DO it and thanks for the helpppp!!!!!!!!!!!!!!

The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:

D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.

The mean of the sampling distribution of p is of:

0.388.

The standard deviation of the sampling distribution of p is of:

0.0184.

The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:

As long as these two conditions are respected:

The values of the parameters in this context are given as follows:

N = 30000, n = 700, p = 0.388.

Hence the conditions are:

Then the shape is approximately normal and option D is correct.

The mean of the distribution is of:

\(\mu = p = 0.388\)

The standard error of the distribution is of:

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184\)

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Answer:

B

Step-by-step explanation:

Answer:

No, it is not.

Step-by-step explanation:

X has 2 3's. X's shouldn't repeat for it to be a function or else it will overlap.

The tent has a volume of 86 cubic feet.

The tent owned by Dante is in the shape of a triangular prism, which means it has two identical equilateral triangle bases that measure 5 feet each. The tent's length is 8 feet, and its height is 4.3 feet.

To calculate the tent's volume, we can use the formula for the volume of a triangular prism, which is \(V = (1/2) * b * h * l\), where b is the base, h is the height, and l is the length of the prism.

Plugging in the given values, we get \(V = (1/2) * 5 * 4.3 * 8\) = 86 cubic feet. The volume of a tent is an important consideration when deciding which one to purchase or use for a particular activity, as it determines how much space is available inside for people and belongings.

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Answer:

Step-by-step explanation:

3^2*5^2= 225

9*25=225

Three to the 2nd power times 5 to the 2nd power.

The surface area is approximately 161.47 square units.

To find the surface area generated by revolving the curve about the x-axis, we can use the formula:

S = 2π∫[a,b] f(x)√(1+[f'(x)]^2) dx

where f(x) is the given curve.

Here, f(x) = 36 - 2√(x^2+1) and we need to revolve it about the x-axis.

To find the limits of integration, we note that the curve is symmetric about the y-axis and therefore we can find the surface area of one half of the curve and multiply it by 2. So, we need to integrate from 0 to 4.

S = 2π∫[0,4] (36 - 2√(x^2+1))√(1+((x(-2x))/((x^2+1)^2))) dx

S = 2π∫[0,4] (36 - 2√(x^2+1))√((x^4+4x^2+1)/(x^4+1)^2) dx

Simplifying the integrand,

S = 2π∫[0,4] (36(x^4+1) - 2(x^2+1))√((x^4+4x^2+1)/(x^4+1)^2) dx

S = 2π∫[0,4] (36x^4-70x^2+34)√((x^4+4x^2+1)/(x^4+1)^2) dx

This integral is difficult to evaluate analytically, but it can be approximated using numerical integration techniques. Using a calculator or software, we find that the surface area is approximately 161.47 square units.

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It's impossible to say Sean should base his decision on the marginal cost and marginal benefit of creating another table. The marginal cost of making a table is not the same as the average cost of making a table. As a result, there is insufficient information to determine what Sean should do.

The opportunity cost of an activity is the value of what must be sacrificed in order to engage in the activity (plus the cost). A cost that cannot be recovered at the time a decision must be made.

The science of decision-making is often used as a crude definition of economics. This stems from the fact that economics is frequently concerned with making the best decision in the most efficient manner. One way to quantify this is to consider total costs and total benefits.

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Answer:

13.5 in^2

Step-by-step explanation:

6 = 1/2(B)(H) = 1/2(2)(H)

H = 6

H x 1.5 =9

area = 1/2(3)(9) = 13.5

Answer:

2.7 square inches

Answer:

it would be 14/39

Step-by-step explanation:

Answer:

\(\text{C. }1.3\)

Step-by-step explanation:

The area of a rectangle with width \(w\) and length \(l\) is given by \(A=lw\).

What we're given:

Substituting given values, we get:

\(1.04=0.8w,\\w=\frac{1.04}{0.8}=\boxed{\text{C. }1.3}\)

\(f(x) = \frac{10}{9}x + 11 \\ \)

So :

\(y = \frac{10}{9}x + 11 \\ \)

Subtract the sides of the equation minus 11

\(y - 11 = \frac{10}{9}x \\ \)

Multiply the sides of the equation by 9

\(9(y - 11) = 10x\)

\(9y - 99 = 10x\)

Divided the sides of the equation by 10

\( \frac{9y - 99}{10} = x \\ \)

So :

\( {f}^{ - 1}(x) = \frac{9x - 99}{10} \\ \)

_________________________________

And we're done.

Thanks for watching buddy good luck.

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Answer:

x-5

Step-by-step explanation:

Answer:

$20.00

Step-by-step explanation:

Let x be the money Carrie had at the start of the week.

Add/Subtract from this amount (x) for the events occurring during the week:

     x    Start

-3.50   1 book

+1.25   Sugardaddy income

-7.50   Batman movie

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

The end of the week Carrie has $10.25

Put this into one equation:

x - 3.50 + 1.25 - 7.50 = 10.25

x = 10.25 + 3.50 - 1.25 + 7.50

x = $20.00

The amount raised by a booster club compared with the number of  raffle tickets sold shows a constant rate of change;

A constant rate of change is realized when a change in one situation always results in a change in another. In the scenario of a booster club that regularly sells raffle tickets, the more tickets it sells, the higher the club gets.

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Answer:

(1,-1)

Step-by-step explanation:

-2x-1 = x+2

-3x = 3

x = -1

substitute

y = (-1) + 2

y = 1

point: (1,-1)

The rule for the pattern is to add 6 to each number.

