Lorna Hall’s real estate tax of $2,010.88 was due on December 14, 2017. Lorna lost her job and could not pay her tax bill until February 27, 2018. The penalty for late payment is 61/2% ordinary interest. (Use Days in a year table.)

a. What is the penalty Lorna must pay? (Round your answer to the nearest cent.)



b. What is the total amount Lorna must pay on February 27? (Round your answer to the nearest cent.)

Answer:

P(x) = 0.7 [tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x

Step-by-step explanation:

given a polynomial with roots x = a and x = b , then the factors are

(x - a) and (x - b)

If x = a is of multiplicity 2 then factor is (x - a)²

the polynomial is then the product of the factors

p(x) = a(x - a)(x - b) ← a is a multiplier

give x = 4 is a root with multiplicity 2 then (x - 4)² is the factor

x = 0 has factor (x - 0) , that is x

x = - 1 has factor (x - (- 1)) , that is (x + 1)

the polynomial is then the product of the factors

P(x) = ax(x + 1)(x - 4)² ← expand squared factor using FOIL

       = ax(x + 1)(x² - 8x + 16)

       = a(x² + x)(x² - 8x + 16) ← distribute

       = a([tex]x^{4}[/tex] - 8x³ + 16x² + x³ - 8x² + 16x)

      = a([tex]x^{4}[/tex] - 7x³ + 8x² + 16x)

to find a substitute (5, 21 ) into P(x)

21 = a([tex]5^{4}[/tex] - 7(5)³ + 8(5)² + 16(5))

21 = a(625 - 875 + 200 + 80)

21 = 30a ( divide both sides by 30 )

0.7 = a

then

P(x) = 0.7([tex]x^{4}[/tex] - 7x³ + 8x² + 16x) ← distribute parenthesis

P(x) = 0.7[tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x

Answer:

$34.20

Step-by-step explanation:

Since each pie is $12.50 but the assistant gets $1.10 for each pie, Johannes will get $11.40 for each pie sold.

We know that there were 3 pies sold so you must solve the equation below

11.40*3

The answer is $34.20

The single fraction in its lowest terms will be;

⇒ - 7(2x - 1)/2

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Or, A number which is expressed as a quotient is called fraction.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2

Now,

Solve the fraction as;

The fraction is,

⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2

⇒ 3 (2x - 1)/5 - (4x - 2)

⇒ 3 (2x - 1)/5 - 2 (2x - 1)

⇒ (2x - 1) (3/5 - 2)

⇒ (2x - 1) (3 - 10)/2

⇒ (2x - 1) (- 7/2)

⇒ - 7(2x - 1)/2

Thus, The single fraction in its lowest terms will be;

⇒ - 7(2x - 1)/2

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The cost to rent chair is $1.5  and table is $8.5  .

In the question ,

it is given that

the cost to rent 12 chairs and 2 tables [tex]=[/tex] $35

and the cost to rent 3 chairs and 5 tables  [tex]=[/tex] $47

let the cost for 1 chair ne "c"

and let the cost for 1 table = "t"

So , according to the question ,

the equations are

12c + 2t = 35      ....equation(1)

3c + 5t = 47         ....equation (2)

On multiply equation (2) by 4 and then subtracting equation (1) from it ,

we get

(12c + 20t) - (12c + 2t) = 188 - 35

12c + 20t - 12c -2t = 153

18t = 153

t = 153/18

t = 8.5

and 12c + 2(8.5) = 35

12c + 17 = 35

12c = 18

c = 18/12

c = 1.5

Therefore , The cost to rent chair is $1.5  and table is $8.5  .

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The number of 3 / 16 yards pieces that can be cut from 3 / 4 yard of ribbon is 4.

The actual length of the ribbon is 3 / 4 yards.

He wants to cut 3 / 16 yards pieces from the actual length of the ribbon.

Therefore, the number of 3 / 16 yard that can be cut from 3 / 4 yard of ribbon can be calculated as follows;

number of pieces of ribbon = 3 / 4 ÷ 3 / 16

number of pieces of ribbon = 3 / 4 × 16 / 3

number of pieces of ribbon =  48 / 12

Therefore,

number of pieces of ribbon =  4 yards

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The graph of this proportional relationship would look like this: A line passes through the point (0, 0) and continues through the point (14, 7).

