Use the summation notation to write the series

10+5+0+(-5)+(-10)+(-15)

Answer:

your answer is 242 in^2

A=22+52+168

The sequence converges to 5 as n goes to ∞. We can prove this rigorously:

The claim is that, for [tex]n\in\Bbb N[/tex],

[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = 5[/tex]

By definition of the limit, this means for any ε > 0, there exists some N such that for any n larger than N, we have

[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| < \varepsilon[/tex]

In order to ensure this inequality, we work backwards to find N in terms of ε :

[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| = \left| \dfrac{5n-1 - 5(n+1)}{n+1} \right| = \dfrac4{|n+1|} < \varepsilon[/tex]

n is a natural number, so n + 1 > 0 and |n + 1| = n + 1. Then

[tex]\dfrac4{n+1} < \varepsilon \implies \dfrac{n+1}4 > \dfrac1\varepsilon \implies n+1 > \dfrac4\varepsilon \implies n > \dfrac4\varepsilon - 1[/tex]

Let N be the smallest natural number greater than or equal to 4/ε - 1, i.e.

[tex]N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]

Then the proof follows: suppose

[tex]n \ge N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]

Then

[tex]n \ge \left\lceil\dfrac4\varepsilon - 1\right\rceil \implies n > \dfrac4\varepsilon - 1 \\\\ \implies n+1 > \dfrac4\varepsilon \\\\ \implies \dfrac4{n+1} < \varepsilon \\\\\implies \left|\dfrac{5n-1}{n+1}-5\right| < \varepsilon[/tex]

as required.

Or we can avoid the rigor and use some facts we know about limits:

[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = \lim_{n\to\infty} \frac{5-\frac1n}{1+\frac1n} = 5[/tex]

since 1/n converges to 0 as n goes to ∞.

Answer:

12

Step-by-step explanation

Answer:

x=40,y=22

Step-by-step explanation:

62/2=31

31+9=40

31-9=22

40+22=62

The given equation is a quadratic equation with a degree of 2 and leading coefficient of 1. The solution to the given quadratic equation are -20 and 20

The given equation is a quadratic equation with a degree of 2 and leading coefficient of 1.

Given the expression

x^2 - 1 = 399

Add 1 to both sides

x^2 = 399 + 1

x^2. = 400

Take the square root of both sides

x = ±√400
x = ±20

Hence the solution to the given quadratic equation are -20 and 20

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Answer: 6.36lb

Step-by-step explanation:

Step-by-step explanation:

Total Weight of the package = weight of product + weight of box

Weight of empty box =0.88lb

Total weight of the box is =7.24lb

Let Weight of product inside box=w

Let wet of empty box =y

Total weight = F

Then,

F=y+w

Since F=7.24lb. y=0.88

Then, w=F-y

w=7.24-0.88

w=6.36lb

The weight of the product is 6.36lb

hope this helps :)

Answer:

[tex]x=3.18[/tex] [tex]cm[/tex]

Explanation:

[tex]x=3.18[/tex] [tex]cm[/tex]

Substitute [tex]y=6 cm[/tex] into  [tex]\frac{}{AC} =y:\frac{}{AC} =6cm[/tex]

Substitute [tex]0=32[/tex] into ∠[tex]CAB=0:[/tex] ∠[tex]CAB=32^o[/tex]

sinA=leg opposite ∠A/hypotenuse : [tex]sin(CAB)=\frac{\frac{}{BC} }{\frac{}{AC} }[/tex]

Substitute [tex]\frac{}{BC} =x,\frac{}{AC}=6cm,[/tex] ∠[tex]CAB=32^o[/tex]

into sin(∠[tex]CAB[/tex]) [tex]=\frac{\frac{}{BC} }{\frac{}{AC} }:sin(32^o)=\frac{x}{6}[/tex]

Calculate [tex]sin(32^o)=\frac{x}{6} :x=3.18cm[/tex]

Answer:

D. octagon

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Basically, when you have a product to two factors set equal to 0, you can use the Zero Product Property and make two separate equations, both set equal to 0, to find the roots for each factor:

[tex]2x+10=0\\2x=-10\\x=-5[/tex]

[tex]x-7=0\\x=7[/tex]

Notice that by plugging these roots back into the equation, either factor will be 0, making the whole expression 0:

[tex](2x+10)(x-7)=0\\(2(7)+10)(7-7)=0\\(24)(0)=0\\0=0[/tex]

[tex](2x+10)(x-7)=0\\(2(-5)+10)(-5-7)=0\\(0)(-12)=0\\0=0[/tex]

Answer:

a)

[tex] \frac{2}{5} [/tex]

b)

Step-by-step explanation:

slope formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

[tex] \frac{4 - 9}{ - 2 - 8} [/tex]

=

[tex] \frac{2}{5} [/tex]

b) using point (-2,4)

[tex]y - y1 = m(x - x1)[/tex]

[tex]y - 4 = \frac{2}{5} (x - ( - 2)[/tex]

Now distribute

[tex]y - 4 = \frac{2}{5} x + \frac{4}{5} [/tex]

add 4 to each side

[tex]y = \frac{2}{5} x + \frac{24}{5} [/tex]

can use the other point given if you want

Answer:

Step-by-step explanation:

Formula

d = speed * time

d = s * t

Givens

t = 1 hour

t2 = 3 hours

s = 5 miles / hour

Solution

t = 1 hour

d = s * t

d = 5 mph * 1 hour

d = 5 miles

t = 3 hours

d = s * t

d = 5 miles / hour * 3 hours

d = 15 miles

Answer

d = s * t

d = 5 miles

d = 15 miles

Answer:

... There isnt answer choices...

