For the given geometric sequence the seventh term is equal to 19/81 and the 12th term is equal to "-57" the value of the 15th term is 1539.
What is a geometric sequence?
One particular sort of sequence is a geometric sequence. It is a sequence in which each term, with the exception of the first, is multiplied by a fixed integer to obtain the following term. The common ratio must be multiplied by the current term in the geometric sequence to obtain the next term, and the common ratio must be divided by the current term to obtain the previous term.
Solution Explained:
We know, a7 = 19/81, a12 = -57
So, ar^7 = 19/81 and ar^12 = -57 (r= common ratio)
Since r< a15 < 0 [the sign alternate]
Ignoring the signs,
r^12 = r^7 X r^5
57 = 19/81 X r^5
(57 X 81)/19 = r^5
243 = r^5
r = the fifth ratio of 243 = 3
therefore, r = -3
So, a15 = a12 X r^3
= -57 X (-3)^3
= 1539
Hence, the value of the 15th term is 1539.
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2 step equation:12. Amy wants to start taking gymnastics. There is a one-time fee of $35 to sign up, then it costs $85 per month. If Amy saves up $225, how many months of gymnastics can she take?
The number of months Amy can take the Gymnastic = 2 months.
Amy wants to start taking gymnastics.
The fee structure of the gymnastics is divided into two parts.
There is a one time fee payment of 35$ and there is a monthly payment that costs 85$ per month.
So the first month fee of the gymnastics = 35 + 85 = 120$
Savings of Amy = 225$
If Amy pays the 1st month fee ,
then the she will be left with the savings = 225$ - 120$ = 105 $
It means Amy can join the gymnastics for one more month .
Hence the number of months Amy can take the Gymnastic = 2 months .
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What are the solutions to the equation 3k² + k-3=0?
Approximate the value of both solutions. Round each answer to two decimal places. Enter your answers as
a list of numbers, separated with commas. Example: 3.25,4.16
k=
The answer will be 0.33 using quadratic equation.
What is quadratic equation
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The equation given 3k² + k -3=0
(3k-1)(k+3)=0
k =1/3
k=0.33
Hence the value of k is 0.33.
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y=-2x^2+20x-2 what is the maximum or minimum value of the function
The Minimum value is y(min) = 48 , x = 5 and The maximum value is [tex]y = -2(x -5)^2+48[/tex]
Given,
In the question:
The given Function is :
[tex]y = -2x^2 + 20x -2[/tex]
To find the maximum or minimum value of the function:
Now, According to the question:
For maximum value:
The given Function is :
[tex]y = -2x^2 + 20x -2[/tex]
Take out the leading coefficient is :
[tex]y = -2(x^2 + 10x) -2[/tex]
Complete the square:
[tex]y = -2(x^2 + (2(-5))x +(-5)^2+(-2-(-2).(-5)^2)[/tex]
Express the function in vertex form:
[tex]y = -2(x -5)^2+48[/tex]
For Minimum Value:
y(min) = 48
x = 5
Hence, The Minimum value is y(min) = 48 , x = 5 and The maximum value is [tex]y = -2(x -5)^2+48[/tex].
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126=2×3×3×k
Solve for k
[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]
Step-by-step explanation:-
[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 18 \times k}}[/tex]
[tex]{ \sf{126 = 18k}}[/tex]
Divide both the sides by 18 in order to find the value of k. Then,
[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]
[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]
Drag each tile to the correct box. Not all tiles will be used.
Find the equations with unit rates greater than the unit rate of the graph. Then arrange these equations in order from least to greatest unit rate.
The equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x
How to determine the equations with unit rates greater than the unit rate of the graph?
