What is the surface of a sphere with a radius of 13 units?

Answer:

Sn = ∑ 4(-6)^n, from n = 0 to n = n

Step-by-step explanation:

* Lets study the geometric pattern

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

- The sum of n terms is Sn = [tex]\frac{a(1-r^{n})}{(1-r)}[/tex], where

 a is the first term , r is the common ratio between each two

 consecutive terms and n is the numbers of terms

- The summation notation is ∑ a r^n, from n = 0 to n = n

* Now lets solve the problem

∵ The terms if the sequence are:

  4 , -24 , 144 , -864 , ........

∵ [tex]\frac{-24}{4}=-6[/tex]

∵ [tex]\frac{144}{-24}=-6[/tex]

∴ There is a constant ratio between each two consecutive terms

∴ The pattern is geometric

- The first term is a

∴ a = 4

- The constant ratio is r

∴ r = -6

∵ Sn = [tex]\frac{a(1-r^{n})}{(1-r)}[/tex]

∴ Sn = [tex]\frac{4(1-(-6)^{n})}{(1-(-6))}=\frac{4(1-(-6)^{n})}{(1+6)}=\frac{4}{7}[1-(-6)^{n}][/tex]

- By using summation notation

∵ Sn = ∑ a r^n , from n = 0 to n = n

∴ Sn = ∑ 4(-6)^n

Answer:

[tex] a_n = (4)(-6)^{n-1}, n =1,2,3,4,.... [/tex]

And we can verify:

[tex] n=1 , a_1 = 4 (-6)^{1-1}= 4[/tex]

[tex] n=2 , a_2 = 4 (-6)^{2-1}= -24[/tex]

[tex] n=3 , a_3 = 4 (-6)^{3-1}= 144[/tex]

[tex] n=4 , a_4 = 4 (-6)^{4-1}= -864[/tex]

And finally we can write the summation like this:

[tex] S_n = \sum_{i=1}^n 4 (-6)^{n-1} , n =1,2,3,... [/tex]

Step-by-step explanation:

For this case we have the following pattern of numbers :

4-24+144-864+...

And we want to express the sum in terms of a summation.

We can use the fact the the general term for the sum can be expressed as:

[tex] a_n = a_1 r^{n-1}[/tex]

And for this case we can identify the value of r dividing successive terms like this:

[tex] r = \frac{|24|}{|4|}= \frac{|144|}{|24|}=\frac{|864|}{|144|}= 6[/tex]

So for this case we know that the value of r =6 and the initial value 4 would represent [tex] a_1 = 4[/tex]

Since the sequence is alternating with + and - signs we can express the general term like this:

[tex] a_n = (4)(-6)^{n-1}, n =1,2,3,4,.... [/tex]

And we can verify:

[tex] n=1 , a_1 = 4 (-6)^{1-1}= 4[/tex]

[tex] n=2 , a_2 = 4 (-6)^{2-1}= -24[/tex]

[tex] n=3 , a_3 = 4 (-6)^{3-1}= 144[/tex]

[tex] n=4 , a_4 = 4 (-6)^{4-1}= -864[/tex]

And finally we can write the summation like this:

[tex] S_n = \sum_{i=1}^n 4 (-6)^{n-1} , n =1,2,3,... [/tex]

Answer:

4.4 is the answer hope it help you

Answer:

4.4 is the answer round it to the nearest ten

Answer:

A) The equation in factored form is (4t + 1)(t - 2) = 0

B) The solutions of the equation are t = -1/4 and t = 2

C) It will take 2 seconds for the rocket to hit the ground

Step-by-step explanation:

