The amount of George's income that is subject to withholding is $75,000, which excludes the alimony income.
What is alimony income?Alimony income represents the amount received from a spouse or a former spouse under a divorce or separation instrument.
What are the incomes subject to withholding?The incomes subject to withholding include the following:
Regular CommissionsVacation payReimbursementsOther expense allowances PensionsBonusesDividendsGambling winnings.Data and Calculations:Wages income = $50,000
Gambling winning = $20,000
Alimony income = $10,000
Dividend income = $5,000
Income subject to withholding = $75,000 ($20,000 + $20,000 + $5,000)
Thus, George's income that is subject to withholding is $75,000, excluding the alimony income.
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graph the solution to the system of inequalities in the coordinate plane 3y>2x+122+y<-5
The graph is shown in the attached image.
sinx + siny=a
cosx + cosy=b
Find cos(x+y/2)
Using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].
What are the formulas for (sin x + sin y) and (cos x + cos y)?The formula for the addition of two Sine functions ([tex]\sin x+\sin y[/tex]) is [tex]\sin x + \sin y = 2\sin\frac{x+y}{2}\cos\frac{x-y}{2}[/tex].The formula for the addition of two Cosine functions ([tex]\cos x+\cos y[/tex]) is [tex]\cos x + \cos y = 2\cos\frac{x+y}{2}\cos\frac{x-y}{2}[/tex].Given that
[tex]\sin x + \sin y = a\\\cos x + \cos y = b[/tex]
Then using the above formulas, we get:
[tex]2\sin\frac{x+y}{2}\cos\frac{x-y}{2}=a[/tex] (1)
[tex]2\cos\frac{x+y}{2}\cos\frac{x-y}{2}=b[/tex] (2)
Dividing the equation (1) by (2), we get:
[tex]\dfrac{\sin\dfrac{x+y}{2}}{\cos\frac{x-y}{2}}=\dfrac{a}{b}\\\Longrightarrow \tan\dfrac{x+y}{2}=\dfrac{a}{b}[/tex] (3)
Now, we know that [tex]\cos\theta=\dfrac{1}{\sqrt{1+\tan^2\theta}}[/tex].
Thus, using the above formula, we get from (3):
[tex]\cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\tan^2\dfrac{x+y}{2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\dfrac{a^2}{b^2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex]
Therefore, using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].
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KI's net income for 2021 is _____.
a.
$188.2 million
b.
$118.5 million
c.
$149.3 million
d.
$162.8 million
cd+(-6c)=150 when d=4
Answer:
c = -75
Step-by-step explanation:
cd + (-6c) = 150
d = 4
c(4) + (-6c) = 150
4c - 6c = 150
-2c = 150
c = -75
Using the graph as your guide, complete the following statement.
The discriminant of the function is
Because the parabola intercepts the x-axis only once, we conclude that the discriminant is 0.
What can we say about the discriminant?
For a quadratic equation:
y = a*x^2 + b*x + c
The discriminant is:
D = b^2 - 4ac
If D = 0, there is only one real zero.If D > 0, there are two real zeros.If D < 0, there are two complex zeros.In the graph we can see that the parabola intercepts the x-axis in its vertex, then the parabola has only one real zero, then we conclude that the discriminant is equal to zero.
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The first five terms of a quadratic sequence are 3, 12, 25, 42, 63.
Find the nth term of this sequence.
Since we know the sequence is quadratic, we expect the [tex]n[/tex]-th term to have the general form
[tex]x_n = an^2 + bn + c[/tex]
Plug in the first 3 known values of the sequence to form a system of equations.
[tex]x_1 = 3 = a + b + c[/tex]
[tex]x_2 = 12 = 4a + 2b + c[/tex]
[tex]x_3 = 25 = 9a + 3b + c[/tex]
Eliminating [tex]c[/tex] gives
[tex](4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9[/tex]
[tex](9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11[/tex]
Eliminating [tex]b[/tex] gives
[tex](4a + b) - (3a + b) = 11 - 9 \implies a = 2[/tex]
Solving for [tex]b,c[/tex], we get
[tex]4a + b = 11 \implies b = 11-4\cdot2 = 3[/tex]
[tex]a+b+c=3 \implies c=3-2-3 = -2[/tex]
So, the [tex]n[/tex]-th term of the sequence is
[tex]x_n = \boxed{2n^2 + 3n - 2}[/tex]
Mathematics problem..