On a graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:
Slope = y2-y1 / x2-x1
Thus, we can any two convenient points on the graph and use it calculate the slope:
Let's pick points (5, 10) and (12, 25)
This implies x1 = 5, y1 = 10 and x2 = 12, y2 = 25
Slope = y2-y1 / x2-x1
Slope = 25-10 / 12-5 = 15/7
Thus, the unit rate of the graph is 15/7 = 2.143
Find the equations with unit rates greater than the unit rate of the graph:
y = 19/8x: unit rate = 19/8 = 2.375
y = 27/13x: unit rate = 27/13 = 2.077
y = 21/9x: unit rate = 21/9 = 2.333
y = 11/5x: unit rate = 11/5 = 2.200
y = 15/17x: unit rate = 15/17 = 0.882
y = 31/15x: unit rate = 31/15 = 2.067
y = 13/6x: unit rate = 13/6 = 2.167
The equations with unit rates greater than the unit rate of the graph are y = 19/8x, y = 21/9x, y = 11/5x and y = 13/6x
Therefore, the equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x. Drag each tile to the correct box accordingly
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Please help asap!! Please please please
Yes, I agree with Jorge.
Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.
Jorge could improve his proof by stating his explanation in terms of mathematics.
He could have used the SAS similarity to show that the given triangles are similar.
What is the similarity test of two triangles?
If the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal, the two triangles are similar.
In the given figures, the length of side AB is equal to the length of side DE.
Side AB = Side DE ----------(I)
Similarly, the length of side BC is equal to the length of side EF.
Side BC = Side EF ----------(II)
And the measure of angle ABC is equal to the measure of angle DEF.
∠ ABC = ∠ DEF -------(III)
From (I), (II), and (III), and by using the SAS test we can say that
ΔABC ~ ΔDEF ----------- SAS test
Hence,
Yes, I agree with Jorge.
Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.
Jorge could improve his proof by stating his explanation in terms of mathematics.
He could have used the SAS similarity to show that the given triangles are similar.
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C: Determine the average rate of change between day 2 and day 4. Show your work. (4 points)
A) It is an exponential equation.
B) y = 2^x
C) The rate between days 2 and 4 is 6 minutes per station number.
Is the data modeling a linear or an exponential equation?Here we have the following data:
(1, 2), (2, 4), (3, 8), (4, 16)
What you can see is that the x-value of the points increases equially between consecutive pairs (increases of one unit).
while the y-value does not do that.
First, it increases by 2, then by 4, then by 8.
So this is an exponential relation.
B) A general exponential will be of the form:
y = a*(b)^x
Usin the first two pairs (1, 2) and (2, 4) we can write two equations:
2 = a*b^1 = a*b
4 = a*b^2
So we have a little system of equations:
2 = a*b
4 = a*b*b
If we take the second equation and we divide that by the first one we get:
4/2 = (a*b*b)/(a*b)
2 = b
Replacing that in the first equation we get:
2 = a*2
2/2 = a = 1
The equation is:
y = 2^x
C) The average rate of change will be:
R = (2^4 - 2^2)/(4 - 2) = (16 - 4)/2 = 12/2 = 6
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A) It is an exponential equation.
B) y = 2^x
C) The rate between days 2 and 4 is 6 minutes per station number.
Day
(t) No. of Calories
Burned
C(t)
2 314
4 356
6 370
8 386
10 405
12 442
14 516
Amanda goes to the gym every day and cross–trains. Based on a chart at the gym showing the calories expended for various activities, Amanda has kept track of the number of calories she has burned over the last two weeks. She wants to find the rate at which she burned calories on day 8. That is, she needs to find C'(8). Estimate the value.
A.
8.00 calories per day
B.
8.75 calories per day
C.
17.50 calories per day
D.
17.75 calories per day
Answer: In photo below
You're Welcome :)
If she wants to find the rate at which she burned calories on day 8. C'(8) is: B. 8.75 calories per day
How to find the calories per day?First step is to find the upper and lower values for the burned calories on day 8.
Upper value (C'(8) = 405 - 386 /2
Upper value C'(8) = 19/2
Upper value C'(8) = 9.5
Lower value C'(8) = 386 -370/2
Lower value C'(8) = 16/2
Lower value C'(8) = 8
Now let find C'(8)
C'(8) = 9.5+8/2
C'(8) = 17.5/2
C'(8) = 8.75 calories per day
Therefore the correct option is B.
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8 (a) Write 0.000089 in standard form.
