number of home sites obtainable from the 6-acre land :
Total size of land ÷ size of each home site ;
6 ÷ 1/4
6 * 4/1
= 24
Hence, 24 home sites are on the plot of land.
Joe earns a monthly salary of 250 plus a commission on his total sales. Last month his total sales were $7,289 and he earned a total of $1,275. What is his commission rate?
Answer: Joe earns a monthly salary of 250 plus a commission on his total sales. Last month his total sales were $7,289 and he earned a total of $1,275. What is his commission rate?
Step-by-step explanation:
250 + $7,289 + $1,275 = 8814
Consider the circular annulus (a plane figure consisting of the area between a pair of concentric circles) specified by the range: 1 1 cases. b) Find the potential that satisfies the following boundary conditions 1 u (1,0) = sin? (0) ), u (2,0) = 0. ) = + (1 - cos (20),
The potential that satisfies the given boundary conditions in part (a) and (b) is: [tex]\[u(r, \theta) = \sin(\theta)\][/tex] and [tex]\[u(r, \theta) = \sin(\theta)\][/tex] respectively.
Consider the circular annulus (a plane figure consisting of the area between a pair of concentric circles) specified by the range:
[tex]$1 \leq r \leq 2$.[/tex]
a) Find the potential that satisfies the following boundary conditions:
[tex]\[\begin{aligned}u(1,0) &= \sin(\theta) \\u(2,0) &= 0 \\u(\theta, 1) &= 1 + (1 - \cos(2\theta))\end{aligned}\][/tex]
b) Find the potential that satisfies the following boundary conditions:
[tex]\[\begin{aligned}u(1,0) &= \sin(\theta) \\u(2,0) &= 0 \\u(\theta, 1) &= 1 + (1 - \cos(20\theta))\end{aligned}\][/tex]
To solve this problem, we can use separation of variables and assume a solution of the form:
[tex]\[u(r, \theta) = R(r)\Theta(\theta)\][/tex]
Plugging this into Laplace's equation [tex]$\nabla^2u = 0$[/tex] and separating variables, we get:
[tex]\[\frac{1}{R}\frac{d}{dr}\left(r\frac{dR}{dr}\right) + \frac{1}{\Theta}\frac{d^2\Theta}{d\theta^2} = 0\][/tex]
Solving the radial equation gives us two solutions:
[tex]\[R(r) = A\ln(r) + B\quad \text{and} \quadR(r) = C\frac{1}{r}\][/tex]
For the angular equation, we have:
[tex]\[\Theta''(\theta) + \lambda\Theta(\theta) = 0\][/tex]
The general solution to this equation is given by:
[tex]\[\Theta(\theta) = D\cos(\sqrt{\lambda}\theta) + E\sin(\sqrt{\lambda}\theta)\][/tex]
To satisfy the boundary conditions, we can impose the following restrictions on [tex]$\lambda$[/tex] and choose appropriate constants:
For part (a)
[tex]\[\begin{aligned}R(1) &= 0 \implies B = -A\ln(1) = 0 \implies B = 0 \\R(2) &= 0 \implies A\ln(2) + B = 0 \implies A\ln(2) = 0 \implies A = 0 \\\Theta(0) &= \sin(0) \implies D = 0 \\\Theta(0) &= \sin(0) \implies E = 1\end{aligned}\][/tex]
Therefore, the potential that satisfies the given boundary conditions in part (a) is:
[tex]\[u(r, \theta) = \sin(\theta)\][/tex]
For part (b)
[tex]\[\begin{aligned}R(1) &= 0 \implies B = -A\ln(1) = 0 \implies B = 0 \\R(2) &= 0 \implies A\ln(2) + B = 0 \implies A\ln(2) = 0 \implies A = 0 \\\Theta(0) &= \sin(0) \implies D = 0 \\\Theta(0) &= \sin(0) \implies E = 1\end{aligned}\][/tex]
Therefore, the potential that satisfies the given boundary conditions in part (b) is:
[tex]\[u(r, \theta) = \sin(\theta)\][/tex]
Please note that in both parts (a) and (b), the radial solution does not contribute to the potential due to the boundary conditions at r=1 and r=2. Thus, the solution is purely dependent on the angular part.
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A particular high school claims that its students have unusually high math SAT scores. A random sample of 50 students from this school was selected, and the mean math SAT score was 544. Is the high school justified in its claim? Explain since it within the range of a usual event, namely within of the mean of the because the score) sample means (Round to two decimal places as needed)
The school is not justified to make this claim because of the reasons defined.
The following is a statement that might be made about the high school to justify its claim No, because the z-score of Z = 1.06 is not uncommon because it does not fall within the range of a typical event, namely within 2 standard deviations of the sample mean.
