Which of the following is true regarding the sequence graphed below?
an
35
30
25
• (5, 25)
20
15-
• (4. 16)
10 -
• (3,9)
5
• (2, 4)
1 2 3
4
5 6
7 8
9
n
The sequence is arithmetic because the terms have a common difference.
O The sequence is arithmetic because the terms do not have a common difference

Answer:

We want to find:

[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}[/tex]

Here we can use Stirling's approximation, which says that for large values of n, we get:

[tex]n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n[/tex]

Because here we are taking the limit when n tends to infinity, we can use this approximation.

Then we get.

[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}[/tex]

Now we can just simplify this, so we get:

[tex]\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\[/tex]

And we can rewrite it as:

[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}[/tex]

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.

Thus:

[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}[/tex]

Answer:

x = 3, x = -5

Step-by-step explanation:

A perfect square trinomial is represented in the form a^2 + 2ab + b^2. We are already given the a^2 term, x^2, and the 2ab term, 2x. From this we can say:

a^2 = x^2

a = x

Now, we can substitute x for a in the other expression to create the equation:

2ab = 2x

2(x)b=2x

b = 1

From this, b^2 is one, so, to get our trinomial all on one side, we add 1 to both sides:

x^2 + 2x = 15

x^2 + 2x + 1 = 16

Now, we can factor. The perfect square trinomial factors into (a + b)^2. In this case, a is x, and b is one. We can factor and get:

(x + 1)^2 = 16

Now, we take the square root of both sides:

x + 1 = ± 4

We can separate this into two equations and solve:

x + 1 = 4

x = 3

x + 1 = -4

x = -5

Answer:

Step-by-step explanation:

x^2 + 2x = 15

x^2 + 2x + [1/2(2)]^2 = 15 +  [1/2(2)]^2

(x + 1/2(2) )^2 = 15 + [(1/2)(2)]^2

(x + 1)^2 = 15 + 1^2

(x + 1)^2 = 15 + 1

(x+1)^2 = 16                       Take the square root of both sides.

sqrt( (x + 1)^2 ) = sqrt(16)

x + 1 = +/- 4

x + 1 = 4

x = 4 - 1 = 3

x + 1 = -4

x = -4 - 1

x = - 5

So the roots are 3 and - 5

9514 1404 393

Answer:

  True

Step-by-step explanation:

In a geometric sequence, the terms a[n+1] and a[n] are related by the common ratio. If the sequence is otherwise unspecified, two sequential terms may have any a relation you like.* Either could be larger or smaller than the other.

__

* If one is zero, the other must be as well. Multiplying 0 by any finite common ratio will give zero as the next term.

Answer:

Santino rented the canoe for 8 hours.

Step-by-step explanation:

The total bill is represented by the formula r(h) = $10 + ($7.50/hour)h,

where h is the number of hours over which the canoe is rented.

If the total bill is $70, then $70 = $10 +  ($7.50/hour)h.

Solve this for h.  Start by subtracting $10 from both sides, obtaining:

$60 =  ($7.50/hour)h.

Dividing both sides by ($7.50/hour), we get:

           $60

h = --------------------- = 8 hours

      ($7.50/hour)

Santino rented the canoe for 8 hours.

Answer:

Increasing the number of people allows more variety and diversity, which makes the sample more accurate.

9514 1404 393

Answer:

Step-by-step explanation:

The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.

tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16   ⇒   sec = -(1/4)√97

cot(θ) = 1/tan(θ) = -4/9

csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81   ⇒   csc = (1/9)√97

sin(θ) = 1/csc(θ) = (9√97)/97

cos(θ) = 1/sec(θ) = (-4√97)/97

Answer:

[tex]{ \tt{ w = 2hx - 11x}} \\ \\ { \bf{w = x(2h - 11)}} \\ \\ { \bf{x = \frac{w}{2h - 11} }}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = \frac{w}{(2h - 11)} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]w = 2hx - 11x[/tex]

[tex]✒ \: w = x \: (2h - 11)[/tex]

[tex]✒ \: x = \frac{w}{(2h - 11)} [/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