In Mathematics, a graph simply refers a type of chart that is typically used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) increases or decreases, the values on the y-coordinate (y-axis) increases or decreases simultaneously.

By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it passes through both points (0, 0) and (14, 7).

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Using an inequality to represent the problem, Chang must run at least an additional 9 miles or greater than 9 miles

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

To find the number of additional miles he will run, let's set the unknown number equals t

12 + t > 21

t > 21 - 12

t >9

Chang will need to run at least 9 miles

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Answer:

i think, x equal 12 and y equal 20

Answer:

c is ur answer

I hope it's help◉‿◉

1) The height of one of these cylinders if its radius is 2 inches is

115.207 inches.

2) The height of one of these cylinders if its radius is 3 inches is

51.203 inches.

3) The height of one of these cylinders if its radius is 6 inches is

12.800 inches.

1) when radius is 2 inches then:

πr²h = 1447

h = 1447/ (3.14 x 2²) = 115.207 inches

2)when radius is 3 inches then:

πr²h = 1447

h = 1447/ (3.14 x 9²) = 51.202 inches

3) when radius is 6 inches then:

πr²h = 1447

h = 1447/ (3.14 x {36}²) = 12.800 inches

1) The height of one of these cylinders if its radius is 2 inches is

115.207 inches.

2) The height of one of these cylinders if its radius is 3 inches is

51.203 inches.

3) The height of one of these cylinders if its radius is 6 inches is

12.800 inches.

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Answer:

A, C, D, E

Step-by-step explanation:

17 is a positive whole number

All whole numbers are integers and rational

Natural numbers are numbers that are positive whole numbers

It is real since you don't have any negative roots

Answer:

Step-by-step explanation:

4x(power of 5) divided by x(power of 2)

5y(po7) div by y(po2)

not 100% sure as i havent learnt this before lol

Answer:

Step-by-step explanation

so basically you need to see what m<I equals and do the same for the rest of them and you should get your answer and that would be let me see and m<k= -44 degrees and m<I and J= -10 degrees and there you have if this is not right i tried have the same step and ask another person

Answer:

5x-9=26

Step-by-step explanation:

5x=35

5 5

x = 7

mark me on brainliest please follow me to

Answer:

x = 7

Step-by-step explanation:

When five times a number is decreased by 9 ​, the result is 26 . What is the​ number?

5x - 9 = 26

add 9 to both sides:

5x - 9 + 9 = 26 + 9

5x =35

divide both sides by 5:

5x/5 =35/5

x = 7

well now, let's recall the remainder theorem, check your textbook since we know you're Da Bomb and love to check that theorem.

well, we know a factor is (x-2) for the polynomial f(x), that means that f(2) =  0, so let's use that

[tex]f(x)=x^3+x^2-5ax+2a^2\hspace{5em}\stackrel{\textit{a factor of f(x)}}{(x-2)}\qquad thus\qquad f(2)=0 \\\\\\ 0=(2)^3+(2)^2-5a(2)+2a^2\implies 0=8+4-10a+2a^2 \\\\\\ 0=2a^2-10a+12\implies 0=2(a^2-5a+6) \\\\\\ 0=a^2-5a+6\implies 0=(a-2)(a-3)\implies a= \begin{cases} 2\\ 3 \end{cases}[/tex]

Yes these triangles are congruent.

What is congruent triangles?

Two triangles live aforesaid to be congruent if all 3 corresponding sides are equal and every one the 3 corresponding angles are equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruousness is’ ≅’.

Main body:

Firstly we need to find the co-ordinates of each point.

M = (-1,5)                               R= (1,1)

L = (-2,2)                               S= (-5,-1)

N= (5,3)                                Q= (2,-2)

to prove these triangles are congruent we need to show that the distance of their sides are equal.

distance formula= [tex]\sqrt{(x1-x2)^2+(y1- y2)^{2}[/tex]

Now in ΔLMN =

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

ML= [tex]\sqrt{10}[/tex] units

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

LN= [tex]\sqrt{50}[/tex] units

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

MN=[tex]\sqrt{40}[/tex] units

Now in ΔQRS=

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

RS = [tex]\sqrt{40}[/tex] units

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

SQ = [tex]\sqrt{50}[/tex] units

RQ = [tex]\sqrt{(1-2)^{2}+(1+2)^{2} }[/tex]

RQ = [tex]\sqrt{10}[/tex] units.