It has been given to us that:
μ = 511
σ = 119
Sample size (n) = 55
and
s = 119 / √55
= 16.046
As we all know,
Only when z > 2 then, the high school's allegation is valid and warranted.
To locate,
Z's value is
So,
Z = ( X - μ )/σ
by applying the Central Limit Theorem to the values,
z = ( 528 - 511 ) / 16.046
= 1.06
Since, z < 2, as a result, the allegation is unjustified.
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Correct question:
The average math SAT score is 511 with a standard deviation of 119. A particular high school claims that its students have unusually high math SAT scores. A random sample of 55 students from this school was selected, and the mean math SAT score was 528. Is the high school justified in its claim? Explain. ▼ No Yes , because the z-score ( nothing) is ▼ unusual not unusual since it ▼ does not lie lies within the range of a usual event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means. (Round to two decimal places as needed.)
Phil has 5 times as many toy race cars as Richard has. Phil has 425 toy race cars. How many race cars does Richard have? *
Answer:
85
Step-by-step explanation:
425 divided by 8= 85
Answer:
He as 85 race cars.
Step-by-step explanation:
Just divide 425 by 5 and you have your answer.
Pls help this is sooOOOOOOO annoying!!
(07.06)Number line with closed circle on 9 and shading to the left.
Which of the following inequalities best represents the graph above?
a > 9
a < 9
a ≤ 9
a ≥ 9
Answer:
a ≤ 9
Step-by-step explanation:
Closed circle means ≤ or ≥
Shading to the left means left direction < or ≤
The inequality sign that has both is: ≤
a ≤ 9
Answer:
The answer is C
Step-by-step explanation:
I took the test and I got it right
Write 3^4 in expanded form. (3^4 means 3 raised to the fourth power.)
A: 3x3
B :3x3x3
C: 3x3x3x3
D: 3x3x3x3x3
Answer:
c because 3.3.3.3 is 3 to the 4th power expanded
Compute the Laplace transform of the function f on (0,0) defined by f(t) = { i Se4 0 3 Give your answer as a function in the variable s for s > 0. L(f)(s) =___
The Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is L(f)(s) = i S / (2s-4).
Given function is f(t) = i Se^4t
Here, Laplace transform of the function f is given by:
L(f)(s) = ∫[0,∞) e^(-st) f(t) dt
On substituting the given function in the above equation, we get:
L(f)(s) = ∫[0,∞) e^(-st) i Se^(4t) dt
L(f)(s) = i S ∫[0,∞) e^(t(4-s)) dt
We know that the Laplace transform of e^(at) is 1/(s-a).
Therefore, Laplace transform of e^(t(4-s)) = 1/(s - (4-s)) = 1/(2s - 4).
Therefore,L(f)(s) = i S * ∫[0,∞) e^(t(4-s)) dt
L(f)(s) = i S * 1/(2s-4) * [-e^(-(4-s)t)]_0^∞
L(f)(s) = i S * 1/(2s-4) * [0 - (-1)] (since the exponentials evaluated at ∞ is zero)
L(f)(s) = i S * 1/(2s-4) * 1
L(f)(s) = i S / (2s-4)
Therefore, the Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is L(f)(s) = i S / (2s-4).
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Martin recorded the low temperatures at his house for one week. The temperatures are shown below.
-7, -3, 4, 1, 2, 8, 7
Approximately what was the average low temperature for the week?
Α. 7
B. "1
C. 1
D "8
What is the solution to the equation below?
0.5n = 6
It's 12 because if you divide 6 by 0.5 you should get 12, so basically use the opposite operation.
Hope that helps!
What is the slope of a line perpendicular to the line y=2/3 x + 3 ( just find the slope)
help a girl out? please
Answer:
21/20
Step-by-step explanation:
If you left $25.00 on your table for a $21.50 meal, what was the percent of the tip?
A.15.0%
B.14.0%
C.18.4
D.16.3
Answer:
I THINK it would be B.
Step-by-step explanation:
I’m very sorry if I’m wrong.
Answer:
16.3%
Step-by-step explanation:
21.5 times 0.163= 3.5
What is the slope of the line connecting the pair of points (0,7) (4,12)
Answer: 5/4
Step-by-step explanation: That should be right because I have big brain. Mark brainlist please :)
A group of 5 friends sold lemonade. If they sold each cup for $0.50 on Friday and for $0.45 on each other day of the week, how much money did each friend make if they split the money evenly?
Day Number of cups
Monday 15
Tuesday 8
Wednesday 5
Thursday 11
Friday 23
Answer:
69
Step-by-step explanation:
Answer:
Step-by-step explanation:
62.00
Find the slope of the line?
Answer:
m=3/4
Step-by-step explanation:
First, let us remind ourselves of the slope formula: m=rise/run=([tex]y_{2}[/tex]-[tex]y_{1}[/tex])/([tex]x_{2}[/tex]-[tex]x_{1}[/tex])
Let's pick two points from the graph to work with. Let's do (3,-6) and (-1,-9).
