Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = 0.7 and P(B) = 0.4.
A. Could it be the case that P(A ∩ B) = 0.5? Pick one:
i. Yes, this is possible. Since B is contained in the event A ∩ B, it must be the case that P(B) ≤ P(A ∩ B) and 0.5 > 0.4 does not violate this requirement.
ii. Yes, this is possible. Since A ∩ B is contained in the event B, it must be the case that P(B) ≤ P(A ∩ B) and 0.5 > 0.4 does not violate this requirement.
iii. No, this is not possible. Since B is equal to A ∩ B, it must be the case that P(A ∩ B) = P(B). However 0.5 > 0.4 violates this requirement.
iiii. No, this is not possible. Since B is contained in the event A ∩ B, it must be the case that P(A ∩ B) ≤ P(B). However 0.5 > 0.4 violates this requirement.
v. No, this is not possible. Since A ∩ B is contained in the event B, it must be the case that P(A ∩ B) ≤ P(B). However 0.5 > 0.4 violates this requirement.
B. From now on, suppose that P(A ∩ B) = 0.3. What is the probability that the selected student has at least one of these two types of cards?
C. What is the probability that the selected student has neither type of card?
D. In terms of A and B, the event that the selected student has a Visa card but not a MasterCard is A ∩ B' . Calculate the probability of this event.
E. Calculate the probability that the selected student has exactly one of the two types of cards.

The required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

An arrangement of numbers in which the numbers are arranged from smallest to greatest numbers is called ascending order.

Given that, some numbers, 3√2, √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.

We need to order them from least to greatest,

3√2 = 4.24

√3 − 1 = 0.73

√19 + 1 = 5.35

6

2√10 ÷ 5 = 1.26

√14 = 3.74

The order from least to greatest is :-

0.73, 1.26, 3.74, 4.24, 5.35 and 6

i.e.

√3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

Hence, the required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

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The number of cups of milk that Minka pours as a mixed number is found in the attached image.

The total number of cups of milk that Minka pours into her oatmeal is calculated as follows:

First day = 1/4

Second day = 1/4 + 1/4

Second day = 2/4

Third day = 1/4 + 2/4

Third day = 3/4

Fourth day = 1/4 + 3/4

Fourth day = 4/4 or 1

Fifth day =  5/4 or 1/4 + 1

Fifth day = 1 1/4

Sixth day = 1/4 + 5/4

Sixth day = 1 1/2

Seventh day = 1/4 + 6/4

Seventh day = 7/4 or 1 3/4

Eight day = 1/4 + 7/4

Eight day = 8/4 or 2

The completed number line is found in the attached image

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The probability of the different discrete random variable X are;

a) P(x = 3) = 0.12

b) (P x ≤ 2) =  0.239

c)  P(x ≥ 1) =  0.947

d) P(1 ≤ x ≤ 4) = 0.493

a) The probability expressed as P(x = 3) from the table is;

P(x = 3) = 0.12

b) The probability expressed as (P x ≤ 2) is;

(P x ≤ 2) = P(x = 2) + P(x = 1) + P(x = 0)

= 0.093 + 0.093 + 0.053

= 0.239

c) The probability expressed as P(x ≥ 1) is;

P(x ≥ 1) = P(x = 6) + P(x = 5) + P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1)

P(x ≥ 1) = 0.267 + 0.187 + 0.187 + 0.12 + 0.093 + 0.093

P(x ≥ 1) =  0.947

d) The probability expressed as P(1 ≤ x ≤ 4) is;

P(1 ≤ x ≤ 4) = P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1)

= 0.187 + 0.12 + 0.093 + 0.093

= 0.493

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The equation from the graph of the function is g(x) = |x - 1|

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the function

The function is an absolute value function

The parent function of an absolute value function is:

y = |x|

The function y = |x| is shifted right by 1 units

Using the above as a guide, we have the following:

g(x) = f(x - 1)

This represents a translation to the right by 1 unit

So, we have

g(x) = |x - 1|

Hence, the translation is g(x) = |x - 1|

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The minimum product between the two numbers is 0 and the two numbers are 4 and 0.