We can clearly see on side of each triangle is equal to one side of another one.

Hence ΔLMN≅ΔQRS.

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The number of quadrilaterals that can be formed with the vertices of a regular pentagon is given by:

5.

The number of vertices for each polygon is given as follows:

Hence, to build the quadrilaterals, four vertices are taken from the set of five vertices of the pentagon.

The formula to be used is given as follows:

The order of the vertices is not relevant, hence the combination formula is used, given as follows:

[tex]C_{n,x} = \frac{n!}{x!(n - x)!}[/tex]

Which gives the number of different combinations of x elements from a set of n elements.

Hence, in the context of this problem, the number of quadrilaterals is obtained as follows:

[tex]C_{5,4} = \frac{5!}{4!1!} = 5[/tex]

The problem asks for how many quadrilaterals can be formed with the vertices of a regular pentagon.

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The relationship between the number of years that Simon's money is invested and the account balance can be described as 4:The relationship is linear. His account increases each year by a constant value of $28.

The simple interest due to Simon's account every year is:
= Simple interest rate x Amount invested

= 0.4% x 7, 000

= $28

This means that every year, Simon's account would increase by a value of $28.

This represents a linear relationship because in linear relationships, the value of the variables increases by a constant amount each year or period.

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10.5 miles far upstream can Tom's boat go on the Little River in 1.5 hours.

The relative velocity formula is written as follows. V is equal to  

V → = V A B → + V B C →

Where. VAB is the velocity in relation to A and B, VBC is the velocity in relation to B and C, and VAC is the velocity in relation to A and C.

The current on the Little River is 8 mph.

Tom's boat goes 15 mph in still water.

For Upstream

the Velocity of the boat  = 15 mph - 8mph

                    = 7mph

How far upstream

can Tom's boat go on the Little River in 1.5 hours = 7* 1.5 = 10.5 miles

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According to the questions that are asked in the various Government exams that are held across the nation, the boat and stream concept is one of the most frequently covered subjects.

Boat speed in still water = 1/2 (downstream speed + upstream speed).

Boat's speed in still water equals 1/2 (13+7) = 1/2 × 20 = 10 km/hr.

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The 95% confidence interval for the distribution of the difference of proportions, using the z-distribution, is given as follows:

(0.11, 0.146).

The first step is finding the proportion and standard error for each sample, as follows:

For the distribution of differences, the mean and the standard error are given as follows:

The z-distribution is used as we are working with proportions, hence the bounds of the interval are given as follows:

p ± zs.

The critical value for a 95% confidence interval with the z-distribution is of z = 1.96.

Hence the lower bound of the interval is:

0.128 - 1.96 x 0.0092 = 0.11.

The upper bound of the interval is:

0.128 + 1.96 x 0.0092 = 0.146.

The information regarding each sample is given by the image at the end of the answer, and the problem asks for the 95% confidence interval for the differences.

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The function f(x) = -3(x + 2)² + 1 has it's vertex as (-2, 1) and an axis of symmetry x = -2

The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.

In the given function;

f(x) = -3(x + 2)² + 1

Kindly find the attached graph of the function below

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The function is positive and increasing from 0 to 2.5, at negative and decreasing  from 0 to -2.5,  respectively.

How to find returns to scale?

Returns to scale involves an increase in an output more than when all the inputs increase proportionately.

Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5.  this shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.

In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.

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Answer:

  336, 504

Step-by-step explanation:

You want the next two numbers in the sequence beginning 6, 24, 60, 120, 210, ....

When attempting to identify a sequence it is often useful to look at the differences between terms, then at the differences of those, and so on. If The differences at some level are constant, that level tells you the degree of the polynomial that will describe the sequence. If they have a common ratio, then the sequence will be based on an exponential function.

1st differences: 18, 36, 60, 90

2nd differences: 18, 24, 30

3rd differences: 6, 6 . . . . . . . . constant, indicating a cubic function

We can go to the trouble to write four equations in the four coefficients of the cubic describing this sequence, or we can let suitable technology find it for us. The attachment shows a graphing calculator solution for the coefficients. The 10^-14 value for the 'd' coefficient is effectively 0. This value is due to the inexact representation of numbers in the floating point arithmetic used by the calculator.