And let 3=[tex]x_{1}[/tex], -6=[tex]y_{1}[/tex], -1=[tex]x_{2}[/tex], -9=[tex]y_{2}[/tex].
1. Substitute the values into the slope formula: [-9-(-6)]/(-1-3)
2. simplify the expression: [-9-(-6)]/(-1-3)=(-9+6)/-4=-3/-4=3/4
3. As a result, the slope of the line is 3/4
Please help I’m having a hard time :(
Answer:
i think you're right- you seem to have all numbers squared correctly, also every negative value squared becomes a positive number, which means that your answers are correct.. what is your issue?
Step-by-step explanation:
8. The 2% solution of tetracaine hydrochloride is already isotonic. How many milliliters of a 0.9% solution of . sodium chloride should be used in compounding the prescription? Tobramycin 0.5% Tetracaine hydrochloride Sol. 2% 15 mL Sodium chloride qs Purified water ad 30 mL Make isoton, sol. Sig. for the eye
To make the 2% solution of tetracaine hydrochloride isotonic, a 0.9% solution of sodium chloride should be used.
The amount of the 0.9% sodium chloride solution needed can be calculated by setting up a proportion based on the concentration percentages.
Let's assume x represents the volume of the 0.9% sodium chloride solution needed in milliliters.
Since the 0.9% solution is isotonic, it means that the concentrations of tetracaine hydrochloride and sodium chloride should be equal. Therefore, the proportion can be set up as follows:
(0.9 / 100) = (2 / 100) * (x / 30)
Simplifying the proportion, we have:
0.009 = 0.02 * (x / 30)
To solve for x, we can multiply both sides of the equation by 30 and divide by 0.02:
x = (0.009 * 30) / 0.02
x ≈ 13.5 mL
Therefore, approximately 13.5 milliliters of the 0.9% sodium chloride solution should be used in compounding the prescription to make the 2% tetracaine hydrochloride solution isotonic.
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The product of three consecutive non-zero integers is taken. Which statement must be true?
Select one:
O A. The third consecutive integer must be even,
B. The product must be odd,
C. Two of the three integers must be even.
D. The product must be even.
E. Two of the three integers must be odd.
©
Answer:
d
Step-by-step explanation:
integer is a whole number
imagine the sum of the first set of 3 integers = 4 + 5 + 6
product = 4 x 5 x 6 = 120
imagine the sum of the 2nd set of 3 integers = 6 + 7 + 8 = 21
6 x 7 x 8 = 3364
The price of n tickets to a concert is 8n + 9 dollars. What is the cost in dollars for 7 tickets to the concert
Answer: 65
Step-by-step explanation:
8nn+7 is your given expression. Plug in 7 for n, the number of tickets: 8(7)+9=56+9=65
In the figure shown, what is the measure of the indicated angle?
Answer:
60 degrees
Step-by-step explanation:
Each triangle needs to add up to 180 total degrees. 70+50=120,
180
-
120
___
60
Which of the following describes the square root of 41. 5,6 6,7 20,21 40,42
Answer:
6,7
Step-by-step explanation:
the squre root of 41 is 6.403
suppose a hand of four cards is drawn from a STANDARD DECK of playing cards with replacement , determine the probability of exactly one card is jack:
Therefore, the probability of exactly one card being jack when a hand of four cards is drawn from a standard deck of playing cards with replacement is 0.073 or 7.3%.
Suppose a hand of four cards is drawn from a standard deck of playing cards with replacement, the probability of exactly one card being jack can be determined using the following steps:Step 1: Determine the total number of possible outcomes when four cards are drawn from a standard deck of 52 cards with replacement. The total number of possible outcomes = 52 × 52 × 52 × 52 = 7,311,616.Step 2: Determine the total number of ways in which exactly one card can be a jack. There are four jacks in a standard deck of 52 cards, so the total number of ways in which exactly one card can be a jack = 4 × 48 × 48 × 48 = 53,333,632.Step 3: Determine the probability of exactly one card being jack. Probability of exactly one card being jack = Total number of ways in which exactly one card can be a jack / Total number of possible outcomes= 53,333,632/ 7,311,616 = 7.28 ≈ 0.073 or 7.3%.Therefore, the probability of exactly one card being jack when a hand of four cards is drawn from a standard deck of playing cards with replacement is 0.073 or 7.3%.
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Need Help which one is it???
Answer:
the blue one but not sure
Answer:
the third one i think
Step-by-step explanation:
here are the options
∠2and∠4
∠1and∠5
∠3and∠6
Answer:
∠1and∠5
Step-by-step explanation:
Hello There!
