The statement which is true about the graph representing function h is the graph is positive on the intervals (- ∞, - 8) and (- 4, 3). Option D is correct.
We are given;
h(x) = -x^3 - 9x^2 + 4x + 96
The function is a cubic function.
Since the leading coefficient is negative the graph start from second quadrant.
So, the graph must be positive in the second quadrant.
Let us check the option D;
The graph is positive on the intervals (- ∞ , - 8) and (- 4, 3).
The graph is positive in the second quadrant. So, (- ∞ , - 8) satisfy.
Let's choose any point between -4 to 3 and substitute in the given equation.
Put x = -1 in the given equation;
h(x) = -(-1)^3 - 9(-1)^2 + 4(-1) + 96 = 1 - 9 - 4 + 96 = 84
So, h(x) is positive.
So, option D is correct.
Thus, the statement which is true about the graph representing function h is the graph is positive on the intervals (- ∞, - 8) and (- 4, 3). Option D is correct.
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Please help an 8th grader in needdddd!!!
We can find the linear equation by using the given graph, the equation is:
y = 4.8*x + 24
How to write the equation for the line?On the graph we can see the best fit line, remember that a linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
On the graph we can see that the y-intercept is at y = 24, then:
y = m*x + 24
Now, notice that when x = 5, the value of y is 48, replacing these values we get:
48 = m*5 + 24
48 -24 = m*5
24/5 = m
4.8*m
The linear equation is:
y = 4.8*x + 24
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$1,300 at 5% for 6 years
Answer:
$1742.12
Step-by-step explanation:
I'm assuming it would be compounded annually so,
A = 1300(1 + 0.05)^6
A = 1742.12
A monkey gathered 4 coconuts per minute. Is it a rate or unit rate?
Answer: unit rate
Step-by-step explanation:
its obvious
Answer:
I believe it is a unit rate
What is the sum of this geometric series?
Princess can sel an average of
21 muffins per day She needs to earn
$30 per day to meet her fundraising goal.
How much does she need to charge for
each muffin to reach her goal? Round to the
hearest cent.
Step-by-step explanation:
x = price per muffin
21 × x = 30
x = 30/21 = 10/7 = $1.428571429... ≈
≈ $1.43
she needs to charge $1.43 per muffin.
Find a polynomial function of degree 7 with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
The polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial is given with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
Each zero, such as a, corresponds to a linear factor, such as (x a). The repeating of such components is corresponding to multiplicity. The following polynomial thus meets the requirements in our example:
= (x-(-3))³(x-0)¹
=(x³-3x²(-3)+3x(-3)²-(-3)²)(x)
=x³+9x²+27x-9x
=x³+9x²+16x
Thus, the polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.
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7,17,27,37,47,57 whath other observations you can make about the pattern
The observation I can make of the pattern is that the sequence always increase by 10.
How to solve an arithmetic pattern?The sequence above shows an arithmetic pattern. Therefore, the arithmetic formula can be used to solve the next sequence.
7, 17, 27, 37, 47, 57..
Therefore,
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore,
a = 7
d = 17 - 7 = 10
Hence, the arithmetic formula is as follows:
aₙ = 7 + (n - 1)10
aₙ = 7 + 10n - 10
aₙ = 10n - 3
The sequence always increase by 10.
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Factor f(c)=4x^3+19x^2-58x+35 into linear factors given that -7 is a zero of f(k)
The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factors is f(c)=(x-1)(x+7)(4x-5)
To express the polynomial as a product of linear factors we have to find the zeros of the polynomial.