* Lets study the information in the problem

- A child launches a toy rocket from the top of a slide

- The equation of the motion is -16² + 28t + 8 = 0, where t is the time

 of rocket to hit the ground

* Now lets solve the problem

- At first simplify the equation

∵ -16t² + 28t + 8 = 0

∵ Al the terms have a factor 4

- Divide all terms by 4

∴ -4t² + 7t + 2 = 0 ⇒ multiply all terms by -1

∴ 4t² - 7t - 2 = 0

- Lets factorize

∵ 4t² = 4t × 1t ⇒ 1st term in the 1st bracket × 1st term in the 2nd bracket

∵ -2 = 1 × -2 ⇒ 2nd term in the 1st bracket × 2nd term in the 2nd bracket

∵ 4t + -2 = -8t ⇒ product of the extremes

∵ 1t × 1 = 1t ⇒ product of means

∵ -8t + 1t = -7t ⇒ middle term

∴ The factorization of 4t² - 7t - 2 is (4t + 1)(t - 2)

∴ (4t + 1)(t - 2) = 0

A) The equation in factored form is (4t + 1)(t - 2) = 0

- Lets use the zero product property to solve the equation

∵ (4t + 1)(t - 2) = 0

- Equate each factor by 0

∵ 4t + 1 = 0 ⇒ subtract 1 from both sides

∴ 4t = -1 ⇒ divide both sides by 4

∴ t = -1/4

OR

∵ t - 2 = 0 ⇒ add 2 for both sides

∴ t = 2

B) The solutions of the equation are t = -1/4 and t = 2

C) We can not accept the answer t = -1/4 because there is no negative

    value for the time

∴ The answer is t = 2 only

* It will take 2 seconds for the rocket to hit the ground

Answer:

Step-by-step explanation:

36.7

Applying the Heron's formula, the area of the parallelogram = 36.7 square units.

Heron's Formula = √[s(s - a)(s - b)(s - c)], where:

A diagonal of a parallelogram cuts a parallelogram into two equal triangles.

Thus, we have two equal triangles in the parallelogram given.

Area of the parallelogram = 2(area of triangle)

Find the area of one triangle using the Heron's formula:

a = 5

b = 8

c = 11

s = (5 + 8 + 11)/2 = 12

Area of one triangle = √[12(12 - 5)(12 - 8)(12 - 11)]

= √[12(7)(4)(1)]

= √336

= 18.33 sq. units.

Therefore, area of the parallelogram = 2(18.33) = 36.7 square units.

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Answer:

4.4 in

Step-by-step explanation:

If a radius is perpendicular to a chord, it bisects that chord. You can use Pythagorean theorem here

[tex] {3.7}^{2} + {2.4}^{2} = {x}^{2} [/tex]

Once solved you'll find x to be roughly 4.4 in

Answer:

x = 4.4 in

Step-by-step explanation:

The segment from the centre of the circle to the chord is a perpendicular bisector, hence

7.4 ÷ 2 = 3.7

Consider the right triangle with legs 3.7 and 2.4 and hypotenuse x

Using Pythagoras' identity in the right triangle, then

x² = 2.4² + 3.7² = 5.76 + 13.69 = 19.45

Take the square root of both sides

x = [tex]\sqrt{19.45}[/tex] ≈ 4.4 in

Answer:

44.72 feet

Step-by-step explanation:

Assuming that the bottom of the tree and the ground makes a right triangle-- use the Pythagorean theorem.

x^2 + 40^2 = 60^2

x^2 + 1,600 = 3,600

x^2 = 2,000

x = 44.72 ft

Answer:

C

Step-by-step explanation:

On edge

f(x)+g(x)

f(x)=3x+2 and g(x)=4x

You have:

3x +2 + 4x

Combine like terms:

3x +4x = 7x

The answer becomes 7x +2

Answer:

The first choice is the correct one

Step-by-step explanation:

That funny symbol is the Greek symbol for "the sum of".  Sum means to add, so whatever numbers we have we are definitely adding them.  The index goes from a starting point of 1 up to 4.  That's those 2 numbers, one below and one above the sum symbol.  The "n" in 7/n is what we are replacing with each number starting at 1 and ending at 4.  7/1, 7/2, 7/3, 7/4.  Those are the numbers, now just put them together with plus signs between them and you're done.

