Lola purchases music from two online services. Company A charges Lola a $10
subscription fee plus 89 cents for each song. Company B charges no subscription fee but
$1.19 per song. What is the minimum number of songs Lola would have to purchase for
Company A to be the cheaper option?

When the sequence limn→∞ (1 n! ∫x t = a f(n+1)(t)(x−t)n d t) converges to zero, as seen on the left side equation the Taylor series will accurately converge to f(x). For the Taylor series of f, this side is known as the integral form of the remainder (x).

Rn(x) = f(n+1)(c) (n + 1); thus, (x a)n + Rn(x)! when there is a c between a and x, (x a)n+1. The Taylor formula is the name given to the second equation. The residual of order n or error term for the Pn(x) over I approximation of f is known as the function Rn(x) (x). To integrate a Taylor Series function, expand the Taylor Series as usual before integrating each term. There is a general expression for the new series. Prior to determining the generic phrase, it is essential to avoid simplification.

Assume that f(x) is a real or composite function and that f(x) is a differentiable function of a real or composite neighborhood number. The following power series is then described by the Taylor series: F (x) = F a F ′ a 1! (x−a)+f”(a)2!

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Answer:

70 degrees

Step-by-step explanation:

Triangle XBC is an isosceles triangle.

From the question given, you already know that angle XBC = 55 degrees. This means that angle XCB = 55 degrees. This is because the two sides XB and XC are of equal length, which means that the angles are also equal to each other.

Using this info, we can calculate angle BXC:

The sum of a triangle adds up to 180, so call the unknown angle x:

55 + 55 + x = 180

110 + x = 180

x = 180 - 110 = 70 degrees

The height of rectangular prism needed to reach the desired volume is 9 inches.

What is the volume of the rectangular prism?

The volume of a rectangular prism is the product of its three dimensions, that is volume = length × width × height.

V= l.w.h

l Length

w Width

h Height

Given :

volume of rectangular prism (v) 32,188.04 inches

length  of rectangular prism(l) 59.3 inches

width of rectangular prism(w) 59 inches

Since , V= l.w.h

32,188.04 = 59.3 * 59 * h

or h = 32188.04/59.3 * 59

or h = 32188.04/3498.2

or h = 9.2

Hence , the height of rectangular prism needed to reach the desired volume is 9 inches.

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The big-o estimate for each of these functions are:

nlog(n^2 + 1) = o (n^2 logn)

It is a commonly used notation in algorithms and data structures domain to get an approximate upper bound of the time the algorithm in question will take to run.

For example, if you want to find the maximum element in a list of n elements, the worst case scenario is that the maximum is the last number. Then we write  O(n) .

If the function is not too unweildy, it's pretty easy to do.

Consider the function f(x) = 4x^3 + (7x^2)(log(x)) + 3x +8

Look for the highest order term - the term that grows faster than the other terms, as x gets larger. For this function, that term is 4x^3.

Now just get rid of the constant out front to get x^3.

Then put a Big O in front: O( x^3 ).

So we say that f(x) is O( x^3 ).

Since,

nlog(n^2 + 1 ) + n^2 logn is approximately equals to n^2logn

which implies,

nlog(n^2 + 1) + (n^2 logn) = O (n^2 logn)

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A) The Probability that comic D will perform fourth is; 1/6

B) The Probability that Comic F will perform first and Comic C will perform fourth is;  1/30

C) Probability that the comedians will perform in the following order, D, F, C, E, A, B is;  1/720

D) Probability that Comic A or Comic B will perform third is; 1/15

A) Probability that comic D will perform fourth;

Number of ways that this will succeed = 1 * 5!

Number of possible outcomes normally = 6!

Thus;

P(D is 4th) = 5!/6! = 1/6

B) Probability that Comic F will perform first and Comic C will perform fourth.

Number of ways that this will succeed = 1 * 1 * 4!

Number of possible outcomes normally = 6!

Thus;

P(F is 1st and C is 4th) = 4!/6! = 1/30

C) Probability that the comedians will perform in the following order, D, F, C, E, A, B;

There is only 1 way and as such the probability = 1/6! = 1/720

D) Probability that Comic A or Comic B will perform third;

(2!*4!)/6! = 1/15

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Answer:

ive did the math and its r= 4

Step-by-step explanation:

The first possible date on which she will complete 25 hours of exercise for the year is on March 1.