Here,
We have Given that f(c)=4x^3+19x^2-58x+35 and -7 is a zero of f(k) and we need to find the polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor
Now,
-7 is a zero of f(k)
i.e. (x+7) is a linear factor of f(k)
now,
we will find out the linear factor of f(c)
so,
f(c)=4x^3+19x^2-58x+35
f(c)=4x^3-4x^2+23x^2-23x-35x+35
f(c)=(x-1)(4x^2+23x-35)
f(c)=(x-1)(4x^2+28x-5x-35)
f(c)=(x-1)(4x(x+7)-5(x+7))
f(c)=(x-1)(x+7)(4x-5)
Hence,
The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor is f(c)=(x-1)(x+7)(4x-5)
Thus,
the linear factor of given polynomial is (x-1)(x+7)(4x-5)
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For sake of simplicity, let us assume that you have won exactly three punches for the game AND that no
prizes are removed after each punch. You are then shown the punching board, which contains 50 slots
with the following dollar amounts: (5) $100, (10) $250, (10) $500, (10) $1000, (8) $2500, (4) $5000, (2)
$10000, (1) $25000. You get to punch one slot at a time and either keep the amount you found or
continue with your other punches.
Working backwards, if you have already used and thrown away your first two punches, there is no
strategy for the third punch. You take whatever you get. Now examine the second punch.
QUESTION 1: What is the expected value of your third punch? Again, for sake of simplicity, assume that
your first two punches were put back into the mix. (Essentially no prizes are removed so there are still
50 holes to punch) Show all calculations necessary for you answer.
Also the question in the picture
The expected value of your third punch is 5660.
What is probability?
A linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100% expresses the likelihood that a specific event (or series of events) will occur.
Given that,
This is the third and last punch and also there is no removal of prizes after each punch. Hence, the expected value would be equal to the mean of all the possibilities available.
E(third punch) = Σ x p(x)
= 100× (5/50) + 250 × (10/50) + 500 × (10/50) + 1000 × (10/50) + 2500 ×(8/50) + 5000 × (4/50) + 100000 × (2/50) + 25000 × (1/50)
= 5660
Let us find the median of the given possibilities,
5 100's, 10 250's, 10 500's, 10 1000's, 8 2500's, 4 5000's, 2 100000's, 1 25000
There is a total of 50 possibilities and hence the median will be the average of the 25th and 26th terms.
25th term = 500
26th term = 1000
Median = (500 + 1000) / 2 = 750
The next available possibility greater than 750 is 1000.
Probability of getting more than 1000 in third punch = P (x > 1000) = (No. of terms greater than 1000) / Total no. of possible outcomes = 15 / 50 = 0.3
Probability of getting less than 1000 in third punch = P (x > 1000) = (No. of terms lesser than 1000) / Total no. of possible outcomes
= 25 / 50 = 0.5
Hence, in the second chance of punch, 1000 or anything greater than 1000 is preferred because the probability of getting more than 1000 in the next chance is less than the probability of getting less than 1000.
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-a+√-4+b
a²- b
if a = -2 and b = 8
The value of expression a²-b is 12 and value of equation -a+√-4+b id 10+2i where a is -2 and b is 8.
What is expression?In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.
Here,
if a = -2 and b = 8
a²-b=(-2)²-8
=-4
-a+√-4+b=-(-2)+2i+8
=10+2i
The equation a²-b has a value of 12 and the expression -a+-4+b has a value of 10+2i, where a is -2 and b is 8.
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Raina's penny bank is 1/10 full. After she adds 480 pennies, it is 1/2 full. How many pennies can Raina's bank hold?
Answer:
1,200 pennies
Step-by-step explanation:
You are on vacation in New York City, and you need to get around town to different locations. Below are the rates for 2 different cab companies, locally dubbed "The Red Cabs" and "The Green Cabs".
How many miles would you travel for the cost to be the same for both cabs and how much will that cost you?
What is the difference in cost between the two companies if you need to travel 8 miles?
After seeing all your vacation photos on S n a p b o o k, your cousin decided they wanted to visit New York City also. They asked for some general advice on traveling around the city. What advice would you give them about which cab company they should use when they travel around the city?
Answer:
The costs are equal at 3 miles. It coest $8 for either company
At 8 miles the green cost 13 and the red cost 18.
My advice would be to use the Red compnay if traveling less than 3 miles and the green company is traveling more than 3 miels. At 3 miles the costs are the same.
Step-by-step explanation:
IXL Please Help Fast!
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 8. If there were 8918 total votes, how many yes votes were there?
