[tex] \rm \sum_{n = 1}^{ \infty } \frac{( - {1)}^{n + 1} }{n \binom{2n}{n} } \\ [/tex]​

Answer:

1/2

Step-by-step explanation:

The scale factor is 1/2 because each side length of [tex]\triangle{A'B'C'}[/tex] is 1/2 of the length of the side lengths of [tex]\triangle{ABC}[/tex].

Hope this helps :)

Answer:

1/2

Step-by-step explanation:

took the test

Answer:

Step-by-step explanation:

Let a = tan⁻¹(x), so tan(a) = x,

[tex]\sin(a)=\frac{x}{\sqrt{1+x^2}}, \cos(a)=\frac{1}{\sqrt{1+x^2}},[/tex]

Let b = tan⁻¹(y), so tan(b) = y,

[tex]\sin(b)=\frac{y}{\sqrt{1+y^2}}, \cos(b)=\frac{1}{\sqrt{1+y^2}},[/tex]

sin( tan⁻¹(x) +  tan⁻¹(y)) = sin(a + b)

= sin(a) cos(b) + cos(a)sin(b)

= [tex]\frac{x}{\sqrt{1+x^2}}\times\frac{1}{\sqrt{1+y^2}}+ \frac{y}{\sqrt{1+y^2}}\times\frac{1}{\sqrt{1+x^2}}[/tex]

[tex]=\frac{x+y}{\sqrt{(1+x^2)(1+y^2)}}[/tex]

Answer:

Median: 5

Interquartile range: 4

Have an amazing day!

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Answer:

2 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Step-by-step explanation:

1+1 is 2

Answer:

5

Step-by-step explanation:

Answer:

4-1.5 or 21/5 or 4.2

Step-by-step explanation:

Multiple: 7 * 3/5 = 7 · 3/1 · 5 = 21/5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(21, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven multiplied by three fifths = twenty-one fifths.

Answer:

-4.9

Step-by-step explanation:

Since the number 26.95 has two decimal places, it can be turned into a whole number with a denominator having two zeroes; 100

        2695

         100

Then change -5 1/2 into an improper fraction; = -5 × 2 + 1

                                                                                    2

                                           = -11/2

2695 ÷ ( -11 )

 100         2

  Reciprocate (put denominator as numerator and vice-versa ) the equation after the ÷ sign. After doing so, the ÷ sign changes to × sign.

Hence:   2695 × ( 2 )

                 100      -11

Then, cross multiply.

          100 ÷ 2              50

     -245 ÷ 50

         = -4.9

Answer: its -4.9

Step-by-step explanation:

Answer:

65449.8 cm3

Step-by-step explanation:

We start with the volume formula for a sphere: 4/3 πr3

We start with subbing in 25 to r, then we cube 25, which is equal to 15625.

We multiply 4/3 and pi. And lastly we multiply what we got by 15625 and either round the answer or fphaving fixed your calculator.

Using the permutation formula, it is found that it's number as a ratio of factorials is given by:

[tex]N = \frac{9!}{4!}[/tex]

The order in which the letters are chosen is important, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

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

In this problem, five letters will be chosen from a set of nine, hence:

[tex]N = P_{(9,5)} = \frac{9!}{(9-5)!} = \frac{9!}{4!}[/tex]

More can be learned about the permutation formula at https://brainly.com/question/25925367

Answer:

probably 200

Step-by-step explanation:

or something like that

I'll do the first three questions to get you started.

==========================================================

Question 1

x = horizontal component of the triangle

cos(angle) = adjacent/hypotenuse

cos(theta) = horizontal/hypotenuse

cos(40) = x/30

x = 30*cos(40)

x = 22.98133329 approximately

This is the horizontal force applies to the suitcase.

Work = force*displacement

Work =  22.98133329*120

Work = 2,757.7599948

Work = 2,758

==========================================================

Question 2

Add the drone's relative air velocity and the wind velocity vectors.

v+w = (13i + 3j) + (-7i - 2j)

v+w = (13i-7i) + (3j-2j)

v+w = 6i + j

==========================================================

Question 3

Check out the diagram below. Focus on the smaller triangle. Notice the placement of angle theta.

sin(theta) = opposite/hypotenuse

sin(40) = x/200

x = 200*sin(40)

x = 128.557521937308

x = 128.558

Answer:

[tex]100\pi[/tex]

Step-by-step explanation:

Step 1: Identity the radius.

Since O is the center of the circle, and C and E lie on the circumference, OC and OE are the radii of the circle and thus,

OC=OE.

Step 2: Consider the rectangle.

All diagonals in a rectangle are congruent so this means

DB= OC ( OC is also a diagonal).

Thus, OC= 10 units.

Step 3: Analyze

So this means OE is also 10 units as well.

Since we know the length of the radius, Use the area of circle,

[tex]\pi {r}^{2} [/tex]

[tex]\pi( {10}^{2} ) = 100\pi[/tex]

So the area of a circle is 100 pi.

Answer:

  314.2 square units

Step-by-step explanation:

The diagonals of a rectangle are the same length, so segment OC is the same length as segment DB: 10 units. OC is a radius of the circle, which means the circle's radius is 10 units.