Answer:
a) x + 10 = 45
b) 3 = 6 - x
c) d = s * t
Step-by-step explanation: This is actually pretty simple. Let's put down one theorem.
SYMMETRIC THEOREM OF PROPERTIES: If a equals b, then b must equal a. Thus, a = b and b = a.
This is all we're really doing.
Take a) for example, 45 = x + 10. Let's label (45) as A, and (x + 10) as B. Thus we have A = B. Now we know by the Symmetric Property, we have B = A. Thus, substituting B and A again, we get x + 10 = 45.
Just keep doing this with all the equations.
Hope this helped!
Kendra received a bonus that was 30% of her monthly earnings. If her monthly earnings were $930, how much was Kendra's bonus?
Answer:
$279
Step-by-step explanation:
100% = $930
30% = ???
(30/100) × 930
=$279
Find the length indicated
Show work
Answer: 5 units
Step-by-step explanation:
x+2+2x-7=13
solve for x
3x=18
x=6
∴SR: 2x-7
=2(6)-7
=12-7
=5
Answer:
SR = 5
Step-by-step explanation:
[tex]TR=x+2+2x-7=3x-5[/tex]
[tex]3x-5=13[/tex]
[tex]3x=13+5[/tex]
[tex]x=18/3=6[/tex]
[tex]SR=2x-7=2(6)-7=12-7=5[/tex]
Hope this helps
Find the slope of the line passing through the points (-4,-4) and (2, 5).
Answer:
the slope of the line passing through the points (-4,-4) and (2, 5) m=3/2.
Step-by-step explanation:
Hello!
To find the slope between two points use the formula
m=(y₂-y₁)/(x₂-x₁)... substitute valuesm=(5-(-4))/(2-(-4))m=9/6m=3/2Grandma is making her grandson french toast. The pan can only fit two pieces of bread at a time. To cook each side of the bread it takes one minute( you have to cook both sides). Grandma made three slices of french toast in three minutes, how was she able to do this
Grandma should be able to make three slices of French toast by slicing one of the original slices into two.
How can grandma make three slices of French toast?Put two slices of bread in the pan and cook them for one minute (first minute)Turn both slices over and cook ( second minute)Remove both slices and slice one of this into two. This will mean the new slices will have one side cooked and another one that is not cooked.Cook these thinner slices (third minute).The result would be three cooked slices, although two of them would be thinner.Learn more about French toast in: https://brainly.com/question/11713135
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PLEASE HELP!
Let f be the function given by f (x) = (create an original sinusoidal function with an amplitude not equal to 1, a period not equal to 2π, and non-zero phase and vertical shifts).
ex: F of x equals negative one half times sine of quantity 3 times x plus pi over 2 end quantity minus 2
Part A: State the amplitude and vertical shift.
Part B: Determine the period of f (x), showing all necessary calculations.
Part C: Calculate the phase shift of the sinusoidal function with proper mathematical justification.
Part D: Graph the sinusoidal function by hand, using your answers from parts A–C.
Choose an angle θ, in radians, such that 2π < θ < 4π . Let θ = (create an original angle measure).
ex: Theta equals 13 pi over 6
Part E: Determine the exact value of cos θ using the sum formula. Show all necessary mathematical work.
Part F: Determine the exact value of sin θ using the difference formula. Show all necessary mathematical work.
Part G: Calculate the exact value of tan 2θ, using your answers from parts E – F.