We want to construct a box whose base length is 2 times the base width. The material used to build the top and bottom cost $ 11 per square feet and the material used to build the sides cost $ 3 per square feet. If the box must have a volume of 40 cubic feet determine the dimensions that will minimize the cost to build the box.
The dimensions that will minimize the cost, obtained from the cost function are;
Width = [tex]\sqrt[3]{\frac{45}{11} }[/tex] feet
Length = [tex]2\cdot \sqrt[3]{\frac{45}{11} }[/tex] feet
Height = [tex]\dfrac{20}{\left(\sqrt[3]{\frac{45}{11} }\right)^2 }[/tex]
What is a function?A function is a rule, or law or expression that provides the definition between an input variable and an output variable.
Base length of the box = 2 × The base width of the box
Cost of the material used to build the top and the bottom = $11 per square feet
Cost of the material used to build the sides = $3 per square feet
Volume of the box = 40 cubic feet
Let x represent the width of the base of the box, and let y represent the height of the box
The information from the question indicates;
The length of the base of the box = 2·x
The volume of the box, V = x × 2·x × y = 2·x²·y = 40
V = 2·x²·y = 40
[tex]y = \dfrac{40}{2\cdot x^2} = \dfrac{20}{x^2}[/tex]
The cost of the box which can be obtained from the surface area of the box can be found as follows;
Cost of the top and the bottom = 2 × x × 2·x × 11 = 44·x²
Cost of the material for the sides = (2 × x × y + 2 × 2·x × y) × 3 = 18·x·y
Cost of the box, C = 44·x² + 18·x·y
[tex]C = 44\cdot x^2 + 18\cdot x \times \dfrac{20}{x^2} = \dfrac{44\cdot x^2+360}{x}[/tex]
To minimize the cost of the box, we get;
[tex]C' =\dfrac{d}{dx}\left( \dfrac{44\cdot x^2+360}{x}\right) = 0[/tex]
[tex]\dfrac{d}{dx}\left( \dfrac{44\cdot x^3+360}{x}\right) = \dfrac{x\times 44\times 3 \times x^2 - \left(44\times x^3+360\right)}{x^2} = \dfrac{88\cdot x^3-360}{x^2} =0[/tex]
At the minimum cost, [tex]\dfrac{88\cdot x^3-360}{x^2} =0[/tex]
Therefore; 88·x³ - 360 = 0
88·x³ = 360
[tex]x = \sqrt[3]{\dfrac{360}{88} } =\sqrt[3]{\dfrac{45}{11} }[/tex]
The width of the base of the box that minimizes the cost is; [tex]x =\sqrt[3]{\dfrac{45}{11}}[/tex]
The length of the base of the box that minimizes the cost is; [tex]2\cdot x =2\times \sqrt[3]{\dfrac{45}{11}}[/tex]
The height of the box that minimizes the cost is; [tex]\dfrac{20}{x^2} = \dfrac{20}{\sqrt[3]{\dfrac{45}{11} } }[/tex]
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The Johnson's purchased a car. If the total price, including a 6% sales tax, was $19,674, find the price of the car before tax
Answer:
Step-by-step explanation:
The price of the car before tax was $18,560.3
Let the price of the car be x. Then,
x + 6% of x = $19,674
106x/100 = $19,674
x = $ 19,673*100/106
with BODMAS, we get
x= $18560.3
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The population of a city has increased by 28% since it was last measured. If the current population is 80,000, what was the previous population?
The previous population of the city is 62500
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 3x + 4y = 14, 5x − 4y = 4.
if the previous population is represented by x and the increment by y, then
y= x×28/100
y = 28x/100 equation 1
the new population = previous population+ increment
therefore x+y= 80,000
represent 28x/100 for y in equation 2
x+28x/100= 80000
making the LHS a single fraction
(100x+28x)/100= 80000
128x= 80000×100
divide both sides by 128
x= 8000000/128
x= 62500
therefore the previous population is 62500
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What is the equation of the line shown in the graph?
The equation of the given line is y = 2x + 4
What is the equation of a line?The equation y = mx + c is the general equation of any straight line, where m is the slope of the line and c is the y -intercept.
