Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet. Which integer represents Gemma’s position with respect to sea level?
–32

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]

Step-by-step explanation:

Starting out with the Taylor series,

[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(a)}{n!}(x-a)^n[/tex]

where [tex]f^{(n)}[/tex] is the nth derivative of f(x) and if we set a = 0, we get the special case of the Taylor series called the Maclaurin series:

[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(0)}{n!}x^n[/tex]

Expanding this series up to the 1st 3 terms at a = 0,

[tex]f(x) = f(0) + \dfrac{f'(0)}{1!}x + \dfrac{f''(0)}{2!}x^2[/tex]

Let's find the derivatives of [tex]e^{\frac{x}{2}}[/tex]:

[tex]f'(x) = \frac{d}{dx} (e^{\frac{x}{2}}) = \frac{1}{2}e^{\frac{x}{2}} \Rightarrow f'(0) = \frac{1}{2}[/tex]

[tex]f''(x) = \frac{1}{4}e^{\frac{x}{2}} \Rightarrow f''(0) = \frac{1}{4}[/tex]

We can now write the Maclaurin series for [tex]e^{\frac{x}{2}}[/tex]as

[tex]e^{\frac{x}{2}} = 1 + \frac{1}{2} x + \frac{1}{8} x^2[/tex]

Answer:

36 meters

Step-by-step explanation:

A=1/2b×h

108sq. m=1/2.6m×h

both side canceling meter

h=2×108m/6

h=36m. answer

The height of the triangle is 12 meters, and the base of the triangle is 18 meters.

Let's denote the height of the triangle as "h" meters. According to the given information, the base of the triangle is 6 meters longer than the height, so the base can be represented as "(h + 6)" meters.

The area of a triangle is given by the formula: Area = (1/2) * base * height

We are given that the area of the triangle is 108 square meters, so we can write the equation as:

108 = (1/2) * (h + 6) * h

Now, let's solve for "h":

108 = (1/2) * (h² + 6h)

Multiply both sides by 2 to eliminate the fraction:

216 = h² + 6h

Rearrange the equation in standard quadratic form:

h² + 6h - 216 = 0

Now, let's solve this quadratic equation for "h." We can factor it or use the quadratic formula. Factoring, we get:

(h + 18)(h - 12) = 0

Setting each factor to zero:

h + 18 = 0     or     h - 12 = 0

Solving for "h" in each case:

h = -18 (discard this negative value as height cannot be negative)     or     h = 12

Since height cannot be negative, we take the positive value of "h," which is 12 meters.

Now, we can find the base by using the given relationship: base = height + 6

base = 12 + 6 = 18 meters

So, the height of the triangle is 12 meters, and the base of the triangle is 18 meters.

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Answer:

1) the planning value for the population standard deviation is 10,000

2)

a) Margin of error E = 500, n = 1536.64 ≈ 1537

b) Margin of error E = 200, n = 9604

c) Margin of error E = 100, n = 38416

3)

As we can see, sample size corresponding to margin of error of $100 is too large and may not be feasible.

Hence, I will not recommend trying to obtain the $100 margin of error in the present case.

Step-by-step explanation:

Given the data in the question;

1) Planning Value for the population standard deviation will be;

⇒ ( 50,000 - 10,000 ) / 4

= 40,000 / 4

σ = 10,000

Hence, the planning value for the population standard deviation is 10,000

2) how large a sample should be taken if the desired margin of error is;

we know that, n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²

given that confidence level = 95%, so [tex]z_{\alpha /2[/tex]  = 1.96

Now,

a) Margin of error E = 500

n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²

n = [ ( 1.96 × 10000 ) / 500 ]²

n = [ 19600 / 500 ]²

n = 1536.64 ≈ 1537

b) Margin of error E = 200

n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²

n = [ ( 1.96 × 10000 ) / 200 ]²

n = [ 19600 / 200 ]²

n = 9604

c)  Margin of error E = 100

n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²

n = [ ( 1.96 × 10000 ) / 100 ]²

n = [ 19600 / 100 ]²

n = 38416

3) Would you recommend trying to obtain the $100 margin of error?

As we can see, sample size corresponding to margin of error of $100 is too large and may not be feasible.

Hence, I will not recommend trying to obtain the $100 margin of error in the present case.

Answer:

7.56

Step-by-step explanation:

Kevin should expect to pay approximately $7.56 for 18 juice boxes based on the given information.

To find out how much Kevin should expect to pay for 18 juice boxes based on the given information, we can set up a proportion using the number of juice boxes and the cost:

In general, an expression refers to a combination of symbols, numbers, variables, and operators that represent a specific computation or value. Expressions are a fundamental concept in mathematics, programming, and logic.

Let "x" be the cost of 18 juice boxes.

