A circular water fountain in the town square has a 112-foot circumference. How far is the center of the fountain from the outer edge? Round to the nearest whole number.

Answer:

128/3

Step-by-step explanation:

The sequence follow the rule (1/6)*(4)^(n-1). The 5th term will be (1/6)*(4)^4=128/3

Answer:

128/3

Step-by-step explanation:

1/6, 2/3, 8/3, . . .

1/6, 4/6, 16/6

We are multiplying by 4 each time

1/6 *4 = 4/6

4/6 * 4 = 16/6

This is a geometric sequence with the common ratio of 4

an = a1 (r)^(n-1)

an = 1/6 (4) ^(n-1)

Let n = 5

a5 = 1/6 (4)^(5-1)

a5 = 1/6 (4)^4

a5 = 1/6 * 256

a5 =128/3

Answer:

Step-by-step explanation:

Point-slope equation for line of slope m that passes through (x₀, y₀):

y-y₀ = m(x-x₀)

apply your data

y-2 = 4(x-6)

Answer:

y−2= −2(x−7)

Step-by-step explanation:

khan academy says its right

Answer:

f(x) = ( x+2)(x-5)(x-6)

Step-by-step explanation:

We can write the equation with zeros at b1,b2,b3

f(x) =a( x-b1)(x-b2)(x-b3)  where a is a constant and b1 b2 b3 are the zeros

f(x) = a( x- -2)(x-5)(x-6)

f(x) = a( x+2)(x-5)(x-6)

We can choose a since we are not given any more information about the function.  Let a = 1

f(x) = 1( x+2)(x-5)(x-6)

f(x) = ( x+2)(x-5)(x-6)

Step-by-step explanation:

I(S) = aS / (S + c)

As S approaches infinity, S becomes much larger than c.  So S + c is approximately equal to just S.

lim(S→∞) I(S)

= lim(S→∞) aS / (S + c)

= lim(S→∞) aS / S

= lim(S→∞) a

= a

As S approaches infinity, I(S) approaches a.

Answer:

see explanation

Step-by-step explanation:

Given

[tex]tan^{-1}[/tex]x + [tex]tan^{-1}[/tex]y + [tex]tan^{-1}[/tex] z = π

let

[tex]tan^{-1}[/tex]x = A , [tex]tan^{-1}[/tex]y = B , [tex]tan^{-1}[/tex]z = C , so

x = tanA, y = tanB , z = tanC

Substituting values

A + B + C = π  ( subtract C from both sides )

A + B = π - C ( take tan of both sides )

tan(A + B) = tan(π - C) = - tanC ( expand left side using addition identity for tan )

[tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = - tanC ( multiply both sides by 1 - tanAtanB )

tanA + tanB = - tanC( 1 - tanAtanB) ← distribute

tanA+ tanB = - tanC + tanAtanBtanC ( add tanC to both sides )

tanA + tanB + tanC = tanAtanBtanC , that is

x + y + z = xyz

Answer: 1.609344 kilometers.

Step-by-step explanation:

A mile is an English Unit that is used to measure the length of a linear surface.

Even though the kilometre has replaced it to a large extent as the standard measure of length, it is still the main unit of measurement for distances in the United States, the United Kingdom, Liberia and UK and US oversees territories.

Miles are longer than kilometres as a kilometer is equivalent to only 0.621371 miles.

1 mile is therefore;

= 1/0.621371

= 1.609344 kilometers.

Answer:

[tex]the \: two \: angles \: are \: equal \: so \: this \\ \: triangle \: is \: issosceless \\ then3x - 6 = 12 \\ 3x = 18 \\ x = \frac{18}{3} \\ x = 6 \\ thank \: you[/tex]

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                         P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of Americans who decide to not go to college = 48%

           n = sample of American adults = 331

           p = population proportion of Americans who decide to not go to

                 college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                        of significance are -1.645 & 1.645}  

P(-1.645 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.645) = 0.90

P( [tex]-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\hat p-p[/tex] < [tex]1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90

P( [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90

90% confidence interval for p = [ [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

 = [ [tex]0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] , [tex]0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] ]

 = [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

              [tex]0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }[/tex]

              [tex]\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}[/tex]

              [tex]\sqrt{n}[/tex] = 54.79

               n = [tex]54.79^{2}[/tex]

               n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Answer:

8,8,-8,-8,8, ... is neither arithmetic nor geometric

Step-by-step explanation:

8,8,-8,-8,8, ...

This sequence is neither arithmetic nor geometric

We could also write

8,8,8,8,8, ... this is geometric since we multiply by 1 each time

Answer:

Attachment 1 : Graph B

Attachment 2 : Option B

Step-by-step explanation:

( 1 ) The equation x = t² - 3 is represented by exponential growth, ( t² ) so it's graph will be similar to the first graph, graph 1, in our options. Then again we have to consider the equation y = √t - 2, which will be similar to graph 4, but with a greater slope. This leaves us with a solution of graph b.

