The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of w is 3, so the degree of the polynomial is 3.
The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this case, the leading coefficient is 12.
In summary, the polynomial -9-8w+3w+12w³ has degree 3 and leading coefficient 12.
match the following descriptions with the method. group of answer choices a model is an automatic, flexible, non-linear regression model, not interpretable, and retains all predictor variables although it may limit the effects of some. [ choose ] a model handles outliers well, handles many potential predictor variables easily, and sorts through predictor variables repeatedly to divide the data into groups to best determine the response variable.
decision tree and neutral network
What is decision tree?
The most effective and well-liked technique for categorization and prediction is the decision tree. A decision tree is a type of tree structure that resembles a flowchart, where each internal node represents a test on an attribute, each branch a test result, and each leaf node (terminal node) a class label.
A model is an automatic flexible non linear regression model not interpretable and retains all predictor variables although it may limit the effect of some decision tree
A model is handles outliers well handle many potential predictor variable easy and short through predictor variables repeatedly to divide the data into group to best determine the response variable is neutral network
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Help pls plssssssssssssssssssssssssssssssssssss asap no cap
Maya spent 40% of her savings to pay for a bicycle
How much
money does she have left in her savings after buying the bicycle?
Answer:
60% because the total should be 100% and if you take 40% away you should be left with 60%
A police department collected the statistics for the number of tickets police officers wrote each day over the last 6 weeks.
Mean =5.23
Median =3
Mode =2
What does the median represent in this situation?
It is the average number of tickets police officers wrote per day,
More than half the police officers wrote this number of tickets.
More police officers wrote this number of tickets per day than any other number.
It is the total number of tickets police officers wrote in 6 days.
The median represents here as, Option B; More than half the police officers wrote this number of tickets.
Given,
A police department collected the statistics for the number of tickets police officers wrote each day over the last 6 weeks.
Mean =5.23
Median =3
Mode =2
We have to find the representation of median in this situation;
Median;-
The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.
Here,
The median 3 represents that, More than half the police officers wrote this number of tickets.
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let x and y be i.i.d. unif(0, 1). (a) compute the covariance of x y and x y . (b) are x y and x y independent studysoup
If x and y be i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero
Here x and y be i.i.d. unif(0, 1)
The i.i.d stands for independent and identically distributed
unif means that the uniformly distributed
Here x and y are i.i.d unif (0,1)
The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable
Here we have to find the covariance of x + y and x - y
According to the properties of covariance
Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0
Because Cov(x, x) = Cov (y, y)
Cov(y, x) = Cov(x, y)
Therefore, the covariance of x+y and x - y is 0
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The law allows marketers of herbs and other natural substances to make health claims that are not supported by evidence. Brands of ginkgo extract claim to "improve memory and concentration ." A randomized comparative experiment found no evidence for such effects. The subjects were 230 healthy people over 60 years old. They were randomly assigned to ginkgo or a placebo pill (a dummy pill that looks and tastes the same). All the subjects took a battery of tests for learning and memory before treatment started and again after six weeks.
(a) Following the model of previous figures, outline the design of this experiment.
(b) Use the Simple Random Sample applet, other software, or Table A to assign half the subjects to the ginkgo group. If you use software, report the first 20 members of the ginkgo group (in the applet's "Sample bin") and the first 20 members of the placebo group (those left in the "Population hopper"). If you use Table A, start at line 103 and choose only the first 5 members of the ginkgo group
a) Six-week learning and memory test: Both groups had a six-week learning and memory test.
b) According to Table A, the first five ginkgo trees are 103, 105, 107, 108, and 109.
(A) By randomly allocating people to treatment & control groups, randomized controlled trials are a form of experimental investigation that seeks to reduce bias. In this instance, the treatment group took tablets containing ginkgo extract, whereas the control group took pills containing a placebo. Prior to the initiation of therapy & again after six weeks, both groups underwent memory and learning tests.
The experiment's design may be summarized as follows:
Choosing the research population is folks over 60 who are in good health
Calculate the sample size: 230 people
Place individuals in control and treatment groups at random: The ginkgo group received half of the participants, while the placebo group received the other half.
