Are the two expressions equivalent when x=3 ? 8x + 40 , 5 (2x + 8)

The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).

What is dilation?

A dilation is a function f from a metric space M into itself that, for any points x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real number. Such a dilatation is a resemblance of the space in Euclidean space.

Here, we have

Given

The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin.

We have to find the image after dilation.

The coordinates of an image (-10,-6), dilating the coordinate by 1/2 means reducing the image by multiplying each coordinate by the factor of 1/2.

Image = (1/2(-10), 1/2(-6))

Image = (-5,-3)

Hence, the image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).

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The time that it will take for Kingsfield to have a larger population than Queensville is given as follows:

3.58 years.

The rates of decline and growth are constant, meaning that the populations for each town are modeled by exponential functions.

The rates for each town are given as follows:

Considering the initial population, the exponential functions for the population of each town after t years are given as follows:

Kingsfield will have a larger population than Queensville when:

[tex]7500(1.2)^t > 32000(0.8)^t[/tex]

Hence:

[tex]\left(\frac{1.2}{0.8}\right)^t > \frac{32000}{7500}[/tex]

(1.5)^t > 4.27

tlog(1.5) > log(4.27)

t > log(4.27)/log(1.5)

t > 3.58 years.

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The pair of Linear angles are 51° and 129°.

When two lines intersect at a point then they will form two linear angles. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.

In other words, if the sum of two adjacent angles is 180° then the pair of angles are said to be Linear Angles.

Here we have

Two angles form linear angles

Let x and y be the two angles

=> x + y = 180 ------ (1)  [ since both are linear angles ]  

Given that the sum of one angle plus 27 is equal to two times the sum of the other angle

=> x + 27 = 2y

=> x = (2y - 27) ---- (2)

Substitute (2) in (1)

=> 2y - 27 + y = 180

=> 3y = 153

=> y = 153/3

=> y =  51  

Now substitute y = 51 in (1)

=> x + 51 = 180

=> x = 180 - 51

=> x = 129

The pair of Linear angles are 51° and 129°.

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The given p-series 1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex]) is divergent as the value of is equal to 3/4 ⇒p < 1.

As given in the question,

Given p-series is equal to :

1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex])

As value of 1³ = 1 and fourth root of 1³ is equal to 1.

We can substitute 1 = (1 /fourth root of 1³) which is equal to

= (1/ [tex]\sqrt[4]{1^{3} }[/tex] ) + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex])

Apply nth formula we get,

= [tex]\sum\limits^\infty_0 {\frac{1}{\sqrt[4]{n^{3} } } }[/tex]

⇒ p = 3/4

And 3/4 < 1

⇒ p < 1

⇒P-series is divergent.

Therefore, as the value of p =3/4<1 the given series  1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex]) is divergent.

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The second term of the series will be 27.

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.

Sum to infinity = a/1-r

where s = 300

r = 0.1

a = 300 (1 - 0.1)

a = 300 (0.9)

a = 270

The second term of the progression will be = ar

Second term = 270 x 0.1

Second term = 27

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Answer: t is the dependent variable  and x the independent variable

Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.

x is the independent variable as we can use whatever values we want for x it is not affected by t

The general anti derivative or indefinite integral of the function

cos2x - sec²x is 1/2 sin2x + tan x + C .

The given function is of the form : cos2x - sec²x

Now we will use the indefinite integral on the above expression:

∫cos2x - sec²x

This can be broken into :

∫cos2x -  ∫sec²x

Now we will integrate them separately:

∫cos2x, we will use u-substitution.

Let 2x = u

Differentiation both sides we get:

2 dx = du

or, dx = 1/2 du

Hence we will use this value:

∫cos2x

= ∫cos u · 1/2du

= 1/2 ∫ cos u du

=1/2 sin u + C , where C is a constant.

Again we will do the second part of the integral:

∫sec²x

= tan x + C

Hence the required integral will be:

1/2 sin2x + tan x + C .

Now we will use differentiation to check the integral

d/dx (1/2 sin2x + tan x + C )

= d/dx (1/2 sin2x) + d/dx (tan x) + d/dx (C)

= cos 2x + sec² x

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The final function  after the transformations are applied to the graph of y =√x is y = 2√(x - 5) +1.

