In an axiomatic system, which category do points, lines, and planes belong to?

A.
theorems

B.
axioms

C.
undefined terms

D.
definitions

Continuous random variable is a random variable that can take on a continuum of worth. In alternative words, a random variable is said to be continuous if it supposes a value that falls between a particular interval.

A continuous random variable can be described as a random variable that can take on an infinite number of possible values. Due to this, the probability that a continuous random variable will take on a fixed value is 0.

The probability density function of a continuous random variable can be explained as a function that gives the probability that the value of the random variable will drop between a range of values. Let X be the continuous random variable, then the formula for the pdf, f(x).

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Answer:

y = 4/3x+2

Step-by-step explanation:

We can use the slope intercept form of the equation

y = mx+b

Where m is the slope and b is the y intercept

y= 4/3 x +b

Substitute the point into the equation

6 = 4/3(3) +b

6 = 4 +b

Subtract 4 from each side

2 = b

y = 4/3x+2

what you need help woth owo

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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The butterfly’s change in elevation each minute is 1.5 feet.

Elevation simply had to do with the height above the sea level.

In this case, the butterfly is flying 8.75 feet above ground and descends at a steady rate to a spot 6.25 feet in 1 2/3. minutes.

The change in elevation will be:

= 8.75 - 6.25.

= 2.50

Therefore, the change per minute will be:

= Change in elevation / Number of minutes

= 2.50 / 1 2/3

= 2.50 / 1.67

= 1.5 feet per minute

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Answer:

its b.

Step-by-step explanation:

yea its complicated

Given are three vectors in set B.

To show that B is dependent

The determinant

Hence vectors are dependent

b) The given equation

Let us try parametrically

These 3 vectors are collinear and hence equation would be

c) Basis for B would be only 2 dimensional

i.e. any two vectors out of 3 form basis

The basis would be (1,0,1) and (0,1,2)

The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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The intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

Option (D) is correct.

What is the intersection of two sets?

The intersection of two sets, A and B, is the set of elements that are common to both sets. It is often represented by A ∩ B.

In this case, Set A = {2, 4, 6, 8} and set B = {1, 2, 3, 4, 5, 6, 7, 8}. The set that represents A ∩ B is {2, 4, 6, 8} because these are the elements that are common to both sets A and B.

So the correct answer is {2, 4, 6, 8}

Hence, the intersection of the given sets is represented as A ∩ B = {2, 4, 6, 8}.

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From the first table, we have;

Given that;

But, table II gives;

Given that;

Where b is same positive constant for both equations.

Recall from a law of logarithm that;

Thus;

Also;

from the second table;

Answer:

Third option is the correct answer

Step-by-step explanation:

\(3 {x}^{5} \bigg( 2 {x}^{2} + 4x + 1 \bigg) \\ \\ = 3 {x}^{5} \times 2 {x}^{2} + 3 {x}^{5} \times 4x + 3 {x}^{5} \times 1 \\ \\ = 3 \times 2 {x}^{5 + 2} + 3 \times 4 {x}^{5 + 1} + (3 \times 1) {x}^{5} \\ \\ \red{ \bold{= 6{x}^{7} + 12{x}^{6} +3 {x}^{5} }}\)

Answer:

4/5 of the cattle is left

Step-by-step explanation:

Given,

A farmer sells 2/5 of his cattle

Let "x" be the total number of cattle

Then,

sold = 2 / 5 x

Then,

Remaining = x - 2x / 5

remaining = 3x / 5

He gives 1/3 of the remainder to his son

son = 1 / 3 × 3x / 5

son = x / 5

Then,

Remaining = 3x / 5 - x / 5

Remaining = 4x / 5

Hope this answer helps you :)

Have a great day

Mark brainliest

Thus 4/5 of the cattle is left

Answer: answer

Step-by-step explanation:4/5 of the cattle is left

The number of months to reach 51 can be illustrated as 3060 - 100x = 51.

The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both.

The farmer planted 3,060 tomato plants in his garden.

Let's assume there's a decrease of 100 monthly.

The number of months, x, it will take for the number of tomato plants in his crop to reach 51 = c

This will be:

3060 - 100x = 51.

This illustrates the equation for the number of months.

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9x9x9x9divide by 4x4x4

Answer:

4⁹ / 4³ = 4⁶ = 4096

Step-by-step explanation:

You can solve this by realising that exponents (the 9 and the 3 in this case), simply tell you how many times to multiply the numbers together.

What you're see there then can also be expressed as:

\(\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4}{4 \times 4 \times 4}\)

Because the numerator and denominator are all multiples of the same number repeatedly, you can simply eliminate the bottom three fours from the top and bottom, giving you:

\(\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times (4 \times 4 \times 4)}{(4 \times 4 \times 4)}\\\\= 4 \times 4 \times 4 \times 4 \times 4 \times 4\)

\(4 \times 4 \times 4 \times 4 \times 4 \times 4\)

A simpler way to look at it is to understand that when the same number is being raised to different bases, and then multiplied or divided, you can simply add or subtract the exponents.  For example, speaking very generically:

\(x^a \times x^b = x^{a + b}\)

and

\(x^a \div x^b = x^{a - b}\)

In this case then, we can simply say:

\(\frac{4^9}{4^3} = 4^{9 - 3} = 4^6\)

So when simplified, the expression is equal to 4⁶, or 4096.