Answer:

the new points/coordinates would be (3,0) and (3,-3) and (-3,-3)

Step-by-step explanation:

this is because you use column vectors and draw a cross at the centre of enlargement then find out how many spaces you need to go right and up for each of the coordinates. then times that by -3 and use your answers to go left and down from the centre (3,3)

The domain of the given relation will be { - 1,2,3,4}.

The domain of the function is defined as the set of all the possible values of the function.

So here we have the ordered pairs given as:-

{ (-1,- 6), (2, - 6), (3,5), (4,0), (4,7)}

Here the possible values for the input of the functions are { - 1,2,3,4}.

Therefore the domain of the given relation will be { - 1,2,3,4}.

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Answer:

Answer:

Right angles.

Step-by-step explanation:

When an angle's measurements equal 90 degrees, it is called a right angle.

Answer:

Right angles

Step-by-step explanation:

For instance a a triangle with an angle of 90 ° is a right trangle because is has a right angle in it.

          [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

       What is the slope of the line through (-5, 13) and (2, -1) ?

  [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

We can use the slope formula :-

[tex]\Large\text{$\displaystyle\frac{y_2-y_1}{x_2-x_1}$}[/tex]

Now , We replace letters with numbers ,

[tex]\Large\text{$\displaystyle\frac{-1-13}{2-(-5)}$}[/tex]

On simplification,

[tex]\Large\text{$\displaystyle\frac{-14}{2+5}$}[/tex]

On further simplification ,

[tex]\Large\text{$\displaystyle\frac{-14}{7}$}[/tex]

[tex]\diamond[/tex] Finally, We get

[tex]\longmapsto\sf\underline{\boxed{\tt{slope=-2}}}[/tex]

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[tex]\rule{300}{1}[/tex]

The slope of the line joining the points (a,b) and (c,d) is given by

Putting the values, we have:

[tex]{:\implies \quad \sf m=\dfrac{-1-13}{2-(-5)}}[/tex]

[tex]{:\implies \quad \sf m=\dfrac{-14}{2+5}}[/tex]

[tex]{:\implies \quad \sf m=\dfrac{-14}{7}=\boxed{\bf{-2}}}[/tex]

Answer:

Qualities variable, because eye color is something you observe from a study on someone. Eye color cannot be observed very well from a quantitive variable, because quantitive variables record height, weight, and other statistics other than eye color.

Answer:

Elena incorrectly used the slant height instead of the height.

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

i got it right

Answer:

8.50

Step-by-step explanation:

it’s 8.50 this is because if you need to round it to the nearest tenth, you just think is 9 closer to 10? Yes and so you make 48 into 8.50

Answer:

sorry this question is do not understand

[tex]q = \frac{gx {}^{2} - px + 2}{x} \\ [/tex]

[tex]p= \frac{gx {}^{2} - qx + 2}{x} [/tex]

The Weekly Sales for 30 shelf spaces is 3.04

The proper table is added as an attachment.

Next, we determine the regression equation using a graphing calculator.

From the graphing calculator, we have the following calculation summary:

The regression equation is represented as:

y = bx + a

Where

b = SP/SSX = 46/750 = 0.06133

a = MY - bMX = 2.12 - (0.06*15) = 1.2

So, we have:

ŷ = 0.06133x + 1.2

When x =30, we have:

ŷ = 0.06133 * 30 + 1.2

Evaluate

ŷ = 3.04

Hence, the Weekly Sales for 30 shelf spaces is 3.04

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Answer:

  40

Step-by-step explanation:

The sum of exterior angles of a convex polygon is 360°. This relation lets you write an equation for x.

__

Clockwise from the bottom, the sum of exterior angles is ...

  90° +(x +35)° +(x +15)° +(2x -20)° +(2x)° = 360°

  120° +6x° = 360° . . . . . . . simplify

  6x = 240 . . . . . . . . . . divide by °, subtract 120

  x = 40 . . . . . . . . . . divide by 6

The value of x is 40.

Answer:

x = 40°

Explanation:

The shape is a pentagon. Any polygon's exterior angles sum up to 360°.

Now, they all sum up to 360° :

⇒ (x + 35) + (x + 15) + (2x - 20) + 2x + 90 = 360°

⇒ x + x + 2x + 2x + 35 + 15 -20 + 90 = 360°

⇒ 6x + 120° = 360°

⇒ 6x = 360° - 120°

⇒ 6x = 240°

⇒ x = 240°/6

⇒ x = 40°

Answer:

The team sold 91 hats.

Step-by-step explanation:

$3,094 ÷ %34 = 91

Answer:

y = -5x + 4.

Step-by-step explanation:

y = mx + c  is the general form

- where m = the slope of the line and c is the y-value where the graph cuts the y-axis.

The graph passes through the points (0, 4) and (1, -1) so the slope

= (Y2 - y1) / (x2 - x1)

= (-1-4) / (1-0)

= -5 = m.

and c = 4.

Answer:

Since RT is equal to 16, we know that RU would be half that amount since SQ goes directly through the middle.  Therefore RU = 16/2 would just give us 8.

Answer:

IT IS 43./45455/.34 LIKE WHEN U ADD 10 TIMES 10 AND DIVIDED 2,000 FROM 20 U THAT ANSWER