( 2 ) We have the following system of equations at hand here.

{ x = 5 cot(t), y = - 3csc(t) + 4 }

Now instead of isolating the t from either equation, let's isolate cot(t) and csc(t) --- Step #1,

x = 5 cot(t) ⇒ x - 5 = cot(t),

y = - 3csc(t) + 4 ⇒ y - 4 = - 3csc(t) ⇒ y - 4 / - 3 = csc(t)

Now let's square these two equations, adding them --- Step #2

We know that csc²θ - cot²θ = 1, so let's subtract the equations

( y - 4 / - 3 )² = (csc(t))²

- ( x - 5 / 1 )² = (cot(t))²

___________________

(y - 4)² / 9 - x² / 25 = 1

And as we are subtracting the two expressions, this is an example of a hyperbola. Therefore your solution is option b.

Answer:

A

Step-by-step explanation:

I just used a graphing calculator.

Just type in all the functions and pick the graph and function pair that match the picture.

I hope this helps!

pls ❤ and mark brainliest pls!

Assuming you want x to approach negative infinity, you have the correct answer. It is choice A.

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

Explanation:

The root x = -2 leads to the factor x+2. That means the answer is between A and B.

As x approaches negative infinity, i.e. as we move to the left, we're going down the red curve and y = f(x) is going to approach negative infinity as well.

In terms of symbols, we'd write [tex]x \to -\infty, \ f(x) \to -\infty[/tex]

Informally, we could say "it falls to the left" as a way to describe this left end behavior.

Answer:

Given f(x)=8sin(x)+cot(x) for -pi<x<pi :

Note that:

f'(x)=8cos(x)-csc^2(x)

f''(x)=-8sin(x)+2csc^2(x)cot(x)

(1) To find the intervals where f(x) is increasing or decreasing we use the first derivative test; if the first derivative is positive on an interval the functio is increasing, negative implies the functio is decreasing.

Using technology we find the approximate zeros of f'(x) on -pi<x<pi :

x~~-1.443401

x~~-.3752857

x~~.3752857

x~~1.443401

Plugging in test values on the intervals yields:

f'(x)<0 on (-pi,-1.443401)

f'(x)>0 on (-1.443401,-.3752857)

f'(x)<0 on

Plz correct me if wrong

Answer:

b ≈ 9.2

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

b² = a² + c² = 6² +7² = 36 + 49 = 85 ( take the square root of both sides )

b = [tex]\sqrt{85}[/tex] ≈ 9.2 ( to the nearest tenth )

Answer:

9.22

Step-by-step explanation:

Since it's a 90° triangle [tex]c^{2} =a^{2} +b^{2}[/tex].

In this example they labeled the hypotenuse as b instead of c are equation is still the same just put the correct variables in the right places.

[tex]b = \sqrt{6^{2} +7^{2} }[/tex]

b = 9.22

Answer:

4th option

Step-by-step explanation:

The relationship is linear,

putting the value of x in the right side of the equation of option 4, you'll get the value of the left side

putting, x=1

y+4=-1/2(x-1)

y=-1/2(1-1)-4

y=-4

putting, x=7

y+4=-1/2(7-1)

y=-1/2(6)-4

y=-6/2-4

y=-3-4

y=-7

Answer:

  $74,748.11

Step-by-step explanation:

In order to make use of the amortization formula, we need to find the equivalent monthly interest rate.

When 12% interest is compounded continuously, the annual multiplier is ...

  e^0.12 ≈ 1.127497

The equivalent multiplier when the interest is compounded monthly is the 12th root of this,

  (e^0.12)^(1/12) = e^0.01 ≈ 1.0100502 = 1 + r

___

The amortization formula tells us that monthly payment amount A will pay off principal P in n months:

  P = A(1 -(1 +r)^-n)/r = $900(1 -1.0100502^-180)/0.0100502

  P = $74,748.11

The customer can pay off a 12% loan of $74,748.11 at the rate of $900 per month for 15 years.

Answer:

3x^2+x+2

Step-by-step explanation:

Let's simplify step-by-step.

2x2+3x−1+x2−2x+3

=2x2+3x+−1+x2+−2x+3

Combine Like Terms:

=2x2+3x+−1+x2+−2x+3

=(2x2+x2)+(3x+−2x)+(−1+3)

Answer:

Point A.

.................

Answer:

It is the Picture B.

