express the log in terms of 3 and 7.

ln441

Answer:

A'(4, -2)

B'(3, 0)

C'(1, -2)

Step-by-step explanation:

Coordinates of the vertices of the given triangle are,

A(-4, 2), B(-3, 0) and C(-1, 2)

ΔABC is transformed by the rotation of 180° about the origin.

Rule for the rotation will be,

(x, y) → (-x, -y)

Coordinates of the image triangle A'B'C' will be,

A(-4, 2) → A'(4, -2)

B(-3, 0) → B'(3, 0)

C(-1, 2) → C'(1, -2)

The line represented by the table is:

y = 2x + 40

A general linear relationship is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We can use the first two pairs:

(6, 52) and (9, 58)

Then we will get:

a = (58 - 52)/(9 - 6)

a = 6/3 = 2

y = 2x + b

To find the value of b, we replace the values of one of the points, if we use the first one (6, 52), then we will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b

40 = b

The line is:

y = 2x + 40

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Answer:

132 cm²

Step-by-step explanation:

To find the area of the figure, start by dividing the figure into smaller rectangles.

Area of figure

= area of shaded rectangle +area of unshaded rectangle

\(\textcolor{steelblue}{\text{Area of rectangle= length ×breadth}}\)

Shaded rectangle

Length= 4 cm

Breadth= 6 cm

Area

= 4(6)

= 24 cm²

Unshaded rectangle

Length= 9 cm

Breadth= 12 cm

Area

= 9(12)

= 108 cm²

After finding the area of each rectangle, we can add the two areas together to obtain the total area of the figure.

Area of figure

= 108 +24

= 132 cm²

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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The first major trade route to connect the eastern and western parts of the world is c. the Silk Road.

The Silk Road was an ancient network of trade routes that connected China with the Mediterranean region, facilitating the exchange of goods, ideas, and cultures between the East and the West. It played a significant role in the development of civilizations and global trade during ancient times.

The Silk Road was a network of trade routes that spanned thousands of miles and connected various regions of the ancient world. It got its name from the valuable silk that was one of the major commodities traded along this route.

The Silk Road began around the 2nd century BCE and remained active for many centuries. It linked the civilizations of East Asia (particularly China) with the Middle East, Central Asia, and Europe. The route consisted of both land and sea routes, with caravans and ships carrying goods and facilitating cultural exchange. The correct answer is C.

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The required surface area of the tetrahedron is 4 + 4√2, as of the given condition.

To find the surface of the tetrahedron, we can divide it into four triangular faces and calculate the area of each face. Let's denote the vertices of the tetrahedron as follows:

A = (0, 0, 0)

B = (0, 2, 0)

C = (0, 0, 2)

D = (4, 2, 0)

Now, we can calculate the area of each face:

Face ABC:

This face is formed by vertices A, B, and C. We can calculate the cross product of the vectors AB and AC to find the normal vector of the face, which will give us the area.

Vector AB = B - A = (0, 2, 0) - (0, 0, 0) = (0, 2, 0)

Vector AC = C - A = (0, 0, 2) - (0, 0, 0) = (0, 0, 2)

Normal vector \(N_{ABC} = AB * AC\)

= (0, 2, 0) x (0, 0, 2)

= (4, 0, 0)

Area of face \(ABC = 1/2 * ||N_{ABC}||\)

= 1/2 * ||(4, 0, 0)||

= 1/2 * 4

= 2

Similarly

Area of face ABD = 2

Area of face BCD =  2√2

Area of face CAD =m2√2

Now, we can find the surface area of the tetrahedron by summing up the areas of all four faces:

Surface Area of the Tetrahedron = Area of face ABC + Area of face ABD + Area of face BCD + Area of face CAD

= 2 + 2 + 2√2 + 2√2

= 4 + 4√2

Therefore, the surface area of the tetrahedron is 4 + 4√2.

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The question is incomplete, the complete question is:

Vertices of tetrahedron: (0,0,0),(0,2,0),(0,0,2), and (4,2,0).
To find out the surface area of the tetrahedron.

In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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A team that controls decisions about and execution of a complete range of tasks, including acquisitions, operations, quality control, maintenance, and shipping, is known as a cross-functional team. This type of team consists of individuals from different functional areas or departments within an organization who come together to work collaboratively on specific projects or goals.

Cross-functional teams are designed to break down silos and foster cooperation and communication between different departments or functions. By including representatives from various areas, such as finance, marketing, operations, and logistics, cross-functional teams bring together diverse perspectives, expertise, and skills to address complex issues and achieve common objectives.

