Determine whether the series converges or diverges
Please, check the image

The required equation is y = - 3.5x + 8.5 (in slope-intercept form) of the line passing through the points with the given coordinates.

The slope of a line is defined as the gradient of the line.

Given that the line that passes through two points (1,5), and (3,−2)

Let the required equation of the line will be as :

y - 5 = [(-2 - 5)/(3-1)](x - 1)

y - 5 = (-7/2)(x - 1)

y - 5 = - 3.5(x - 1)

y - 5 = - 3.5x + 3.5

y = - 3.5x + 3.5 + 5

y = - 3.5x + 8.5

Thus, the required equation is y = - 3.5x + 8.5 (in slope-intercept form) of the line passing through the points with the given coordinates.

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There are total 4*5*3 = 60 ways of wearing one each.

What is Fundamental Counting Principle?

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle.

Solution:

Let,

for three events A, B, and C, number of outcomes be a,b, and c respectively.

So, the total number of outcomes is given by the product of outcomes of all the events i.e. by using Fundamental Counting Principle.

In the question mentioned,

a = 4

b = 5

c = 3

So, total outcomes = 4*5*3 = 60 ways

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In terms of fractions, 2/5 of the icicle was eaten by the boy.

In mathematical term:

A boy ate three fifth of an icicle = 3/5

A boy gave = 1/3

So, Icicle eaten by the boy = 3/5 - 1/3

= (9 - 3) / 15

= 6/15

= 2/5

Hence, In terms of fractions 2/5 of the icicle was eaten by the boy.

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Answer: x - 2y = -10.

Step-by-step explanation:

The correct statements regarding the functions are given as follows:

Regarding the type of function, we have that:

The y-intercepts are the values of y for which x = 0, hence they are given as follows:

Hence function g(x) starts less than f(x), but it eventually exceeds function f(x), as it is exponential, meaning that it has a greater average rate of change.

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Answer:

48000

Step-by-step explanation:

I multiplied the length times width time height (20x40x60) to get 48000.

[tex]\displaystyle \lim_{\theta \to 0}\cfrac{\tan^2(\theta )-\sin(\theta )}{\theta 4}\implies \stackrel{\textit{\Large L'Hopital's rule}}{\lim_{\theta \to 0}\cfrac{\frac{d}{d\theta }[\tan^2(\theta )-\sin(\theta )]}{\frac{d}{d\theta }[\theta 4]}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{d}{d\theta }[\tan^2(\theta )-\sin(\theta )]\implies \cfrac{d}{d\theta }[[\tan(\theta )]^2-\sin(\theta )]\implies \stackrel{chain~rule}{2\tan(\theta )\cdot \sec^2(\theta )} ~~ -\cos(\theta ) \\\\\\ 2\tan(\theta )\cdot \cfrac{1}{\cos^2(\theta )}-\cos(\theta )\implies \cfrac{~~ \frac{2\sin(\theta) }{\cos(\theta) } ~~}{\cos^2(\theta )}~~ -\cos(\theta ) \\\\\\ \cfrac{2\sin(\theta) }{\cos^3(\theta) }~~ -\cos(\theta )\implies \cfrac{2\sin(\theta)-\cos^4(\theta)}{\cos^3(\theta)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{d}{d\theta}[4\theta]\implies 4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\displaystyle \lim_{\theta \to 0}\cfrac{\tan^2(\theta )-\sin(\theta )}{\theta 4}\implies \lim_{\theta \to 0}\cfrac{ ~~ \frac{2\sin(\theta)-\cos^4(\theta)}{\cos^3(\theta)} ~~ }{4}\implies \lim_{\theta \to 0}\cfrac{2\sin(\theta)-\cos^4(\theta)}{4\cos^3(\theta)} \\\\\\ \displaystyle \lim_{\theta \to 0}\cfrac{2\sin(0)-\cos^4(0)}{4\cos^3(0)}\implies \lim_{\theta \to 0}\cfrac{2(0)-1^4}{4(1^3)}\implies {\Large \begin{array}{llll} -\cfrac{1}{4} \end{array}}[/tex]

Answer:

A or C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of (y-x) when (x-y) = 3 is -3.

According to the question,

We have the following equation:

x-y = 3

Now, we have to find the value of (y-x). We can easily do this by multiplying both sides of this equation by -1.

We know that the multiplication of two negative integers always gives us the positive results and the multiplication of one negative and one positive integer give us the negative results.