In general, dates can refer to a specific day on the calendar, such as January 1 or December 31. Dates can also refer to a specific point in time, such as a specific hour, minute, or second. In some cases, dates can also refer to a specific period of time, such as a year, month, or week.

Since Nora plans to do a 45-minute workout four times a week,

she will exercise for a total of 4 * 45 minutes = 180 minutes per week.

This means that each week, she will exercise for a total of 180 / 60 = 3 hours.

To complete 25 hours of exercise for the year,

Nora will need to exercise for a total of 25 / 3 = 8.3 weeks.

The first possible date on which she will complete 25 hours of exercise is therefore 8.3 weeks after Jan 1,

Which is approximately 8.3 * 7 = 58 days after Jan 1.

Therefore, the first possible date on which Nora will complete 25 hours of exercise is 58 days after Jan 1, which is on March 1.

Overall, if Nora sticks to her New Year's resolution to exercise four times a week, the first possible date on which she will complete 25 hours of exercise for the year is on March 1.

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Value of x is 30 and y is 30, if angle A is (2x), angle B is (y+x), and angle C is (y-x).

The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.

Given

Angle A = 2x

Angle B = y + x

60 =  y + x

y = 60 - x

Angle C = y - x

60 = y - x

60 + x = y

As we know, sum of triangle is 180

2x + 60 - x + 60 + x = 180

2x - x + x = 180 - 120

2x = 60

x - 30

For value of y, equating value of x in y = 60 - x

y = 60 - 30

y = 30

Value of x is 30 and y is 30, if angle A is (2x), angle B is (y+x), and angle C is (y-x).

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The attached picture is of a similar problem. But different radii.

Notice how you can form 2 equilateral triangles, and that there are 4 semi circles (at AC, AD, BC, BD).

This is because points C and D lie on the circumference of the circles. So distance from centres( A and b) to C and D are the radius

To get the area of your shaded section, you would just need to add up the areas of the 4 semi circles and 2 equi. triangles.

To get the area of a semi circle, work out the area of one of the sectors, i.e sector ABC, then subtract area of an equilateral triangle.

(Note, due to symmetry all semi circles have same area)

________________________________________________________

For example, for the picture below:

Area of equi triangle = absinC = 1*1*sin60 = √(3)   --> (C is angle)

Area of sector = (angle/360) * πr² = (60/360) * π * (1)² = π/6

So area of 1 semi circle = Area of Sector - Area of equi triangle

                                       = π/6 - √(3)

Now you would just add the areas of 4 semi circles, and 2 equi triangles, and compare coefficients to get a, b, c.
______________________________________

Now you would do the same for your question, except radius is now 6cm instead of 1cm.

Answer:

-4

Step-by-step explanation:

[tex]-3*2 + 2=-4[/tex]

Step-by-step explanation:

To find the number of years it will take for Enola's investment to triple in value, we can use the formula for simple interest:

I = P * r * t

where I is the total interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the number of years.

Since the investment will triple in value, the total interest earned will be equal to two times the initial investment, or 2 * $8,600.00 = $17,200.00. Substituting these values into the formula and solving for t, we get:

$17,200.00 = $8,600.00 * 5.1% * t

t = $17,200.00 / ($8,600.00 * 5.1%) = 3.28 years

Rounding this value to the nearest tenth of a year, we get t = 3.3 years. Therefore, it will take approximately 3.3 years for Enola's investment to triple in value.

The volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution is 1.176 ml.

Volume is a degree of the quantity of area that be counted occupies. Matter is described as a bodily substance that occupies area and has a mass. In bodily sciences like chemistry, the usual unit of extent is cubic metres (m3). From this, different gadgets are derived inclusive of litre (L) and millilitre (mL).

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If during the year, Salaries Payable decreased by $12,000. Using the direct method of reporting cash flows from operating activities, if Salaries Expense amounted to $450,000 for the year, the cash paid to employees is $462,000.

Cash paid can be defined can be defined as the amount that is payable to an employee by an employer.

Using this formula to find the cash paid to employees

Cash paid to employees = Salaries payable decreased + Salaries Expense

Where:

Salaries payable decreased = $12,000

Salaries expense = $450,000

Let plug in the formula

Cash paid to employees = $450,000 + $12,000

Cash paid to employees = $462,000

Therefore the Cash paid to employees  is the amount of $462,000.

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Step-by-step explanation:

(a). Radius = WX, WY or WT as they are all points going from the centre of the circle.

(b). Diameter = TX or XT as it goes through the circle points.

