Suppose that the probability of event A is 0.4 and the probability of event B is 0.5. What is P A B ( ) ? if A and B are mutually exclusive? What is P A B ( ) ? if A and B are independent?

Answer:

Step-by-step explanation:

\(\angle R+\angle S+ \angle T =180\)       (angle sum of a triangle is 180°)

\(2x+11+3x+23+x+42=180\)

                              \(6x+76=180\)

                                      \(6x=104\)

                                        \(x=17.667\)

\(\text{So we get: } \angle R= 46.33,\angle S=76,\angle T=59.667\)

In ascending order:

   \(\angle R= 46.33,\angle T=59.667,\angle S=76\)

Answer:

x≤1

Step-by-step explanation:

sqrt( 3-2x) ≥ zero

3-2x  ≥ zero

3 ≥ 2x

3/2 ≥ x

x ≤ 3/2

sqrt( 1-x) ≥ zero

1-x ≥ zero

1 ≥ x

x ≤ 1

We need the more restrictive domain since we are adding the two functions

x≤1

Therefore, the maximum displacement of the particle is 4 units, and it occurs at time t = 1.

To find the maximum displacement, we need to first determine the particle's velocity and acceleration.

The velocity of the particle is given by the derivative of its position function:

\(v(t) = y'(t) = 3t^2 - 12t + 9\)

The acceleration of the particle is given by the derivative of its velocity function: a(t) = v'(t) = 6t - 12

Now, to find the maximum displacement, we need to find the time at which the particle comes to rest.

This occurs when its velocity is zero:

\(3t^2 - 12t + 9 = 0\)

Simplifying this equation, we get:

\(t^2 - 4t + 3 = 0\)

This quadratic equation factors as:

(t - 1)(t - 3) = 0

So the particle comes to rest at t = 1 or t = 3.

Next, we need to determine whether the particle is at a maximum or minimum at each of these times.

To do this, we look at the sign of the acceleration:

When t = 1, a(1) = 6(1) - 12 = -6, which is negative.

Therefore, the particle is at a maximum at t = 1.

When t = 3, a(3) = 6(3) - 12 = 6, which is positive.

Therefore, the particle is at a minimum at t = 3.

Finally, we need to find the displacement of the particle at each of these times:

\(y(1) = 1^3 - 6(1)^2 + 9(1) = 4\)

\(y(3) = 3^3 - 6(3)^2 + 9(3) = 0.\)

For similar question on displacement.

https://brainly.com/question/1581502

#SPJ11

Answer:

Solve for √3−2x.

√3−2x=4√x

To remove the radical on the left side of the equation, square both sides of the equation.

√3−2x²=(4√x)²

Simplify each side of the equation.

3−2x=16x

Solve for x.

=> x=16

Step-by-step explanation:

Answer:

x = \(\frac{1}{6}\)

Step-by-step explanation:

Given

\(\frac{\sqrt{3-2x} }{\sqrt{4x} }\) = 2 ( square both sides )

\(\frac{3-2x}{4x}\) = 4 ( multiply both sides by 4x )

3 - 2x = 16x ( add 2x to both sides )

3 = 18x ( divide both sides by 18 )

\(\frac{3}{18}\) = x , that is

x = \(\frac{1}{6}\)

It’s discriminant is zero, so it has one real solution statement is true for  x²-2x +1=0.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x²+1=2x

This can also be written as x²-2x +1=0

a=1, b=-2 and c=1

The expression b² − 4ac is called the discriminant, and can be used to determine whether the solutions are real, repeated, or complex.

(-2)² − 4(1)(1)=4-4

b² − 4ac= 0

A discriminant of zero indicates that the quadratic has a repeated real number solution.

It’s discriminant is zero, so it has one real solution.

Hence, It’s discriminant is zero, so it has one real solution statement is true for  x²-2x +1=0.