Answer:

3u - 2v + w = 69i + 19j.

8u - 6v = 184i + 60j.

7v - 4w = -128i + 62j.

u - 5w = -9i + 37j.

Step-by-step explanation:

Note that there are multiple ways to denote a vector. For example, vector u can be written either in bold typeface "u" or with an arrow above it [tex]\vec{u}[/tex]. This explanation uses both representations.

[tex]\displaystyle \vec{u} = \langle 11, 12\rangle =\left(\begin{array}{c}11 \\12\end{array}\right)[/tex].

[tex]\displaystyle \vec{v} = \langle -16, 6\rangle= \left(\begin{array}{c}-16 \\6\end{array}\right)[/tex].

[tex]\displaystyle \vec{w} = \langle 4, -5\rangle=\left(\begin{array}{c}4 \\-5\end{array}\right)[/tex].

There are two components in each of the three vectors. For example, in vector u, the first component is 11 and the second is 12. When multiplying a vector with a constant, multiply each component by the constant. For example,

[tex]3\;\vec{v} = 3\;\left(\begin{array}{c}11 \\12\end{array}\right) = \left(\begin{array}{c}3\times 11 \\3 \times 12\end{array}\right) = \left(\begin{array}{c}33 \\36\end{array}\right)[/tex].

So is the case when the constant is negative:

[tex]-2\;\vec{v} = (-2)\; \left(\begin{array}{c}-16 \\6\end{array}\right) =\left(\begin{array}{c}(-2) \times (-16) \\(-2)\times(-6)\end{array}\right) = \left(\begin{array}{c}32 \\12\end{array}\right)[/tex].

When adding two vectors, add the corresponding components (this phrase comes from Wolfram Mathworld) of each vector. In other words, add the number on the same row to each other. For example, when adding 3u to (-2)v,

[tex]3\;\vec{u} + (-2)\;\vec{v} = \left(\begin{array}{c}33 \\36\end{array}\right) + \left(\begin{array}{c}32 \\12\end{array}\right) = \left(\begin{array}{c}33 + 32 \\36+12\end{array}\right) = \left(\begin{array}{c}65\\48\end{array}\right)[/tex].

Apply the two rules for the four vector operations.

[tex]\displaystyle \begin{aligned}3\;\vec{u} - 2\;\vec{v} + \vec{w} &= 3\;\left(\begin{array}{c}11 \\12\end{array}\right) + (-2)\;\left(\begin{array}{c}-16 \\6\end{array}\right) + \left(\begin{array}{c}4 \\-5\end{array}\right)\\&= \left(\begin{array}{c}3\times 11 + (-2)\times (-16) + 4\\ 3\times 12 + (-2)\times 6 + (-5) \end{array}\right)\\&=\left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle\end{aligned}[/tex]

Rewrite this vector as a linear combination of two unit vectors. The first component 69 will be the coefficient in front of the first unit vector, i. The second component 19 will be the coefficient in front of the second unit vector, j.

[tex]\displaystyle \left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle = 69\;\vec{i} + 19\;\vec{j}[/tex].

[tex]\displaystyle \begin{aligned}8\;\vec{u} - 6\;\vec{v} &= 8\;\left(\begin{array}{c}11\\12\end{array}\right) + (-6) \;\left(\begin{array}{c}-16\\6\end{array}\right)\\&=\left(\begin{array}{c}88+96\\96 - 36\end{array}\right)\\&= \left(\begin{array}{c}184\\60\end{array}\right)= \langle 184, 60\rangle\\&=184\;\vec{i} + 60\;\vec{j} \end{aligned}[/tex].

[tex]\displaystyle \begin{aligned}7\;\vec{v} - 4\;\vec{w} &= 7\;\left(\begin{array}{c}-16\\6\end{array}\right) + (-4) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}-112 - 16\\42+20\end{array}\right)\\&= \left(\begin{array}{c}-128\\62\end{array}\right)= \langle -128, 62\rangle\\&=-128\;\vec{i} + 62\;\vec{j} \end{aligned}[/tex].

