If events A and B are independent, what must be true?A.) P(AB) = P(B)
B.) P(A/B) = P(A)
C.) P(A) = P(B)
D.) OP(AB) = P(BIA)

Answer:

Option B

Answered by GAUTHMATH

Answer:

V ≈ 615.75

r Radius 7

h Height 4

Answer:

[tex]x=17[/tex]

Step-by-step explanation:

[tex](6x+10)(x+17)(4x-34)[/tex]

[tex]6x+10+x+17+4x-34=180[/tex]

Add:- [tex]6x+x+4x=11x[/tex]

and [tex]10+17-34=-7[/tex]

So, [tex]11x-7=180[/tex]

Add 7 to both sides:-

[tex]11x=187[/tex]

Divide both sides by 11:-

[tex]\frac{11x}{11}=\frac{187}{11}[/tex]

[tex]x=17[/tex]

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Answer:

The expected total amount of time in minutes the operator will spend on the calls each day is of 174.8 minutes.

The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is of 17.4356 minutes.

0.3085 = 30.85% approximate probability that the total time spent on the calls will be less than 166 minutes.

The value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95 is [tex]c = 203.4816[/tex]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

n instances of a normally distributed variable:

For n instances of a normally distributed variable, the mean is:

[tex]M = n\mu[/tex]

The standard deviation is:

[tex]s = \sigma\sqrt{n}[/tex]

Calls to a customer service center last on average 2.3 minutes with a standard deviation of 2 minutes.

This means that [tex]\mu = 2.3, \sigma = 2[/tex]

An operator in the call center is required to answer 76 calls each day.

This means that [tex]n = 76[/tex]

What is the expected total amount of time in minutes the operator will spend on the calls each day?

[tex]M = n\mu = 76*2.3 = 174.8[/tex]

The expected total amount of time in minutes the operator will spend on the calls each day is of 174.8 minutes.

What is the standard deviation of the total amount of time in minutes the operator will spend on the calls each day?

[tex]s = \sigma\sqrt{n} = 2\sqrt{76} = 17.4356[/tex]

The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is of 17.4356 minutes.

What is the approximate probability that the total time spent on the calls will be less than 166 minutes?

This is the p-value of Z when X = 166.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem:

[tex]Z = \frac{X - M}{s}[/tex]

[tex]Z = \frac{166 - 174.8}{17.4356}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085.

0.3085 = 30.85% approximate probability that the total time spent on the calls will be less than 166 minutes.

What is the value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95?

This is X = c for which Z has a p-value of 0.95, so X = c when Z = 1.645. Then

[tex]Z = \frac{X - M}{s}[/tex]

[tex]1.645 = \frac{c - 174.8}{17.4356}[/tex]

[tex]c - 174.8 = 1.645*17.4356[/tex]

[tex]c = 203.4816[/tex]

The value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.95 is [tex]c = 203.4816[/tex]

Answer:

1320 m^2

Step-by-step explanation:

area of ground = π r ^2

= (22/7) × (137/2)^2

= 14,747.0714286 m^2

area of ground and path

=( 22/7)(143/2)^2

= 16,067.0714286 m^2

area of path

=16,067.0714286 -14,747.0714286

= 1320 m^2

note :

r = radius = diameter /2

area of a circle = π r^2

diameter of circle created with path and ground = 137 + 2 × width of path

= 137 + 2× 3 = 143 m

Step-by-step explanation:

8 men can do 60 man days of work by dividing 60 man days by the 8 men, which gives us 60/8 = 7 1/2 da

Answer:

f(g(x)) = 9x^2 + 15x - 6

Step-by-step explanation:

We are using function g(x) = 3x - 1 as the input to function f(x) = x^2 + 7x.

Starting with f(x) = x^2 + 7x, substitute g(x) for x on the left side and likewise substitute x^2 + 7x for each x on the right side.  We obtain:

f(g(x)) = (3x - 1)^2 + 7(3x - 1).

If we multiply this out, we get:

f(g(x)) = 9x^2 - 6x + 1 + 21x - 7, or

f(g(x)) = 9x^2 + 15x - 6

Answer:

7/10

Step-by-step explanation:

Total number = 17+3+8+12 = 40

The ones that are large are 17 and 8

The ones that are blue are 17 and 3

Do not count the 17 twice

P(large or blue) = (17+3+8)/40

                          = 28/40

                         =7/10

Answer:

[tex]15y^9 - 7y^3 + y[/tex]

Nonic polynomial

Step-by-step explanation:

Given

[tex]y - 7y^3 + 15y^9[/tex]

Required

Write in standard form

The standard form of a polynomial is:

[tex]ay^n + by^{n-1} + ......... + k[/tex]

So, we have:

[tex]y - 7y^3 + 15y^9[/tex]

The standard form is:

[tex]15y^9 - 7y^3 + y[/tex]

And the name is: Nonic polynomial (because it has a degree of 9)

Answer:

Remember that for a circle centered in the point (a, b) and with a radius R, the equation is:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the submarine is located at the point (0, 0)

And the radar range has the equation:

2*x^2 + 2*y^2 = 128

You can see that this seems like a circle equation.

If we divide both sides by 2, we get:

x^2 + y^2 = 128/2

x^2 + y^2 = 64 = 8^2

This is the equation for a circle centered in the point (0, 0) (which is the position of the submarine) of radius R = 8 units.

The graph can be seen below, this is just a circle of radius 8.

We also want to see if the submarine's radar can detect a ship located in the point (6, 6)

In the graph, this point is graphed, and you can see that it is outside the circle.

