If events A and B are independent, what must be true?

P(A|B) = P(B)
P(A|B) = P(A)
P(A) = P(B)
P(A|B) = P(B|A)

An x-intercept of the continuous function in the table is (-1, 0)

The x-intercept of a line is the point where the line crossed the x-axis or the  point where the value of y is zero.

From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)

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The volume of the cylinder will be equal to 1017.87 cubic feet.

Volume is defined as the space occupied by any object in the three-Dimensions. For the cylinder, the volume will be calculated by radius and the height of the cylinder.

Given that:-

The volume of the cylinder will be calculated by using the formulas below:-

V = πr²h

V = π ( 9 )² 4

V = 1017.87 cubic feet.

Therefore the volume of the cylinder will be equal to 1017.87 cubic feet.

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Answer:

Step-by-step explanation:

From the information,we get:

Two stacks of books together are = 7 1/2 inches tall.

One stack is given,that is = 4 3/4 inches.

To Find:

Solution:

Let us assume that the other height of the book be x.

Then the equation will be:

[tex] 4\cfrac{3}{4} + x = 7\cfrac{1}{2} [/tex]

Convert the mixed fractions to fractions:

[tex] \implies \: \cfrac{19}{4 } + x = \cfrac{15}{2} [/tex]

Subtract 19/4 from both sides:

[tex] \implies \: x + \cfrac{19}{4} - \cfrac{19}{4} = \cfrac{15}{2} - \cfrac{19}{4} [/tex]

[tex] \implies \: x = \cfrac{11}{4} =\boxed{ 2 \cfrac{3}{4} \rm \: inches}[/tex]

Hence, we can conclude that:

The height of the other book is 2 3/4 inches.

The probability that a student is a female or major in civil engineering is 62%

At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?

Let A represent Female and B represents civil engineering.

The above representation means that the given parameters are:

The required probability is calculated as:

P(A or B) = P(A) + P(B) - P(A and B)

This gives

P(A or B) = 49% + 21% - 8%

Evaluate

P(A or B) = 62%

Hence, the probability that a student is a female or major in civil engineering is 62%

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Answer:

Add 3 to both sides

Property: Addition property of equality

Step-by-step explanation:

Action: Add 3 to both sides.

⇒ x - 3 =               12

(cancel out)+ 3     + 3

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

     x    =        15  

The property used:

→ equation is true and the same #is added to each side the resulting equation is true. for any #s a,b,c,if a=b then a+c=b+c.

After 15 seconds rocket reaches to maximum height is 225 units.

Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.

Here, the given equation of height

            h(t) = -t² + 30t

             y = -t² + 30t

Now, on differentiating both side with respect to t, we get

        dy/dt = -2t + 30

put dy/dt = 0, we get

       0 = -2t + 30

        2t = 30

        t = 15

Now, at t = 15 sec. rocket reach at its maximum height.

maximum height at t = 15 sec is

     h(15) = -(15)² + 30(15)

     h(15) = -225 + 450

    h(15) = 225

Thus, after 15 seconds rocket reaches to maximum height is 225 units.

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Hi student, let me help you out! :)

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

We are asked to factor out the GCF in the expression

[tex]\star~\star\mathrm{6x^3+3x}~\star~\star[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So let's divide.

But first. we should work out the GCF.

Both terms have 3x in common, so we divide both terms by 3x:

[tex]\mathrm{6x^3+3x}[/tex]

[tex]\mathrm{3x(2x^2+1)}[/tex]

To ensure that we've factored correctly, we can always use the distributive property, distribute 3x and see whether or not we end up with [tex]\mathtt{6x^3+3x}[/tex].

So the answer is

[tex]\mathrm{3x(2x^2+1)}[/tex]

Notice I put parentheses around 2x²+1. This indicates that 3x is multiplied times both 2x² and 1.

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

The coordinates, to the nearest tenth, of the relative maximum of the graph is (-1.8,13.2)

The equation of the function is given as:

y = x^3 + x^2 – 6x + 5

Next, we plot the graph of the function (see attachment)

From the attached graph, we have the relative maximum to be at:

(x,y) = (-1.8,13.2)

Hence, the coordinates, to the nearest tenth, of the relative maximum of the graph is (-1.8,13.2)

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Answer:

18 inches = 1.5 feet

8 inches = 2/3 foot

y = 1.5 + (2/3)x

Answer:

B

Step-by-step explanation:

A right triangle must have one of its 3 angles equal to 90°

the only triangle with an angle of 90° is Triangle C

Answer:

B:Triangle

Step-by-step explanation:

The length of the intervals of the given frequency table is

500 ft.

The given list shows the lengths in feet of the 25 longest bridges in the United States.

we have to determine the median and mode of the bridge data.

The median is the middle number of the data set arranged in ascending order.

1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260.

The median is 1750.

Mode is the number that appears most often in the data set.

1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260

The mode is 1600.

Therefore the correct option is Median: 1750, Mode: 1600

So the length of the intervals of the given frequency table is

500 ft.

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[tex]\text{Nth term of an arithmetic series} = a +(n-1)d \\\\\text{Nth term of an geometric series}= ar^{n-1}\\\\\text{where,}\\\\\text{a = first term.}\\\\\text{d = common difference.}\\\\\text{r = common ratio.}[/tex]

Step-by-step explanation:

Scale factor red to blue meaning 42 to 7

42÷7=6

Scale factor is 6

Perimeter of the blue quadrilateral = ?