The equation of the function f(x) is f(x) = 2 sin(π/2(x + 6)) - 3
How to create the sine function?A sine function is represented as:
f(x) = A sin(B(x + C)) + D
Where
A = Amplitude
Period = 2π/B
C = Phase shift
D = Vertical shift
The requirements in the question are:
Amplitude not equal to 1Period not equal to 2πNon-zero phase and vertical shiftsSo, we can use the following assumptions
A = 2
Period = 4
C = 6
D = -3
So, we have:
f(x) = 2 sin(B(x + 6)) - 3
The value of B is
4 = 2π/B
This gives
B = π/2
So, we have:
f(x) = 2 sin(π/2(x + 6)) - 3
The amplitude, vertical shift, period of f(x)and the phase shiftUsing the representations in (a), we have:
Amplitude = 2Vertical shift = -3Period = 4Phase shift = 6The graph of the functionSee attachment for the graph of f(x)
The value of cos θLet θ = 3π
So, we have:
cos(3π)
This is calculated as:
cos(3π) = cos(2π + π)
Expand
cos(3π) = cos(2π) *cos(π) - sin(2π) *sin(π)
Evaluate
cos(3π) = -1
The value of sin θLet θ = 3π
So, we have:
sin(3π)
This is calculated as:
sin(3π) = sin(2π + π)
Expand
sin(3π) = sin(2π) *cos(π) + cos(2π) *sin(π)
Evaluate
sin(3π) = 0
The value of tan 2θLet θ = 3π
So, we have:
tan(2 * 3π)
tan(6π)
This is calculated as:
tan(6π) = tan(3π + 3π)
Evaluate
tan(3π) = 0
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The next model of a sports car will cost 4.4% more than the current model. The current model costs $49,000. How much will the price increase in dollars? What will be the price of the next model?
Answer: $51156
Step-by-step explanation:
a = b x p%
how much will the price increase
a = 49,000 x 4.4%
= 49,000 x 0.044
= $2156
price of next model
49,000 + 2156 = $51156
(-4) (-2) +2 (6+5) if anyone knows pls tell due dates tomm for homework
Thanks,
Unknownaz05
Answer:
21
Step-by-step explanation:
(-4)(-2)+2(6+5)
(8)+2(11)
10+11
21
Hope this helps! :)
Answer:32
Step-by-step explanation: First, we do parentheses. 6+5 = 11. Next, we have to do multiplication (-4)(-2) is positive 8 because there are two negatives. 8+2 is 10 + 2(11) is 10+22 which is 32
The functions fand g are defined as follows. f(x) = 3x-1 g(x)=3x³ +5 Find f(-6) and g (-4). Simplify your answers as much as possible. ƒ(-6) = g (-4) =
Answer:
f(-6)= -19 and g(-4)= -187
what is Z in the rhombus?
Answer: 27°
Step-by-step explanation:
The easiest way to find the measure of angle Z is to know that in a rhombus, the diagonals are perpendicular bisectors of each other. This means that all the four angles in the center are 90°.
Since we know that all angles in a triangle add up to 180°, we can set the sum of z, 63, and 90 to be 180 and solve for z.
[tex]z+63+90=180\\z+153=180\\z=27[/tex]
Hence, z is 27°.
Please help!!!!!!!!!!!!!!!!
Answer: Option (3)
Step-by-step explanation:
[tex]\frac{1}{6a^2}-\frac{5b}{3a^3}+\frac{b^2}{4a}\\\\=\frac{2a}{12a^3}-\frac{20b}{12a^3}+\frac{3a^2 b^2}{12a^3}\\\\=\frac{3a^2 +b2 +2a-20b}{12a^3}[/tex]
what is - 1/5 ( -2 1/4) ?
Attached as picture. Please read fully
a. The velocity t = [tex]v = Ce_{n} (\frac{mo}{mo - kt} ) - gt[/tex]
b. v60 = 7164
How to solve for the velocitymdv/dt = ck - mg
dv/dt = ck/m - mg/m
= ck/m - g
dv = [tex](\frac{ck}{Mo-Kt} -g)dv[/tex]
Integrate the two sides of the equation to get
v [tex]-\frac{ck}{k} e_{n} (Mo- kt)-gt+c[/tex]
[tex]v = Ce_{n} (\frac{mo}{mo - kt} ) - gt[/tex]
b. fuel accounts for 55% of the mass
So final mass after fuel is burned out is = 0.45
c=2500
g=9.8
t=60
v = -2500ln0.45 - 9.8 x 60
= 7752 - 588
= 7164
Complete questionA rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the rocket will satisfy the equation where g is the acceleration due to gravity.
dv dt m =ck - mg
(a) Find v(t) keeping in mind that the mass m is a function of t.
v(t) =
m/sec
(b) Suppose that the fuel accounts for 55% of the initial mass of the rocket and that all of the fuel is consumed at 60 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.]
v(60) =
m/sec [Round to nearest whole number]
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The accompanying data are the caloric contents and the sugar contents (in grams) of 11 high-fiber breakfast cereals. Find the equation of the regression line. Then construct a
scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not
meaningful to predict the value of y, explain why not.