[tex]\displaystyle \begin{aligned}\;\vec{u} - 5\;\vec{w} &= \left(\begin{array}{c}11\\12\end{array}\right) + (-5) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}11-20\\12+25\end{array}\right)\\&= \left(\begin{array}{c}-9\\37\end{array}\right)= \langle -9, 37\rangle\\&=-9\;\vec{i} + 37\;\vec{j} \end{aligned}[/tex].

Answer:

Moderate Negative Correlation

Step-by-step explanation:

I got 100% on Homework...

The strength of the correlation between the hours spent exercising and the hours spent playing video games moderate negative relationship.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

If Irina spends more time playing video games she will have less time to spend exercising, therefore, we can conclude that if she plays more video games the time spent on exercising will be less and vice versa. Thus, there exists a negative correlation coefficient between the two variables.

Since in a day there is limited time available, therefore, if time is spent on video games, there will be very less or no time left for exercising, hence, the relationship between the two is moderate and dependent.

Hence, the strength of the correlation between the hours spent exercising and the hours spent playing video games moderate negative relationship.

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For this case we must resolve the following expression:[tex]log_ {0.5} (16)[/tex]

We have to:

[tex]log_ {a} (x) = \frac {log_ {b} (x)} {log_ {b} (a)}[/tex]

The base change rule can be used if a and b are greater than 1 and are not equal to x.

We substitute the values in the base change formula, using [tex]b = 10[/tex]

[tex]\frac {log (16)} {log (0.5)} = - 4[/tex]

Answer:

-4

Option A

Answer:

(a, 0)

Step-by-step explanation:

Point S has the same x-coordinate as does Point R:  a.

Point S has the y-coordinate 0, as Point S lies on the x-axis.

Correct final answer:  (a, 0) represents Point S.

The fully simplified product of (b-2c)(-3bc) has 2 terms and a degree of 3. The number of negative terms in the simplified product depends on the values of b and c, which are not provided.

When simplifying the expression (b-2c)(-3bc), we use the distributive property to multiply each term in the first parenthesis by each term in the second parenthesis. However, since the two terms -2c and -3bc will multiply to produce a term with a higher degree than b times -3bc, the simplified expression does not have 4 terms, but rather only 2 terms. The correct simplified form is -3b^2c + 6c^2. There are two terms, and the highest degree of any term, which is the sum of the exponents of the variables in that term, is 3 (b^2c having degree 3, since 2+1=3).

Therefore, the correct statements about the fully simplified product of (b-2c)(-3bc) are:

Answer:

C) An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?  

Step-by-step explanation:

Note that in this question:

x = amount of containers to be purchased.

50,000 =  the amount given

< means that the amount in total must be less than (& not equal to) 50000

1200 = the amount of the container cost.

C) is your best answer.

~

Answer:

It is C

Step-by-step explanation:

An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?

1,200x < 50,000

x < 41.67

Thus, only 41 containers can be purchased, so that the purchase remains under $50,000.

The statement "the expense must be less than $50,000" means that the total cost must be less than $50,000.

Explanation:

The altitude CH divides triangle ABC into similar triangles:

ΔABC ~ ΔACH ~ ΔCBH

Angle bisector AL divides the triangle(s) into proportional parts:

BL/BA = CL/CA

HD/HA = CD/CA

Of course, the Pythagorean theorem applies to the sides of each right triangle:

AH^2 +CH^2 = AC^2

DH^2 +AH^2 = AD^2

LC^2 + AC^2 = LA^2

AC^2 +BC^2 = AB^2

And segment lengths sum:

HD +DC = HC

AD +DL = AL

AH +HB = AB

CL +LB = CB

Solving the problem involves picking the relations that let you find something you don't know from the things you do know. You keep going this way until the whole geometry is solved (or, at least, the parts you care about).