Administering care: Pills containing ginkgo extract were given to the ginkgo group, whereas placebo pills were given to the placebo group.
Prior to starting therapy, both groups had their learning and memory skills tested.
Both groups underwent learning and memory ability tests six weeks later.
(b) According to the basic random sample applet, the first 20 members of the ginkgo Biloba subpopulation are:
11, 13, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35
first 20 subjects using a placebo Those that participated are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 23, 31, 36, 37, 38, 39, and 40.
5 people: 103, 105, 107, 108, and 109
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2) If you wish to save up $220,000 using an annuity, what monthly payment is required into the
annuity if the annuity has an APR of 8.0% compounded annually and you wish to reach your
savings goal in 30 years?
The monthly payment required into the annuity with an APR of 8.0% compounded annually and you wish to reach your savings goal in 30 years is $156.19.
How the monthly payment is determined?The monthly payment is required for 360 months (30 years x 12).
We can compute this periodic payment using an online finance calculator by inputting the parameters below:
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 8%
PV (Present Value) = $0
FV (Future Value) = $220,000
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 1
Results:
Monthly Payments (PMT) = $156.19
Sum of all periodic payments = $56,228.40
Total Interest = $163,771.60
Thus, to reach a future value of $220,000, the monthly annuity deposit should be $156.19 for 30 years at 8%.
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If c(x) = 5/x-2 and d(x) = x + 3, what is the domain of (cd)(x)?
A-all real values of x
B-all real values of x except x = 2
C-all real values of x except x = –3
D-all real values of x except x = 2 and x = –3
Answer:
B
Step-by-step explanation:
You always choose the most limited domain in these answers. And for c(x) the domain is all real numbers except 2, and the domain for d(x) is all real numbers.
So the domain is all real numbers except for 2 (most limited)
The domain of the function is all real values of x except x = 2. Therefore, option B is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Given that, c(x)=5/(x-2) and d(x)=x+3.
Here, (c·d)(x)=c(x)×d(x)
= 5/(x-2) × (x+3)
= 5(x+3)/(x-2)
= (5x+15)/(x-2)
Find the domain by finding where the expression is defined.
Interval Notation: (-∞,2)∪(2,∞)
Set-Builder Notation: {x|x≠2}
Therefore, option B is the correct answer.
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#9.
The table represents some points on the graph of linear function f.
Which function represents f ?
f(x)=32(3 x-1)
f(x)=-32(x-3)
f(x)=-2(32 x-3)
f(x)=16(2 x-1)
The function represents f ( x ) is f ( x ) = 32 ( 3x - 1 )
Given :
The table represents some points on the graph of linear function f.
Table :
x -2 1 5 10
f ( x ) -224 64 448 928
take two points ( 5 , 448 ) and ( 1 , 64 )
slope m = 64 - ( 448 ) / 1 - ( 5 )
= 64 - 448 / 1 - 5
= -384 / -4
= 384 / 4
= 192 / 2
= 96
( 1 , 64 ) on
y - 64 = 96 ( x - 1 )
y - 64 = 96x - 96
y = 96x - 96 + 64
y = 96x - 32
take 32 as common
= 32 ( 3x - 1 )
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Hi please order the side lengths from least to greatest thank you
Answer:
Step-by-step explanation:
ok
alr
Answer:
below
Step-by-step explanation:
Largest angle = largest opposite side , smallest angle = smallest opposite side
EF < ED <DF
First use appropriate properties of logarithms to rewrite f(x) and then find f’(x)
Answer:
f(x) = 6ln(8) -6ln(x)f'(x) = -6/xStep-by-step explanation:
You want to rewrite f(x) and differentiate it for f(x) = 6·ln(8/x).