The equation of the n-th term a[n] is ...

  a[n] = n³ +3n² +2n

The next two terms are ...

  a[6] = 336

  a[7] = 540

__

Additional comment

The equations for the coefficients of y = ax³ +bx² +cx +d will use the given sequence values and x values of 1..4. Here they are:

  6 = a·1 +b·1 +c·1 +d

  24 = a·8 +b·4 +c·2 +d

  60 = a·27 +b·9 +c·3 +d

  120 = a·64 +b·16 +c·4 +d

The second attachment shows a calculator solution for these four equations. (a, b, c, d) = (1, 3, 2, 0)

y + 2 = 5/2 (x - 6) ; 5x-2y=34 ; y=5/2x-17 is the equations of the line that goes through the point (6,-2) and is perpendicular to the line y+2=-2/5(x-10), Hence the correct options are B, C and F.

The standard forms of the equation of a line are:

Slope-intercept form:

y = mx + c

Where m indicates the slope of the line and c is the y-intercept

Intercept form:

x/a + y/b = 1

General form of the equation of the straight line, i.e. Ax+By+C = 0

x/(-C/A) + y/(-C/B) = 1

where a = -C/A and b = – C/B

Normal form:

The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:

x cos α+y sin α = p

Given,

Point = (6,-2) = (x2,y2)

Equation of line = y+2=-2/5(x-10)

General equation of the line = y - y1 = m ( x-x1 )

After comparing we get,

Slope of the given line = -2/5

As we know both the lines are perpendicular to each other so, product of their slopes must be equal to -1.

m1 × m2 = -1

-2/5 × m2 = -1

We get m2 = 5/2

So the equation of the line having slope  5/2 and passing through  (6,-2) is:

y - y2 = m2 ( x-x2 )

y -(-2) = 5/2 (x - 6)

y + 2 = 5/2 (x - 6)

Hence, we get equation of the line as y + 2 = 5/2 (x - 6) .

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Answer: Marks bakery

Step-by-step explanation:

divide 450 by 3 = 150 loaves of bread Ann baked per day

divide 560 by 4= 140 loaves of bread Mark bakes per day

Thus Marks bakery bakes bread at a faster rate.

The area of the city block is 13.23 kilometers².

The city block is 3 times as long as it is wide. In this case, the width can be represented by w. The length will be 3w.

Therefore, perimeter will be:

= 2(length + width)

= 2(3w + w) = 16.8

8w = 16.8

Divide

w = 16.8 / 8

w = 2.1

Length = 3w = 3 × 2.1 = 6.3km

The area will be:

= Length × Width

= 6.3 × 2.1

= 13.23km²

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Answer:

The area of the city block is 13.23 kilometers².

Step-by-step explanation:

The horizontal asymptote is y = [tex]\frac{9}{4}[/tex].

Let f(x) = [tex]\frac{9x^{3}-5x-9}{4x^{3}-9x+4}[/tex]

Line y = L is a horizontal asymptote of the function y=f(x), if either [tex]\lim_{x \to \infty} f(x) = L[/tex] or, [tex]\lim_{x \to -\infty} f(x) =L[/tex] and L is finite.

We will calculate limits :

[tex]\lim_{x \to \infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]

[tex]\lim_{x \to -\infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]

Hence, horizontal asymptote is y = [tex]\frac{9}{4}[/tex].

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The probability that the sample proportion will differ from the population proportion by more than 3% is 0.8948

The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.

In this case, the sample proportion:

= ✓[p(1 - p)/n]

= ✓(0.13 × 0.87)/329

= 0.01854.

The probability will be:

P(-0.03 / 0.01854) < z < (0.03 / 0.01854)

P(-1.62 < z < 1.62)

Looking at the z table, the probability is 0.08948

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well, the reduction in value is £12500 - £11625 = £875.

if we take 12500 to be the 100%, what is 875 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 12500 & 100\\ 875& x \end{array} \implies \cfrac{12500}{875}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{100}{7}=\cfrac{100}{x}\implies 100x=700\implies x=\cfrac{700}{100}\implies x=7[/tex]

Answer: El porcentaje de reducción exacto es de: 7%, con esto el precio de descuento es de €875.