So, we will have the following expression:

-x+y = -3

It can rewritten as follows:

y-x = -3

Hence, the value of (y-x) when (x-y) = 3 is -3.

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The value of 3xy³ + 2xy³z + xyz + xz = 0

To find the value of a given equation or expression replaces each variable with the given value.

For example, a = 1 and b = 3 then find 3a + 2b.

=>  3(1) + 2(3) = 3 + 6 = 9

Therefore, the value of 3a + 2b = 9

Multiplying any number with zero will give zero i.e 3 × 0 = 0. No matter how large the number is when we multiply it by zero the result will be zero.

Here we have

x = 0, y = 3 and z = 5

We need to find the value of 3xy³ + 2xy³z + xyz + xz

Substitute given values in the given expression

=> 3(0)(y)³ + 2(0)y³z + (0)yz + (0)z     [ x × 0 = 0  ]

=> 0 + 0 + 0 + 0

=> 0

Therefore,

The value of 3xy³ + 2xy³z + xyz + xz = 0

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The factored form of 8x²⁴-27⁶ is (2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)

Equations may be solved and x-intercepts can be found very quickly when a quadratic expression is in factored form and equal to 0. You may also find vertices and maximum and minimum values of the expression.

The four main methods of factoring are the Grouping method, Difference in Two Squares, Sum or Difference in Cubes, and Greatest Common Factor (GCF).

It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant. Examples of factors include ((5x + 2)(3x-1)) and ((2(x-1)(x+3)).

Given,

8x²⁴-27⁶

=(2x⁸)³-(3y²)³

=(2x⁸-3y²)((2x⁸)²+2x⁸×3y²+(3y²)²

=(2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)

Therefore, the factored form of 8x²⁴-27⁶ is (2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)

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Check the picture below.

Answer:

9 and 10

Step-by-step explanation:

To three decimal places

[tex]7 \sqrt{2} = 9.899[/tex]

So 7√2 is between 9 and 10 (closer to 10).

The vertex form of Parabola is y= 1/4(x + 2)² -4 .

The general equation of a parabola is given by y = a(x – h)² + k or

x = a(y – k)² +h. Here (h, k) is vertex.

Given:

focus at (–2,–3) and a directrix at y = –5.

We know, the standard form is (x - h)² = 4p (y - k),

where the focus is (h, k + p) and the directrix is y = k - p

So, (h, k + p) = (-2, -3)

h = -2, k + p = -3

Directrix is y = k - p:

k - p = -5

k + p = -3

so, 2k = -8

k = -4

and, p = -3+ 4 = 1

Thus, the vertex is at (-2, -4) and p = 1, the equation is:

(x + 2)² = 4(y+  4)

1/4(x + 2)² =  y+4

y= 1/4(x + 2)² -4

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The largest number of boxes that can fit into the crate is 27.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

From the given data in the question,

The dimension of the crate is: 28 × 18 × 15

Volume of crate = 6480 cm³

And the dimensions of packs = 8 × 6 × 5

the volume of packs = 240 cm³

Then, the number of boxes that fit into the crate = 6480/240

= 27

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Answer:

The associative property of multiplication states that the product of three or more numbers remains the same regardless of how the numbers are grouped. For example, 3 × (5 × 6) = (3 × 5) × 6.

Step-by-step explanation:

The value of x is x=p(m-n).

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Given expression: m=n+(x/p)

To find: Make x the subject.

To make x the subject we have to separate the x to one side.

Expression m=n+(x/p)

Take n to another side,

(x/p)=m-n

Cross multiply,

x=p(m-n)

Therefore, the value of x is x=p(m-n).

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Answer: How many cards are there tho?

Step-by-step explanation:

Value of x rounded to nearest tenth is 25.5 units.

Given in question,

Right angled triangle CDE

θ = 20°

CD = perpendicular = 24 units

CE = Hypotenuse = x

Therefore,

cosθ = Perpendicular/Hypotenuse

cos 20 = 24/x

0.9397 = 24/x

         x = 24/0.9397

            = 25.54

Hence, value of x rounded to nearest tenth is 25.5 units.

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It is a rhombus kind of quadrilateral.

What is quadrilateral?

A quadrilateral has four sides, is two-dimensional (flat), closed (the lines join up), and has straight sides.

A rhombus is a four-sided quadrilateral with all of the features of a parallelogram.