Rules of logarithmsThe log of a ratio is the difference of logs:
ln(a/b) = ln(a) -ln(b)
ApplicationUsing this to rewrite f(x), we have ...
f(x) = 6ln(8/x) = 6(ln(8) -ln(x))
f(x) = 6·ln(8) -6·ln(x)
DerivativeThe derivative of the constant is zero, so ...
f'(x) = -6/x
Find the critical values, to, to test the claim that H, H2. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. Assume that of to. Use a = 0,05 ny = 25, n = 30, X = 23, X2 = 21,5 = 1.5,82 = 1.9 OA 2064 OB 2.797 Oct2492 OD 1.711
The critical values for the following sample are ±2.0064.
Here it is given that α = 0.05,
To calculate the critical values we will use the t-statistic.
Here n₁ = 25 and n₂ = 30
Hence, the degrees of freedom
d.f = n₁ + n₂ - 2 [Since it's a 2-sample test]
= 25 + 30 - 2
= 53
Now our significance level is α = 0.05,
To know the critical value we will make use of a t-distribution table and look up the value corresponding to a 0.05 significance level and 53 degrees of freedom.
Here we will get the critical values ±2.0064
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Investment The future value S of an investment earning 6% compounded continuously is a function of the principal P and the length of time t that the principal has been invested. It is given by
S = f(P, t) = Pe0.06t
Find f(2000, 20), and interpret your answer.
The value of f(2000 , 20) is $6640.24 and the interpretation is "if 2000 was invested initially then $6640.24 will be the amount after 20 years" .
In the question ,
it is given that,
the future value (S) on investment earning is compounded continuously at 6% .
the function of the principal P and the length of time t that the principal has been invested is given by
S = f(P, t) = P×[tex]e^{0.06 \times t}[/tex]
to find f(2000 , 20) ,
we substitute P = 2000 and t = 20 ,
we get ,
f(2000 , 20) = 2000×[tex]e^{0.06 \times 20}[/tex]
Simplifying further ,
we get ,
= 6640.2338
≈ 6640.24
Its interpretation is "if 2000 was invested initially then $6640.24 will be the amount after 20 years .
Therefore , the value of f(2000 , 20) is $6640.24 .
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The following age structure diagrams were created for various counties in the United States from 2000 census data. Which of the following statements best describes the pattern seen in age structure diagram C?
There is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.
Which age structure diagram represents a population's ages the best?
However, it is generally agreed that using a population pyramid is the most effective technique to graphically depict the age and sex distribution of a certain population. A population pyramid displays the numbers or percentages of men and women in each age group using a paired bar chart-style image.Age structure diagrams in nations with high population increase have a sharp pyramid shape.Age structure diagrams in nations with rapid growth have a pyramidal shape, indicating a majority of younger people, many of whom are of reproductive age.Hence, there is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.
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assuming no employees are subject to ceilings for their earnings, calculate salaries payable and employer payroll tax expense.
Assuming no employees are subject to ceilings for their earnings IS $7,450
The computation of Salaries Payable is shown below:-
Gross Payroll $10,000
Less:
Federal income tax withheld $1,800
Social security rate at 6% -$600
Medicare rate at 1.5% -$150
Total deduction -$2,550
Salary Payable $7,450
We simply deduct three above taxes from the gross payroll so that we get to know for the salary payable amount
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You are given the rate of investment dI/dt. Find the capital accumulation over a five-year period by evaluating the definite integral Capital accumulation = 5 dI dt dt 0 where t is the time in years. (Round your answer to two decimal places.) dI dt = 16,000t (t2 + 2)2
Evaluate the definite integral.
Evaluate the definite integral.
Use any basic integration formula or formulas to find the indefinite integral. (Use C for the constant of integration.)
capital accumulation is 3,973,910.14.
To evaluate the definite integral, we will have to find the indefinite integral. We use integral by substitution to find the indefinite integral.