These teams are responsible for making decisions related to their assigned tasks, executing plans, and ensuring the successful completion of the project or initiative. Their comprehensive range of responsibilities allows for greater efficiency, coordination, and integration across different functions, leading to improved outcomes and performance.

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To examine the relationship between two variables, the variables must be measured from the same population.

When conducting research, it's critical to ensure that the variables being measured are from the same population. Two variables are said to have a relationship when their values are related to one another in some way. The relationship between two variables is measured to determine how strong the correlation is and how much variation is present.

The measure of correlation or relationship is frequently done using statistical methods, which rely on the assumption that the variables being tested are from the same population. This is because samples drawn from different populations may not be comparable and can have different values for the same variable.

Therefore, to properly compare and assess the relationship between two variables, they must be measured from the same population.

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Answer:82 cm squared

Step-by-step explanation:

Just draw imaginary lines on the shape to turn it into a bunch of squares and rectangles, then find the area of those and add them together.

Kinda hard to explain since there are multiple ways to do it, but I hope that this still helps!

Answer:

Both of the arrowed ones are the sides

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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Answer:

3.2

Step-by-step explanation:

Two small metal spheres are 35. 1 cm apart. The spheres have equal amounts of negative charge and repel each other with forces of magnitude 0. 0360 n. The charge on each sphere \(Q = 1.4 \times 10^{-12}\) c.

According to coulombs law force between two charges is given by  

\(F = \dfrac{1}{4\pi \epsilon }\dfrac{Qq}{r^2}\)

Here, R is the distance between both the charges Q and q.

Two small metal spheres are 35. 1 cm apart.

The spheres have equal amounts of negative charge and repel each other with forces of magnitude 0. 0360 n.

We have given force F =0.036 N

R is the distance between both the charges which is given as 25 cm

So  

\(F = \dfrac{1}{4\pi \epsilon }\dfrac{Qq}{r^2}\)

\(0.036 = \dfrac{1}{4\times 3.14\times 8.85\times 10^{-12} }(\dfrac{Q^2}{35. 1})\)

\(Q = 1.4 \times 10^{-12}\) c

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Answer:

(a) The exponential function representing the number of people who had watched the video \(t\) hours after the initial observation is \(n(t) = 129\cdot 1.3^{\frac{t}{3} }\).

(b) As \(n(120) < 5\times 10^{6}\), we conclude that this video is not going "viral".

Step-by-step explanation:

Statement is incomplete. The complete statement is:

An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.

(a) Write an exponential function for the number of people A who had watched the video n hours after the initial observation.

(b) A video is said to go "viral" if the number of people who have watched the video exceeds 5 million within 5 days (120 hours). Would this video be considered to have gone viral?

(a) From the statement of the problem we get the following relationship:

\(\frac{n_{i+1}}{n_{i}}= r^{[(i+1)-i]}\) (Eq. 1)

Where:

\(n_{i}\) - i-th number of people watching a video, dimensionless.

\(n_{i+1}\) - (i+1)-th number of people watching a video, dimensionless.

\(r\) - Increase ratio, dimensionless.

For Induction Theorem, we get the following relatioship for \(i = 0\):

\(\frac{n_{1}}{n_{o}} = r^{1-0}\) (Eq. 2)

For \(i = m\), the following relationship is constructed:

\(\left(\frac{n_{1}}{n_{o}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+1}}{n_{m}} \right) = r^{m}\)

\(\frac{n_{m+1}}{n_{o}} = r^{m}\)(Eq. 3)

And for \(i = m+1\), we have the following expression:

\(\left(\frac{n_{1}}{n_{0}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+2}}{n_{m}} \right) = r^{m+1}\)

\(\frac{n_{m+2}}{n_{0}} = r^{m+1}\)(Eq. 4)

If we multiply (Eq. 3) by the (m+1)-th ratio based on (Eq. 1):

\(\left(\frac{n_{m+1}}{n_{o}}\right)\cdot \left(\frac{n_{m+2}}{n_{m+1}} \right) = r^{m} \cdot r\)

\(\frac{n_{m+2}}{n_{o}} = r^{m+1}\)

Which is (Eq. 4) and the exponential function is represented by:

\(n_{i+1} = n_{o}\cdot r^{i}\), \(i\in \mathbb{N}_{O}\) (Eq. 5)

As the number of people is increased at constant rate every 3 hours, we get that \(i\) is:

\(i = \frac{t}{3}\), \(t \in \mathbb{R}\), \(t \geq 0\) (Eq. 6)

Where \(t\) is the time, measured in hours.

Then, the exponential function is:

\(n(t) = n_{o}\cdot r^{\frac{t}{3} }\) (Eq. 7)

Where \(n_{o}\) is the initial number of people watching the video, dimensionless.

