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Use the probability distribution table to answer the question.

What is P(X ≥ 2)?



Enter your answer, as a decimal, in the box.

Answer:

D

Step-by-step explanation:

The arcsine ([tex]\sin^{-1}[/tex]) function of x is defined as the inverse sine function of x when -1≤x≤1.

So, when

[tex]-4\le x\le 4,[/tex]

we have that

[tex]-1\le \dfrac{1}{4}x\le 1.[/tex]

This gives us the domain [tex]-4\le x\le 4[/tex] of the function [tex]y=\sin^{-1}\left(\dfrac{1}{4}x\right).[/tex]

The range of the function [tex]y=\sin^{-1}x[/tex] is [tex]-\dfrac{\pi }{2}\le x\le \dfrac{\pi }{2},[/tex] so the range of the function [tex]y=\sin^{-1}\left(\dfrac{1}{4}x\right)[/tex] is the same (options A and C are false).

When x=-4,

[tex]y=\sin^{-1}\left(\dfrac{1}{4}\cdot (-4)\right)=\sin^{-1}(-1)=-\dfrac{\pi}{2}.[/tex]

So, option B is false and option D is true.

Answer:

  B) [tex]\left[\begin{array}{cc}1&0\\0&-1\end{array}\right][/tex]

Step-by-step explanation:

When the coordinates are represented by a column vector, the vertical reflection transformation (x, y) ⇒ (x, -y) looks like the matrix of answer choice B.

Answer:

Shift to the right 3 units.

Answer:

Shift to the right 3 units

Step-by-step explanation:

Translations are a type of rigid transformation of functions, in which the position of the graph of a function is modified. The general form of the graph of a function moves up, down, left, or right.

Vertical translations:

Let:

[tex]a >0[/tex]

[tex]y=f(x)+a[/tex]  shifts the graph [tex]a[/tex] units up

[tex]y=f(x)-a[/tex] shifts the graph [tex]a[/tex] units down

Horizontal translations:

Let:

[tex]b>0[/tex]

[tex]y=f(x+a)[/tex] shifts the graph [tex]b[/tex] units to the left.

[tex]y=f(x-a)[/tex] shifts the graph [tex]b[/tex] units to the right.

Using the previous information we can conclude that the function:

[tex]f(x-3)[/tex]

Is a Horizontal translation in which the graph was shifted [tex]b=3[/tex] units to the right.

[tex]f(x-3)=(x-3)^3[/tex]

I leave you the graphs, so you can corroborate the answer easily.

Answer:

Step-by-step explanation:

(1)

[tex]a_i = a_{i-1} + 1[/tex]

(2)

The initial condition is [tex]a_1 = 1[/tex]

(3)

Infinitely many.

a) The recurrence relation is sₙ = sₙ₋₁ + sₙ₋₂ + ... + s₂ + s₁.

b) the initial condition s₂ = 1.

c) Clearly the solution to this recurrence relation and initial condition is sₙ = 2n-2 for all n >= 2.

Here, we have,

Let sₙ be the number of such sequences.

A string ending in n must consist of a string ending in something less than n, followed by an n as the last term.

Therefore the recurrence relation is sₙ = sₙ₋₁ + sₙ₋₂ + ... + s₂ + s₁.

This is equivalent to sₙ = 2sₙ-1.

b) We need two initial conditions if we use the second formulation above, s₁ = 1 and s₂ = 1.

There's one sequence which ends in 1,

and there is only the sequence 1,2 ending in 2.

If we use the first formulation above, then we can get by with just the initial condition s₂ = 1.

c) Clearly the solution to this recurrence relation and initial condition is sₙ = 2n-2 for all n >= 2.

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Answer:

 I think its B

The outcomes which are in A or B are Tokyo, Houston, New York, Tijuana and Canada.

An event is defined as something that occurs or is perceived to occur; an occurrence, especially one of some significance.

In the table it is clearly visible:

Event A = Tokyo, Houston, New York, Tijuana

Event B =  Houston, New York, Tijuana and Canada

We have to choose outcomes which are either in A or in B

Hence the outcomes are Tokyo, Houston, New York, Tijuana and Canada.