Capital Accumulation = ∫ dI/dt dt
= ∫ 16,000t (t^2 + 2)^2dt
If u = t^2 + 2 then du = 2t dt so the integral is
Capital accumulation = ∫ 16,000t (t^2 + 2)^2 dt
= ∫ 16,000 × (u - 2) × u^2 du/2
= ∫ 16,000u^3 - 64,000u^2 + 64,000udu/2
= 8,000u^4/4 - 32,000u^3/3 + 32,000u^2/2 + C
= 2,000u^4 - 10,667.7u^3 + 16,000u^2 + C
Substituting u again gives us:
Capital Accumulation = 2,000(t^2 + 2)^4 - 10,667.7(t^2 + 2)^3 + 16,000(t^2 + 2)^2 + C
To evaluate the definite integral, we need to find the values of this expression at t=0 and t=5 and subtract the two.
Capital Accumulation = [2,000(5^2 + 2)^4 - 10,667.7(5^2 + 2)^3 + 16,000(5^2 + 2)^2] - [2,000(0^2 + 2)^4 - 10,667.7(0^2 + 2)^3 + 16,000(0^2 + 2)^2]
= [2000(27)^4 - 10667.7(27)^3 + 16000(27)^2] - [2000(2)^4 - 10667.7(2)^3 + 16000(2)^2]
= 4,607,143.47 - 1,333,333.33 + 691,200
= 3,973,910.14
Therefore, the five-year capital accumulation is 3,973,910.14.
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Community center sells a total of 297 tickets
Adult tickets are $3
Student tickets are $1
They collect $479 in ticket sales
How many of each type of ticket were sold ?
They sold $479 in ticket sales and they had a total of 297 tickets sold, so they must have sold $479/297 = $<<479/297=1.61>>1.61 per ticket.
There are two types of tickets, adult tickets and student tickets, and adult tickets are $3, so the student tickets are $1.61 - $3 = $<<1.61-3=-1.39>>-1.39.
However, a ticket cannot be negative so we know that all of the tickets must have been adult tickets and they sold 297 tickets for $479, so they sold 297 tickets * $3/ticket = $<<297*3=891>>891 worth of adult tickets. Answer: \boxed{891}.
solve 4x + 3.5 = 2(2x +2) for x. show your work!!:)
The given linear equation 4x + 3.5 = 2(2x + 2) has no solution.
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
The given linear equation is
4x + 3.5 = 2(2x + 2)
Now,
4x + 3.5 = 2(2x + 2)
4x + 3.5 = 4x + 4
3.5 = 4 which is not possible
So the equation does not have any solution
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Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x3(3 + x4)6 dx, u = 3 + x4 Evaluate the integral by making the given substitution. (Use C for the constant of integration.)
dt(1 â 3t)6, where u = 1 â 3t
The answer to this integration is - [tex]\frac{u^{7} }{28} + c[/tex] .
u = 3 + x⁴
differentiate both sides,
⇒ du = 0 + 4x³ dx
⇒ du = 4x³ dx
⇒[tex]dx = \frac{du}{4x^{3} }[/tex] ..........(1)
The integration is :
[tex]\int x^{3} ( 3 +x^{4} )^{6} dx[/tex]
Substitute the values from equation (1)
= [tex]\int x^{3} u^{6} \frac{du}{4x^{3} }[/tex]
= [tex]\frac{1}{4} \int u^{6} du[/tex]
=[tex]\frac{1}{4} . \frac{u^{7} }{7} + c[/tex] ( c = integration constant )
= [tex]\frac{u^{7} }{28} + c[/tex]
Hence, the answer to this integration is - [tex]\frac{u^{7} }{28} + c[/tex] .
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Between which two consecutive whole numbers does the value of √389 lie?
Answer:
19 and 20
Step-by-step explanation:
Take the square root of 389
[tex]\sqrt{389} = 19.723...[/tex]
solve the problem. a statistical study indicates that the fraction of the electric toasters manufactured by a certain company that are still in working condition after t years of use is approximately what fraction of the toasters can be expected to fail during the fourth year of use? 0.3012 0.0993 0.2019 0.0666
0.2019 is a fraction of the toasters that can be expected to fail during the fourth year of use for the given statistical studies
As it is the fraction of toasters that can be expected to fail during the fourth year of use. This is determined from a statistical study, which indicates that the fraction of electric toasters manufactured by a certain company that is still in working condition after t years of use is approximately 0.3012. To calculate the fraction of toasters expected to fail during the fourth year of use, we simply subtract 0.3012 from 1, which gives us 0.2019. This means that, according to the statistical study, approximately 20% of the electric toasters manufactured by the company can be expected to fail during the fourth year of use.