here 1st number is x

and 2nd number is y

and the difference between twice a number and another number is 8 so 2x-y = 8

minimum value of

xy

= x(2x-8)

here the eqn is x(2x-8)

and we have to find its minima

If we have a formula expressed as y= ax2+bx+c , we can find the minimum of the quadratic equation according to the following formula: The minimum value is min= c-b2 /4a.

and the minima is at x=4

here the minimum value will be 0

so either value of x=0  or x= 4;

first number is 4 and second is 0

and product of x*y = 0;

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Using linear function, the slope of -1 means that when one of the ratio of dimension is increased by 1, the other is decreased by 1.

A linear function is modeled by:

y = mx + b

Here, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

Also shown as b is the y-intercept, which is the value of y when x = 0.

Given that the lengths and the widths are interchangeable, that is, either can be considered as the input or as the output.

The slope of -1 means that when the input in increased by 1, the output is decreased by -1, that is;

=  length/width

This is increased by 1, and the other is decreased by 1.

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Answer:

No

Step-by-step explanation:

At least two sides will have to be the same.

Answer:

Step-by-step explanation:

The inequality |3x| >= 0 simply states that the absolute value of 3x must be greater than or equal to zero.

Since the absolute value of any number must always be non-negative, this inequality is always true. That means any real number x satisfies the inequality |3x| >= 0.

Therefore, the solution to the inequality |3x| >= 0 is x ∈ R, where R represents the set of all real numbers.

Answer:

Step-by-step explanation:

23x

Answer:

I'm not sure, but the quotient is divided, so 5016/11

Step-by-step explanation:

5016/11, and then 50/11, and find out the answer.

Applying the knowledge of sets, the number of people that have been to Australia but not Europe is calculated as: 2.

Let's call the number of people who have been to Europe "E" and the number of people who have been to Australia "A". We know that:

E = 11

A = 7

We also know that 5 people have been to both Europe and Australia, so they are counted in both E and A:

E = 11

A = 7

E ∩ A = 5

To find the number of people who have been to Australia but not Europe, we can use the formula:

A - (E ∩ A) = A - 5 = 7 - 5 = 2

Therefore, the 2 people have been to Australia but not Europe.

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Answer:

B) Annually

Step-by-step explanation:

If interest is compounded once every 12 months, it is compounded annually.

Answer:

B) Annually

Step-by-step explanation:

Compounded means to calculate interest on the borrowed amount and on previous interest.

Monthly means to be done one every month.

Annually means to be done yearly or every year.

Let's break this down. Semi means half or a partial of something. Annually, as we already discussed, means yearly or every year. Now, when we put it together, it creates half a year. So, semiannually means half a year.

We know a quarter, as in, the coin, is 25 cent. if we multiply 25 cents by four, we get a dollar. So a quarter coin is one fourth, or, a quarter of a dollar. Now, applying that to years, since a year is twelve months and a quarter is one fourth, we can divide twelve by four to get three. Three months is one quarter of a year.

With this in mind, twelve months is equal to a year. So, the interest is compounded every year.

A is incorrect because it says monthly. We have already figured out that the interest is compounded yearly, so it is incorrect.

B is correct because the definition of Annually is yearly or every twelve months.

C is incorrect because semiannually means half or part of a year, not a full year.

D is incorrect because quarterly means one fourth of a year, or, three months.

Identifying the theorem is the most important step while working with circle theorems.

        x² + y² = r²

Given are the points about circle theorems.

While working with circle theorems, identifying the theorem by looking at the information provided is the most important step.

Therefore, identifying the theorem is the most important step while working with circle theorems.

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The probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively is 7/8.

In probability theory, the likelihood of a particular event occurring is measured in terms of probability. When it comes to tossing a coin, there are two possible outcomes: heads or tails.