Step-by-step explanation:

[tex] 24 = 3 \cdot 2^3 [/tex]

[tex]96=3\cdot 2^5 [/tex]

[tex] 384=3\cdot2^7[/tex]

hence it is a geometric progression, with a multiplied constant [tex]3[/tex]

Sum of G.P. of [tex]n[/tex] terms [tex] S_n = a\dfrac{r^n-1}{r-1}\quad \text{where } r \text{ is the common ratio and } a \text{ is the first term} [/tex]

and [tex] r=-2^2=-4[/tex]

Note that the constant should be separated, so

[tex] a= -8 [\tex]

after plugging the values, you'll get the answer

[tex] -26216 \times 3 [/tex]

which option C

Answer:

C

Step-by-step explanation:

-24+96-384+...

a=-24

r=96/(-24)=-4

[tex]s_{7}=a\frac{1-r^7}{1-r} \\=-24\frac{1-(-4)^7}{1-(-4)}\\=-24\frac{1+4^7}{1+4} \\=-24\frac{1+16384}{5} \\=-24\frac{16385}{5} \\=-24 \times 3277\\=-78648[/tex]

Answer:

9: tens place

4: tenths place

Step-by-step explanation:

let the function be [tex]y=ax^2+bx+c[/tex]

put $x=0, \, y=6$ , to get $c=6$

put $x=2, \, y=16$ , $16=4a+2b+6\implies 2a+b=5$

put $x=3, \, y=33$ , $33=9a+3b+6\implies 3a+b=9$

subtract the two equation, to get $a=4$

now substitute $a$ in first equation, to get $b=5-2\cdot4=-3$

so, $f(x)=4x^2-3x+6$

Answer:

[tex]\sqrt{280}[/tex] = 2[tex]\sqrt{70}[/tex]

37^2 = 1369

33^2 =1089

1369-1089 = 280

Step-by-step explanation:

9514 1404 393

Answer:

  see below

Step-by-step explanation:

  [tex]\text{A. point: }X\\\\\text{B. ray through Y: }\overrightarrow{XY}\\\\\text{C. line through Z: }\overleftrightarrow{XZ}\\\\\text{D. plane: plane } XYZ[/tex]

__

Additional comment

When you don't have the benefit of typesetting, you can refer to the geometry by name: ray XY, line XZ,

Answer:

12 - 6 x (0 + 15) = 34

How I got my answer

First, how i got my answer was that I had to solve the equation first, ignoring the answer. I got 0 x 6 = 0, then I did 124 - 0 = 124, then I did 124 - 15 = 109, which clearly isn't 34. I figured that we have to put the parentheses around the zero because if we don't, we are going have to multiply something by zero, which always gets zero. After that, I decided that I should put the parentheses around either the 6, or the 15. I did both, and saw which one was correct. If we put it around the 6, we get, 124 - (6 x 0) + 15 = 124 - 0 - 15 = 124 - 15 = 109, which isn't 34. Then I checked 124 - 6 x (0 + 15) = 124 - 6 x 15 = 124 - 90 = 34, and we just got the answer.

P.S. Sorry if it was confusing, I didn't really know how to explain it

Answer:

Hello the options to your question is missing below are the options

 A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles

B.the unknown population mean is definitely between 10 and 16 miles

C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians

D.the unknown population mean is between 10 and 16 miles with probability .95

Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians  ( c )

Step-by-step explanation:

95%  confidence

interval = 10 to 16 miles

To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians

confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,

Answer:

b

Step-by-step explanation:

because its right dummy

Answer: Search Results

Featured snippet from the web

In triangle sum of 2 sides must be greater than the 3rd side. So, the third > 8 - 6 = 2 and also the third < 8 + 6 = 14. So, the answer is 2 < third side < 14. The third side lies between(2,14).

Step-by-step explanation: Brainlyest please

Answer:

statistics are when data analyzed in order to make decisions about the population behind the data.

The correct answer to the question is Statistics (Option D).

What is statistics?

Statistics is a field of study in mathematics which deals with raw data. It is a tool which refines the data to produce meaningful results and a pathway to better understanding of it.

Some examples of raw data can be population sample which loves to see a particular TV show or a sample of students getting so and so marks in Math test.

Data is analyzed mainly by three different measure of central tendency that is mean, median and mode.

Therefore, Statistics the correct answer.

To know more about statistics refer:https://brainly.com/question/10734660

#SPJ2

Answer:

800700

Step-by-step explanation:

800000 + 00000 + 0000 + 000 + 00 + 0

000000 + 00000 + 0000 + 700 + 00 + 0

------------------------------------------------------------

= 800700

Answer:

Hey there!

800000+700=800700

Hope this helps :)

Answer:

3.25

Step-by-step explanation:

Answer:

  36

Step-by-step explanation:

Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.

The new figure has 12+24 = 36 edges.