___

We can use the Pythagorean theorem to find AH right away, since we already know AD and DH.

DH^2 +AH^2 = AD^2

4^2 + AH^2 = 8^2 . . . . . . . substitute known values

AH^2 = 64 -16 = 48 . . . . . . subtract 16

AH = 4√3 . . . . . . . . . . . . . . take the square root

Now, we can use this with the angle bisector relation to tell us how CD and CA are related.

HD/HA = CD/CA

4/(4√3) = CD/CA . . . . . substitute known values

CA = CD·√3 . . . . . . . . . cross multiply and simplify

Using the sum of lengths equation, we have ...

CH = HD +CD

CH = 4 + CD

From the Pythagorean theorem ...

AH^2 +CH^2 = AC^2

(4√3)^2 + (4 +CD)^2 = (CD√3)^2 . . . . . substitute known values

48 + (16 +8·CD +CD^2) = 3·CD^2 . . . . . simplify a bit

2·CD^2 -8·CD -64 = 0 . . . . . . . . . . . . . . . put the quadratic into standard form

2(CD -8)(CD +4) = 0 . . . . . . . . . . . . . . . . factor

CD = 8 . . . . . only the positive solution is useful here

Now, we know ...

∆ADC is isosceles, so ∠ACH = ∠CAD = ∠DAH = ∠CBA

CH = 8+4 = 12

AC = 8√3 . . . . . = 2·AH

Then by similar triangles, ...

AB = 2·AC = 16√3

BC = AC·√3 = 24

Answer:

The normal price is $90

Step-by-step explanation:

Let

x-----> the normal price

we know that

100%-10%=90%=90/100=0.90

so

0.90x=$81

Solve for x

x=$81/0.90

x=$90

Answer:0.001

x=the number of workers taking the bus to work

p= probability of success =(15/100) = 0.15

q= probability of failure =1- p = 0.85

P(X=6) = 10C6(0.15)^6(0.85)^4

            = 0.001

Answer: 0.001

Step-by-step explanation:

Binomial probability formula :

[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of exactly x successes in n trials.

Given : The probability of city workers take the bus to work =15%=0.15

The sample size :n= 10

Now, the probability that exactly 6 put of 10 workers take the bus to work :-

[tex]P(6)=^{10}C_6(0.15)^{6}(1-0.15)^{10-6}\\\\=\dfrac{10!}{6!(10-6)!}(0.15)^6(0.85)^4\\\\=0.0012486552627\approx0.001[/tex]

Therefore , the probability that exactly 6 workers take the bus to work = 0.001

The correct option will be No, she made an error in step 2, she should have found y=0.5

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have been Given the system of linear equations:

-3x + 2y = 8 --- eqn. 1

3x + 2y = -6 ---eqn. 1

First add both equations together

4y = 2

Now, divide both sides by 4:

y = 2/4

y = 0.5

Thus Kaitlyn got y = 2 instead of 0.5 in this second step. The solution she would get will be incorrect due to an error has occurred here.

Therefore, the error made by Kaitlyn while solving the equations is in step 2. Her solution will be incorrect.

The correct option will be: No

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Answer:

The correct answer is letter C

Answer:

[tex]x^{\frac{21}{4} }[/tex]

Step-by-step explanation:

Given expression is:

[tex](\sqrt[8]{x^7} )^{6}[/tex]

First we will use the rule:

[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]

So for the given expression:

[tex]\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }[/tex]

We will use tha property of multiplication on powers:

[tex]=x^{7*\frac{1}{8} }[/tex]

[tex]= x^{\frac{7}{8} }[/tex]

Applying the outer exponent now

[tex](x^{\frac{7}{8} })^6[/tex]

[tex]= x^{\frac{7}{8}*6 } \\= x^{\frac{42}{8} }\\= x^{\frac{21}{4} }[/tex]

Answer:

lets say you mark the dice your answer would be 4.