To calculate the probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively, we need to use the concept of complementary events. Complementary events are two events that make up the whole sample space

Let's first calculate the probability of not getting at least one head and at least one tail. The only way to not get at least one head and at least one tail is to get either three heads or three tails. The probability of getting three heads or three tails in a row is (1/2)³ or 1/8 since there are 8 possible outcomes when a coin is tossed thrice successively.

Now we can calculate the probability of obtaining at least one head and at least one tail by subtracting the probability of not getting at least one head and at least one tail from 1.

1 - 1/8 = 7/8

Therefore, the probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively is 7/8.

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If A is a matrix of order m × n, then

Rank of A + Nullity of A = Number of columns in A = n

Now, According to the question:

The rank-nullity theorem states that the dimension of the domain of a linear function is equal to the sum of the dimensions of its range (i.e., the set of values in the codomain that the function actually takes) and kernel (i.e., the set of values in the domain that are mapped to the zero vector in the codomain).

The range null-space decomposition is the representation of a vector space as the direct sum of the range and the null space of a certain power of a given matrix.

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The given question is incomplete,

So, The question is:

What is rank nullity theorem and range and null space ?

The equations must intersect at a single point then it have the unique solution and the value of h and k are h = -1 and k = 6

A system has no solution if the equations are inconsistent, meaning there is no way to satisfy both equations simultaneously. It has a unique solution if the equations intersect at a single point, meaning there is only one set of values that satisfies both equations.

Let's take a look at the first system of equations, 19.

Equation 1: x + hx = 2

Equation 2: 4x + 8x = k

For the system to have no solution, the equations must be inconsistent. This means they must be parallel and never intersect. To achieve this, we can set the slopes of the lines to be equal but the y-intercepts different. In other words, we need to choose h and k such that:

h = -2 and k = 5

Substituting these values into the equations, we get:

Equation 1: x - 2x = 2

Equation 2: 4x + 8x = 5

You can see that these two equations do not have a common solution. They are inconsistent, meaning there is no point that satisfies both equations.

For the system to have a unique solution, the equations must intersect at a single point. This means the slopes and y-intercepts must be different. To achieve this, we can choose h and k such that:

h = -1 and k = 6

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Answer:

L = 4.5

Step-by-step explanation:

You can rewrite the equation as 2L^2 + L - 45 = 0 and then solve using the quadratic formula

L = (-1 plus or minus the sq root of 361) / 4

L = (-1 plus or minus 19) / 4

L = -5 or 4.5 but lengths can't be negative so the length is 4.5

Answer: 2

Step-by-step explanation:

The python methods that can be used to perform simple linear regression on a data set are -  

A. linregress method from scipy module

C. ols method from statsmodels module

The linregress method from the module is the most simplest and effortless method for performing simple linear on the data set. It consists of two arrays one represents the independent variables and the second represents the dependent variables.

The relationship between two variables can be modeled using simple linear regression, where the first variable is treated as the independent variable and the other as the dependent variable. Finding the line of best fit that lowers the squared sum of the residuals is the goal.

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Assuming that each face is equally likely to come up.

(a) The sample space for this experiment  = {1, 2, 3}

(b) P(odd number) = 2/3

(c) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces:

(i) The probability of the single events, P(3) = 2/7

(ii) P(even number) = 1/3

(a) The sample space for this experiment is the set of all possible outcomes, which are the numbers 1, 2, and 3 that can appear on the face of the die.

Sample space = {1, 2, 3}

(b) To find the probability of getting an odd number, we need to find the probability of getting a 1 or a 3. There are 3 faces with the number 1 and 1 face with the number 3, so there are 3 + 1 = 4 faces that result in an odd number. There are 6 faces total, so the probability of getting an odd number is 4/6 = 2/3.

P(odd number) = 2/3

(c)

(i) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces, then each of the other five faces would have a probability of 1/7 of coming up, and the face with the 3 on it would have a probability of 2/7 of coming up.

P(1) = P(2) = 1/7

P(3) = 2/7

(ii) To find the probability of getting an even number, we need to find the probability of getting a 2. There are 2 faces with the number 2, so there are 2 faces that result in an even number. There are 6 faces total, so the probability of getting an even number is 2/6 = 1/3.