Answer: 0.000089
Step-by-step explanation: 0.000089 is already in standard form, if you want 0.000089 in the scientific form then that would be...
8.9 x 10⁻⁵
-353.92 - (-283.56) -131.29
-353.92-(-283.56)-131.29= -20,165
Suppose the government has a balanced budget and wants to increase spending without changing tax rates. The government enters the loanable funds market to borrow $150 billion for economic stimulus spending. How much money is available for private investment after this action has shifted the demand curve as shown in the figure?
The money available for private investment is $250 billion dollar
What is demand curve ?
The demand curve is a graphical representation of the connection between the cost of a commodity or service and the amount that is demanded over time. The price will often be shown on the left vertical axis in a representation, and the amount needed will typically be shown on the horizontal axis.
Refer to the attachment for graph:
Once investments and government borrowing are added together, the total is = $400
if borrowing from the government is= $150
private investment
=( investment and and government borrowing) - (government borrowing )
= $400 - $150 = $250
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Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72. Which of the following are still outstanding?
The amount that is outstanding when Brett tallies up the transactions in his check.is $9.19.
How to calculate the value?From the information, Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72.
The amount that is outstanding will be the difference between the amount given. This will be:
= Bank statement - Total balance
= $257.72 - $248.53
= $9.19
This is the outstanding amount.
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) Nike deposits N5,000.00 in a savings bank account. If she is paid an interest rate of 5% per annum for 2 years, how much is the simple interest? NOO. O
The simple interest that Nike will receive after 2 years is $500.
The principal amount =$5000
Rate = 5% = 0.05
Time = 2 years
Now simple interest = PRT = 5000 × 0.05 × 2 = 500
Hence the simple interest earned by Nike is $500
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.
Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.
A loan is a sum of money that a person obtains from a bank or another type of financial institution in order to pay bills. A few types of loans are personal, student, auto, and mortgage loans.
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step by step explanation to-4x = -x + 3
The value of x is -1 for equation -4x = -x + 3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -4x = -x + 3
In the given equation minus four times of x equal to minus x plus three
x is the variable
Plus and minus are operators
-4x = -x + 3
Take the variables to one sides
Add +x on both sides
-4x+x=-x+x+3
-3x=3
Divide both sides by -3
x=-1
Hence, the value of x is -1 for equation -4x = -x + 3
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
What is Equation of Circle?The location of a circle in the Cartesian plane is represented by a circle equation. We can write the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.
The standard equation of a circle with center at
(a, b) and radius is r.
So, the standard equation circle is
(x -a)² + (y- b)² = r²
Given:
As, we know the standard form for equation of a circle is
(x-a)² + (y-b)² = b =r²
where (a, b) is the center of the circle and r is the radius of the circle.
We have
diameter = 12 units
radius = 12/2 = 6 units
So, the center will be at (0, 3)
Thus, the equation of circle
(x-0)² + (y-3)² = 6²
x²+ (y-3)² = 36
Hence, the Equation of Circle is x²+ (y-3)² = 36.
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ERROR ANALYSIS Describe and correct the error in finding m/1. X 115° +39° + m/1 = 360° 154° +m1 = 360° m1= 206
-1/2u+3/5=1/6 What is u?
_____________________
[tex]\huge\blue{\mid{\fbox{\tt{Answer}}\mid}}[/tex]
[tex]u=\frac{13}{15}[/tex][tex]\huge\blue{\mid{\fbox{\tt{Explanation}}\mid}}[/tex]
DefinitionsMultiplication - Multiplication, otherwise known as the inverse of division repeats a certain number's value into what it has been multiplied by. Ex. [tex]4\cdot4=16[/tex]
Fraction - A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.
Algebra - Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all mathematics
Reciprocal - In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by [tex]\frac{1}x[/tex] or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction [tex]\frac{a}b[/tex] is [tex]\frac{b}a[/tex]. For the multiplicative inverse of a real number, divide 1 by the number.