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Answer:

b = 9 1/6

Step-by-step explanation:

b + 5/6 = 10

Subtract 5/6 from each side

b + 5/6 -5/6= 10-5/6

b = 10 -5/6

Borrow 1 from the 10 in the form of 6/6

b = 9 +6/6 - 5/6

b = 9 +1/6

b = 9 1/6

Answer:

D

Step-by-step explanation:

The question is on negative exponents

Given that;

F(x)=2^x

From the general formulae a^-n =1/a^n

Hence

F(-4)= 2⁻⁴

F(-4)= I/ 2⁴

=1/16

Answer:

H(t)= -16t^2+40t+1.2

Step-by-step explanation:

H(t) = -16t^2 + vt + s

I hope this is what you were looking for.

p/2=7.74

This was a trick question. P is the variable that represents the total cost of the pizza. To normally find the total cost of pizza using the cost each of the two people spent, you would simply multiply 7.74*2=p. Since that wasn’t in the choices, you can divide by two on each side to get p/2=7.74.

Answer:

D

Step-by-step explanation:

Answer:

Answer 2

Step-by-step explanation:

We start with (log to the base x of 8) = y and want to find the value of y.

Obviously the base here is x.

Therefore,

 (log to the base x of 8)            y

x                                           =  x

The quantity on the left side of this equation simplifies to 8.

                                 y

Then we have 8 = x

We'll need to solve this equation for y.  To do so, take the common log of both sides, obtaining:

                                               log 8

log 8 = y log x, so that   y =  -----------    This corresponds to given answer 2.

                                                 log x

Answer:

10 cm

Step-by-step explanation:

Answer:

10 cm

Step-by-step explanation:

Since, the volume of a cuboid is,

V = l × w × h,

Where,

l = length,

w = width,

h = height,

∵ The shape of the aquarium must be cuboid,

We have, l = 20 cm, w = 12 cm, V = 2400 cm³,

By substituting the values,

2400 = 20 × 12 × h

2400 = 240h

[tex]\implies h = \frac{2400}{240}=10[/tex]

Hence, the height of the water in Nemo's aquarium would be 10 cm.

Convert to cylindrical coordinates:

[tex]x=x[/tex]

[tex]y=r\cos\theta[/tex]

[tex]z=r\sin\theta[/tex]

Then [tex]E[/tex] is the set of points [tex](r,\theta,x)[/tex] such that [tex]0\le r\le1[/tex], [tex]0\le\theta\le2\pi[/tex], and [tex]7y^2+7z^2\le x\le7[/tex] or [tex]7r^2\le x\le7[/tex].

Now

[tex]\displaystyle\iiint_E5x\,\mathrm dV=5\int_0^{2\pi}\int_0^1\int_{7r^2}^7xr\,\mathrm dx\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{245\pi}3}[/tex]

To evaluate the triple integral, convert to cylindrical coordinates and use the given bounds. Plug in the limits of integration and calculate the integral.

To evaluate the triple integral ∫ 5x dv, where E is bounded by the paraboloid x = 7y^2 + 7z^2 and the plane x = 7, we can use cylindrical coordinates. Let's express x in terms of y and z:

x = 7y^2 + 7z^2

Substitute this expression for x in the integral:

∫5x dv = ∫35(y^2 + z^2) dv

Now, convert the integral to cylindrical coordinates:

∫35(r^2sin(θ)rdrdθdz

Since the region E is bounded by x = 7, the limits of integration for r and z are 0 to 7. For θ, the limits are 0 to 2π. Plug in these limits and evaluate the triple integral to find the answer.

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Answer:

D

Step-by-step explanation:

The ⅓ power means cube root.

5^⅓ = ∛5

Answer D.

Answer: Option D

[tex]3m-\frac{4}{3}-\frac{2}{m}[/tex]

Step-by-step explanation:

The initial expression is:

[tex]\frac{9m^2 - 4m - 6}{3m}[/tex]

The first step is:

[tex]\frac{9m^2}{3m} - \frac{4m}{3m} - \frac{6}{3m}[/tex]

Now we must simplify the 3 fractions.