(a) x = 160 cal
(b)x= 90 cal
(c)x= 175 cal
(d)x=198 cal
Click the icon to view the table of caloric and sugar contents.
The regression equation based on the information given about the sugar contents will be 0.18x - 20.84.
How to explain the regression?It should be noted that from the information, the accompanying data are the caloric contents and the sugar contents of 11 high-fiber breakfast cereals.
The sugar content will be:
a. 160 calories
= 0.18x - 20.84.
= 0.18(160) - 20.84
= 7.96
b. 90 calories
= 0.18x - 20.84.
= 0.18(90) - 20.84
= -4.64
c. 175 calories
= 0.18x - 20.84.
= 0.18(175) - 20.84
= 10.66
d. 208 calories
= 0.18x - 20.84.
= 0.18(208) - 20.84
= 16.6
Therefore, the sugar contents is illustrated above.
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Solve rs + t = u for the variable s
Answer:
[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]
Step-by-step explanation:
You have to move the variables (r and t) with u to isolate s.
[tex]rs+t=u[/tex]
[tex]-t[/tex] [tex]-t[/tex]
------------------------
[tex]rs=u-t[/tex]
÷ [tex]r[/tex] ÷ [tex]r[/tex]
------------------------
[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]
A recent food drive distributed 6,298 pounds of stoneground cornmeal to 1,007 people. Approximately how many pounds did each person receive? Round to the hundredths.
Answer: 6.25
Step-by-step explanation: Here, you want to find how much of 6,298 pounds of food each person got. You can do this by dividing. 6,298/1,007 should get you the answer because it shows how the 6,298 pounds were distributed amongst the 1,007 people.
What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
The length of the apothem of the regular pentagon shown is 5.2 meters
How to determine the length of the apothem?Represent the central angle of the regular pentagon using x
The value of the central angle of the regular pentagon is then calculated as:
x = 360/n
Where n represents the number of sides
i.e n = 5
So, we have:
x = 360/5
Evaluate the quotient
x = 72
Represents the apothem with y.
The apothem is then calculated as:
tan(x/2) = (Side length/2)/Apothem
This gives
tan(72/2) = (7.6/2)/y
Evaluate the quotient
tan(36) =3.8/y
Multiply both sides by y
y tan(36) = 3.8
Divide both sides by tan(36)
y = 3.8/tan(36)
Evaluate the quotient
y = 5.2
Hence, the length of the apothem of the regular pentagon shown is 5.2 meters
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Determine the point (x,y) ( x , y ) on the unit circle associated with the following real number s. Write the exact answer as an ordered pair. Do not round. s=−11π6
The required coordinates of the unit circle for s = -11π/6 is (√3/2, 1/2). Using trigonometric functions, the required answer is calculated.
What are the trigonometric functions?There are six trigonometric functions.
They are sin θ, cos θ, tan θ, sec θ, cosec θ, and cot θ.
Where θ - 0 to 360° or 0 to 2π
Calculation:For a unit circle, the coordinates are given in the form of trigonometric functions as below:
x = cos θ and y = sin θ
Here it is given that s = θ = -11π/6
So, on substituting,
x = cos θ = cos (-11π/6)
⇒ x = √3/2
y = sin θ = sin (-11π/6)
⇒ y = 1/2
Thus, the required coordinate pair is (√3/2, 1/2).
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Hi,
Could anyone help with this please?
Many thanks,
Length: 2.6 meters
Width: 1.8 meters
Area: 4.68 meters
Since the scale is 1/40, we can multiply the centimeter measurements by 40 thus making it our scale factor.
Length
2.6 x 40 = 260
260 cm = 2.6 m
Width
4.5 x 40 = 180
180 cm= 1.8 m
Area
1.8 x 2.6 = 4.68 m
Length: 2.6 meters
Width: 1.8 meters
Area: 4.68 meters
Write your answers as fractions in the format 1/2.
If a learner is picked at random, what is the probability that they are
female and use public transport?
The learner rejoins their class mates and another learner is picked at
random. What is the probability that they are female and walk/cycle to
college?