[tex]y=\frac{5}{2}x-14[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]y=\frac{5}{2}x-10[/tex]

In the given equation, [tex]\frac{5}{2}[/tex] is in the place of m, making it the slope. Because parallel lines have the same slope, the line we're currently solving for therefore has a slope of [tex]\frac{5}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:

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

2) Determine the y-intercept (b)

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

Plug in the given point (-6,-29) and solve for b

[tex]-29=\frac{5}{2}(-6)+b[/tex]

Simplify -6 and 2

[tex]-29=\frac{5}{1}(-3)+b\\-29=(5)}(-3)+b\\-29=-15+b[/tex]

Add 15 to both sides to isolate b

[tex]-29+15=-15+b+15\\-14=b[/tex]

Therefore, the y-intercept is -14. Plug this back into [tex]y=\frac{5}{2}x+b[/tex]:

[tex]y=\frac{5}{2}x-14[/tex]

I hope this helps!

Answer:

The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)

Step-by-step explanation:

Hey there!

The probability of first getting a red marble is 1/3 since we have 1 red marble out of 2 + 1 = 3 total.

We put the marble back. The probability of then choosing a black marble is 2/3, since we have 2 black marbles out of 3 total.

So we get 1/3 * 2/3 = 2/9

The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)

Hope this helps, please mark brainliest if possible. Have a nice day. :)

Answer:

[tex]2x + 8[/tex]

Step-by-step explanation:

Area of triangle equal

[tex] \frac{b \times h}{2} = a[/tex]

where b is the base and h is the height.

Plug in what we know.

[tex] \frac{b \times 6x}{2} = 6 {x}^{2} + 24x[/tex]

Multiply 2 by both sides.

[tex]b \times 6x = 2(6 {x}^{2} + 24x)[/tex]

Divide 6x by both sides.

[tex]b = \frac{12 {x}^{2} + 48x }{6x} = 2x + 8[/tex]

Answer:

silly question...I used technology to "cheat"

it is 11/23

34155 32775 33649 34485

72105 72105 72105 72105

Step-by-step explanation:

Answer:

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{101}{\sqrt{90}} = 27.4[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 436 - 27.4 = 408.6.

The upper end of the interval is the sample mean added to M. So it is 436 + 27.4 = 463.4.

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Answer:

f ( -4 ) = 1024 + 8 + 9

Step-by-step explanation:

f ( x ) = 4x⁴ - x² + 9

If f ( - 4 ) then we get

f ( -4 ) = 4 ( -4)⁴ - ( - 4)² + 9

Expand the exponents

f ( - 4 ) = 4 ( 256 ) + 8 + 9

multiply the numbers

f ( -4 ) = 1024 + 8 + 9

9514 1404 393

Answer:

  $2505.80

Step-by-step explanation:

After the first exchange, the tourist has ...

  $3000(12.90 R/$) = R38,700

After 7 days, she has ...

  R38,700 -7(R900) = R32,400

After the second exchange, she has ...

  R32,400 × ($1/R12.93) = $2505.80

She gets $2505.80 at the second exchange.

Answer:

Step-by-step explanation:

[tex] \frac{3}{2} \div 5[/tex]

[tex] = \frac{3}{2} \times \frac{1}{5} [/tex]

[tex] = \frac{3}{10} [/tex]

= 0.3 (Ans)

Answer:

3/10

Step-by-step explanation:

3/2÷5

3/2÷5/1

3/2÷10/2 ( LCM of denominators)

3/2×2/10 ( Reciprocal of 10/2)

3/10 (Cancelling 2 by 2)

Answer:

Answer is 42

Step-by-step explanation:

2^5 + 10

2*2*2*2*2 + 10

32 + 10

42

Answer:

x = 3

Step-by-step explanation:

Assuming the acute angle are 45degrees

Hypotenuse = 3√2

Opposite = x

According to SOH CAH TOA

Sin 45 = opposite//hypotenuse

Sin 45 = x/3√2

1/√2 = x/3√2

Cross multiply

√2x = 3√2

x = 3

Hence the value of x is 3

Answer:

... ..... C is the answer

Answer:

since it's the lhs we are concerned about, i. e., Y axis, so it must be either up or down. now look at the question, it says 8x2 - (1), it means one lower value of y i. e., 1 unit down

Answer:It is shifted 1 unit down.