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john wants to make 100 ml of a 5% alchohol solution by mixing a 2% alchohol solution with a 7% alchohol solution. wirte a system and solve to find how many ml of each solution will he need
We will need 40ml of 2% alcohol and 60ml of 7% alcohol to generate a solution of 100ml of 5% alcohol.
What is alchohol ?
Alcohol has addictive qualities and is a harmful, psychoactive drug. Alcoholic drinks are a common aspect of the social environment for many people in many modern nations. This is especially true for those who frequent highly visible, globally influential social settings where drinking often goes hand in hand with socialising. It is simple to ignore or minimise the harm that drinking does to one's health and society under this situation.
Let x and y be the quantities of the 2% and 7% alcohol solutions to be used to make 100ml of 5%, here we get the equation as,
[tex]x+y=100\\y=100-x[/tex]
Now, we can solve the problem to determine how many solutions there are:
[tex]2x+7y=5*100\\2x+7(100-x)=500\\-5x=-200\\x=40\\y=100-x\\y=100-40\\y=60[/tex]
We will need 40ml of 2% alcohol and 60ml of 7% alcohol to generate a solution of 100ml of 5% alcohol.
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g an independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. they collected information on the percentage of the bill left as a tip for 25 randomly selected bills. the average tip was 14.3% of the bill with a standard deviation of 2.7%. assume that the tips are approximately normally distributed. construct an interval to estimate the true average tip (as a percent of the bill) with 95% confidence. round the endpoints to two decimal places, if necessary.
An interval to estimate the true average tip is (14.84,13.76).
What is standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance.
confidence interval = sample mean ± standard deviation /(n)^1/2
substitute the values in it then
confidence interval = 14.3 ± 2.7/(25)^1/2
confidence interval = 14.3 ± 2.7/5
confidence interval = 14.3 ± 0.54
confidence interval = 14.3 + 0.54 , confidence interval = 14.3 - 0.54
confidence interval = (14.84,13.76)
So, an interval to estimate the true average tip is (14.84,13.76).
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Can a probability sum to 1.07 or does it have to be exactly 1?
Answer:
Step-by-step explanation:
probability ≤|1|
or -1≤ probability ≤1
Answer:
No
Step-by-step explanation:
The sum of the probabilities in a probability distribution is always 1.
Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
The possible values of B in the number line are option A, C, D and E
Number LineA number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.
In this problem, the value of B is between 3 and 2 since B is located between them.
Checking the given options;
A = 2.5
This is possible because B can be at the middle between 2 and 3
B = 2/5
This fraction isn't possible because the value of B is greater than this.
C = 5 / 2
This fraction is possible because the decimal value is 2.5 which is the same as option A
D = 25 / 10
This fraction is also possible because the decimal value is 2.5 which is same as option A and C
E = 2.49
This is also a likely possibility as this can be approximated to 2.5
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prove if f is a function from [0,1] to r and f is continuous then there exists an x in [0,1] such that f(x)
If f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.
What is a function?
In mathematics, a function is a rule that assigns a unique output to each input in a set. A function is continuous if the output value changes smoothly as the input value changes, without any sudden jumps or breaks.
To prove that if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem.
The intermediate value theorem states that if a function f is continuous on a closed interval [a,b], and if y is any value between f(a) and f(b), then there exists at least one x in the interval [a,b] such that f(x) = y.
In our case, f is a function from [0,1] to R, which is a closed interval, and f is continuous on this interval. Therefore, the intermediate value theorem applies to f.
To prove that there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem with y = 0. Since 0 is between f(0) and f(1), the intermediate value theorem guarantees that there exists at least one x in [0,1] such that f(x) = 0.
Hence, if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.