The area of a circle is given by ...

  A = πr²

  A = π(10 units)² = 100π units²

  A ≈ 314.2 units²

The area of circle O is about 314.2 square units.

Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.

At the null hypothesis, we test if the proportion is of 50.3%, hence:

[tex]H_0: p = 0.503[/tex]

We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:

[tex]H_1: p \neq 0.503[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, the parameters are:

[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]

Hence:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]

[tex]z = 2.32[/tex]

Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.

More can be learned about the z-distribution at https://brainly.com/question/26454209

Answer:

Hope the picture will help you

Check by using sum of angles of triangle = 180°

Answer:

I think so Option D is the correct answer

Answer:

80 Percent

Step-by-step explanation:

Since she has done 6/30 pages, she has 24/30 more pages to complete. Convert 24/30 to a decimal by dividing 24 by 30 to get the percentage, which is 80 percent

Hopefully this helps - let me know if you have any questions!

Answer:

x=6 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

The cost of the mortgage is $81250

Interests are percentages of a principal

Given the following parameters

Principal = $65000

Rate = 7% = 0.07
Time = 5 years

I = PRT/100
I = 65000*0.07*25
I = 16,250

Cost of mortgage = Principal + Interest

Cost of mortgage = 65000 + 16250
Cost of mortgage = 81,250

Hence the cost of the mortgage is $81250

Learn more on mortgage here: https://brainly.com/question/22846480

Answer:

$72,823

Step-by-step explanation:

just took test

[tex]f(x,y)=x^2+y^3\implies \left.\cfrac{}{} 2x+3y^2 \right]_{\stackrel{\textit{\small x=2}}{\textit{\small y=1}}}\implies 2(2)+3(1)^2\implies 7[/tex]

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:

Perimeter of rectangle = 2(L + B)

→ 64 = 2(3x + x)

→ 64 = 2(4x)

→ 64/2 = 4x

→ 32 = 4x

→ 32/4 = x

→ 8 = x

Hence,

Answer:

⠀

Step-by-step explanation :

⠀

As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,

⠀

Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .

⠀

Now, According to the Question :

⠀

[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{2 (3 x + x )= 64 }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{8x= 64 }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{64}{8} }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar[/tex]

⠀

Therefore,

⠀

Now, We are to find the length of the rectangle:

[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}[/tex]

⠀

[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}[/tex]

⠀

[tex]{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar[/tex]

⠀

Therefore,

⠀

[tex]18 = 2\times 3 \times 3\\\\30 = 2 \times 3 \times 5\\\\\text{HCF}~ = 2\times 3 = 6[/tex]

Step-by-step explanation:

f(x) goes through the point (0, 1).

g(x) goes through (2, 1) for the same y value.

that means g(x) is f(x) translated 2 units to the right.

but we could also look at the same x value (0).

then g(x) goes through (0, -5).

and that means g(x) is f(x) translated 6 units down.

since it is a line function, shifting it left/right or up/down makes no difference to the shape or position of the new curve itself.

as it looks like you don't have 6 in the drop-down menu, then 2 units (to the right) is the desired correct result.

that means g(x) = f(x-2) = 3(x-2) + 1 = 3x - 6 + 1 = 3x - 5

and that is what the graph is showing us.

Answer: C. [tex]\pi[/tex]

=======================================================

Explanation:

The x intercept always occurs when y = 0.

Use the unit circle to determine that [tex]\cos(\theta) = 0[/tex] when [tex]\theta = \frac{\pi}{2} \text{ and } \theta = \frac{3\pi}{2}[/tex]

So if [tex]x = \pi[/tex], then we have

[tex]y = \cos\left(\frac{1}{2}x\right)\\\\y = \cos\left(\frac{x}{2}\right)\\\\y = \cos\left(\frac{\pi}{2}\right)\\\\y = 0\\\\[/tex]

which shows us that [tex](\pi, 0)[/tex] is the location of one of the infinitely many x intercepts for this function.

Answer:

4 ÷ 1,000 = 0.004

Rounding up to 0 as the nearest whole number

[tex]\orange\bigstar \bold{ solution}[/tex]

[tex]\bold{f(x) = x³ - \frac{1}{x³ } }[/tex]

[tex]\bold{f ( \frac{1}{x} )= \frac{1}{x³} -x³ } [/tex]

[tex]\bold{f (x) + f (\frac{1}{x}) = (x³- \frac{1}{x³} ) + ( \frac{1}{x³} -x³)}[/tex]

[tex]\bold{ = 0 }[/tex]

Answer: 3 11/12

Step-by-step explanation:

1 1/3 * 2 = 2 2/3

5/8 * 2 = 1 1/4

2 2/3 + 1 1/4 = 3 11/12

It is a tool as it represents the language of patterns.

It is also a means of working with abstract notions and then applying them, which frequently leads to the formation of generalisations and insights outside of the original context.

Answer:

28

Step-by-step explanation:

I assume the polygon is a trapezoid with parallel bases of 2 yd and 5 yd, and an altitude of 8 yd.

area of trapezoid = (base1 + base2)h/2

area = (2 yd + 5 yd)(8 yd)/2

area = 28 yd²