P(even number) = 1/3

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Answer:

Rounding to the nearest cent, the total amount after 9 years is $3182.67.

Step-by-step explanation:

The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

where:

A = final amount

P = principal amount (initial investment)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

In this case, P = 2000, r = 0.053, n = 2 (compounded semiannually), and t = 9.

Plugging in these values, we get:

A = 2000(1 + 0.053/2)^(2*9)

= 2000(1.0265)^18

≈ 3182.67

Rounding to the nearest cent, the total amount after 9 years is $3182.67.

The weight of the beagle D. Erin has weighs 35 pounds.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information, Let the weight of the beagle is 'x'.

So, the weight of a Great Dane is (2x + 2) pounds.

Therefore, 2x + 2 = 72.

2x = 70.

x = 35 pounds.

So,  The beagle weighs 35 pounds.

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The true statement is: The difference in height between the whale and the plane is 11,835 feet.

We can calculate this difference by subtracting the height of the whale from the height of the plane:

= Height of plane - Height of whale

= 10,300 feet - (-1,535 feet)

= 11,765 feet

Therefore, the difference in height between the whale and the plane is 11,765 feet.

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The coordinates of all the points generated from (x, y, z) by repeatedly applying the operations in the order given are: (a) (x, -y, z); (b) (x, y, -z); (c) (-x, y, -z); (d) (-x, z, y); and (e) (x, -z, -y).

For (a), a mirror perpendicular to the y-axis and passing through the origin reflects the coordinates in the y-axis, so the new coordinates will be (x, -y, z).

For (b), a four-fold rotation whose axis is coincident with the x-axis and passing through the origin rotates the coordinates around the x-axis by 90 degrees, so the new coordinates will be (x, y, -z).

For (c), a 4 roto inversion whose axis is coincident with the x-axis and passing through the origin inverts the coordinates in the x-axis, so the new coordinates will be (-x, y, -z).

For (d), a three-fold rotation whose axis passes through the origin and the point (1,1,1) rotates the coordinates around the axis by 120 degrees, so the new coordinates will be (-y, -z, x).

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The required point of the beginning is given as Point A. Option B is correct.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

When you move 5 units north, you increase the y-coordinate by 5. When you move 3 units west, you decrease the x-coordinate by 3. So, if you start at an unknown point and move 5 units north and 3 units west, your final position would be at a point with the coordinates (x - 3, y + 5).

Since you ended at point D, and the final coordinates are not given, we cannot determine the starting point without more information.

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Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

Pythagorean theorem and its converse to prove that triangle ABC is a right triangle.

The converse of Pythagorean theorem states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.

Let's begin by visualizing the given triangle ABC and the line CN that is perpendicular to side AB. Since CN is perpendicular to AB, we can say that triangle ACN and triangle BCN are right triangles (as the angle at C is 90 degrees).

Now, let's focus on the point H that is the geometric mean of points D and E. This means that DH multiplied by HE is equal to CH squared (as per the definition of geometric mean).

We can represent this relationship using the Pythagorean theorem as well. Since triangle CDH and triangle CEH are right triangles (as angle C is 90 degrees), we can say that:

CD² + DH² = CH² (using Pythagorean theorem for triangle CDH)

CE² + EH² = CH² (using Pythagorean theorem for triangle CEH)

From the given relationship of geometric mean, we can substitute CH² in the above equations and get:

CD² + DH² = HE*DH

CE² + EH² = HE*EH

Adding these two equations, we get:

CD² + CE² + DH² + EH² = HE*(DH + EH)

AB² = 4HE² (using the fact that DH + EH = DE = 2HE)

This equation gives us an important insight about the triangle ABC. It tells us that the sum of the squares of the sides (AB²) is equal to four times the square of the length HE (4HE²).

Now, we can use the converse of Pythagorean theorem to prove that triangle ABC is a right triangle.

In our case, we have AB² = 4HE², which satisfies the converse of Pythagorean theorem. Therefore, we can conclude that triangle ABC is a right triangle.

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