Given a line passing through points (-1, 2) and (-3, -2)
We know (y - y1) = [(y2−y1)/(x2−x1)](x - x1).
Therefore, y - 2 = [(-2-2)/(-3+1)](x+1)
y-2 = 2x + 2
y = 2x + 4
Hence, The equation of the given line is y = 2x + 4
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about μ if the sample size, n, is 13. (b) Construct an 80% confidence interval about μ if the sample size, n, is 26. (c) Construct a 98% confidence interval about μ if the sample size, n, is 13. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
The confidence intervals for this problem, using the t-distribution, are given as follows:
a) 80% confidence level, n = 13: (106.24, 113.76).
b) 80% confidence level, n = 26: (107.42, 112.58).
c) 98% confidence level, n = 13: (102.56, 117.44).
d) These intervals could not be computed if the population had not been normally distributed, as the sample size is less than 30.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical values, using a t-distribution calculator, for the two-tailed 95% intervals, are given as follows:
80% confidence, n = 13, 12 df: t = 1.3562.80% confidence, n = 26, 25 df: t = 1.3163.98% confidence, n = 13, 12 df: t = 2.681.The mean and the standard deviation are given as follows:
[tex]\overline{x} = 110, s = 10[/tex]
For item a, with n = 13, the bounds of the interval are given as follows:
110 - 1.3562 x 10/sqrt(13) = 106.24.110 + 1.3562 x 10/sqrt(13) = 113.76.For item b, with n = 26, the bounds of the interval are given as follows:
110 - 1.3163 x 10/sqrt(26) = 107.42.110 + 1.3163 x 10/sqrt(26) = 112.58.For item c, with n = 13, the bounds of the interval are given as follows:
110 - 2.681 x 10/sqrt(13) = 102.56.110 + 2.681 x 10/sqrt(13) = 117.44.The Central Limit Theorem states that the intervals can be obtained for non-normal populations only if the sample size is equal or greater than 30.
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Order these numbers from least to greatest. 7.209, 7.23, 7.3, 7.1032
Answer:
7.1032,7.209,7.23,7.3.
so we can not put the dot and imagine like 71032 72090 we not put the 0 but it's can not be with no 0 72300 and we not put 0 73000 it most greatest so
i write answer on the top!
A bottle holds 96 fluids ounce of lemonade. How much is this in pints?
Answer:
12 pints
Step-by-step explanation:
[tex]\frac{1}{8}[/tex] = [tex]\frac{8}{96}[/tex]
8 ounces is equal to 1 pint. 8 x 12 = 96, so 1 x 12 is 12
Mai has 5 loves of bread and jeff has 3 loves.Mia and Jeff decide to share their bread witha hungry stranger.they all sit down and they have an equal amount of bread. the stranger gives them 8 coins to split for there generosity. describe the most equitable way mia and jeff should split the coins based on how much bred they gave
The most equitable way to share the coin between Mai and Jeff is ratio 5:3. Mai will have 5 coins and Jeff 3 coins
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b.
Mai dropped 5 loaves and Jeff 3 loaves. This means that the ratio of brad dropped by Mia and Jeff is 5:3.
The stranger dropped 8coins. the most equitable way to share the coin is to share it in ratio 5:8
Using this ratio, the total ratio is 8
therefore Mia will have 5/8×8=5coins
Jeff will have 3/8×8= 3coins
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Which expression is equivalent to (3x4y5)-²?
Answer:Equivalent expressions Calculator Get detailed solutions to your math problems with our Equivalent expressions step-by-step calculator. Practice your math skills and learn step by step.
Answer:
Answer:Equivalent expressions Calculator Get detailed solutions so your math problems with ur Equivalent expressions
Step-by-step explanation:
Graph the solution to the equation y=1/4+2 and y=–2x–7
Answer:
Step-by-step explanation:
y= 1/4x+2
y=-2x-7
Graphs below
Solve the system. 2x + y = 3 −2y = 14 − 6x Write each equation in slope-intercept form. y = -2 x + 3 y = 3 x + -7 How do the slopes and y–intercepts of the two equations compare?
The slopes and the y-intercepts of two equations are different.
