Dante is a software salesman. Let represent his total pay (in dollars). Let represent the number of copies of History is Fun he sells. Suppose that and are related by the equation 2400+120x=y

The positive square roots of the number 151,321 according to the task content can be determined by means of division as; 389.

It follows from.the task content above that the number given is; 151,321 whose positive square roots is to be determined.

Upon testing different integers as divisor on the number 151,321; it is concluded that the only positive integer by which 151,321 can be divided to result in a whole is; 389.

Hence, the positive square root of the number 151,321 is; 389.

Consequently, it can be concluded that the positive square root of the number, 151,321 as in the task content is; 389 which is itself a prime number as it is only divisible by 1 and itself.

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a. By replacing [tex]x[/tex] with [tex]-x^2[/tex] in the power series, we get

[tex]\displaystyle \frac1{1+x^2} = \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n}[/tex]

Integrate both sides to recover [tex]\arctan(x)[/tex] on the left.

[tex]\displaystyle \int \frac{dx}{1+x^2} = \int \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n} \, dx[/tex]

[tex]\displaystyle \arctan(x) = C + \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

By letting [tex]x=0[/tex] on both sides, we find [tex]C=0[/tex], so that

[tex]\displaystyle \arctan(x) = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

Then dividing both sides by [tex]x[/tex] gives

[tex]\displaystyle \boxed{\frac{\arctan(x)}x = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n} \, dx}[/tex]

b. Let [tex]x=\frac1{\sqrt3}[/tex]. Then

[tex]\displaystyle \frac{\arctan\left(\frac1{\sqrt3}\right)}{\frac1{\sqrt3}} = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} \left(\dfrac1\sqrt3\right)^{2n}[/tex]

[tex]\displaystyle \sqrt3 \arctan\left(\frac1{\sqrt3}\right) = \sum_{n=0}^\infty \frac1{2n+1} \left(-\frac13\right)^n[/tex]

Taking the first few terms from the infinite series, we can approximate

[tex]n=0 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1[/tex]

[tex]0\le n\le1 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1+\dfrac13\left(-\dfrac13\right) = \dfrac89[/tex]

which together suggest the value we want is bounded between 8/9 and 9/9 = 1, hence [tex]\boxed{p=8}[/tex].

Since the series is alternating and converges on [tex]-1<x<0\cup0<x<1[/tex],

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^0 a_n \right| < |a_1| = \left|\frac13 \left(-\frac13\right)^1\right| = \frac19[/tex]

and

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^1 a_n \right| < |a_2| = \left|\frac15 \left(-\frac13\right)^2\right| = \frac1{45}[/tex]

which tells us the first approximation is off by at most 1/9 from the actual value of [tex]\frac\pi{2\sqrt3}[/tex], whereas the second approximation is off by at most 1/45 from the actual value. In other words, the second approximation is closer, so [tex]\frac\pi{2\sqrt3}[/tex] is closer to [tex]\frac p9[/tex] :

[tex]\dfrac89 \approx 0.8889[/tex]

[tex]\dfrac{\pi}{2\sqrt3}\approx0.9069[/tex]

[tex]\dfrac99 = 1[/tex]

Based on the random sample of beach lengths taken, the probability of a randomly selected beach having a length of 12 miles is C. 0.

Beach length is considered a continuous variable which takes a numerically positive form because it can have any one of infinite possible values.

As a result, there is no possibility that a beach chosen at random will have a given length of 12 miles which means that the probability is 0.

In conclusion, the probability that a selected beach has a length of 12 miles is 0.

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If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.

We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.

Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.

let the number of movies be x and the number of songs be y.

According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.

It will be as under:

85x+4y<1000.

Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

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The table that represents exponential growth is the second table.

Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.

In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the Xs increase by 1, the Ys increase by a multiple of 4.

One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.