(c). Chord = UV or TX as it is two points that originate from the centre of the circle.

(d).  The diameter is two times the radius, as the radius (WY = 3) we can find out that the diameter is 3 * 2 so 6.

Answer: (3,-6) x=3 y=-6

Step-by-step explanation:

Option (d) i.e y = 2x is correct option as this function is satisfying given values of y and x.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially offered the standard concept of function in 1837.

y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x).

We need to check by substituting value of y in every equation to check correct option.

(a) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = 3x= 3×3=9

L.H.S≠R.H.S

So, it is not a correct option.

(b) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = x-3= 3-3=0

L.H.S≠R.H.S

So, it is not a correct option.

(c) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = x+2= 3+3=5

L.H.S≠R.H.S

So, it is not a correct option.

(d) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = 2x= 2×3=6

L.H.S=R.H.S

So, it is correct option.

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The simple interest rate that Levi is being charged, given that he will have to pay back $ 45 and $ 15. 25 in 5 months, is  81.3 %

The simple interest rate can first be found by finding the monthly amount that Levi has to pay in fees which is :

= 15. 25 / 5 months

= $ 3. 05 fee per month

The amount that the fee would have been in a year is :

= 3. 05  x 12

= $ 36. 60

The simple interest rate is therefore :

= 36. 60 / 45

= 81.3 %

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Answer:

you would times them both so 4x543 =2172

Step-by-step explanation:

543 cubic centimeters has 0.543 L approximate displacement.

Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.

Basic formula to calculate engine displacement is =

V = π/4 x D² x H x N

Where :

D = Bore Diameter

H = Length of Stroke

N = Number of Cylinder

Since the question has already stated cubic centimeter, it has already shown the displacement. So, we can ignore above formula and the 4-cylinder engine information.

First, we state what is known. It is the displacement at cubic centimeter.

Cubic centimeter = 543 cc

Next, we change the unit of cubic centimeter (cc) into liter (L)

Displacement = cc / 1000 L

= 543 / 1000 L = 0.543 L

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Geometric mean will be a line segment with length x such that x² = a × c.

Geometric mean of two line segments p and q is a line x such that it satisfies the formula x² = a × b or x/a = b/x.

To construct geometric mean, first simply draw a line segment and mark a point P anywhere on this line.

Mark the length of the line segment 'a' from the point P and mark the endpoint of 'a' as A. Now, in the same line, from the point P, mark the length of the given line 'c' and mark its endpoint as C.

Now, draw a perpendicular bisector of the resulting line PC. Then we get the midpoint of PC. Let this point be O.

Draw a semicircle with center O and the endpoints P and C.

Now draw a vertical perpendicular line from the point A until it cuts the semicircle. Let N be the point where this line touches the semicircle.

Now join P with N.

The line PN will be the geometric mean x such that a × c = x².

Hence the line segment PN is the geometric mean with length x.

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The angles m∠CEA and m∠AED are supplementary .hence the value of x will be 10 has been proved.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays known as the vertex—is referenced as an angle's sides.

We are Given that m∠CEA and m∠AED are only two angles on a straight line thus they will be supplementary.

Therefore, we have

m∠CEA + m∠AED = 180°

8x + 10 + 6x + 30 = 180

14x + 40 = 180

14x = 140

x = 10

Hence "The value of x will be 10 that proved the angles m∠CEA and m∠AEDare complementary".

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The shape of the graph of a function is the shape assumed by the graph of the function after the dataset generated by using the function is plotted on the coordinate plane. The shape in the graph of the question is a triangular shape.

A function is a direction used to map the values of an input variable of the function to the output variables.

The points in the attaches graph which are connected by lines are;

(0, 1.5), and (4.5, 0)

The joining of the above points in the attached graph, and the origin forms a triangular shape.

Details about the shape of the graph of a function

The graph of a function such as f(x) = -x² + 2·x + 3, is obtained by finding the values of the output values of the function, f(x) for each input value of the function, x as follows;

x     [tex]{}[/tex]             f(x)

0     [tex]{}[/tex]              3

1     [tex]{}[/tex]               4

2     [tex]{}[/tex]              3

3     [tex]{}[/tex]              0

4     [tex]{}[/tex]              -5

5     [tex]{}[/tex]              -12

6     [tex]{}[/tex]              -21

7     [tex]{}[/tex]              -32

8     [tex]{}[/tex]              -45

Please find attached the graph of the sample function created with MS Excel

The graph of the function f(x) = -x² + 2·x + 3 has the shape of a parabola, which is the shape of a quadratic function.

