give an indexed family of sets that is pairwise disjoint but the intersection over it is nonempty

Answers

Answer 1

The intersection over the indexed family {A_i} is nonempty, as there are no elements that belong to all three sets:
⋂(A_i) = A_1 ∩ A_2 ∩ A_3 = ∅ (empty set)

An indexed family of sets that is pairwise disjoint but has a nonempty intersection can be represented as follows:

Consider an indexed family of sets {A_i} where i belongs to the index set I, with I = {1, 2, 3}. Define the sets A_i as:

A_1 = {1, 2}
A_2 = {2, 3}
A_3 = {1, 3}

The sets are pairwise disjoint since no two sets share any common elements:
A_1 ∩ A_2 = {2} (not empty)
A_1 ∩ A_3 = {1} (not empty)
A_2 ∩ A_3 = {3} (not empty)

However, the intersection over the indexed family {A_i} is nonempty, as there are no elements that belong to all three sets:

⋂(A_i) = A_1 ∩ A_2 ∩ A_3 = ∅ (empty set)

In this example, the indexed family of sets is pairwise disjoint, but the intersection over the family is nonempty.

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Related Questions

Let a and b be the events of the fda approving and rejecting a new drug to treat hypertension, respectively. The events a and b are:_____.
a. independent.
b. unilateral.
c. conditional.
d. mutually exclusive.

Answers

The correct option is (d) Mutually exclusive events.

Let a and b be the events of the fda approving and rejecting a new drug to treat hypertension, respectively. The events a and b are mutually exclusive events.

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, provide a clear illustration.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.

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Kawan buys some protein bars at $0.90 each and bottled water at $0.70 each for a group hike. He buys twice as many bottles of water as protein bars. If he spends $46 in total, how many bottles of water and protein bars does he buy? Let x= the number of protein bars

Answers

Answer:

he buts 20 protein bars and 40 water bottles

Step-by-step explanation:

so first u set up an equation like this

46=.90x+.70(2x)

next you multipy

46=.90x+1.4x

Then add

46=2.3x

then divide by 2.3 to solve for x

x=20 so u have 20 protein bars

and 20 times 2 to find the amount of water bottles

Answer:

20 Protein bars and 40 waters.

Step-by-step explanation:

Let x = protein bars and y = waters

y = 2x          .9x + .7 y = 46

Looking at the second equation, I would rather not work with decimals, so I will multiple the whole equation through by ten.  That now gives m

9x + 7y = 460 Substitute in 2x for y (from my first equation above)

9x + 7(2x) = 460

9x +14x = 460  Combine 9x and 14x

23x = 460  Divide both sides by 23

x = 20  This is the number of protein bars.  To find y plug 20 into the first equation above.

y = 2x

y =20(2)

y = 40

Write an expression, of the type A log(x B), for the transformed logarithmic function shown below:

Answers

The equation of the logarithmic function is y = log(x - 1)

How to write the equation of the transformed function?

The points are given as:

(0,3) and (2,0)

The equation is represented as:

y = A log(x + B)

Substitute (2,0) in y = A log(x + B)

y = A log(x + B)

This means that:

0 = A log(2 + B)

This means that:

A = 0 or log(2 + B) = 0

Take the antilog of both sides of log(2 + B) = 0

2 + B = 1

Solve for B in 2 + B = 1

B = -1

Substitute B = -1 in y = A log(x + B)

y = A log(x - 1)

Substitute (0,3) in y = A log(x - 1)

3 = A log(0 - 1)

So, we have:

3 = A log(-1)

The above equation is undefined.

Hence, the equation of the logarithmic function is y = log(x - 1)

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Complete question

Write an expression, of the type A log(x + B), for the transformed logarithmic function shown below:

(0,3) and (2,0)

Which is a factor of f(x) = 60x4 86x3 – 46x2 – 43x 8? use the rational root theorem to help you find your answer.

Answers

The correct option is (2)  [tex]\frac{8}{5}[/tex] and (3)  [tex]\frac{1}{6}[/tex].

The factor of equation  f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

Rational Root Theorem:  

The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.

For the given polynomial, the roots are given as;

[tex]$$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.[/tex]

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only   [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex] can be written in the form:  

[tex]\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}[/tex]

Therefore, the rational roots of polynomial f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

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The complete question is-

Which is a factor of f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8? use the rational root theorem to help you find your answer.

x – 6 => 65x – 8 =>   [tex]\frac{8}{5}[/tex] 6x – 1 =>   [tex]\frac{1}{6}[/tex]8x + 5 => [tex]\frac{-5}{8}[/tex]

A machine in a candy company creates 9,328 pieces of candy each hour. if a box holds 98 pieces of candy, how many boxes can be filled in one hour?