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Answer: B

Step-by-step explanation:

See attachment for the graph of the function y = 5 sin(4x)

The trigonometry function is given as:

y = 5 sin(4x)

To plot the graph, we use the following domain:

x > 0

This represents the minimum value of x

Also, we use

x < π/2

This represents the maximum value of x

When the domain are combined, we have:

0 < x < π/2

This means that the domain that gives a complete cycle is 0 < x < π/2

See attachment for the graph of the function

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[tex]f(x)=\left( \cfrac{3x^2-2}{2x+3} \right)^3\implies \cfrac{df}{dx}=\stackrel{\textit{\LARGE chain~ ~~ rule}}{3\left( \cfrac{3x^2-2}{2x+3} \right)^2\underset{quotient~rule}{\left( \cfrac{6x(2x+3)~~ - ~~(3x^2-2)2}{(2x+3)^2} \right)}} \\\\\\ \cfrac{df}{dx}=3\left( \cfrac{3x^2-2}{2x+3} \right)^2\left( \cfrac{12x^2+18x-6x^2+4}{(2x+3)^2} \right) \\\\\\ \cfrac{df}{dx}=3\left( \cfrac{3x^2-2}{2x+3} \right)^2\left( \cfrac{6x^2+18x+4}{(2x+3)^2} \right)[/tex]

[tex]\cfrac{df}{dx}=3 \cfrac{(3x^2-2)^2}{(2x+3)^2} \left( \cfrac{2(3x^2+9x+2)}{(2x+3)^2} \right)\implies \cfrac{df}{dx}=\cfrac{6(3x^2-2)^2(3x^2+9x+2)}{(2x+3)^4}[/tex]

now, we could expand the polynomials, but there isn't much simplification, so no much point doing so.

Answer:

(the figure is poorly drawn)

Step-by-step explanation:

find y

180 - 120 = 60°

find x

180 - 60 - 30 = 90°

Answer:

A, C

Step-by-step explanation:

See attached image.

[tex]given \: that \: its \: linear \\ m = \frac{15 - 3}{3 - 0} = \frac{12}{3} = 4 [/tex]

[tex]b = y(0) = 3 \\ y = 4x + 3 \: [/tex]

Answer:

D) y = 4x + 3

Step-by-step explanation:

   [tex]\sf \boxed{\bf y = mx +b}[/tex]

Here, m is the slope and b is y intercept.

At y intercept, x = 0

         From the table, y intercept  = 3

Choose any two points from the table to find the slope.

(0 ,3)  & (3,15)

[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

           [tex]\sf =\dfrac{15-3}{3-0}\\\\=\dfrac{12}{3}\\\\=4[/tex]

m = 4 ; b = 3

 Equation of line:

                 y = 4x  + 3

Answer: 56.1 kilograms

Step-by-step explanation:

Solution 1: Multiply 51 by 10% and we'll get 5.1. Then, add 51 and 5.1 and we'll get 56.1

Solution 2: Multiply 51 by 110% and we'll get 56.1

(we can multiply 51 by 1 + 10% because multiplying 51 by 1 is the same thing as multiplying 51 by 100%. So you can just use this slicker formula for solving problems like this)

Part a

The domain is the set of x-values, which is [tex](-\infty, \infty)[/tex]

Part b

The range is the set of y-values, which is [tex](-\infty, -2][/tex]

Part c

The x-intercepts is when y=0, which there are none of.

Part d

The y-intercept is when x=0, which is at (0, -2).

Using proportions, it is found that the two cities are 27.5 miles apart.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the given scale, we have that each inch of distance represents 10 miles. Hence the distance in miles for a distance of 2 and 3/4 miles = 2.75 miles is given by:

D = 10 x 2.75 = 27.5 miles.

Hence, the two cities are 27.5 miles apart.

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By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

Herein we have a trigonometric equation which has to be simplified. Simplification procedure consists in applying trigonometric expressions and algebra properties to transform the function from the form f(cos 12x) to the form f(cos 6x). Now we present the solution in detail:

By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

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Answer:

39916800

Step-by-step explanation:

1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11

Answer:

Angle x= 60°

Step-by-step explanation:

For the triangle HIL, you're going to add 30+90=120

Angles in a triangle add up to 180.

So, therefore,

180-120=60   so angle L must equal 60.

HJ is a straight line and angles in a straight line add up to 180.

180-90=90

Angle JIL is equal to 90.

To find y you add 90+45 which equals 135.

Again, angles in a triangle add up to 180.

180-135=45

So,

y = 45

Now we are told that IJK is a right angle and that we are given that IJL is 45. 45 is half of 90 so LJK must be 45.

To find angle JLK we must add angle L and angle y.