The image shown below shows an example of what corresponding angles look like
Properties of corresponding angles
Must be on the same side of the transversalMust be congruentangles 2 and 4 are on the same side of the transversal however they are supplementary angles not congruent
angles 2 and 4 are an example of adjacent angles therefore this is not the answer
angles 1 and 5 are on the same side of the transversal and they are most definitely congruent
This might be our answer but lets check the last answer just to be sure
Angles 3 and 6 are congruent but they are not on the same side of the transversal
angles 3 and 6 are an example of alternate interior angles therefore this is not the correct answer
So we can conclude that angles 1 and 5 are corresponding angles
Consider the system of equations shown below 2x₁ + 3x₂ + 3x3 = 20 3x₁ +5x₂ + 2x3 = 9 -x₁ + 3x₂ + 5x3 = 4. What is the coefficient matrix for this system of equations?
The coefficient matrix is a square matrix with dimensions equal to the number of variables in the system of equations.
The coefficient matrix is a matrix of the coefficients of the variables in a system of linear equations.
Now, we arrange these coefficients in a matrix format by placing them row-wise. This gives us the coefficient matrix:
[tex]2x + 3y + 3x3 = 20[/tex]
[tex]3x + 5y + 2x3 = 9[/tex]
[tex]-x + 3y + 5x3 = 4[/tex]
Each row of the coefficient matrix corresponds to an equation in the system, and each column represents the coefficients of a specific variable (x₁, x₂, x₃).
In summary, the coefficient matrix for the given system of equations is:
[tex]| 2 3 3 |[/tex]
[tex]| 3 5 2 |[/tex]
[tex]|-1 3 5 |[/tex]
This matrix provides a compact representation of the coefficients in the system, which can be further used for various operations and calculations.
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I’m sorry for the spam questions but I need help
Answer:
x = 30
Step-by-step explanation:
2x + x = 90
3x = 90
x = 30
Danny has a scale drawing of his house. If
3 inches (in) on the scale drawing equals
7 feet on the real house, what is the actual
height of the house?
5.4 in
Answer:
151.2
Step-by-step explanation:
7x12=84
84/3=28
28x5.4=151.2
Decide whether the composite functions, fog and g • f, are equal to x. f(x) = *25, g(x) = 2x - 5 2 O No, no O Yes, yes Yes, no O No, yes
The composite functions fog and g • f are not equal to x. The function fog simplifies to 4x² - 20x + 25, while g • f simplifies to 45. Therefore, neither composite function equals x.
To determine whether the composite functions fog and g • f are equal to x, we need to evaluate each expression separately and compare the results.
1. fog (or f(g(x))):
f(g(x)) = f(2x - 5)
To compute f(2x - 5), we substitute (2x - 5) into the function f(x) = x²:
f(2x - 5) = (2x - 5)²
Expanding this expression, we get:
f(2x - 5) = 4x² - 20x + 25
Therefore, fog is not equal to x since f(2x - 5) simplifies to 4x² - 20x + 25, not x.
2. g • f (or g(f(x))):
g(f(x)) = g(25)
To compute g(25), we substitute 25 into the function g(x) = 2x - 5:
g(25) = 2(25) - 5
g(25) = 50 - 5
g(25) = 45
Therefore, g • f is not equal to x since g(25) evaluates to 45, not x.
In conclusion, neither fog nor g • f is equal to x. The composite functions do not simplify to x; fog simplifies to 4x²- 20x + 25, and g • f simplifies to 45.
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A train travels along a horizontal line according to the function s(t) = –13 + 3t2 – 4t – 4 where t is measured in hours and s is measured in miles. What is the velocity of the train after 4 hours?
The velocity of the train after 4 hours is 20 miles per hour.
To find the velocity of the train after 4 hours, we need to differentiate the given function s(t) with respect to t.
Velocity is the derivative of position with respect to time.
That is,v(t) = ds(t)/dtTo differentiate s(t) = –13 + 3t² – 4t – 4, we differentiate each term separately.v(t) = d/dt(-13) + d/dt(3t²) - d/dt(4t) - d/dt(4)v(t) = 0 + 6t - 4
The velocity of the train after 4 hours is given by substituting t = 4 in the above equation.v(4) = 6(4) - 4 = 20
The velocity of the train after 4 hours is 20 miles per hour.To sum up, the velocity of the train after 4 hours is 20 miles per hour.
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−8x 4y>3 6x−7y<−5 is (2,3) a solution of the system?
The ordered pair (2,3) is not a solution of the system
How to determine if (2,3) a solution of the system?From the question, we have the following parameters that can be used in our computation:
−8x + 4y > 3
6x - 7y < −5
The solution is given as
(2, 3)
Next, we test this value on the system
So, we have
−8(2) + 4(3) > 3
-4 > 3 --- false
This means that (2,3) is not a solution of the system
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