We know that by properties of the division of exponents of the same base:

[tex]\frac{a^n}{a^h}= a^{n-h}[/tex]

Then for the expression:

[tex]\frac{9m^2}{3m}[/tex]

In this case

[tex]a=m\\n=2\\h=1[/tex]

[tex]\frac{9m^2}{3m} = 3m^{2-1}=3m[/tex]

Then for the expression:

[tex]\frac{4m}{3m}[/tex]

[tex]a=m\\n=1\\h=1[/tex]

[tex]\frac{4m}{3m}= \frac{4}{3}m^{1-1}=\frac{4}{3}[/tex]

Then for the expression:

[tex]\frac{6}{3m}[/tex]

[tex]a=m\\n=0\\h=1[/tex]

[tex]\frac{6}{3m}=\frac{2}{m}[/tex]

Finally

[tex]\frac{9m^2}{3m} - \frac{4m}{3m} - \frac{6}{3m}=3m-\frac{4}{3}-\frac{2}{m}[/tex]

Answer:

The last choice is your answer

Step-by-step explanation:

Plot your point in an x/y coordinate plane.  We are in QII where x is negative and y is positive.  From that point, if you drop an altitude to the negative x axis, you have a right triangle with a base measure of -2, a height of 5 and a hypotenuse that is unknown as of right now.  We will find it using Pythagorean's Theorem.  [tex]5^2+(-2)^2=c^2[/tex]

The length of the hypotenuse is √29.  That means that the cosine of that angle is the side adjacent over the hypotenuse.  Rationalizing the denominator gives us [tex]-\frac{2\sqrt{29} }{29}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Reflection because it's one of them

Answer:

The answer is AB.

Choice D.

Step-by-step explanation:

We are given four blood types and the number of females and males having each of the blood type. We are to determine the blood type that is independent of the gender.

It is evident that the disparity in the number of males and females in the blood types A, B and O is large.

Only in the blood type AB, the difference is very small. The number of males and females having AB blood type is more or less same. So, we can conclude that blood type AB is independent of gender.

Answer:

B

Step-by-step explanation:

The study doesn't prove a causation, only a correlation.  So we can conclude that cities with good air quality do not have traffic jams.

Answer:

Step-by-step explanation:

If an environmental organization releases a report where they state that the cities with the worst traffic jams have the worst air pollution, then we can deduct from this conclusion its anti-thesis, which is the cities without traffic jams have better air quality.

We deduct this because the given statement is a relation between two variables: traffic jam and air pollution. When we set a relationship between variable and we draw a conclusion, we have to determine all the deduction that can be made, like in this case.

Basically, the given relationship between variables is directly proportional, the more traffic jams, the more air pollution. Which also can be stated as the less traffic jams, the less air pollution.

Therefore, the conclusion that describes best the conclusion draw from the study is B. Cities with good air quality do not have traffic jams.

Answer:

[tex]72\pi\ in^{3}[/tex]

Step-by-step explanation:

step 1

Calculate the volume of the cylinder (flower vase)

The volume is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=6/2=3\ in[/tex] -----> the radius is half the diameter

[tex]h=12\ in[/tex]

substitute the values

[tex]V=\pi (3)^{2}(12)=108\pi\ in^{3}[/tex] ------> exact value

step 2

Calculate  2/3 of the volume

[tex]V=(2/3)108\pi=72\pi\ in^{3}[/tex]

Answer:

$12.50

Step-by-step explanation:

she has $100. 3/4 of that would be $75. what she has left would be $25. half of that would be $12.50. so she has $12.50 left.

C because it would be the best amount

Answer:

d

Step-by-step explanation:

Answer:

V = 6, E = 9, F = 5 is the answer

The relation between vertices, edges, and faces is F + V = E + 2.

You have to count the faces, vertices and edges of a polyhedron.

A polyhedron is a 3-dimensional solid made by joining together polygons. Face: The flat surfaces that make up a polyhedron

Edges: It is a line segment formed when two faces meet up.

Vertices: It is the point of intersection of the edges of the polyhedron. Taking an example of Tetrahedron.

It has 4 faces, 4 vertices and 6 edges. Recall Euler's formula which states  F + V = E + 2

where F, V, and E represent the number of faces, edges, and vertices of the polyhedron respectively. Verifying the Euler's formula for tetrahedron F = 4V = 4E = 6

so 4 + 4 = 6 + 2

Hence we can verify the Euler's formula.

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Answer:

Left ends is +ve infinity and Right end is -ve infinity. however both tends to be infinity.

Step-by-step explanation:

Let us under stand the basics of determining the end behavior of a graph , by just analyzing the degrees and coefficient of a polynomial.Please refer to the image we have shared with this for a better understanding also.

The rule is bifurcated in two broad category and and two sub category in them.

Category .

The nature of degree (Even / Odd )

Subcategory .