The probability that they are female and use public transport is [tex]\mathbf{=\dfrac{1}{3}}[/tex]
The probability that they are female and walk/cycle to college is [tex]\mathbf{=\dfrac{1}{9}}[/tex]
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is too probable to occur or how probable a statement is to be true.
Probability is synonymous with possibility. It is a mathematical field that is concerned with the occurrence of a random event. The value ranges from zero to one. The definition of probability is to predict the degree to which something is likely to occur. To determine the likelihood of a particular event occurring, we must first determine the total number of possible outcomes.
Mathematically:
[tex]\mathbf{Probability = \dfrac{number \ of \ required \ outcomes}{total \ number \ of \ possible \ outcomes}}[/tex]
From the table in the image attached below.
The probability that they are female and use public transport is:
[tex]\mathbf{=\dfrac{9}{27}}[/tex]
[tex]\mathbf{=\dfrac{1}{3}}[/tex]
Also, the probability that they are female and walk/cycle to college is:
[tex]\mathbf{=\dfrac{3}{27}}[/tex]
[tex]\mathbf{=\dfrac{1}{9}}[/tex]
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PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
Considering it's discriminant, it is found that:
A. The classmate is wrong, as the discriminant is of zero, hence the equation has one solution.
B. The quadratic equation has 1 x-intercept.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
y = ax^2 + bx + c
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], it has 2 real solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has 1 real solutions.If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.In this problem, the equation is:
y = 9x² - 6x + 1.
The coefficients are a = 9, b = -6 and c = 1, hence the discriminant is:
[tex]\Delta =(-6)^2 - 4(9)(1) = 36 - 36 = 0[/tex]
Since the discriminant is zero, the classmate is wrong, as it means that the equation has one solution = one x-intercept.
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About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
If the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
Given sample size be 300 and about 5% of the population has a particular genetic mutation.
We are required to find the standard deviation for the number of people with the genetic mutation in groups of 300.
Sample size=300
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation=[tex]\sqrt{np(1-p)}[/tex]
Use the known values in the above formula.
Standard deviation=[tex]\sqrt{300*0.05(1-0.05)}[/tex]
=[tex]\sqrt{14.25}[/tex]
=3.77
Hence if the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
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MY NOTES
lim
n18
ASK YOUR TEACHER
Use the Limit Comparison Test to determine the convergence or divergence of the series.
00
n=1
n3
converges
O diverges
n+ 3
n+ 3
n3-5n+8
- 5n+ 8
Need Help?
-
=L>0
Read It
9,433
PRACTICE ANOTHER
Watch It
AUG
3
tv♫♬
(a
A
Part 1) [tex]\displaystyle \frac{1}{n^2}[/tex] or 1/(n^2) goes in the box.
Part 2) The series converges
======================================================
Work Shown:
[tex]\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\[/tex]
[tex]\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\[/tex]
Because L is finite and positive, i.e. [tex]0 < L < \infty[/tex], this means that the original series given and the series
[tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/tex]
either converge together or diverge together due to the Limit Comparison Test.
But the simpler series is known to converge (p-series test).
Therefore, the original series converges as well.
The two series likely don't converge to the same value, but they both converge nonetheless.
The mean of a normally distributed data set is 110, and the standard deviation is 15.
a) Use the Empirical Rule to find the probability that a randomly-selected data value is greater than 95.
b) Use the Empirical Rule to find the probability that a randomly-selected data value is greater than 125.
Step-by-step explanation:
68% of all values are within 1 SD (110 ± 15).
95% of all values are within 2SD (110 ± 2×15 = 30)
99.7% of all values are within 3 SD (110 ± 3×15 = 45)
a)
95 is 110 - 15, so exactly 1 SD apart from the mean value.
68% or 0.68 is the probability of all values between 95 and 125.
so, 34% or 0.34 is the probability of all values between 95 and 110. and 50% or 0.5 is the probability of all values larger than 110.
so, the probability of all values larger than 95 is
0.34 + 0.5 = 0.84
b)
125 is 110 + 15, so exactly 1 SD apart from the mean value.
so, as per a) 34% or 0.34 is the probability of all values between 110 and 125. and 50% or 0.5 is the probability of all values larger than 110.
so, the probability of all values larger than 125 is
0.5 - 0.34 = 0.16