How to calculate the slope-intercept form of the equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.How to determine the slopes and y–intercepts of the two equations?From the information provided, we have the following equations:
2x + y = 3 ....equation 1.
−2y = 14 − 6x ....equation 2.
In slope-intercept form, the first equation can be written by subtracting 2x from both sides as follows:
2x + y - 2x = 3 - 2x
y = 3 - 2x
y = -2x + 3
Therefore, m = -2 and c = 3.
For the second equation, we would divide both sides by -2 as follows:
−2y/-2 = 14/-2 − 6x/-2
y = -7 + 3x
y = 3x - 7
Therefore, m = 3 and c = -7.
In this context, we can reasonably and logically deduce that the slopes and the y-intercepts are quite different.
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Answer:
y = -2x + 3
y = 3x + -7
The slopes and the y-intercepts are different.
The system represents lines that Intersect at one point
Exactly one solution
Step-by-step explanation:
Edge2022
get me brainliest
Make the subject of
9x = u
Which ordered pair in the form (x, y) is a solution of this equation?
x + 7y= 10
Answer: (3, 1)
Step-by-step explanation:
Plug in each coordinate and see if the equation holds true:
[tex](13, 2)\\13+2(7)=13+14=27\neq 10[/tex]
[tex](2, 1)\\2+7(1)=2+7=9\neq 10[/tex]
[tex](4, 1)\\4+7(1)=4+7=11\neq 10[/tex]
[tex]3+7(1)=3+7=10[/tex]
In 5-7 Sentences, please explain each of these vocabulary terms. You may give an example or write the definition: 1.Outlier 2.Cluster 3.Positive linear association 4.Negative linear association 5.No association 6.Non-linear association
Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.
What is an outlier?An outlier, to put it simply, is a data point in a data graph or dataset you're dealing with that is abnormally high or abnormally low in comparison to the nearest data point and the rest of the nearby coexisting values.
The vocabulary term is explained as,
1.Outlier - Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.
2. Cluster - An identifiable cluster of values in a numerical variable's distribution that is close to one another and appears notably more frequently than values on either side of them.
3. Positive linear association - When the variable on the x-axis grows as the variable on the y-axis increases, a positive linear connection exists. An upward-sloping linear regression line demonstrates this.\
4. Negative linear association - A negative linear correlation exists when one variable rises while the other falls. An upwardly sloping straight regression line illustrates this.
5.No association - There is a "negative correlation" when one variable rises while the other one falls. The points in the scatterplot have no connection if there is no correlation between the variables.
6. Non-linear association - When two variables have a nonlinear relationship, the slope of the curve illustrating the relationship alters when the value of one of the variables varies. Any curve whose slope alters when one of the variables' values changes is said to be nonlinear.
Thus, extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.
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Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y=a( x− ℎ)^2+k and how they can be identified from the equation.
Please help
When a quadratic equation is given in the form y = a( x− ℎ )^2 + k the easily seen features are
coordinates of the vertex = v(h, k) the axis of the parabola - y axisthe opening of the curve in the axis - open upwardWhat is equation of a parabola?Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation
The quadratic equation in the factored form is written as
y = a ( x − ℎ )^2 + k
This equation shows the coordinates of the vertex which is v(h, k)
The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis
"a" helps to determine if the curve opens upwards or downwards. when a is:
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Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the amount of taxes owed on a taxable income of $38,520.
The effective tax rate for a taxable income of $75,400 is 24%.
What is the Marginal tax rate?The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate.
WE have Given that;
Marginal Tax Rate Chart Tax Bracket
$0 –$10,275 10%
$10,276 –$41,175 12%
$41,176 –$89,075 22%
$89,076 –$170,050 24%
$170,051 –$215,950 32%
$215,951 –$539,900 35%
> $539,901 37%
Hence, the effective tax rate for income of $95, 600 lies in the range of a marginal tax rate of; 24%.
thus, the effective tax rate;
= 72,026/ 95600
= 24 %
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Answer:
4,416.90
Step-by-step explanation:
12% tax bracket: $38,520 - 10,725 = 27795(0.12) = 3335.4
1027.50+3335.4 = 4416.90