The coefficient of term containing degree ( Negative/Positive )

Rule 1 :

Degree : Even

If coefficient is

Rule 1(a) : Positive ⇒Both ends are towards +ve infinity

Rule 1(b) : Negative⇒Both ends are towards -ve infinity

Rule 2 :

Degree : Odd

If coefficient is

Rule 2(a) : Positive ⇒ Left ends is -ve infinity and Right end is +ve infinity

Rule 2(b) : Negative ⇒ Left ends is +ve infinity and Right end is -ve infinity

Let us see our function f(x) = [tex]-2x^3 + 3x[/tex] now

Here

Degree is 3 which is Odd

Its coefficient is (-2) which is negative

Hence we go to rule 2(b)

That is the Left ends is +ve infinity and Right end is -ve infinity. however both tends to be infinity.

Answer:

A

Step-by-step explanation:

Given a sinusoidal function (sine function or cos function) in the form

y = A Cos (Bx), we can say that A is the amplitude.

Amplitude defines the function's maximum and minimum.

The maximum of this form of function is A and the minimum is -A.

The function given is y = -Cos(8x), so A is -1

Thus, maximum value is 1 and minimum value is -1.

Correct answer is A

Answer:

The sigma notation of the series is 8∑n=2 [1/2(1/2)^n-2]

Step-by-step explanation:

* Lets revise the meaning of sigma notation

- A series can be represented in a compact form, called summation or

 sigma notation.

- The Greek capital letter, ∑ , is used to represent the sum.

# Ex:

- The series 4 + 8 + 12 + 16 + 20 + 24 can be expressed 6Σ(n=1) 4n  

- The expression is read as the sum of 4n as n goes from 1 to 6

- The coefficient of n is 4 because the common difference is 4

- The variable n is called the index of summation.

# Look to the attached figure to more understand

* Now lets solve the problem

∵ The series is 1/2 + 1/4 + 1/8 + ........... + 1/128 and n = 2

- There is a constant ratio between each to consecutive terms

∴ The series is geometric

∴ a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , ..........

∵ an = a(r)^n-1, where a is the first term, r is the common ratio and n

  is the position of the number in the series and the first n is 1

∵ 1/4 ÷ 1/2 = 12 , 1/8 ÷ 1/4 = 1/2

∴ The constant ratio is 1/2

∵ The first term is 1/2

∵ The last term is 1/128

∵ 1/128 = 1/2^7

∴ 1/128 = (1/2)^7

- There are seven terms in the sequence

∵ The n of the first term is 2

∴ The n of the last term = 7 + 1 = 8

* Now lets write the sigma notation

∴ 8∑n=2 [1/2(1/2)^n-2] ⇒ put them like the attached figure

- To generate the terms of the series given in sigma notation above,

  replace n by 2 , 3 , 4 , 5 , 6 , 7 , 8

Answer:

[tex]\large\boxed{a=4\sqrt3}[/tex]

Step-by-step explanation:

We have the triangle 30° - 60° - 90°.  In that triangle sides are in proportion

1 : √3 : 2 (look at the picture).

We have

[tex]a\sqrt3=12[/tex]         multiply both sides by √3   (use √a · √a = a)

[tex]3a=12\sqrt3[/tex]       divide both sides by 3

[tex]a=4\sqrt3[/tex]

[tex]b=2a\to b=2(4\sqrt3)=8\sqrt3[/tex]

Answer: Option A

The Amplitude is

[tex]A = \frac{1}{2}[/tex]

Then the period is

[tex]\frac{2}{3}\pi[/tex]

Step-by-step explanation:

The general sine function has the following form  

[tex]y = Asin(bx) + k[/tex]

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.  

[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

In this case we have the following function

[tex]f(t)=\frac{1}{2}sin(3t)[/tex]

Thus:

[tex]b=3[/tex]

Then the period is

[tex]\frac{2\pi}{3}=\frac{2}{3}\pi[/tex]

The Amplitude is

[tex]A = \frac{1}{2}[/tex]

The answer is Option A

Answer:

a. amplitude: [tex]\displaystyle \frac{1}{2};[/tex]period: [tex]\displaystyle \frac{2}{3}\pi[/tex]

Explanation:

[tex]\displaystyle f(t) = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{3}\pi \\ Amplitude \hookrightarrow \frac{1}{2}[/tex]

With the above information, you now should have an idea of how to interpret graphs like this.

I am joyous to assist you at any time.

Answer:

A square root is a number that produces a specific quantity when multiplied by itself.

Step-by-step explanation:

For example, 9 is the square root of 81, as 9*9=81

Answer:

a number which produces a specified quantity when multiplied by itself.

Step-by-step explanation:

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