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compute the determinate of a either bu chooseing a row or colim for codactor expansion or bu applying row operations
Choose a row or column and perform Gaussian Elimination to reduce the matrix to row/column echelon form.Once the matrix is in row/column echelon form, the determinant can be found by multiplying the diagonal elements.
Let's take the matrix
A =
[1, 2, 3]
[4, 5, 6]
[7, 8, 9]
Choose the first column and perform Gaussian Elimination to reduce the matrix to row echelon form:
A =
[1, 2, 3]
[0, -3, -6]
[0, -6, -12]
The determinant of the matrix is found by multiplying the diagonal elements, which in this case is (1)(-3)(-12) = 36.
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Al is single, age 60, and has gross income of $140,000, of which $120,000 is salary and $20,000 is rental income. His deductible expenses are as follows:
Charitable contributions 4,000
Contribution to a traditional IRA 6,000
Expenses paid on rental property 7,500
Interest on home mortgage and property taxes on personal residence 7,200
State income tax 2,200
What is Al's AGI?
a.$140,000.
b.$126,500.
c.$114,000.
d.$134,000.
Al's AGI is $126,500.
What is gross income?
Before any deductions or taxes, gross income is the total of all wages, salaries, profits, interest payments, rentals, and other sources of income. It differs from net income, which is calculated as gross income less any applicable taxes and other deductions.
Here, we have
Given
Gross income of $140,000
Fewer Deductible expenses :
Alimony ($20,000)
Contribution to a traditional IRA ($6,000)
Expenses paid on rental property ($7,500)
AGI = Gross income - Contribution to a traditional IRA- Expenses paid on rental property
AGI = $140,000 - $6,000 - $7,500
AGI = $126,500.
Hence, Al's AGI is $126,500.
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The designers of a water park have sketched a preliminary drawing of a new slide. The length of the ladder is I - 40 feet, and its angle of elevation is 60 (segure). 60 (a) Find the height of the slide. (Round your answer to two decimal places) - (b) Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance ander travels (c) Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30°. Find an interval for how far ander travels hortzontally (round me values to one decimal place. Enter your answer using interval notation
(a) The height of the slide is 34.64 feet .
(b) The angle of depression is θ = tan⁻¹(34.64/d)
(c) The interval for which the rider travels horizontally is (60 , 74.3) .
In the question ,
it is given that ,
the length of the ladder is = 40 feet .
the angle of elevation is 60° .
From the figure given below.
Part(a) :
Let the height of the slide be = h.
From the triangle ABC ,
Sin(60°) = h/l
So , h = 40×0.8660
h = 34.64 feet .
Part(b) :
let θ be the angle of depression .
So , From the triangle DEF ;
tanθ = DF/DE
tanθ = h/d
So , θ = tan⁻¹(34.64/d)
Part(c) :
Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30° .
let θ = 25° , then
tanθ = 34.64/d
So , tan25° = 34.64/d
d = 34.64/tan25°
d = 34.64/0.4663
Simplifying further ,
we get ,
d = 74.3 feet .
and θ = 30° , then
tan30° = 34.64/d
d = 34.64/tan30°
d = 34.64/0.5773
So , d = 60 feet .
So , the interval for which the rider travels horizontally is (60 , 74.3) .
Therefore , (a) The required height is 34.64 feet , (b) angle of depression is tan⁻¹(34.64/d) and (c) the interval is (60 , 74.3) .
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onvert the integral below to polar coordinates and evaluate the integral. instructions: please enter the integrand in the first answer box, typing theta for . depending on the order of integration you choose, enter dr and dtheta in either order into the second and third answer boxes with only one dr or dtheta in each box. then, enter the limits of integration and evaluate the integral to find the volume. a
Evaluation of the integral is [tex]\frac{81}{16}[/tex]
In mathematics, an integral is either a definite value representing the region under a function's graph for a certain interval or a new function whose derivative represents the original function (indefinite integral). The fact that a definite integral of any function that can be integrated may be found using the indefinite integral and a corollary to the calculus fundamental theorem connects these two interpretations.
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