Answers

Answer:

Step-by-step explanation:

9,328 and you would divide that by 98 and the answer would be 95.18367347 boxes

If a researcher needs a sample that is representative of the population they are studying, they could utilize a _______.

Answers

The researchers could utilize a probability sample.

Meaning of a Probability Sample

Every member of a population must have an equal chance of being chosen for a study in order for a sample to be considered a probability sample, and the researcher must be aware of this likelihood. The most typical type of sampling used in public opinion research, election polling, and other studies whose findings will be generalized to a larger population is probability sampling in which probability samples are made use of.

Probability Sample as the Representative of Population Sample

Here, a sample that qualifies for a representative of the population the researchers are studying, must consist of members having equal chances to be chosen for the study. Thus, a probability sample is the best representative of their study population.

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help help help help help help pleaseeeeeee

Answers

the maximum height is 180ft.

How to find the maximum height of the rocket?

The height of the equation is modeled by:

[tex]y = 60t - 5t^2[/tex]

Notice that this is a quadratic equation with a negative leading coefficient, which means that the maximum is at the vertex, then the maximum is at:

[tex]t = -60/(2*-5) = 6[/tex]

To get the maximum height, we need to evaluate the function in t = 6, we will get:

[tex]y = 60*6 - 5*6^2 = 180[/tex]

This means that the maximum height is 180ft.

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write the slope-intercept form of the equation of each line

1. x-3y = 6

2. 4x-y = 1

3. 6x+5y = -15

4. 13x- 11y =-12

Answers

Answer:

y = [tex]\frac{1}{3}[/tex]x - 2y = 4x - 1y = -[tex]\frac{6}{5}[/tex]x - 3y = [tex]\frac{13}{11}[/tex] + [tex]\frac{12}{11}[/tex]

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m represents the slope and b represents the intercept.

x - 3y = 6

3y = x - 6

y = [tex]\frac{1}{3}[/tex]x - 2

4x - y = 1

y = 4x - 1

6x + 5y = -15

5y = -6x - 15

y = -[tex]\frac{6}{5}[/tex]x - 3

13x - 11y = -12

11y = 13x + 12

y = [tex]\frac{13}{11}[/tex] + [tex]\frac{12}{11}[/tex]

In simplified form, we can write $\sqrt[3]{\sqrt[3]{54}+\sqrt[3]{250}}$ as $a\sqrt[b]{c}$, where $a$, $b$, and $c$ are all positive integers. what is $a+b+c$?

Answers

The sum of a+b+c = 307.

According to the statement

[tex]$\sqrt[3]{\sqrt[3]{54}+\sqrt[3]{250}}$[/tex] is written as [tex]$a\sqrt[b]{c}$[/tex]

now we find the sum of these

in these terms a=54 and b=3 and c=250

Then

a+b+c = 54+3+250

a+b+c = 307

So, The sum of a+b+c = 307.

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Can someone help me out with these two problems having trouble please !!

Answers

Answer:

1.

x=-10

x=-6

2.

x=10

x=-3

Step-by-step explanation:

to find the zeros of a function you need to set it equal to zero:

x^2+16x+60=0

then you factor

(x+10)(x+6)=0

then you have to finish factoring/simplifying

x+10=0

  -10

x=-10

x+6=0

 -6

x=-6

and the same thing for number 2

x^2-7x-30=0

(x-10)(x-3)=0

x=10, x=3

Answer:

1.) x = -10, x = - 6

2.) x = 10, x = -3

Step-by-step explanation:

1.) factorize and set the equation to zero by multiplying a and c and finding factors of it that will result in b once added/subtracted

[tex]x^2+16x+60\\(x+10)(x+6)\\(x+10)(x+6)=0\\x=-10, x=-6[/tex]

2.) do the same for number 2:

[tex]x^2-7x-30\\(x-10)(x+3)\\(x-10)(x+3)=0\\x = 10, x = -3[/tex]

i hope this helped!

What is the slope?
Please help!! Thankss

Answers

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0,2) ← 2 points on the line

m = [tex]\frac{2-0}{0-(-1)}[/tex] = [tex]\frac{2}{0+1}[/tex] = [tex]\frac{2}{1}[/tex] = 2

In the past, schools in Los Angeles County have closed an average of three days each year for weather emergencies. What is the probability that schools in Los Angeles County will close for four days next year

Answers

The probability that the schools in Los Angeles will be closed for four days next year is 0.1680.