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The relation between variables is represented by an equation ; y = 2.5x+15

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Alexa joined a program at some coffee shop which offers her $15 per month, after which she will get her coffee at a discount rate which $2.5

We can represent the relationship as ;

y = 2.5x+15

Where, x (number of coffee) is an independent variable because it does not depend on any condition, and y (cost) is a dependent variable because it depends on the value of x.

Hence, the relation is described as y = 2.5x+15

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Answer:

4y = (1/2)^x -5

Step-by-step explanation:

The first three equations are lines. All the variables have a power of just one (power of one is a math number that is not written) They are actually all written in slope-intercept form even. Line equations are linear function. Yay the words match!

You get a curve (not linear) when you have exponents, square roots or variables in the denominator of a fraction. Or as here, a variable for an exponent!

see the attached solution

Answer:

[tex]\dfrac{-2x^4-6}{(x+1)(x-1)(x^2+1)}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{2}{x+1}-\dfrac{2x}{x-1}+\dfrac{4}{x^2+1}[/tex]

The least common multiplier of the denominators is:

[tex](x+1)(x-1)(x^2+1)[/tex]

Adjust the fractions based on the least common multiplier:

[tex]\implies \dfrac{2(x-1)(x^2+1)}{(x+1)(x-1)(x^2+1)}-\dfrac{2x(x+1)(x^2+1)}{(x+1)(x-1)(x^2+1)}+\dfrac{4(x+1)(x-1)}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{a}{c} \pm \dfrac{b}{c}=\dfrac{a \pm b}{c}:[/tex]

[tex]\implies \dfrac{2(x-1)(x^2+1)-2x(x+1)(x^2+1)+4(x+1)(x-1)}{(x+1)(x-1)(x^2+1)}[/tex]

Simplify:

[tex]\implies \dfrac{2(x^3-x^2+x-1)-2x(x^3+x^2+x+1)+4(x^2-1)}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{2x^3-2x^2+2x-2-2x^4-2x^3-2x^2-2x+4x^2-4}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{-2x^4+2x^3-2x^3-2x^2-2x^2+4x^2+2x-2x-2-4}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{-2x^4-6}{(x+1)(x-1)(x^2+1)}[/tex]

Answer:

36647.36

Step-by-step explanation:

Lease payment =$1000

interest rate= 6%, compounded monthly

Time = 4 years

We have to calculate the present value

PV = 10000 + 10000/(1+ 0.06/12)^12 + 10000/(1+0.06/12)^24+ 10000(1+0.06/12)^36 = 36647.36

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One pair of vertical angles are 2 and 3.

One pair of supplementary angles are 1 and 3.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Vertical angles are:

1 and 4

2 and 3

6 and 7

5 and 8

Supplementary angles are:

1 and 3.

2 and 4.

6 and 8.

5 and 7.

Thus,

Vertical angles are 2 and 3.

Supplementary angles are 1 and 3.

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Answer:

RS, SQ, QR

Step-by-step explanation:

The three angles in a triangle add up to 180° Two angles are given, so we can find the third angle.

11 + 40 + S = 180

51 + S = 180

subtract 51

S = 129°

S is the biggest angle, so the biggest side will be opposite from S. QR is the biggest side.

AngleQ is 11°, the smallest angle. The smallest side will be opposite from the smallest angle. The smallest side is RS.

The 40° angle, AngleR is in the middle. The medium length side is opposite from the medium size angle. SQ is the medium length side.

From small to big:

RS, SQ, QR

Answer:

The 4th answer down

RS, SQ, RQ

Step-by-step explanation:

There is a relationship between the angle measurement and the length of the side opposite of the angle.  The side opposite of the largest angle measurement has the longest side opposite to that angle, the same is true for the middle angle and the smallest angle.

Answer:

$5,851.88

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ A = P(1 + rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for P:

[tex]\implies 6000=P\left(1+0.02375 \times \dfrac{389}{365}\right)[/tex]

[tex]\implies P=\dfrac{6000}{1+0.02375 \times \dfrac{389}{365}}[/tex]

[tex]\implies P=\dfrac{6000}{1+0.0253116438...}[/tex]

[tex]\implies P=\dfrac{6000}{1.0253116438...}[/tex]

[tex]\implies P=5851.87931....[/tex]

Therefore, you would need to deposit $5,851.88 in your account now.