Step-by-step explanation:

9514 1404 393

Answer:

  -3840t^4

Step-by-step explanation:

The k-th term, counting from k=0, is ...

  C(5, k)·(4t)^(5-k)·(-3)^k

Here, we want k=1, so the term is ...

  C(5, 1)·(4t)^4·(-3)^1 = 5·256t^4·(-3) = -3840t^4

__

The program used in the attachment likes to list polynomials with the highest-degree term last. The t^4 term is next to last.

Answer:

y = 5x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 5, then

y = 5x + c ← is the partial equation

To find c substitute (2, 3) into the partial equation

3 = 10 + c ⇒ c = 3 - 10 = - 7

y = 5x - 7 ← equation of line

Answer:

[tex]Width = 59[/tex]

Step-by-step explanation:

Given

The above data

Required

The class width

To do this, we simply calculate the difference between the class limits of any one of the classes.

Taking 1187–1246 as a point of reference, the class width is:

[tex]Width = 1246 - 1187[/tex]

[tex]Width = 59[/tex]

Answer:

75 hombres y 125 mujeres

Step-by-step explanation:

lo siento, yo no hablo español bien

Answer:

√-2 ≈ 1.41i

Step-by-step explanation:

√-2 = i√2 = i × 1.414.. ≈ 1.41i

Answer:

[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]

The inverse function is to calculate the number of rides; given the amount paid

Step-by-step explanation:

Given

[tex]Admission = 15[/tex]

[tex]Ride = 3[/tex] per ride

Required

Explain the inverse function

First, we calculate the function

Let x represents the number of rides

So:

[tex]f(x) = Admission + Ride * x[/tex]

[tex]f(x) = 15 + 3 * x[/tex]

[tex]f(x) = 15 + 3x[/tex]

For the inverse function, we have:

[tex]y = 15 + 3x[/tex]

Swap x and y

[tex]x = 15 + 3y[/tex]

Make 3y the subject

[tex]3y = x - 15[/tex]

Make y the subject

[tex]y =\frac{x}{3} - 5[/tex]

Replace y with the inverse function

[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]

The above is to calculate the number of rides; given the amount paid

Answer:

They went over their goal for the last six months by 34 minutes per month.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all values in the data-set divided by the size of the data-set.

529, 499, 651, 652, 1,163, and 310 minutes on their cell phone plan.

The mean is:

[tex]M = \frac{529+499+651+652+1163+310}{6} = 634[/tex]

By how many minutes did they go over their goal in the last six months?

The mean was of 634 minutes, and they wanted to keep it below 600. So

634 - 600 = 34

They went over their goal for the last six months by 34 minutes per month.

Answer:

the quotient of x and 3

Step-by-step explanation:

x divided by 3

division answers are called quotients

Answer:

Step-by-step explanation:

x/3

• the difference of x and 3

• the quotient of 3 and x

• the product of 3 and x

• the quotient of x and 3  is correct.  We are dividing x into 3, not 3 into x.

[tex]f'(4) = 43[/tex]

Explanation:

Given: [tex]f(x)=5x^2 + 3x + 3[/tex]

[tex]\displaystyle f'(x)= \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}[/tex]

Note that

[tex]f(x+h) = 5(x+h)^2 + 3(x+h) + 3[/tex]

[tex]\:\:\;\:\:\:\:= 5(x^2 + 2hx + h^2) + 3x + 3h +3[/tex]

[tex]\:\:\;\:\:\:\:= 5x^2 + 10hx + 5h^2 + 3x + 3h +3[/tex]

Substituting the above equation into the expression for f'(x), we can then write f'(x) as

[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{10hx + 3h + 5h^2}{h}[/tex]

[tex]\displaystyle\:\:\;\:\:\:\:= \lim_{h \to 0} (10x +3 +5h)[/tex]

[tex]\:\:\;\:\:\:\:= 10x + 3[/tex]

Therefore,

[tex]f'(4) = 10(4) + 3 = 43[/tex]