What is Poisson's distribution formula?

In order to comprehend separate events that happen at a steady pace over the course of a specified amount of time, Poisson's distributions are frequently utilized.

Formula for Poisson's distribution:

f(x) = ((λ^x)/x!).(e^(-λ))

x = Event to be calculated for

λ = Expected number of occurrences

P(X = x) = ((λ^x)/x!).(e^(-λ))

Here λ = 3 and x = 4

P(X = 4) = (81 / 4!).(e^(-3))

P(X = 4) = (81 * e^(-3))/24

P(X = 4) = (81 * 0.049)/24

P(X = 4) = 0.1680

Hence, the probability that schools in Los Angeles will be closed for four days next year is 0.1680.

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Which is an equivalent form of the expression 1800(1.2)^-t

Answers

Answer:

1800(5/6)^t

Step-by-step explanation:

I don't see any answer choices, but this would be another form if it is listed. The negative exponent means that you get the reciprocal of the fraction (in this case 1.2). This turns 1.2 into (1/1.2), which is equivalent to 5/6.

The Smith family bought carpet for their basement. It originally cost $1,600. The company offered and installment plan for 12 monthly payments of $150. How much was the carpet?​

Answers

Answer:

$1,800

Step-by-step explanation:

If the Smiths agree to the installment plan and pay $150 every month for 12 months, it will add up to $1,800 at the end of the year.

Help please!!! Due in 10 mins

Answers

Answer:

2.0

Step-by-step explanation:

Emma has money in two savings accounts. One rate is 6% and the other is 14%. If she has $950 more in the 14% account and the total interest is $342, how much is invested in each savings account?

Answers

The amount invested in the account that has a rate of 14% is $1767

The amount invested in the account that has a rate of 6% is $1425.

What are the linear equations that represent the question

0.06a + 0.14b = 342 equation 1

b - a = $950 equation 2

Where:

a = amount invested in the account that has a rate of 6%

b =  = amount invested in the account that has a rate of 14%

How much was invested in each account?

Multiply equation 2 by 0.06

0.06b - 0.06a = 57 equation 3

Subtract equation 3 from equation 2

285 = 0.2a

a = 285 / 0.2

a = 1425

Substitute for a in equation 2

b - 1425 = 342

b = 1425 + 342

b = $1767

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2. If you use AB as the base to find the area of ABCD shown at the right, what should you use as the height?

Answers

The height that should be used is DE

Area of a parallelogram

From the question, we are to determine what should be used as the height

The area of a parallelogram is given by the formula,

A = b × h

Where A is the area

b is the base

and h is the perpendicular height

In the given diagram, if AB is used as the base, then the height that would be used will be DE. This is because DE is perpendicular to AB

Hence, the height that should be used is DE

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pls help i’ll give brainliest

Answers

Answer: y=-1/5x+ 8/5    (Third one down)

identify and shade the following regions on separate venn diagram

Answers

The attached figures represent the shaded areas of the given set operations

How to identify the shaded regions?

To shade the given regions of the sets, we need to highlight the following set operations

Intersection: This represents the elements that are common between two or more setsUnion: This represents the totality of all elements in two or more sets (without repetition of elements)Complement: This represents the elements that are not present in the given set

Using the above definition of set operations and the Venn diagram, we have the following values:

X U Y' = Y'X n Y' = ∅ i.e an empty set(X U Y)' = X' n Y'(X n Y)' = U i.e. the universal setX' U Y' = X' n Y'X' n Y' = X' U Y'(X' U Y)' = X(X U Y')' = Y

See attachment for the shaded areas of the above set operations

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(?) James is following this recipe to make flapjacks.
James uses 650 g of margarine.
How many flapjacks is James making?
Recipe: Makes 8 flapjacks
50 g sugar
100 ml syrup
125 g oats
130 g margarine
65 g sultanas

Answers

I hope this helps.
Remember find how much is for one person and divide it by how much grams it uses to find how many people it’s making it for

Jessica and her best friend found some money under the couch. they split the money evenly, each getting $16.32. how much money did they find?

Answers

Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

How much did Jessica and her friend find?