The minimal surface area box has the following measurements: side of base = 5√2/2, height = 5√2, and minimal surface area = 25√2 + 50.

(a) Let x be the side of the square base and y be the height of the box. Then the volume of the box is given by V = x²y = 125, and the surface area is given by S = 2x² + 4xy. We want to minimize S subject to the constraint that V is fixed at 125.

Using the volume equation, we can solve for y in terms of x: y = 125/x². Substituting this expression for y into the surface area equation, we get S(x) = 2x² + 4x(125/x²) = 2x² + 500/x.

To minimize S(x), we take the derivative with respect to x and set it equal to zero:

S'(x) = 4x - 500/x² = 0

Solving for x, we get x = 5√2/2. Substituting this value into the expression for y, we get y = 5√2.

Therefore, the dimensions of the box with minimal surface area are: side of base = 5√2/2, height = 5√2, and minimal surface area = 25√2 + 50.

(b) Let x be the side of the square base and y be the height of the box. Then the surface area of the box is given by S = 2x² + 4xy = 44, and we want to maximize the volume V = x²y.

Using the surface area equation, we can solve for y in terms of x: y = (44 - 2x²)/4x. Substituting this expression for y into the volume equation, we get V(x) = x²(44 - 2x²)/4x = (11x² - x⁴/2).

To maximize V(x), we take the derivative with respect to x and set it equal to zero:

V'(x) = 22x - 2x³/2 = 0

Solving for x, we get x = √11. Substituting this value into the expression for y, we get y = (√11 - √2)²/2.

Therefore, the dimensions of the box with maximal volume are: side of base = √11, height = (√11 - √2)^²/2, and maximal volume = 11(√11 - √2)²/4.

(c) Using Newton's Method, we can approximate the root of f(x) = x³ - 12 starting with an initial guess of x₀ = 2:

x₁ = x₀ - f(x₀)/f'(x₀) = 2 - (2₃ - 12)/(32₂) = 1.833333

x₂ = x₁ - f(x₁)/f'(x₁) = 1.833333 - (1.833333³ - 12)/(31.833333²) = 2.005917

x₃ = x₂ - f(x₂)/f'(x₂) = 2.005917 - (2.005917³ - 12)/(3*2.005917²) = 2.000007

Therefore, the approximated root of f(x) = x³ - 12 using Newton's Method with an initial guess of 2 is x₃ = 2.000007.

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Answer:

at first put the value of X

after that do the equation.

Step-by-step explanation:

hope it will help you

Answer:

a = 2

Step-by-step explanation:

substitute x with the number 5.

5+8a=25+5a-7a

subtract 5a from both sides

5+3a=25-7a

add 7a to both sides

5+10a = 25

subtract 5 from both sides

10a=20

divide both sides by 10

a = 2

The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:

Theorist Approach to Learning Key Concepts

Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.

Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.

Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.

While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

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Answer:

C: One soda cost $2

Step-by-step explanation:

One soda costs $2. As you can see, which each soda you buy, X and Y go up by two. The relationship of X and Y is x=2y, with X being sodas and Y being dollars

Complete question is;

​In a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​adults, complete parts​ (a) through​ (c).

(a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as​ needed.)

​(b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is _______?(Round to three decimal places as​ needed.) ​

(c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models ______? (Round to three decimal places as​ needed.)

Answer:

A) 0.062

B)0.564

C)0.436

Step-by-step explanation:

There are 800 US adults sampled and 199 think that most celebrities are good role models.

Now, two are selected without replacement.

Thus;

A) Probability that both adults think most celebrities are good role models would be = (199/800) × (198/799) = 39402/639200 = 0.062

B) we want to find probability that neither adult thinks most celebrities are good role models.

Now, since 199 out of 800 think that most celebrities are good role models..

Thus, number that doesn't think most celebrities are good role models = 800 - 199 = 601

probability that neither adult thinks most celebrities are good role models. would be = (601/800) × (600/799)= 180300/319600 = 0.564

C) We want to find the probability that at least one of the two adults thinks most celebrities are good role models.

Now, since we already have the probability that neither of them thinks most celebrities are good role models, we will just subtract that probability from 1.

Thus;

probability that at least one of the two adults thinks most celebrities are good role models = 1 - 0.564 = 0.436

Answer:

K'(2, 1 )

Step-by-step explanation:

EDG 2020

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

The answer is D.) 48

Step-by-step explanation:

I made X stand as 3 so my equations would go as follows.

AC=4(3)+12 and 2(3)+18=BC

After solving for both they both become 24 and since C looks like its half way All I did was add 24 and 24 to get 48 as the answer.

Hope this helps.

A brainliest is always appreciated.

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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The solution to given linear inequality, 6(x1.5) + 30 < 48, is x < 2

From the question, we are to solve the given linear inequality

The given linear inequality is

6(x1.5) + 30 < 48

First, we will write this inequality properly.

The inequality can be properly written as

6(1.5x) + 30 < 48

Now, we will solve the linear inequality

6(1.5x) + 30 < 48

Subtract 30 from both sides of the equation

6(1.5x) + 30 - 30 < 48 - 30

6(1.5x) < 18

Divide both sides of the inequality by 6

6(1.5x)/6 < 18/6

(1.5x) < 3
1.5x < 3

Divide both sides of the inequality by 1.5

1.5x/1.5 < 3/1.5

x < 2

Hence, the solution is x < 2

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