Step-by-step explanation:

1+4=5, 2+3=5, 3+2=5, 4+1=5

Answer:

4 I got it right on Edmentum

Step-by-step explanation:

Hook me up with a 5 star and a Thanks :)

Answer:

42

Step-by-step explanation:

The permutation for that set of data looks like this:

[tex]_{7}P_{2}[/tex]

The formula looks like this:

[tex]_{7}P_{2}=\frac{7!}{(7-2)!}[/tex]

which of course simplifies to

[tex]_{7}P_{2}=\frac{7!}{5!}[/tex]

which further simplifies down to the most basic simplification:

[tex]_{7}P_{2}=7*6[/tex]

since the 5*4*3*2*1 that goes after the 6 in the numerator cancels with the 5*4*3*2*1 in the denominator.

You could also check this on your calculator.  Hit "math", then arrow over to "Prob" and it's under nPr.

Answer:

Step-by-step explanation:

A regular polygon is defined to be a convex polygon with congruent sides and congruent angles.

Convex means that all interior angles are less than 180 degrees.  However, if all interior angles are equal, the polygon has to be convex.

Final answer:

A regular polygon is a convex shape with sides and angles that are all congruent, exemplified by the faces of an icosahedron or an equilateral triangle.

Explanation:

A regular polygon is defined to be a convex polygon with congruent sides and congruent angles. This means that all sides are the same length and all interior angles are equal in measure, which contributes to the polygon's symmetry. As an example from three-dimensional geometry, an icosahedron is a symmetrical, solid shape with 20 faces, each of which is an equilateral triangle.

Answer:

neither

Step-by-step explanation:

The second and 3rd one can be modeled by by y = 100/x but the first one and the fourth one do not follow that, so the answer is neither. The first and fourth are y = 80/x

Put the values in and you will see the equations for yourself.

One

y = 80/2

y = 40

The 80 came from looking at this as an indirect variation. y = k/x

y = 40

x = 2

y = k/x

40 = k/2  Multiply both sides by 2

40 * 2 = k

k = 80

Two

y = k/x

20 = k/5

k = 20 * 5

k = 100

Answer:

x= 8.1

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos⁡ θ= base/hypotenuse

cos⁡ 36=x/10

0.8090=x/10

8.090=x

x=8.090

Rounding off to nearest 10

x=8.1

Answer:

  see below

Step-by-step explanation:

The graph extends to the left more or less horizontally, approaching the line y=3. The only choice that expresses that is the third one.

Answer:

[tex]\frac{inches}{minute}[/tex]

Change the feet to minutes by multiplying by 12, and change the hour to minutes.

Speedy: [tex]\frac{240}{60}[/tex]

Slowpoke: [tex]\frac{80}{30}[/tex]

Cleo: [tex]\frac{96}{10}[/tex]

Speedy is the fastest.

[tex]\frac{feet}{hour}[/tex]

Change minutes to feet by dividing and change the minutes to hours by multiplying.

Hope this helps and have a great day!!!

[tex]Sofia[/tex]

Answer:

The area of the rhombus is [tex]72\ m^{2}[/tex]

Step-by-step explanation:

we know that

To find the area of a rhombus, multiply the lengths of the two diagonals and divide by 2

[tex]A=\frac{1}{2}(6+6)(6+6)=72\ m^{2}[/tex]

Answer:

50

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Substitute 7 for x into the expression 8x−6 and then simplify using order of operations.

8(7)−6

56−6

50

Answer:

x = 12.5

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos ⁡θ= base/hypotenuse

cos⁡ 28=11/x

x=11/cos⁡28  

x=11/0.8829

x=12.45

Rounding off to nearest 10

x=12.5

Subtract 6 from both sides

-x > -1 - 6

Simplify -1 - 6 to -7

-x > -7

Multiply both sides by -1

= A. x < 7

Answer:

a. x<7 is the correct choice.

Step-by-step explanation:

The question is telling that the equation 6-x is larger than 1, so the last three choices are eliminated.