To learn more on Quadratic equation click:

https://brainly.com/question/17177510

#SPJ1

Answer: x = 5 or x = -4

Step-by-step explanation:

Given equation

x² - x = 20

Subtract 20 on both sides

x² - x - 20 = 0

Cross factorize the equation

x          -5

x          4

Factorize the equation

(x - 5) (x + 4) = 0

\(\boxed{x=5}\) or \(\boxed{x=-4}\)

Hope this helps!! :)

Please let me know if you have any questions

Events that have no outcomes in common  are said to be disjoint or mutually exclusive.

Two sets are known to be mutually exclusive when they have no common elements. Mutually exclusive events are those that cannot take place at the same moment.

If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero.

Set A = {2, 4, 6, 8, 10, 12, 14, 16}

Set B = {1, 3, 5, 7, 9, 11, 13, 15}

A and B do not have any numbers in common, so P (A ∩ B) = 0. Therefore, A and B are mutually exclusive.

To know more about Probability

https://brainly.com/question/15583528

#SPJ4

The ball will need to travel 126 feet since it will be dropped from a height of 6 feet and then bounce 10/11 feet.

A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

2*{6/(1-10/11)}-6

2*(6/1/11)-6

2*6*11-6

required distance=126 feet

The required distance will be 126 feet as the ball is dropped from 6 feet and rebounds 10/11 of the distance.

To know more about division,

https://brainly.com/question/28598725

#SPJ4

Answer:

She will save \(\$24.44\) by driving.

Step-by-step explanation:

Given: Jocelyn lives in Granite Falls. She wants to visit Megan in Spokane Valley. She can fly from Seattle to Spokane for \(\$96.20\) round trip or she can drive a total of \(650\) miles round trip. If her car gets \(25\) miles per gallon, and gas costs \(\$2.76\)/gallon.

To find: how much money will she save by driving?

Solution:

The total cost for flying Seattle to Spokane is \(\$96.20\).

Now, in order to find how much money will she save by driving, we need to first find the total cost for driving a total of \(650\) miles round trip.

So, total distance \(=650\) miles.

Car covers \(25\) miles per gallon.

So, to cover \(650\) miles, \(\frac{650}{25} =26\) gallons of gas is required.

Now, gas costs \(\$2.76\)/gallon.

Therefore, total charge \(=26\times2.76=\$71.76\).

So, total money saved\(=\$96.20-\$71.76=\$24.44\)

Hence, she will save \(\$24.44\) by driving.

Answer:

it was viewed as the perfecto spot for trade

Answer:

a

Step-by-step explanation:

Answer:

choice 2

Step-by-step explanation:

a translation is just a copy from one location to another

a) 0 fraudulent records need to be resampled if we would like the proportion of fraudulent records in the balanced data set to be 20%.

b) 1600 non-fraudulent records need to be set aside if we would like the proportion of fraudulent records in the balanced data set to be 20%?

(a) How many non-fraudulent records need to be set aside if we would like the proportion of fraudulent records in the balanced data set to be 20%

Ans - 0

(b) How many non-fraudulent records need to be set aside if we would like the proportion of fraudulent records in the balanced data set to be 20%?

Ans 1600

Therefore, fraudulent records is 400 which 4% of 10000 so we will not resample any fraudulent record.

To balance in the dataset with 20% of fraudulent data we need to set aside 16% of non-fraudulent records which is 1600 records and replace it with 1600 fraudulent records so that it becomes 20% of total fraudulent records

Learn more about fraudulent here;

https://brainly.com/question/32930891

#SPJ4

Complete Question:

6. Suppose we are running a fraud classification model, with a training set of 10,000 records of which only 400 are fraudulent.

a) How many fraudulent records need to be resampled if we would like the proportion of fraudulent records in the balanced data set to be 20%?

b) How many non-fraudulent records need to be set aside if we would like the proportion of fraudulent records in the balanced data set to be 20%?

The least-squares regression line equation better predicts the y-value for the point (10, 14) for this dataset.

It should be noted that to determine which regression equation better predicts the y-value for the point (10, 14), we need to evaluate the y-values predicted by each equation at x=10 and compare them.

For the median-median line equation, when x=10:

y = 1.4x + 2.6

y = 1.4(10) + 2.6

y = 16 + 2.6

y = 18.6

For the least-squares regression line equation, when x=10:

y = 0.9x + 4.2

y = 0.9(10) + 4.2

y = 9 + 4.2

y = 13.2

Comparing these two predicted y-values, we see that the least-squares regression line predicts a y-value of 13.2, while the median-median line predicts a y-value of 18.6. Therefore, we can conclude that the least-squares regression line equation better predicts the y-value for the point (10, 14) for this dataset.

Learn more about regression on

https://brainly.com/question/25987747

#SPJ1

The answer is D. 95th percentile is not needed for constructing a box-plot.

A box plot, also known as a box-and-whisker plot, provides a visual representation of the distribution of a dataset. It consists of several key measures, including the following:

A. First quartile (Q1): This is the 25th percentile, which marks the lower boundary of the box.

B. 50th percentile: This is the median, which is the middle value of the dataset when it is ordered from smallest to largest. It is represented by a line within the box.

C. 75th percentile (Q3): This is the upper quartile, marking the upper boundary of the box.

D. 95th percentile: This measure is not typically used in constructing a box plot. It provides information about the value below which 95% of the data falls, but it is not necessary for constructing the basic elements of a box plot.

Therefore, the correct answer is D. 95th percentile.

Learn more about  percentile from

https://brainly.com/question/2263719

#SPJ11

The equilibrium price is the price at the equilibrium price is the price that brings supply and demand into balance, ensuring that the market clears and there is neither a shortage nor a surplus of goods.

The equilibrium price is the price at which the quantity demanded by consumers equals the quantity supplied by producers in a market. It is the point of balance between supply and demand.

At the equilibrium price, there is no shortage or surplus of goods in the market. The quantity demanded by consumers at that price matches the quantity supplied by producers, resulting in a state of market equilibrium.

If the price is set above the equilibrium price, there will be a surplus of goods because the quantity supplied exceeds the quantity demanded. Producers will be left with excess inventory, and they may need to lower the price to sell their goods.

On the other hand, if the price is set below the equilibrium price, there will be a shortage of goods because the quantity demanded exceeds the quantity supplied. Consumers will be willing to buy more goods at the lower price, and producers may need to raise the price to meet the increased demand.

Therefore, the equilibrium price is the price that brings supply and demand into balance, ensuring that the market clears and there is neither a shortage nor a surplus of goods.

To know more about equilibrium:

https://brainly.com/question/30694482#

#SPJ11

The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.

Given readings:

25 psi pressure

13 psi vacuum

6.3 psi vacuum

7.8 psi vacuum

1.9 psi vacuum

2 psi pressure

7.8 psi pressure

Expressed as rational numbers with a common denominator:

25 psi = 25/1

13 psi = 13/1

6.3 psi = 63/10

7.8 psi = 78/10

1.9 psi = 19/10

2 psi = 2/1

7.8 psi = 78/10

Now, let's order these rational numbers from least to greatest:

1.9 psi = 19/10

6.3 psi = 63/10

7.8 psi = 78/10

7.8 psi = 78/10

13 psi = 13/1

25 psi = 25/1

2 psi = 2/1

Ordered from least to greatest:

19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1

Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

for such more question on rational numbers

https://brainly.com/question/19079438

#SPJ8

Answer:

Answer is 10% of 30 = 3

Answer:

x = 2

Explanation:

Given:

BG = 27

AG = 13 + 7x

Note that when three perpendicular bisectors of the sides of a triangle meet at a point, the point is called a Circumcenter.

Also, note that the Circumcenter is equidistant from the vertices of the triangle.

So for the given triangle, G is the circumcenter, and AG = BG = CG.

Let's go ahead and solve for x as seen below;

Let's subtract 13 from both sides of the equation, we'll have;

Let's divide both sides by 7;

So the value of x is 2

Answer:

1/3

Step-by-step explanation:

Answer:

b.1

Step-by-step explanation:

The correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.

What is the system of equations?

A system of equations is a set of two or more equations with the same variables. The goal of a system of equations is to find the values of the variables that simultaneously satisfy all the equations in the system.

The given equations are

3x + y = 12

x + 4y = 4

To graph the system of equations, we can start by finding the x-intercepts and y-intercepts of each line.

The x-intercept is the point where the line crosses the x-axis, which means that the y-value is 0. To find the x-intercept, we can set y = 0 and solve for x:

3x + y = 12

3x + 0 = 12

3x = 12

x = 4

So, the x-intercept of the first line is (4, 0).

Next, we can find the y-intercept, which is the point where the line crosses the y-axis, meaning that the x-value is 0. To find the y-intercept, we can set x = 0 and solve for y:

3x + y = 12

0 + y = 12

y = 12

So, the y-intercept of the first line is (0, 12).

We can repeat this process for the second line to find its x-intercept and y-intercept:

x + 4y = 4

x + 4 * 0 = 4

x = 4

So, the x-intercept of the second line is (4, 0).

Next, we can find the y-intercept by setting x = 0:

x + 4y = 4

0 + 4y = 4

4y = 4

y = 1

So, the y-intercept of the second line is (0, 1).

Now that we have found the x-intercepts and y-intercepts of each line, we can plot these points on a coordinate plane and draw lines through them to obtain the graph of the system of equations.

The graph shows a line with an x-intercept at (4, 0) and a y-intercept at (0, 12). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 1).

Therefore, the correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.

To learn more about the system of equations, visit:

https://brainly.com/question/13729904

#SPJ1

The probability that the committee contains at least one man is 1 - (probability of selecting only women).

To find the probability, we need to determine the total number of possible committee combinations and the number of combinations with at least one man. There are 9 people (6 women + 3 men) to choose from, and we want to choose a committee of 4.

Total combinations = C(9,4) = 9! / (4!(9-4)!) = 126
Combinations of only women = C(6,4) = 6! / (4!(6-4)!) = 15

To find the probability of at least one man, we'll subtract the probability of selecting only women from 1:

P(at least one man) = 1 - (15/126) = 1 - 0.119 = 0.881

The probability that the committee contains at least one man is approximately 0.881, or 88.1%.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

The derivative of the function f(x) = 4x³ - 8x, evaluated at x = 4, is f'(4) = 184. This means that at x = 4, the rate of change of f(x) is 184 units per unit of x.

The derivative of a function measures the rate at which the function is changing at a specific point. In this case, we are given the function f(x) = 4x³ - 8x and asked to find its derivative at x = 4, denoted as f'(4).

To find the derivative of f(x), we can apply the power rule of differentiation. According to the power rule, if we have a term of the form axⁿ, the derivative is given by d/dx(axⁿ) = naxⁿ⁻¹. Applying this rule to each term in f(x), we get:

f'(x) = d/dx(4x³) - d/dx(8x)

      = 3(4)(x²) - 8

      = 12x² - 8

Now, to find f'(4), we substitute x = 4 into the derivative expression:

f'(4) = 12(4)² - 8

     = 12(16) - 8

     = 192 - 8

     = 184

Therefore, the main answer is f'(4) = 184.

Learn more about derivative

brainly.com/question/29144258

#SPJ11

Answer:

2\(x^3\) - 7\(x^2\) + 8x -3

Step-by-step explanation:

To multiply a binomial (2 terms) by a trinomial (3 terms):

Multiply the first term of the binomial by the each term of the trinomial.

Multiply the second term of the binomial by each term of the trinomial.

Combine the expressions and simplify.

(2x-3)*(\(x^2\)-2x+1)

(2x * \(x^2\)) + (2x * -2x) + (2x * 1)

(2\(x^3\)) + (-4\(x^2\)) + (2x)

(2x-3) * (\(x^2\)-2x+1)

(-3 * \(x^2\)) + (-3 * -2x) + (-3 * 1)

(-3\(x^2\)) + (6x) + (-3)

[2\(x^3\) + -4\(x^2\) + 2x] + [-3\(x^2\) + 6x + -3]

2\(x^3\) - 7\(x^2\) + 8x -3

give me brainliest please

Solving the equation for the price, P, we have; P= 100S/(1-D)

According to the question;

To solve for the price, P; we have;

By cross product;

By dividing through by (1-D); we have;

Read more on subject of formula;

https://brainly.com/question/11000305

The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

Answer:

see below

Step-by-step explanation:

1) adjacent angles are 2 angles right next to each other and are labeled with 3 letters, not 2.  

Examples in the picture would include <ABE, <ABD

Vertical angles are angles opposite of each other, so 2 examples are ABE and DBC

2) adjacent angles: PQT and QTR

vertical angles: PQR and SQR

3) a) adjacent

b) neither

c) vertical

d) vertical

e) adjacent

f) neither

hope this helps!

Answer:

The possible dimensions are;

If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units

Step-by-step explanation:

Let;

Length of Rectangle A be a

Width of Rectangle A be b

Length of Rectangle B be c

Width of Rectangle B be d

Thus;

Area of Rectangle A = a × b

Area of Rectangle B = c × d

We are told that the area of Rectangle A is twice the area of Rectangle B:

Thus;

2cd = ab - - - - - eq. 1

perimeter of Rectangle A = 2a + 2b

perimeter of Rectangle B = 2c + 2d

We are told that the perimeter of Rectangle A is 20 units greater than the perimeter of Rectangle B. Thus, we now have;

20 + 2c + 2d = 2a + 2b - - - - eq. 2

We have 4 unknowns which are (a, b, c and d) but only 2 equations, so we need to reduce to 2 unknown variables and calculate the other ones. In this way, one of the infinite solutions is obtained.

Let's assume that c = 1 and d = 2, we obtain:

From eq 1, we have;

2 * 1 * 2 = a*b

ab = 4 or a = 4/b

From eq 2, we have;

20 + 2(1) + 2(2) = 2a + 2b

26 = 2a + 2b

Putting a = 4/b into this, we have;

26 = 2(4/b) + 2b

Multiply through by b to get;

26b = 8 + 2b²

So,we have;

2b² -26b + 8 = 0

Using quadratic formula for this,

b = 0.315 or 12.685

When, b = 12.685, a = 4/12.685 = 0.315

When, b = 0.315, a = 4/0.315 = 12.685

So, the possible dimensions are;

If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units

Using Algebra operation,

the total revenue from ticket sales on that day is $ 3444..

We have given the following information,

timing of museum for entry is 9:00 am to 5:55pm. i.e 8 hours 55 minutes .

price of ticket for a regular admission= $10

price of ticket for a student admission = $6

30 people's admission in every 5 minutes so,

inclusive there are 9×12=108 five-minute intervals, total of tickets were sold = 108× 30

= 3240

let x student and 3x regular tickets were sold on that day.

then, x+3x= 108× 30 –> x= 3240/4 = 810

put x= 7560 in above formula, for regular admission, 3x=3× 81 = 243

So, the total revenue from ticket sales that day was 243×$10 + 810×$6 = $2430 + $4860

= $7290

Hence, total revenue from tickect sales is $7290.

To learn more about Algebra operation, visit:

https://brainly.com/question/395066

#SPJ4

Answer:

165 cm

Step-by-step explanation:

We solve using the rule

Shadow of ruler/Length of ruler = Shadow of the girl /Length of the girl

Shadow of ruler = 20cm

Length of ruler = 30cm

Shadow of the girl = 110cm

Length of the girl = x

Hence:

20/30 = 110/x

Cross Multiply

20x = 30 × 110

x = 30 × 110/20

x = 165 cm

Therefore, Sierra(the girl) is 165cm tall

Answer:

A

Step-by-step explanation:

We are given the function:

\(f(x) = x^2 - 4x\)

And we want to find:

\(\displaystyle f(2b^2)\)

Substitute:

\(\displaystyle f(2b^2) =(2b^2)^2 -4(2b^2)\)

And evaluate:

\(\displaystyle \begin{aligned} f(2b^2) &=(2b^2)^2 -4(2b^2) \\ &=(4b^4) +(-8b^2) \\ &= 4b^4 - 8b^2 \end{aligned}\)

In conclusion, our answer is A.