What is transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Rule of transformation:

g(x) = c f(x+a) + b

If c > 1, then f(x) vertically starched by c factor. If 0< c < 1, then f(x) vertically compressed by c factor.

If a>0, then f(x) is shifted horizontally a unit right side. If a<0, then f(x) is shifted horizontally a unit left side.

If b>0, then f(x) is shifted vertically b unit upward. If a<0, then f(x) is shifted vertically b unit downward.

Putting c = 2, a = -5, b = 1, and f(x) = √x

y = 2√(x - 5) +1

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The null hypothesis cannot be rejected.

Given that,

A study is done to determine the average cost difference between utilizing two different statistical tools to analyze data. 15 data sets are used to do this. Each program performs an analysis on each, and the cost of the analysis is noted.

To test if cost is same, we test mean difference of scores =0

H0: d=0

H0: d != 0

z0 = 0-(-05467) / 0.039976

= 1.367

z score for alpha = .05 is 1.96

Since, z0 < z score, we cannot reject the null hypotheses

Therefore, the null hypothesis cannot be rejected.

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The value of y when X value is -1 would be = -5

The substitution equation method is the method of solving equation whereby a value is being simplified and substituted into the second equation to obtain the next unknown value.

From the given equation:

(x-2)²/16 - (y-4)²/9 = 1

Take X = -1 and substitute X for -1 into the given equation,

(-1-2)²/16 - (y-4)²/9 = 1

9/16 - (y-4)²/9 = 1

(y-4)²/9 = 9/16- 1

(y-4)²/9 = -7/16

Cross multiply

(y -4)² = 9(-7)/16

y²+16 = -63/16

16(y²+16) = -63

16y²+256 = -63

16y² = -319

y² = -319/16

y² = -20

y= -√20

y = -4.5

y = -5

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The probability that the mean height x is between 68 and 70 inches is found as 37.28%.

The z-score is written as follows:

z = (x - μ)/σ

In which,

x =  between 68 and 70 inches.

μ = mean 69 inches

σ = standard deviation 6 inches

Put the values in the formula,

Probability that the mean height x is between 68 and 70 inches

P(68 < x < 70) = (68 - 69 / 6) < z < (70 - 69 / 6)

P(68 < x < 70) = (-0.16) < z < (0.16)

P(68 < x < 70) = 0.4364 - 0.0636

P(68 < x < 70) = 0.3728

P(68 < x < 70) = 37.28%

Thus, the probability that the mean height x is between 68 and 70 inches is found as 37.28%.

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In order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies from great desserts inc. to be enforceable, the agreement must be in writing if the pies cost at least $500.

What is an Agreement?

This refers to the legally binding contract that exists between two or more entities where the terms of the contract have been drawn up and the terms have been agreed upon by all parties involved, subject to certain conditions before it can be enforceable.

Hence, we can see that in order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies and because they are a limited liability company, there needs to be a minimum threshold and this can be done, if the cost of the pies is at least $500.

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Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by

f(x) = Σ[∞], n=1 cnyn(x)

To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).

cn = (f,yn) = ∫[0,4]f(x)yn(x)dx

Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by

cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx

Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.

cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx

= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx

= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx

= 1/2 ∫[0,2] (x+2)yn(x) dx

Therefore, the coefficient Cn is given by

Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

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4% is  the percentage rate of increase or decrease in exponential function.

What exactly makes a function exponential?

A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.

                    The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

We have,

y = 420( 1.04)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is

y(x)= a(1-r)^x such that r is the growth percent.

    1 + r = 1.04

      r = 0.04 ⇒  4%

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From the given Isosceles trapezoid ABCD, the three correct statements are:

∠ADC ≅ ∠BCD

AD ≅ BC

AC ≅ BD

An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths.

Particularly in isosceles trapezoids, there are unique correlations. "Equal legs" is what the term "isosceles" denotes. Non-parallel sides on isosceles trapezoids have the same lengths. The "legs" are another name for these equal sides.

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. A triangle with two congruent sides is referred to as being isosceles, in other words.