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

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Give the center and radius of a circle with the equation: (x+1)²+(y-2)²=100
A-The center is (-1. 2) and the radius is 10
B-The center is (1, -2) and the radius is 50
C- The center is (1, -2) and the radius is 10
D- The center is (-1, 2) and the radius is 50

Answers

OPTION A is the correct answer

Help ASAP!!! Geometry, “fill in the blanks”

Answers

Skew lines and parallel lines do not intersect

How to determine the skew lines?

As a general rule, skew lines are lined that are not on the same plane; they are not parallel to each other and they do not intersect

Using the above definition as a guide, the skew lines in the figure are:

CG and BDAE and FHEG and DH

The difference between skew lines and parallel lines

Parallel lines and skew lines are different in the following ways:

Skew lines are on different planesParallel lines are on the same plane

The likeness between skew lines and parallel lines

Parallel lines and skew lines are alike in the following way:

Skew lines and parallel lines do not intersect

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given that 5x:9=7:3 calculate the value of x. give your answer in its simplest form.

Answers

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

x = 21/5

Step-by-step explanation:

___________________________

Given →

5x:9 = 7:3

So,

→ 5x/9 = 7/3

→ x = (7 × 9)/(3 × 5)

→ x = 21/5

___________________________

Hope it helps you!!

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

At approximately what angle does the wire meet the ground?
33.6°
39.8°
50.2°
56.4°

Answers

Using relations in a right triangle, it is found that the tree meets the wire at an angle of 56.4º.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, we have that:

The opposite side to the angle is of 10 feet.The hypotenuse is of 12 feet.

Hence:

[tex]\sin{\alpha} = \frac{10}{12}[/tex]

[tex]\alpha = \sin^{-1}{\left(\frac{10}{12}\right)}[/tex]

[tex]\alpha = 56.4^\circ[/tex].

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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each expression to make pairs of equivalent expressions.

Answers

The equivalent expressions indicated are;

1) 1/a^6b^4

2) a^6/b^6

3) a^6/b^5

4) b^6/a^6

5) a^5b^3

What is the result of the equivalent expressions?

We have to note that when we talk about the equivalent expressions, we mean the expressions that we have to get from each other when we carry out a little computational work on the original expression.

Thus, the equivalent expression has shown that the expression that is in the bracket is the same as the original expression by the use of the laws of exponents.

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I really need help for my hw please

Answers

Answer:

5.46

111

86

367.2

49

467

use labels

Step-by-step explanation:

1. [tex]\frac{39}{2} times . 0.28[/tex]

[tex]\frac{39}{2} times \frac{28}{100} =\frac{1092}{200} \\[/tex]

[tex]\frac{1092}{200} = \frac{273}{50}[/tex]

Answer 273/50 or 5.46 inches

2. [tex]\frac{97}{87} times \frac{100}{1} =\frac{9700}{87}[/tex]

Answer 9700/87= 111%ft

3. [tex]\frac{146}{1} divided \frac{170}{1}[/tex]

[tex]\frac{146}{1}times\frac{1}{170} =\frac{146}{170}[/tex]

Answer=146/170=73/85=

86%tons

4. [tex]\frac{136}{1} times\frac{270}{100} =\frac{36720}{100}[/tex]

Answer=367.2%ft

5 .[tex]\frac{60}{123}[/tex]=49%inches

6.[tex]\frac{56}{1} times\frac{100}{12} =[/tex]467%inches

please help me solve this

Answers

Answer:

1.5, -1.5

Step-by-step explanation:

Using the quadratic formula, you should have a plus, and minus solution. These should be your answers.

From the top of a 16 m tall building, the angle of depression to a car on the road is 35°. To the nearest metre, how far is the car from the base of the building?

Answers

The distance of the car from the tall building to the nearest meter is 23m.

How far is the car from the base of the building?

Given the data in the question;

Angle of depression θ = 35°Height of building = 16mDistance of car from building = x

We use trigonometric ratio since the scenario forms a right angle triangle.

tanθ = opposite / adjacent

tanθ = opposite / adjacent

tan( 35° ) = 16m / x

x = 16m / tan( 35° )

x = 16m / 0.7002

x = 23m

Therefore, the distance of the car from the tall building to the nearest meter is 23m.

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3. There are 50 girls and 50 boys at a party, all of
whom have written down their names on sheets
of paper for a chance to win a raffle prize. Of all
the girls and boys, 10 girls have braces and 15
boys have braces. What is the probability that
the child randomly chosen to win the raffle will
be a boy without braces?

Answers

There is a 25% chance that a child with braces will be chosen.
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