If perimeter of red = 204

Then we use this following proportion

[tex]204 \div 42 = x \div 7[/tex]

[tex] \frac{204}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=7×204

42x=1428

x=34

Area of the blue quadrilateral = ?

If area of the red quadrilateral = 2880

Then we use the following proportion

[tex]2880 \div 42 = x \div 7[/tex]

[tex] \frac{2880}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=2880×7

42x=20160

x=480

Answer:

see the attachment photo!

Answer:

Answer: -3/2

Step-by-step explanation:

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for an angle of 780°, we can say that is really a 360° + 360° + 60°, so two full revolutions plus an extra 60°. Check the picture below, with the coterminal in green.

The advantages and disadvantages of the kind of technology we have access to in the early 21st century include:

Advantages:

The improvement of productivity.

Better and easier communication between people.

Disadvantages:

Can be bad for the environment.

Technology might be able to replace humans in jobs.

Technology is the result of accumulated knowledge and the application of skills, and processes used in industrial production and scientific research.

Technology is embedded in the operation of all machines for the intended purpose of an organization.

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Answer:

√121 = 11

Explanation:

11 × 11 = 121

Answer:

11

Step-by-step explanation:

The square root of 121 is 11.

= 11*11 = √(121)

= 121 = 11

done

Answer:

Step-by-step explanation

Sorry but your answer is a fake question which I can't answer

Answer:

Yes, x = 0 is a solution to the given equation

Step-by-step explanation:

Hi Student!

The goal of this question is to determine x = 0 is a solution of the expression that was provided.  The first step that we must take is input 0 into all of the x's that we have in the expression.  Then we just simplify both sides and determine if the end expression is true and if it is then x = 0 is a solution.

Plug in the values

Simplify both sides

Looking at the final expression, we can see that 1 is indeed equal to 1 and since the expression is true, we can say that x = 0 is a solution of the expression that was provided in the problem statement.

Answer:

none of the above

Step-by-step explanation:

4x + 7 = x + 2

4x - x + 7 = x - x + 2

3x + 7 = 2

3x + 7 - 7 = 2 - 7

3x = -5

3x / 3 = -5 / 3

x = -5 / 3 = -1.667

5x - 8 = x + 4

5x - x - 8 = x - x + 4

4x - 8 + 8 = 4 + 8

4x = 12

4x / 4 = 12 / 4

x = 3

3x + 2 = 5x + 2

3x - 5x + 2 = 5x - 5x + 2

-2x + 2 = 2

-2x + 2 - 2 = 2 - 2

-2x = 0

x = 0

Integers, As a whole number that can be written without a remainder,

x = 3

x = 0

(Mixed) Fraction

x = -5 / 3 = -1.667

Nani wait what I don't know

Answer:

I think maybe u=6.71 but I'm not sure. wait for another answer

Some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.

Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a experiment. To avoid any ambiguity or surprise, a experiment must be properly defined.

A) Because human experimentation is immoral, animal research has been employed as a research approach.

However, using animals is unethical because they are subjected to unpleasant and hazardous procedures, as well as stress and injury. The use of non-animal methods to substitute animal methods as much as possible will provide both ethical and technical benefits. Researchers should make the use of non-animal methods for a top priority experiments.

B) Even though the purpose of an experiment is to ensure success in rabbits, this is incorrect in people because action is what will operate properly.

The absence of thyroid-stimulating hormone in rabbit serum is a mistaken notion. As a result, it is preferable to test the drug further, and it was a success. As a result, there will be no dysfunctionality for humans.

Thus, some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.

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The total area with land based on the information given is 3x² + 60x.

Let the width = x

Let the length = (1.5 × x) = 1.5x

Area = 1.5x × x = 1.5x²

The area along with land:

Width = x + 20

Length = 3 × x = 3x

The total area with land:

= Length × Width

= 3x(x + 20)

= 3x² + 60x.

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The solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

The figure is not given;

However, the question can still be solved without it

The given parameters are:

a = 31, b = 23, and c = 20

Calculate angle A using the following law of cosine

a² = b² + c² - 2bc * cos(A)

So, we have:

31² = 23² + 20² - 2 * 23 * 20 * cos(A)

Evaluate

961 = 929 - 920 * cos(A)

Subtract 929 from both sides

32 =- 920 * cos(A)

Divide both sides by -920

cos(A) = -0.0348

Take the arc cos of both sides

A = 92.0

Calculate angle B using the following law of sine

a/sin(A) = b/sin(B)

So, we have:

31/sin(92) = 23/sin(B)

This gives

31.0189 = 23/sin(B)

Rewrite as:

sin(B) =23/31.0189

Evaluate

sin(B) =0.7415

Take arc sin of both sides

B = 47.9

Calculate angle C using:

C = 180 - 92.0 - 47.9

Evaluate

C = 40.1

Hence, the solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

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Answer:

A graph shows zeros to be ±3. Factoring those out leaves the quadratic

 (x-2)² +1

which has complex roots 2±i.

The function has roots -3, 3, 2-i, 2+i.

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

The function is :

f(x) = x⁴ - 4x² - 5

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

Plotting on a graph :

⇒ Once plotted on graph, check where the line of the function intersects the x-axis

⇒ Those will be the zeros of the function

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

Solution :

⇒ x = -2.236

⇒ x = 2.236

Answer:

  d

Step-by-step explanation: