Consider two events A and B such that P(A) = 1/3 and P(B) = 1/2. Determine
the value of P(B ∩ Ac) for each of the following conditions:
(a) A and B are disjoint;
(b) A ⊂ B;
(c) P(A ∩ B) = 18

Equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5 is (x+3)²/25+(y-5)²/16=1

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

Given,

center −3, 5,

Major axis of length 8

Endpoint of minor axis 0, 5.

Standard form of equation for an ellipse with vertical major axis:

(x-h)²/b²+(y-k)²/a²=1, a>b

(h,k)=(x,y) coordinates of center.

(-3, 5) are coordinates of centre

given length of vertical major axis:=8=2a=4

a=4

a²=16

Length of minor axis=b=5

b²=25

Hence,  equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5 is (x+3)²/25+(y-5)²/16=1

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The force exerted by her biceps to allow her hold the tray is 282 N.

Force is the product of mass and acceleration.

To calculate the force the biceps must exert to allow her hold the tray, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for F'

Hence, the force exerted by her biceps is 282 N.

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After solving the equation the jet is descending vertically at 12 mph.

The Pythagorean Theorem is a mathematical statement that states that in a right triangle the sum of the squares of the lengths of the two sides that make up the right angle are equal to the square of the length of the hypotenuse. This theorem is named after the ancient Greek mathematician, Pythagoras. It can be expressed as the equation: a2 + b2 = c2, where 'a' and 'b' are the lengths of the two sides adjacent to the right angle and 'c' is the length of the hypotenuse. The Pythagorean Theorem is a fundamental tool used in geometry and trigonometry, and it is used to calculate the lengths of the sides of a right triangle. It can also be used to calculate the distances between two points or to calculate the area of a triangle.

The jet is descending at 12 mph. This can be calculated by using the Pythagorean Theorem. Since the jet is approaching the oil depot horizontally at 738 mph and descending diagonally at a constant speed of 750 mph, we can use the Pythagorean Theorem to calculate the vertical component of the jet's descent.
750^2 = 738^2 + x^2
x = √(750^2 - 738^2)
x = 12 mph
Therefore, the jet is descending vertically at 12 mph.

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Answer:

10.37

Step-by-step explanation:

3 in the thousandths place is lower than 5 therefore you have to turn the thousandths into a 0 and don't change the forenumber

Since type I error is to reject the null hypothesis when null is true that's why the Correct option is C.

The researchers believe that more than or less than 65% of college students will graduate with debt, when in fact, 65% will.

The null hypothesis is true if the experimental result matches the predicted theoretical result. The null hypothesis is disproved and we examine an alternative one if there are any variations in the observed parameters between the samples. The null hypothesis was rejected, which opens the door for additional study but does not imply that the first experimentation was flawed. Usually, the null hypothesis is used to gauge the strength of the evidence.

Hence we get the required answer and the correct option is c.

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We are given the following data set:

10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20

Standard deviation = 8.043

Confidence level = 1 - Significance Level = 1 - 99.74% = 4.56% = 0.0456

According to the data provided, the regression line equation is given by

y=2.83+0.52x.  The non-linear characteristics of data is ignored by the regression line.

The most popular statistical method for simulating a link between two sets of variables is linear regression. As a result, a linear regression equation that can be applied to data is created.

The required formula is:

[tex]y= a + b_{yx}x[/tex]

[tex]b_{yx} = \frac {n \sum xy - \sum x \sum y}{n \sum x ^ {2} - (\sum x) ^ {2}}[/tex]

[tex]a = \bar y - b_{yx} \bar x[/tex]

[tex]\bar x = 8.81 \\\bar y = 7.45\\\sum x ^ {2} =947\\\sum xy = 770.95[/tex]

[tex]b_{yx} = 0.52[/tex]

[tex]a=2.83[/tex]

y=2.83+0.52x .

In scatter plot, Non-linear characteristics is ignored by the regression line.

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The relation between these three variables is demonstrated by

the formula for Ohm's Law: E = (I)(Z) is 12i.

What is Ohm's Law?

According to Ohm's law, the resistance of the circuit and the current or energy travelling through the resistance are both exactly proportional to the voltage or potential difference between two places. V=IR is the equation for Ohm's law.According to Ohm's Law, assuming the temperature and other physical parameters don't vary, the current flowing through a conductor is precisely proportional to the potential difference applied across its ends. Through a resistor, current is inversely proportional to the voltage difference.

(3+3 i)(2+2 i)

Apply complex arithmetic rule: (a+b i)(c+d i)=(a c-b d)+(a d+b c) i

=(3 .2-3. 2)+(3 .2+3 . 2) i

Simplify [tex]$(3 \cdot 2-3 \cdot 2)+(3 \cdot 2+3 \cdot 2) i: \quad 12 i$[/tex]

[tex]$=12 i$[/tex]

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The correct statement regarding how can a translation and a rotation be used to map triangle HJK to triangle LMN is given as follows:

The translation just changes the position of the figure, hence it has to be among equivalent vertices of the triangles.

The equivalent vertices are given as follows:

The equivalent sides are given as follows:

HK and LN.

Thus the rotation is about K until HK lies on the line containing LN, and the third option is correct.

The problem is given by the image shown at the end of the answer.

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The algebraic equation representing cost can be given as C= 85n+1500.

What is an equation in one variable and power one?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers and x is a variable. This equation has only one solution which can be found by separating the constant and variable terms in the equation.

We are given that A banquet hall charges $1500 to rent the hall and $85 per guest that attends.

Let the number of guests be n

Hence, The equation can be given as

C = 85n+1500

Where C is the cost, n is the number of guests attending.

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The Maclaurin Series of xe²ˣ: x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

Given that,

f(x) = xe^2x

Taylor series of function f(x) at a is defined as:

f(x) = f(a) + f'(a)/1!/(x-a) +f''(a)/2! (x-a)² +....

Maclaurin series of Function F(x) is a Taylor series of Function f(x) at: a=0

f(x) = f(0) + f'(0)/1! /(x) +f''(0)/2!/ (x)² +....

Apply the Maclaurin Formula

= 0 +d/dx (xe²ˣ)(0)/1! x + d²/dx² (xe²ˣ)(0)/2! x² +....

Evaluate the derivatives :

= 0 + 1/1! x + 4/2! x² + 12/3! x³ + ...

Refine :

= x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

So, the Maclaurin series for f(x) = xe^2x is  x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....

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Answer:

114

Step-by-step explanation:

120% of 95 = 1.2 × 95 = 114

Answer:

Step-by-step explanation:

x>y

-x<-y

98>59

-98<-59

59>1

-59<-1

any negative value <any positive value (including 0)

combining

-98<-59<-1<51

The slope of the line is 9/13 according to the given line.

The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.

The steepness, incline, or grade of a line can be approximated by the slope's absolute value. The slope of a line in the plane including the x and y axes is typically symbolized by the letter m and is defined as the difference in the y coordinate by the equivalent difference in the x coordinate between two different places on the line. The following equation encapsulates this:

Slope=rise/run

Rise=y₂-y₁

=-1-(-10)

=9

Run=x₂-x₁

=9-(-4)

=13

Therefore, slope=9/13

Hence, the slope of the line is 9/13.

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the matrix A, which is composed of all scalar multiples of the vector [6 3], and represents the reflection about the line L in R2.A = [[-6/7, 9/7],[9/7, 6/7]]

Let L be the line in R^2 which consists of all scalar multiples of the vector [6 3], then the equation of the line is y= (3/6)x.

We need to find the matrix A which represents the reflection about the line L.

Let (x1, y1) be any point on the line L and let (x2, y2) be its reflection about the line L.

Now, we know that the slope of the line L is 3/6, hence the slope of the normal to the line L is -6/3.

So, the equation of the normal to the line L is y = -(6/3)x. Now, we can use the point-slope form of the line equation to calculate the equation of the line passing through (x1, y1) and its reflection (x2, y2).

The line that connects (x1, y1) and (x2, y2) has the following equation:

y-y1 = (y2-y1)/(x2-x1) (x-x1)

=> y-y

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The addition property of equality states that if two values are equal to a third value, then they are also equal to each other. In this case, 4 is equal to 5+2, so 4 must also be equal to 2+5. However, Mark wrote the equation incorrectly, so the correct statement would be 4 = 5 + 2.

The addition property of equality is a key concept in mathematics, and it is important to understand and use it correctly. In this case, 4 is equal to 5+2, so the correct statement would be 4 = 5 + 2. This is because the addition property of equality states that if two values are equal to a third value, then they are also equal to each other. Therefore, Mark's statement of 4 = 2 + 5 was incorrect, and the correct statement was 4 = 5 + 2. Understanding and applying the addition property of equality is essential for success in math.

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The solution to the differential equation subject to the given initial condition is  log P = 0.07t + log(30)

Differential equation in which the variables can be separated from one from one another are called separable differential equations

A general form to write a separable differential equation is

dy/dx = f(x)g(y)

where the variable x and y can be separated from each other

According to the question,

We have to solve dP/dt=0.07P by using separation of variable

=> dP/dt=0.07P

Dividing P both sides and multiplying dt

=> dP / P = 0.07 dt

Now Integrating both the sides

=> [tex]\int\limits {\frac{1}{P} \, dP = \int\limits {0.07} \, dt[/tex]

=> log P = 0.07t + c ------(1)

It is given that  P(0)=30

which means at t = 0 , the value of P = 30

Substituting t = 0 and P = 30

log(30) = 0 + c

=> c = log(30)

Substituting the value of c back to equation (1)

log P = 0.07t + log(30)

=> log(P / 30) = 0.07t is our solution

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The probability density function will be expressed as f_M(x) = n * x^(n-1) and cumulative density function is f_Z(z) = n * (1-z)^(n-1).

To find the probability density function of M, we need to find the probability that M takes on a particular value x, which is equal to the probability that all of the random variables U1, ..., Un are less than or equal to x. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is less than or equal to x. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is less than or equal to x is simply x. Therefore, the probability that M takes on a particular value x is equal to x^n.

This means that the probability density function of M is given by:

f_M(x) = n * x^(n-1)

for x in the range [0, 1].

For the second part of the question, we want to find the cumulative distribution function (c.d.f.) and probability density function (p.d.f.) of Z = min(U1, ..., Un). We can find the c.d.f. of Z by finding the probability that Z is less than or equal to a particular value z. This is equal to the probability that all of the random variables U1, ..., Un are greater than or equal to z. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is greater than or equal to z. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is greater than or equal to z is simply 1-z. Therefore, the probability that Z is less than or equal to z is equal to (1-z)^n.

This means that the cumulative distribution function of Z is given by:

F_Z(z) = (1-z)^n

for z in the range [0, 1].

To find the probability density function of Z, we can differentiate the cumulative distribution function with respect to z. This gives us:

f_Z(z) = n * (1-z)^(n-1)

for z in the range [0, 1].

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MP = 16 ,, where NP = 13

therefore : MP - NP = MN <=> MN = 16 - 13 <=> MN = 3

MP = 16 ,, where MO = 9

therefore : MP - MO = OP <=> 16 - 9 = MO <=> MO = 7

MO = 7 & MN = 3

therefore : MO - MN = NO <=> NO = 7 - 3 <=> NO = 4

Answer:

F = (9/5)C + 32

Step-by-step explanation:

C = 5/9(F-32)        **you wrote the fraction wrong in your question, it's 5/9, not 5/6

C = (5F)/9 - 160/9

C + 160/9 = (5F)/9

9C + 160 = 5F

(9C + 160)/5 = F

F = (9/5)C + 32

Answer:                   F = (6C/5) + 32

To express F in terms of C, rearrange the equation to isolate 'F'.

To rearrange the equation, we want 'F' to be by itself. To move numbers to the other side, we do the other pair of inverse operation to both sides. This cancels out what we don't need while keeping the left and right sides equal.

Pairs of inverse operations

[tex]\displaystyle { C = \frac{5}{6}*(F-32) }[/tex]                  Start with the equation in the question.

[tex]\displaystyle { C = \frac{5*(F-32)}{6} }[/tex]                  Rewrite. This is the same as the question.

[tex]\displaystyle { 6C = \frac{5*(F-32)}{6}*6 }\\[/tex]           Multiply both sides by 6.

[tex]\displaystyle { 6C = 5*(F-32) }[/tex]                 Cancelled out 6 on the right.

[tex]\\\displaystyle { \frac{6C}{5} = \frac{5*(F-32)}{5} }[/tex]                Divide both sides by 5.

[tex]\displaystyle { \frac{6C}{5} = (F-32) }[/tex]                      Cancelled out 5 on the right.

[tex]\displaystyle { \frac{6C}{5} = F-32 }[/tex]                         We don't need the brackets if 'F - 32' is alone.

[tex]\displaystyle { \frac{6C}{5}+32 = F-32+32 }[/tex]         Add 32 to both sides.

[tex]\displaystyle { \frac{6C}{5}+32 = F }[/tex]                         Cancelled out 32 on the right.

[tex]\displaystyle { F = \frac{6C}{5}+32 }[/tex]                         Keep lone variables on the left side.

Therefore, the equation to convert Celsius to Fahrenheit is:

           [tex]\displaystyle { F = \frac{6C}{5}+32 }[/tex]

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8

x = 6

9

x=7

10

x= 15

see explanation in image

because you know that m and n are parralell you can use the vertical angle theorem as well as the fact that lines in a straight angle add to 180

if you have any questions just comment

A stochastic matrix A's steady state is an eigenvector w with eigenvalue 1, such that the elements are positive and add up to 1. The theorem of Perron-Frobenius...

A square matrix A is stochastic if all of its entries are nonnegative, and the elements of each column total to 1. If all of the elements in a matrix are positive integers, the matrix is positive.

A stochastic matrix is a square matrix with probability vector columns. A probability vector is a numerical vector with entries that are real values ranging from 0 to 1 and whose sum equals 1.

(Stochastic processes, mathematics) A square matrix of rows of nonnegative real values, with each row adding up to A Markov chain's transitions are described by its element in the 'th row and 'th column, which describes the probability of moving from state to state in one time step.

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Points H, J and K are collinear and I'll choose K, J, and H as the non-collinear points

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

Points H, J and K are collinear as they are on the same line. Pick either K or K to fill out the answer box. I'll go with point K.

it through. Imagine if the flat piece of paper could revolve about this axis (like a propeller). The fact that the points are not all on the same line ensures that we build exactly one individual plane.

I'll choose K, J, and H as the non-collinear points to give the object the name Plane KJH. There may be further options.

Hence, Points H, J and K are collinear and I'll choose K, J, and H as the non-collinear points

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The following pricing strategies could be ethical in many situations is price discrimination.

Predatory pricing is a strategy in which a company establishes a price that is too low to get new customers.

Price baiting is a strategy in which businesses make customers believe that they will have to pay less than the actual price of the product.

Price gouging is when a company puts a price that is too high for a product in a level that is not reasonable and this is considered to be unethical.

Price discrimination is a strategy in which businesses charge different prices to different customers based on what they believe that a group of customers would be willing to pay.

For example, when an airline sees that a specific route has a high demand, it increases the price of the ticket.

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Answer:

D. Price discrimination

They walk 810 m on 21 day and 1,200 m on 60th day.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

She has decided to walk 10 m more every day on day 20 she walked 800 m.

Now,

Since, She has decided to walk 10 m more every day on day 20 she walked 800 m.

Hence, The amount of meters she walk everyday can be given as a linear function, and, the rate of variation is a constant (10 m/day):

⇒ 10 m / day

This constant (10 m/day) is the slope of the linear function.

And, We know that;

One point of the linear function (D(20) = 800) and the slope, so we can calculate the y-intercept:

⇒ D (t) = 10t + b

⇒ 800 = 10 × 20 + b

⇒ 800 - 200 = b

⇒ b = 600

So, The equation become;

⇒ D (t) = 10t + 600

Hence, For day t = 21;

⇒ D (21) = 10 x 21 + 600

⇒ D (21) = 810 m

And, For day t = 60;

⇒ D (60) = 10 x 60 + 600

⇒ D (60) = 1,200 m

Thus, They walk 810 m on 21 day and 1,200 m on 60th day.

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Answer:

The slope is [tex]\frac{-2}{3}[/tex]

Step-by-step explanation:

An order pair is in the form (x y).  The slope is the change in y over the change in x.  From the 2 points our y's are 2 and 4.  From the 2 points our x's are  1 and -2.  to find the change you subtract.

[tex]\frac{2-4}{1 - -2}[/tex] = [tex]\frac{-2}{1 + 2}[/tex] [tex]\frac{-2}{3}[/tex]

According to the triangle inequality theorem; D)2,3,6 can not be the lengths of the sides of a triangle

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side of that triangle  

If the two shortest sides are put end to end, they should be longer than the longest side to be able to angle up to form a triangle.

Therefore applying this theorem in this case;

A) 2,3,4: The sum of 2 and 3 = 5; which is greater than 4

B) 2,3,2: The sum of 2 and 2 = 4; which is greater than 3

C) 2,3,3: The sum of 2 and 3 = 5; which is greater than 3

D) 2,3,6: The sum of 2 and 3 = 5; which is not greater than 6; therefore according to the triangle inequality theorem these cannot be the lengths of the sides of a triangle.

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The ratio a : b represented in the table of values is (c) 3 : 5

From the question, we have the following table of values that can be used in our computation:

a b

1.5 2.5

51 85

99 165

Remove the last two entries in the table

So, we have the following representation

a b

1.5 2.5

Express the remaining entries as a ratio

So, we have the following representation

Ratio = a : b

Substitute the known values in the above equation, so, we have the following representation

Ratio = 1.5 : 2.5

Divide the ratio by 0.5

So, we have the following representation

Ratio = 1.5/0.5 : 2.5/0,5

Evaluate the quotients

So, we have the following representation

Ratio = 3 : 5

Hence, the ratio is (c) 3 : 5

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