A rhombus has three more characteristics: consecutive sides that are congruent; diagonals that bisect pairs of opposite angles; and diagonals that are perpendicular to one another.

Moving clockwise, beginning at point A in the top left corner of a hypothetical rhombus ABCD, you can see that side AB is congruent to side BC and side CD is congruent to side DA.

Additionally, you can see that diagonals AC and DB are perpendicular to one another and that the rhombus' diagonals split pairs of opposing angles.

Hence, It is a rhombus kind of quadrilateral.

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[tex]\cfrac{5x^6 5x^{-2}125x 2x^4 2x^{-5}}{2x^5 5x^{-3} 2x^6}\implies \cfrac{5\cdot 5\cdot 125\cdot 2\cdot 2}{2\cdot 5\cdot 2}\cdot \cfrac{x^6 x^{-2}x x^4 x^{-5}}{x^5 x^{-3} x^6} \\\\\\ \cfrac{ 5\cdot 125}{1}\cdot \cfrac{x^{6-2+1+4-5}}{x^{5-3+6}}\implies 125\cdot \cfrac{x^4}{x^8}\implies 125\cdot \cfrac{1}{x^8 x^{-4}}\implies \cfrac{125}{x^{8-4}}\implies {\Large \begin{array}{llll} \cfrac{125}{x^4} \end{array}}[/tex]

The statement that is true for the function, h is h(2) = 16

It is given that there is a function h

The range of function, h is [tex]1\leq h(x)\leq 25[/tex]

The domain of the function, h is [tex]-3 \leq x\leq 11[/tex]

And it is also given that h(8) = 19 and h(-2) = 2

Now,

The 1st option is h(-3) = -1

But the range of h is between 1 to 25, hence, this option is not true.

The 2nd option is h(8) = 21

But it is already given that h08) = 19, thus this option is not true.

The 3rd option is h(13) = 18

But the domain of h is between -3 and 11, So, this option is not true as well.

The fourth option is h(2) = 16

In this the values of range and domain are correct.

Thus, h(2) = 16.

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Answer: The pickles are $3.99

Step-by-step explanation:For percents,this is always done by simply dividing the percent (in this case 15%) by 100%. So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number. 0.15 x $152.00=$3.99

The largest possible total area of the three pens is 15312.5sq.units.

What is a rectangular area?

The quantity of space occupied by a flat surface with a specific shape is referred to as the area.

Area of a Rectangle = (Length × Breadth) square units.

Here,

We let x be the length and y be the breadth of a rectangle area.

Given equation : 2y + 4x = 700

y + 2x  = 350

y = 350 - 2x .......(1)

Area of rectangular field (A)= xy

A = x(350 - 2x)

A = 350x - 2x²

Differentiating w.r.t x we get,

A' = 350 - 4x

Again, differentiating w.r.t x we get,

A" = -4

Let A' = 0

350 - 4x = 0

4x = 350

x = 87.5

A is maximum at 87.5feets.

Hence, the largest possible total area of the three pens = XY = 87.5×175 = 15312.5 sq. units.

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The coordinates of the starting point is  (12, 5)

Ordered pairs refers to the arrangement of 2 numbers in the form (a, b)

The rule to move ordered pair one unit left 1 will be subtracted in the x coordinates

(5, 5) → one unit left → ( 5 - 1, 5 ) = (4, 5)

The rule to move ordered pair 8 units left, 8 will be added in the x coordinates

(4, 5) → one unit left → ( 4 + 8, 5 ) = (12, 5)

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Answer:

-15530

Step-by-step explanation:

plug it in to a calculator

why so random numbers

Answer:

Step-by-step explanation:

2(5+777x60/6x(-1))

2(5-7770)

2x(-7765)

-15530

Answer:

6 [tex]\frac{2}{3}[/tex] Hours

Step-by-step explanation:

Distance = rate times time

Let t = time

1 = .15t   Divide both sides by .15

6.666... = t  The 6 is repeating so as a fraction it would be

6 [tex]\frac{2}{3}[/tex]

The number of minutes that the executive use the phone is 131 minutes.

From the information, the cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use.

Let the number of minutes be m.

This will be illustrated as:

35 + 0.40m = 87.80

Collect like terms

0.40m = 87.80 - 35

0.40m = 52.80

Divide

m = 52.40 / 0.40

m = 131

The number of minute is 131 minutes.

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