_____________________
Now we can solve this equationStep one - Subtract: [tex]-\frac{1}{2} u=\frac{1}{6}-\frac{3}{5}[/tex]Step two - Simplify: [tex]-\frac{1}{2} u=-\frac{13}{30}[/tex]Step three - Multiply by the reciprocal of [tex]-\frac{1}2[/tex]: [tex]-\frac{1}{2}u\cdot -\frac{2}{1}=-\frac{13}{30}\cdot -\frac{2}{1}[/tex]Step four- Simplify: [tex]u=\frac{13}{15}[/tex]Your answer is [tex]u=\frac{13}{15}[/tex]What other congruence is needed to prove that △QRP≅△QFP by ASA?
QR≅QF
∠R≅∠F
∠QPR≅∠QPF
PR≅PF
On an architect's blueprint, 1 inch corresponds to 4 feet. Find the length of a wall represented by a line 1 inches long on the blueprint
The length of wall in real life is 4 feet.
Given that on an architect's blueprint, 1 inch corresponds to 4 feet.
In this architect's plan, a wall represented by a line 1 inches long on the blue print.
So, the length of wall in real life is = 4 feet.
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Answer:
4ft
Step-by-step explanation:
If 1 inch corresponds to 4 ft on the blueprint. The ratio is 1 inch on the blue print for every 4 ft in real life.
Select the correct answer. What is this equation rewritten in logarithmic form? 9x = 3
A. log9 3 = x
B. logx 3 = 9
C. log3 9 = x
D. log3 x = 9
Answer:
A. [tex]\log_9{3}=x[/tex]
Step-by-step explanation:
[tex]y=e^x\rightarrow\log_e{y}=x[/tex]
Therefore,
[tex]3=9^x\rightarrow\log_9{3}=x[/tex]
Complete the following ratios: Current assets = $13,000 Inventory = $4,400 Current liabilities = $10,000 Net income = $7,700 Net sales = $24,400 A. Profit margin on net sales (round to nearest tenth percent) B. Acid test (round to nearest tenth percent.)
The completion of the following accounting ratios is as follows:
A. Profit margin on net sales is 31.6%.
B. Acid test is 86.0%.
What are accounting ratios?Accounting ratios enable financial analysts to understand the relative magnitude of one financial statement account to another.
By their nature, accounting ratios compare or represent an entity's financial performance or position in relative terms.
Current assets = $13,000
Inventory = $4,400
Current liabilities = $10,000
Net income = $7,700 Net sales = $24,400
The profit margin on net sales = Net Income ÷ Net Sales x 100
= $7,700 ÷ $24,400
= 31.6%
Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities
= ($13,000 - $4,400) ÷ $10,000
= 0.86
= 86%
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Please help 25 points
Answer: 6x - 4 = 68
Step-by-step explanation:
Vertical angles are congruent to each other. The two angles given, 6x - 4 and 68, are vertical angles. This means we can set them equal to each other for our equation. Using this logic, the answer is;
6x - 4 = 68
Find the values of x and y
X= 20 & Y= 70 in right-angled triangle .
What is right angle triangle?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The longest of the three sides, known as the hypotenuse, is the third side.2X + 140 = 180
2X = 40°
X = 20°
X + Y = 90°
Y = 70°
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2. Write each of the following as a power function in the form f(x) = kx^p.
f(x) = -3/2x^5
The simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .
What is power function ?
A function having a single term that is the sum of a real number, a coefficient, and a variable raised to a fixed real number is called a power function. Consider functions for area or volume as examples (a number that multiplies a variable raised to an exponent is known as a coefficient). A power function is a function where y = x n, where n is any real constant number. In reality, many of our parent functions, including linear and quadratic functions, are power functions.
Here ,
a) f(x) = [tex]\frac{-3}{2x^5}[/tex]
To write in the form of f(x)= [tex]kx^p[/tex]
=> f(x) = [tex]\frac{-3}{2}* \frac{1}{x^5}[/tex]
=> f(x) = [tex]\frac{-3}{2} x^-5[/tex]
b) g(x) = 5[tex]\sqrt[3]{x}[/tex]
Here we know that [tex]\sqrt[n]{a} = a^\frac{1}{n}[/tex] , then
=>g(x)=5[tex]x^\frac{1}{3}[/tex]
Hence the simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .
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a.) find the test statistic
b.) what is the p-value
c.)what is the conclusion about the null hypothesis
d.) what is the final conclusion?
a) The test statistic is: t = 1.85.
b) The p-value is: 0.0648.
c) The null hypothesis is not rejected.
d) There is not sufficient evidence to conclude that the population mean is different of 4.
What is the test statistic?The standard deviation is known only for the sample, hence the t-distribution is obtain the test statistic.
The test statistic of the t-distribution is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the variables of the equation are given as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the hypotheses.s is the standard deviation of the sample.n is the sample size.For this problem, the values of these parameters are as follows:
[tex]\overline{x} = 4.32, \mu = 4, s = 4.24, n = 600[/tex]
Hence the test statistic is obtained as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{4.32 - 4}{\frac{4.24}{\sqrt{600}}}[/tex]
t = 1.85.
P-value and conclusionThe p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, with 600 - 1 = 599 df and t = 1.85, hence it is of 0.0648.
Since the p-value is greater than the significance level of 0.01, it is found that the conclusion regarding the null hypothesis is that it is not rejected, meaning that the sample does not give sufficient evidence to conclude that the population mean is different of 4.
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Solve for x.
-8x+14 ≥ 60 OR - 4x + 50 < 58
Choose 1 answer:
(A
E
x≤-
x≤
-
23
4
23
4
x>-2
or x>-2
There are no solutions
All values of a are solutions
Answer:
[tex]x\leq -7 or x > -2[/tex]
Step-by-step explanation:
-8x+14 ≥ 60 or - 4x + 50 < 58
-8x ≥ 56 or - 4x < 8
[tex]x \leq -7[/tex] or [tex]x > -2[/tex]
Whats the answer to this?
The required image of points (-4, 6) is (-6, -4) as per the given condition,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
As the image of the point (5, -1) is mapped as, (1, 5),
Which implies a function that (x, y) mapped as (-y , x)
So for (-4, 6) mapped as (-6, -4)
Thus, the required image of points (-4, 6) is (-6, -4) as per the given condition,
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Show that the terms of the series ∑n=1log 5r are in AP. Hence, find the sum of the first twenty terms of the series and also the least value of n for which the sum to n terms exceeds 400
The required sum of the first twenty terms of the series ∑n=1log 5r are in AP will be 32.37.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
We have been given that the terms of the series ∑n=1log 5r are in AP.
As per the given question,
∑n(log(5r)) = log(5·1)+log(5·2)+log(5·3)+...+log(5·n)
n = 20
∑log(5r) = log(5·1)+log(5·2)+log(5·3)+...+log(5·20)
Using the property of logarithmic logₐ(xy) = logₐx + logₐy,
∑log(5r) = (log(5)+log(1)) + (log(5)+ log(2))+(10g(5)+Log(3))+ ...(10g(5)+Log(20))
∑log(5r) = (log(5)+log(5)+log(5)+...+log(5)
∑log(5r) = 20·1og(5)+((log(1)+log(2)+log(3)+...+log(20)
Using property of logarithmic logₐ(xy) = logₐx + logₐy,
∑log(Sr)=20·1og(5)+log(1×2×3×...20)
∑log(5r) = 20-log(5)+log(201)
∑log(5r) = 32.365524703598
Rounded to the nearest hundredth decimal,
∑log(5r) = 32.37
Thus, the required sum of the first twenty terms of the series ∑n=1log 5r in AP will be 32.37.
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0°F; drops 15° what’s the new temperature
The new temperature is given as -15°F.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The present temperature is 0°F.
And, the drop in the temperature is 15°.
The new temperature after the drop can be found by subtracting the amount of drop from the initial temperature as follows,
0 - 15°F
= -15°F
Hence, the new temperature after the drop is -15°F.
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Michel is taking 4 credit hours of courses at his local community college. Each credit hour costs $110.50. He is also to pay three technology fees of $19.25. Determine the total amount that he will pay in tuition.
Total: 499.75
Step-by-step explanation:
4 × 110.5 = 442
3 × 19.25 = 57.75
442 + 57.75 = 499.75