Thus, three correct statements are -

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For binary class classification, assumptions are necessary in a way:

Given that

From Boyer Naive classifier,

We evaluate (ai | vj) is given below

(ai | vj) = n(e) + m(p) / n + m

Here,

m = equivalent sample size

n(e) = number of training examples

for which v = vj and a = ai

n(i) = number of training example for which v = vj

P = a prior estimate for P(ai | vj)

Here, we calculate that

P(SUV | yes), P(Red | yes), P(Domestic | yes)

P(SUV | no), P(Red | no), P(Domestic | no)

We evaluating this value like

yes:

RED :                             SUV:                            DOMESTIC:

n = 5                              n = 5                             n = 5

n(c) = 3                          n(c) = 1                           n(c) = 2

P = 0.5                          P = 0.5                           P = 0.5

m = 3                              m = 3                            m = 3

Therefore, with the above calculation we can justify that the simplifying assumptions are necessary in a binary class classification.

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Answer:

Read explanation :)

Step-by-step explanation:

Activity 1: When it says direction it refers to the tiles going horizontal and vertical for example the 4 and 9 going vetical to make vertical you must first add 4 + 9 which equals 13 then add a 2 under the 9 so it equals 15. And for 8 and 4 horizontal you must add 8 + 4 which equals 12 so add a three in between the 8 and 4 and for the 7 there is a two on the right of it so add 7 + 2 to equal 9 then add 6 to equal 15 then add a 1 in between the 8 and the 6 to equal 15 and add the 5 in the middle.

Activity 2: On the addition table on the left side of the table the number is the number you add to the number on top for example: the 2 at the top of the table plus the 6 on the same vertical line going down so it would be 2 + 6 which equals 8 as it tells you the answer and for 7 on the left side of the table and 3 at the top of the table with the vertical line would be 7 + 3 which equals 10.

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The distance the ride will go for birr 1350 is 130 kilometres.

The ride cost birr 50 to pick up and 10 birr per km. The distance you can go with birr 1350 can be calculated as follows;

Let's use equation to represent the total amount spent on the distance covered.

Therefore,

let

Hence,

y = 50 + 10x

Therefore,

where

y = 1350

y = 50 + 10x

1350 = 50 + 10x

1350 - 50 = 10x

1300 = 10x

divide both sides by 10

x = 1300 / 10

x = 130 km

Therefore, the ride will go 130 km.

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The equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.

What is an equation of a circle?

A circle can be characterized by its centre's location and its radius's length.

Let the center of the considered circle be at the (h, k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The center of the circle is at (-2, 1) and the radius of the circle is 2 units. Then the equation of the circle will be
(x - (-2))² + (y - 1)² = 2²

        (x + 2)² + (y - 1)² = 2²

        (x + 2)² + (y - 1)² = 4
Hence, the equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.

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The number of sections that are most likely on each color on the spinner are

From the question, we have the following parameters that can be used in our computation:

Number of times the spinner is spun = 50 times

The outcomes are

Number of sections = 10

The section of each color is then calculated as

Color = Color outcomes/Number of times * Number of sections

Using the above as a guide, we have the following:

Red = 19/50 * 10 = 3.8

Green = 11/50 * 10 = 2.2

Black = 4/50 * 10 = 0.8

Orange = 16/50 * 10 = 3.2

Approximate

Red = 4

Green = 2

Black = 1

Orange = 3

The above represents the possible sections

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Answer:

Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)

Good luck;)

Step-by-step explanation:

The simplified form of the given logarithmic expression as required in the task content bis Choice B; 2log8.

It follows from the task content that the simplified form of the logarithmic expression is to be determined as a single log term.

On this note, since the given expression is;

2log2 + 2log4

It follows from factorisation that we have;

2 ( log 2 + log 4 )

Therefore, the expression in the parentheses can be simplified as a single log term using the sum of logarithms law as follows;

= 2 ( log ( 2 × 4 ) )

= 2 log 8.

Ultimately, the answer choice which represents the simplified form of the expression as a single log term is; Choice B; 2 log 8.

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Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient

Let f:R⇒S be a surjective homomorphism of rings with identity.

We have to find if R is a PID, prove that every ideal in S is principal.

We know that,

Let I be the ideal of S

Since f is sufficient homomorphism.

So, f⁻¹(I) is an ideal of R.