This means that it is outside the range of the radar, thus the radar can not detect the ship.

Answer:

Option D

Only the equation in option D matches with the table

Answered by GAUTHMATH

Answer:  Choice B

Explanation:

Everywhere you see an x, replace it with a+2.

[tex]f(x) = 3(x+5)+\frac{4}{x}\\\\f(a+2) = 3(a+2+5)+\frac{4}{a+2}\\\\f(a+2) = 3(a+7)+\frac{4}{a+2}\\\\[/tex]

Answer:

The probability of success is .12

The probability of failure is .88

According to the binomial theorem the probability of 3 success is

10! / (3! * 7!) * .12^3 * .88^7 = .085

We have [tex]f\left(f^{-1}(x)\right) = x[/tex] for inverse functions [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex]. Then if [tex]f(x) = 2x+5[/tex], we have

[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 5 = x \implies f^{-1}(x) = \dfrac{x-5}2[/tex]

Then

[tex]f^{-1}(8) = \dfrac{8-5}2 = \boxed{\dfrac32}[/tex]

Answer:

The leading coefficient is -8 as it is a mix of x and cardinal, if it was x alone then it wouldn't be the coefficient, we would use the next number shown.

If it was just a number and no x then it would still be the coefficient.

The degree is 9 as it is the highest power shown.

Step-by-step explanation:

See attachment for examples

Answer:

the nullity of a matrix A is the demision of its null space:nullity A = dim (n(A).

Let breadth be x

We know

[tex]\boxed{\sf Area_{(Rectangle)}=Length\times Breadth}[/tex]

[tex]\\ \sf\longmapsto x(x+4)=22[/tex]

[tex]\\ \sf\longmapsto x^2+4x=22[/tex]

[tex]\\ \sf\longmapsto x^2+4x-22=0[/tex]

[tex]\\ \sf\longmapsto x=-2\pm\sqrt{26}[/tex]

It doesnot have any real roots

Answer:

2.31 m

Step-by-step explanation:

with marking down to centimeter length, one can only estimate accurately to the nearest  centimeter or hundredth of a meter.

Answer:2.31 meter

Step-by-step explanation: none

Answer:

was assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

Answer:

70.908 is greater than 7.908 .

I hope your day goes nice

Answer:

both are different because of different placement of point.

Answer:  [tex]-2+\sqrt{3}[/tex]

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

Work Shown:

Apply the following trig identity

[tex]\tan(A - B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)*\tan(B)}\\\\\tan(225 - 60) = \frac{\tan(225)-\tan(60)}{1+\tan(225)*\tan(60)}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+1*\sqrt{3}}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\[/tex]

Now let's rationalize the denominator

[tex]\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\tan(165) = \frac{(1-\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\\tan(165) = \frac{(1-\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{(1)^2-2*1*\sqrt{3}+(\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{1-2\sqrt{3}+3}{1-3}\\\\\tan(165) = \frac{4-2\sqrt{3}}{-2}\\\\\tan(165) = -2+\sqrt{3}\\\\[/tex]

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

As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.

Or you can note how

[tex]\tan(165) \approx -0.267949\\\\-2+\sqrt{3} \approx -0.267949[/tex]

which helps us see that they are the same thing.

Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as [tex]\sqrt{3}-2[/tex] but it's the same as above.

Answer:

2 + 109 = 111

Step-by-step explanation:

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

Answer:

28 units²

Step-by-step explanation:

Area of trapezoid =

2(8 + 4)/2 = 12

Area of rectangle =

2 x 8 = 16

16 + 12 = 28

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

7/12

Step-by-step explanation:

total: 12 roses

white roses: 5

pink roses: 7

fraction of pink roses = 7/12

Answer:

Solution given:

equation is:

x²-40x+A=0

when A=200

equation becomes

x²-40x+200=0

Comparing above equation with ax²+bx+c=0 we get

a=1

b=-40

c=200

x=[tex]\displaystyle \frac{-b±\sqrt{b²-4ac}}{2a}[/tex]

substituting value

x=[tex]\displaystyle \frac{-*-40±\sqrt{(-40)²-4*1*200}}{2*1}[/tex]

x=[tex]\displaystyle \frac{40±\sqrt{800}}{2}[/tex]

x=[tex]\displaystyle \frac{40±20\sqrt{2}}{2}[/tex]

taking positive

x=[tex]\displaystyle \frac{40+20\sqrt{2}}{2}[/tex]

x=34.14

taking negative

x=[tex]\displaystyle \frac{40-20\sqrt{2}}{2}[/tex]

x=5.86

[tex]\\ \rm\longmapsto cot40=\dfrac{7.6}{EF}[/tex]

[tex]\\ \rm\longmapsto EF=\dfrac{7.6}{cot40}[/tex]

[tex]\\ \rm\longmapsto EF=\dfrac{7.6}{1.19}[/tex]

[tex]\\ \rm\longmapsto EF=6.38units[/tex]

Answer:

[tex]\displaystyle 6,38\:units[/tex]

Step-by-step explanation:

You would set your proportion up like so:

[tex]\displaystyle \frac{7,6}{EF} = cot\:40° \\ \\ 7,6 = EFcot\:40° → 6,3771571969... = \frac{7,6}{cot\:40°} \\ \\ 6,38 ≈ EF[/tex]

I am joyous to assist you at any time.

Answer:

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Answer:

The area of a triangle is:

Area = 1/2(bh)

Area = 1/2(70)

Area = 35 square inches

Let me know  if this helps!