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

Proof:

We'll break the proof into two cases which I'll label A and B

-----------

Case A: 'a' is even

k = some integer

a = 2k = some even integer

a+1 = 2k+1

a(a+1) = 2k(2k+1) = 2(2k^2+k) = 2*(some integer)

Since 2 is a factor of that last expression, this shows that a(a+1) is even when 'a' is even.

-----------

Case B: 'a' is odd

k = some integer

a = 2k+1 = some odd integer

a+1 = (2k+1)+1 = 2k+2

a(a+1) = (2k+1)(2k+2) = 2(2k+1)(k+1) = 2(some integer)

This shows that a(a+1) is even when 'a' is odd.

-----------

Therefore, for any integer 'a', the expression a(a+1) is always even.

Some examples:

-----------

Here's a slightly different way to interpret why the proof works.

a(a+1) consists of factors 'a' and 'a+1'

Either way, we'll have 2 as a factor somewhere in a(a+1).

Answer:

f(2.11) = 13.9867 or 13.99 in²

Step-by-step explanation:

Given the radius ( r ) of 2.11 inches, we can determine the area of a circle by substituting the value of the radius into the following function:

f(r ) = πr²

f(2.11) = π(2.11)²

f(2.11) = π(4.4521)

f(2.11) = 13.9867 or 13.99 in²

Therefore, the area of the circle with a radius of 2.11 inches is 13.99 in².

Among all triangles inscribed in a circle, the equilateral triangle maximizes the product of the magnitudes of its sides.

To prove this statement using Lagrange multipliers, let's consider a triangle inscribed in a circle with sides of lengths a, b, and c. The area of the triangle can be expressed using Heron's formula:

Area = √[s(s-a)(s-b)(s-c)],

where s is the semi-perimeter given by s = (a + b + c)/2. We want to maximize the product of the side lengths a, b, and c, which can be written as P = abc.

To apply Lagrange multipliers, we need to set up the following equations:

∇P = λ∇Area, where ∇P is the gradient of P and ∇Area is the gradient of the area function.

Constraint equation: g(a, b, c) = a^2 + b^2 + c^2 - R^2 = 0, where R is the radius of the inscribed circle.

Taking the partial derivatives and setting up the equations, we get:

∂P/∂a = bc = λ(∂Area/∂a),

∂P/∂b = ac = λ(∂Area/∂b),

∂P/∂c = ab = λ(∂Area/∂c),

a^2 + b^2 + c^2 - R^2 = 0.

From the first three equations, we have bc = ac = ab, which implies a = b = c (assuming none of them is zero). Substituting this back into the constraint equation, we get 3a^2 - R^2 = 0, which gives a = b = c = R/√3.

Therefore, the equilateral triangle with sides of length R/√3 maximizes the product of its side lengths among all triangles inscribed in a circle.

In conclusion, using Lagrange multipliers, we have shown that the equilateral triangle is the triangle that maximizes the product of its side lengths among all triangles inscribed in a circle.

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Answer:

the answer is G G(X)=F(X+2)

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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Answer:

17×6=102 because he gave 2 boxes to his brother so he have 6 boxes

Answer:

y=1/3t

Step-by-step explanation:

For a linear function you can use the formula y=mx+b

m is the slope (also known as the rate of change)

b is the y intercept (the value y is at when x is 0). For this problem the bucket starts out empty so there is no y-intercept that needs to be written in the equation.

To find slope divide the inches of water by the total number of minutes given. 12/36=1/3

Plug your slope and y-intercept into the equation.

y=1/3t+0

Simplify

y=1/3t

Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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Answer:

18 days

Explanation:

To determine the fewest number of days that will pass before both rooms are cleaned again on the same day, we list the multiple of each of the days.

The next multiple 6 and 9 have in common is 18.

Therefore, after 18 days has passed, the two rooms will be cleaned on the same day.

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer:17/20 answer a

Step-by-step explanation:

Greetings from Brasil....

From Pythagoras we have

AB² = AC² + BC²

13² = 12² + X²

Answer:

5 cm

Step-by-step explanation:

Pythagoras theorem gives us:

\(hypotenuse^{2} = side^{2} + side^{2}\)

We know the hypotenuse is 13 cm.

We know one side is 12 cm.

\(13^{2} = 12^{2} + side^{2}\)

\(169= 144 + side^{2}\)

Subtracting 144 from both sides:

\(25 = side^{2}\)

Reversing the sides:

\(side^{2}=25\)

\(\sqrt{side^{2}}= \±\sqrt{25}\)

\(side = \±\sqrt{25}\)

\(side = \±5\)

Since a distance can't be negative:

\(side=5\)

The third side is 5 cm.

Answer: Ksh 6144

Step-by-step explanation:

On Thursday, a fruit vendor bought 1948 oranges on a Thursday and sold 750. The number of oranges left will be: = 1948 - 750 = 1198

On n Friday, he sold 240 more oranges than on Thursday. This means the number of oranges sold is: = 240 + 750 = 990.

The number for f oranges left will then be: = 1198 - 990 = 208

On Saturday, he bought 560 more

oranges, the total oranges that the vendor has now will be:

= 208 + 560 = 768

Since sold all the oranges he had at a price of Ksh. 8 each, the amount if money made will be:

= Ksh 8 × 768

= Ksh 6144

The vendor made Ksh 6144