We have the proportion:

6 juice boxes / $2.52 = 18 juice boxes / x

To solve for "x," we can cross-multiply:

6x = 18 x $2.52

6x = $45.36

Now, divide both sides by 6 to isolate "x":

x = $45.36 / 6

x ≈ $7.56

Therefore, According to the data provided, Kevin should budget about $7.56 for 18 juice cartons.

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Answer:

x = 28

Step-by-step explanation:

HFG = EFI

6x - 4 = 164

6x = 164 + 4

6x = 168

x = 168/6

x = 28

Answer:

d = [tex]\frac{2x + 3}{p}[/tex]  - x

Step-by-step explanation:

First divide both sides by p.

then subtract x from both sides

Answer:

[tex]\displaystyle d = \frac{2x + 3}{d} - x[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle p(d + x) = 2x + 3[/tex]

Step 2: Solve for d

a) By Pythagoras theorem , h^2 is = a^2 + b^2 where a is the hypotenuse and a and b are the legs.

=) 15^2 = x^2 + y^2

That is the relation

b) area of triangle = 1/2 x height x base

=) 1/2 * x * y = 30

=) xy = 15cm

Given:

Marginal cost for making 1 mask = $0.50

Total cost to make 100 masks = $62

Revenue per mask = $3

To find:

(a) Linear cost function C(x)

(b) Revenue function R(x)

(c) Break even point

(d) Interval of profit & loss

Solution:

(a) We know that linear cost function is given by,

Total cost = Fixed cost per unit + (Marginal cost per unit)*(Number of units)

Let 'x' denote the number of units

[tex]\Rightarrow[/tex] C(x) = b + mx

It is given that, m = $0.50

[tex]\Rightarrow[/tex] C(x) = b + 0.5x

It is also given that the total cost of making 100 masks is $62

[tex]\Rightarrow[/tex] C(100) = $62

[tex]\Rightarrow[/tex] b +0.5(100) = 62

[tex]\Rightarrow[/tex] b + 50 =62

[tex]\Rightarrow[/tex] b = 62 - 50

[tex]\Rightarrow[/tex] b = 12

[tex]\Rightarrow[/tex] C(x) = 12 + 0.5x

This is the linear cost function, C(x)

(b) We know that,

Total Revenue = Revenue per unit * Number of units

It is given that a mask is sold for $3, i.e., revenue per mask is $3

Let 'x' denote the number of units

Then the revenue function is given by,

R(x) = 3x

This is the revenue function, R(x)

(c) We know that, break even point refers to the point where total cost is equal to the total revenue. Thus, at break even point, we have,

C(x) = R(x)

[tex]\Rightarrow[/tex] 12 + 0.5x = 3x

[tex]\Rightarrow[/tex] 3x - 0.5x = 12

[tex]\Rightarrow[/tex] 2.5x = 12

[tex]\Rightarrow x=\frac{12}{2.5}[/tex]

[tex]\Rightarrow[/tex] x = 4.8

Since, 'x' denotes the number of masks, it must be a whole number and not a fraction. Thus, we will round off our value to get the break even point as 5 masks.

That is, 5 masks must be made to break even.

(d) We know that the profit function is given as the difference of revenue function and cost function. That is, we have,

P(x) = R(x) - C(x)

[tex]\Rightarrow[/tex] P(x) = 3x - (12 + 0.5x)

[tex]\Rightarrow[/tex] P(x) = 3x - 12 - 0.5x

[tex]\Rightarrow[/tex] P(x) = 2.5x -12

Now, we know that there is profit when the value of the profit function is positive & there is loss when the value of profit function is negative. Thus, we can calculate the intervals of profit and loss by finding the intervals where the profit function is positive & negative respectively. Alternatively, since the break even point denotes the point where the value of the profit function is 0, we can find the intervals of profit and loss as the intervals greater than and lesser than the break even point respectively.

That is, since the break even point is x = 4.8, the interval of profit is given as x > 4.8 & the interval of loss is given as x < 4.8

Taking into account that 'x' denotes the number of masks and thus must be a whole number, we have the intervals of profit and loss as,

Loss:= [tex]x \in [0,4][/tex]

Profit:= [tex]x \in [5, \infty)[/tex]

Final answer:

(a) Linear Cost function: C(x) = 12 + 0.5x

(b) Revenue function: R(x) = 3x

(c) 5 masks must be made to break even

(d) Interval of profit: [tex]x \in [5, \infty)[/tex], Interval of loss: [tex]x \in [0,4][/tex]

Given:

The piecewise function is:

[tex]f(x)=\begin{cases}9x & \text{ if } x<-1 \\ x-4 & \text{ if } x\geq -1 \end{cases}[/tex]

To find:

The values of [tex]f(-3),f(0), f(-1)[/tex].

Solution:

In the given piecewise function,

[tex]f(x)=9x[/tex] for [tex]x<-1[/tex] and [tex]f(x)=x-4[/tex] for [tex]x\geq -1[/tex].

Putting [tex]x=-3[/tex] in [tex]f(x)=9x[/tex], we get

[tex]f(-3)=9(-3)[/tex]

[tex]f(-3)=27[/tex]

Putting [tex]x=0[/tex] in [tex]f(x)=x-4[/tex], we get

[tex]f(0)=0-4[/tex]

[tex]f(0)=-4[/tex]

Putting [tex]x=-1[/tex] in [tex]f(x)=x-4[/tex], we get

[tex]f(-1)=-1-4[/tex]

[tex]f(-1)=-5[/tex]

The required values are [tex]f(-3)=27,f(0)=-4,f(-1)=-5[/tex].

Therefore, the correct option is D.

Answer:

Y = 0.0315x + 9.4764

Residual = 2.35

Correlation Coefficient = 0.847

Step-by-step explanation:

From the R output given :

Intercept = 9.4764

Slope = 0.0315

x = number of manufacturing enterprise employing 20 or more workers

y = annual mean concentration of Sulphur dioxide

The regression equation :

y = bx + c

b = slope ; c = intercept

y = 0.0315x + 9.4764

Prediction using the regression equation :

The predicted y value, when x = 250

y = 0.0315(250) + 9.4764

y = 17.3514

The residual, if actual annual concentration = 15

Y residual = 17.35 - 15 = 2.35

The correlation Coefficient value, R

R = √R²

R = √0.717

R = 0.847

Step-by-step explanation:

Here is the answer for your question

i think hhjs is how it goes

Answer:

30. A right triangle has one angle that is 90°

All angles add to 180°

180 - 90 - 60 = 30

Step-by-step explanation:

Answer:

116 degrees

Explanation:

If we divide the triangle from the vertex of the triangle, the vertex angle of each triangle would lie on a straight line in the triangle. Angle on a straight line is 180 degrees.

If the vertex angle of one triangle is 64 degrees then the vertex angle x of the other triangle is 180 degrees - 64 degrees = 116 degrees.

Answer:B

Step-by-step explanation: There is a mathematical way to do this , but the simplest way is just to imagine all of the transformations and choose the most reasonable one. All of the other answers are ridiculous.

Answer:

DM=38\ cmDM=38 cm

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

Triangles DEF and OEN are similar by AA Similarity Postulate

Remember that if two triangles are similar, then the ratio of its corresponding sides is proportional

In this problem

\frac{DE}{OE}=\frac{DF}{ON}

OE

DE

=

ON

DF

substitute the given values

\frac{44}{22}=\frac{DF}{38}

22

44

=

38

DF

2=\frac{DF}{38}2=

38

DF

DF=2(38)=76\ cmDF=2(38)=76 cm

\begin{gathered}DF=2DM\\76=2DM\\DM=38\ cm\end{gathered}

DF=2DM

76=2DM

DM=38 cm

ur welcomeee♥️♥️♥️

Answer:

C

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

264 interest/3 years=88 interest/year

principal x interest rate =interest/year

2200 x interest rate =88

interest rate =88/2200

interest rate =.04 or 4%

Answer: SInce this is multiple choice I won't provide an explanation. The answers are B) (-1, -4) and E) (4, 6)

Answer:

y = 2 / (r/3 - s/5)

Step-by-step explanation:

r/3 - 2/y = s/5

add 2/y to both sides

r/3 = s/5 + 2/y

Subtract s/5 from both sides

r/3 - s/5 = 2/y

multiply both sides by y

y(r/3 - s/5) = 2

Divide both sides by r/3 - s/5

y = 2 / (r/3 - s/5)

Answer:

sssssssss

Step-by-step explanation:

ssssssss

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

Explanation:

The observations are in ascending order, which means the set is sorted from smallest to largest.

The X is at the right-most endpoint, so X is the largest value (aka the max).

The min is 33, so,

max - min = range

X - 33 = 58

X = 58+33

X = 91 is the max

Answer:

Step-by-step explanation:

The range of the data is the highest value - the lowest value.

The lowest in the list is 33 so the highest must be 33 + 58

= 91.

Answer:

16

Step-by-step explanation:

a = 5

b = 3

a - b = 2

▪︎5 - 3 = 2

ab = 15

▪︎5(3) = 15

a^2 - b^2 = ?

5^2 = 25

3^2 = 9

25 - 9 = 16.

a^2 - b^2 = 16.

Answer: $15219.20

Step-by-step explanation:

Based on the information given, firstly we need to calculate the discount which will be:

= 18% × $18560

= 0.18 × $18560

= $3340.80

Then, the amount that Dao will pay will be:

= Sticker price - Discount

= $18560 - $3340.80

= $15219.20

Therefore, Dao will pay $15219.20

Answer:

Patrice does not have sufficient evidence to reject the fast-food chain's claim.

Step-by-step explanation:

unless she already ate some fries, not enough evidence