Since R is PID so ∈ r ∈ R such that

f⁻¹(I) = <r>

I = <f(r)>

Therefore,

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

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By using the division algorithm to divide 116 by 3 will be 38.

The given integers a and b are 116 and 3 respectively.

Let q be the counter variable and r be the variable to store the new dividend after each loop.

Division algorithm,

If a<b

return 0;

else

q = 0;

r = a;

repeat

q = q+1;

r = r-b;

until r<b;

return q, r;

Working:

116 is not less than 3, implies

r = 116 -3 = 113

q = 0+1=1

Repeating until we get q = 38, r = 2 = a

2<3, hence returns q = 38, r =2

The question is incomplete, the complete question is:

use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true.

(a) q = 39   (b) q =32   (c) q = 38

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The n expressed in terms of r and p is n=r/p.

How to solve the word problems?

Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:

You must frequently create two distinct linear equations in two variables in order to solve these issues.

So, it is expressed as:

r=pn

n=r/p

Hence, The n expressed in terms of r and p is n=r/p.

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An expression that shows number of cookies each friend got is c/5.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, Cole has c oatmeal cookies. He lets 5 of his friends share them fairly.

Total number of cookies =c

Sharing among 5 friends

Number of cookies each friend got =Total number of cookies/5

= c/5

Therefore, an expression that shows number of cookies each friend got is c/5.

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The inverse of the function shown is (x + 5).

What is the inverse of the function?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "[tex]f^{-1}[/tex]" or "[tex]F^{-1}[/tex]." Here, (-1) should not be confused with an exponent or a reciprocal.

Coordinates of the given line are (8,3) and (-2,-7)

The function of the given graph for two points form is

[tex]y-y_{1} = \frac{y_{2}-y_{1} }{x_{2} -x_{1}} (x-x_{1} )[/tex]

or, [tex]y-3 = \frac{-7-3 }{-2-8} (x-8 )[/tex]

or, y - 3 = x - 8

or, y = x -8 + 3 = x - 5

y = x - 5

To find the inverse, replace x with y and y with x then, we get

x = y - 5

y = x + 5

[tex]f^{-1}[/tex] = x + 5

Hence, the inverse of the function shown is (x + 5).

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Answer:

5[tex]\sqrt{3}[/tex]i

Step-by-step explanation:

[tex]\sqrt{-5(5)(3)}[/tex]  You can pull out a 5 and you are left with [tex]\sqrt{-1}[/tex] and [tex]\sqrt{3}[/tex].

The [tex]\sqrt{-1}[/tex] = 1

5[tex]\sqrt{3}[/tex] i

Answer: [tex]5\sqrt{3} i[/tex]

Step-by-step explanation:

The square root of -75 is not a real number, because it is not possible to find a real number that when squared results in a negative number.

In mathematics, the square root of a number is defined as the number that, when multiplied by itself, equals the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. Similarly, the square root of 9 is 3, because 3 x 3 = 9.

However, it is not possible to find a real number that, when squared, results in a negative number. This is because any real number multiplied by itself is always positive, regardless of whether the original number was positive or negative. For example, the square of -2 is 4, because    (-2) × (-2) = 4, which is a positive number.

Double however, complex numbers are used to represent numbers that have a non-zero imaginary component, such as the square root of -1. Complex numbers are written in the form a + bi, where a and b are real numbers and i represents the imaginary unit.

Therefore, the square root of -75 can be written in simplified form as  [tex]5\sqrt{3} i[/tex], where [tex]i[/tex] is the imaginary unit. This represents a complex number with a real component of 0 and an imaginary component of [tex]5\sqrt{3}[/tex].

Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.

1 dozen of Rose costs = $30.96

1 dozen of chrysanthemums costs = $17.80

1 dozen of of tulips costs = $ 21.10

Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips

                         = 16 * 30.96 + 40 * 17.80 + 20 *21.10

                         = $1629.36

There is a 6% sales tax on all order = 6% of 1629.36 =  $ 97.76

Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.

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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.

What is Percentage ?
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Use the unitary approach.
by adjusting the fraction's denominator to 100.
It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
                        = 16 * 30.96 + 40 * 17.80 + 20 *21.10
                        = $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 =  $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.

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