60+45=105

Angles in a straight line add up to 180. So,

180-105=75

75 = Angle JLK

75+45=120

Angles in a triangle add up to 180 so,

180-120= 60

Angle x= 60°

Hope this helped, if so please award me with the brainliest if possible. If you require further assistance from me comment below! :)

Answer:

1200 centimeters

Step-by-step explanation:

Hello!

1meter=100centimeters

12meter = ?

[tex]thus \: \frac{12m \times 100cm}{1m} = 1200cm[/tex]

Answer:

1200cm

Step-by-step explanation:

1m=100cm

12m=xcm

by multiplying cris cross

x=12*100

x=1200cm

12m=1200cm

Answer:

Step-by-step explanation:

23

Step-by-step explanation:

b + 35° = 180° ( supplementary angle )

b = 180° - 35°

b = 145°

Answer: [tex]\Large\boxed{b=145^\circ}[/tex]

Step-by-step explanation:

Given information

∡1 = 35°

∡b = ?

Total Angle = 180° (Supplementary Angle)

Derived formula from the given information

∡1 + ∡b = Total Angle

Substitute values into the given formula

(35) + b = 180

Subtract 35 on both sides

35 + b - 35 = 180 - 35

[tex]\Large\boxed{b=145^\circ}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

well, with the assumption that a year has 365 days, that means one day is really just 1/365th of a year, so then 54 days will be 54/365 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$17100\\ r=rate\to 9.65\%\to \frac{9.65}{100}\dotfill &0.0965\\ t=years\dotfill &\frac{54}{365} \end{cases} \\\\\\ I = (17100)(0.0965)(\frac{54}{365})\implies \stackrel{\textit{interest owed}}{I\approx 244.13}~\hfill \underset{amount~owed}{\stackrel{17100~~ + ~~244.13}{\approx 17344.13}}[/tex]

Answer + Step-by-step explanation:

the probability that a child will not fall on any given day :

= (63 × 64 + 27 × 88) ÷ 100

= 64.08 %

the probability that a child will fall in dry weather :

= (27 × 12) ÷ 100

= 3.24 %

The probability that a person in this income bracket will be audited this year is of 3%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that 30 out of 1000 people are audited, hence the probability that a person in this income bracket will be audited this year is given by:

p = 30/1000 = 0.03 = 3%.

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Answer:

the coordinates of equations

1.4x+y=-7

for x =0

f(0,y)=4(0)+y=-7

y=-7

for y=0

f(x,0)=4x+0=-7

4x=-7

x=-7/4

2.x-y=2

for x=0

f(0,y)=0-y=2

-y=2

y=-2

for y=0

f(x,0)=x-0=2

x=2

graph all of the equations coordinates or you can look the image

so the answers are : {-3,-1}

CMIIW

The correct answer which represents the quotient of 20√z⁶ ÷ √16z⁷ in simplest radical form is; (5√z)/z.

The quotient given can be evaluated by means of the laws of indices as follows;

20√z⁶ ÷ √16z⁷

= 20√z⁶ ÷ 4√z⁷

= 5 √(z⁶/z⁷)

= 5 √z^(-1)

= 5 × z^(-1/2)

= 5/√z

Hence, by rationalisation; we have;

= (5√z)/z.

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1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

1) The following trigonometric formulae are used to derive the half-angle formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a half angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a half angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a half angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in rectangular form to polar form are obtained by trigonometric functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in polar form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in rectangular form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the linear function y = 5 · x - 8, we proceed to use the following substitution formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

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The value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

The equation is given as:

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000

From the question, we understand that the expression is to be solved from left to right (without using the pemdas mathematical rule)

So, we start by multiplying 2 and 4

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 8 + 48000 / 8 - 1 x 30 x 2 + 40000

Add 8 and 48000

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 48008 / 8 - 1 x 30 x 2 + 40000

Divide 48008 by 8

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6001 - 1 x 30 x 2 + 40000

Subtract 1 from 6001

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6000 x 30 x 2 + 40000

Multiply 6000 and 30

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 180000 x 2 + 40000

Multiply 180000 by 2

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 360000 + 40000

Evaluate the sum

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 400000

Hence, the value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

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Answer:

I think it would be D

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

To prove two lines parallel, we need to check if the two angles involving the lines acts as some angle pair with defininte property.

In the given figure,

( by Alternate Exterior angle pair )

Hence, the two lines are parallel.

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

18 miles

Step-by-step explanation:

hihihihihiuijihihihi