If we know that \(n_{o} = 129\) and \(r = 1.3\), then the exponential function representing the number of people who had watched the video \(t\) hours after the initial observation is:

\(n(t) = 129\cdot 1.3^{\frac{t}{3} }\)

(b) If we know that \(t = 120\,h\), then we evaluate the exponential function:

\(n (120) = 129\cdot 1.3^{\frac{120}{3} }\)

\(n(120) = 4.659\times 10^{6}\)

As \(n(120) < 5\times 10^{6}\), we conclude that this video is not going "viral".

a) Probability of drawing two cards summing to 21: 1/331

b) Probability of drawing two cards summing to 10: 28/1326

c) Probability of drawing a third card to make the sum strictly larger than 21: 2/25

a) To calculate the probability of drawing two cards that sum to 21, we need to determine the number of favorable outcomes and the total number of possible outcomes.

There are four ways to get a sum of 21 with two cards: drawing an Ace and a face card (4 possibilities).

The total number of possible outcomes is given by the combination of choosing two cards from a deck of 52 cards, which is C(52, 2) = 1326.

Therefore, the probability of drawing two cards that sum to 21 is 4/1326, which simplifies to 1/331 or approximately 0.0030.

b) To calculate the probability of drawing two cards that sum to 10, we need to determine the number of favorable outcomes.

There are several combinations that sum to 10: drawing a 4 and a 6, drawing a 5 and a 5, drawing a 6 and a 4, and drawing a face card and a 10.

The total number of possible outcomes remains the same, which is 1326.

Therefore, the probability of drawing two cards that sum to 10 is (4 + 4 + 4 + 16)/1326, which simplifies to 28/1326 or approximately 0.0211.

c) Given that you have already drawn the 10 of clubs and the 4 of hearts, the sum of these two cards is 10 + 4 = 14.

To find the probability that the sum of all three cards is strictly larger than 21, we need to consider the remaining cards in the deck. Since there are 50 cards left in the deck, we calculate the probability of drawing a card that makes the sum exceed 21.

The only way to exceed 21 is to draw an Ace, which is worth 11. There are four Aces in the deck.

Therefore, the probability of drawing a card that makes the sum strictly larger than 21 is 4/50, which simplifies to 2/25 or approximately 0.08.

Complete question:

Assume that in blackjack, an ace is always worth 11, all face cards (jack, queen, king) are worth 10, and all number cards are worth the number they show. given a shuffled deck of cards:

a) What is the probability that you draw two cards and they sum 21

b) What is the probability that you draw two cards and they sum 10

c) Suppose, you have drawn two cards: 10 of clubs and 4 of hearts. You now draw a third card from remaining 50. What is the probability that the sum of all three cards is strictly larger than 21?

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Answer:

The answer is \(s = - \frac{3}{2}\) .

Step-by-step explanation:

Solve the equation:

\(0.5s + 1 = 7 + 4.5s\)

-Subtract \(4.5s\) from \(0.5s\) :

\(0.5s + 1 -4.5s = 7 + 4.5s -4.5s\)

\(-4s + 1 = 7\)

-Subtract both sides by \(1\) :

\(-4s + 1 - 1 = 7 -1\)

\(-4s = 6\)

-Divide both sides by \(-4\) :

\(\frac{-4s}{-4} = \frac{6}{-4}\)

\(s = -\frac{3}{2}\)

So, therefore, the final answer is \(s = -\frac{3}{2}\) .

Answer:

-3/4

Step-by-step explanation:

The slope of line passes through the points (-9,10) and (-13,13)​ is -3/4.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

(-9,10) and (-13,13)​

So, slope= (13 - 10)/ ( -13 + 9)

slope= 3 / (-4)

slope= -3/4

Hence, the slope of line is -3/4.

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Answer:

a) Area of sector TRV = \( 42.4\: units^2 \)

b) \( 0.8\: units\)

Step-by-step explanation:

a)

In \( \odot R\), TW is diameter.

Therefore,

\( m\widehat {TVW} = 180\degree \)

\( \because m\widehat {TV} +m\widehat {VW} =m\widehat {TVW} \)

\( \therefore m\widehat {TV} +120\degree =180\degree \)

\( \therefore m\widehat {TV} =180\degree - 120\degree \)

\( \therefore m\widehat {TV} = 60\degree \)

\( \because m\angle TRV=m\widehat{TV} \)

(Measure of central angle is equal to the measure of its corresponding arc)

\( \therefore m\angle TRV\:(\theta) =60\degree \)

Radius (r) = RW = 9 units

Area of sector TRV

\( =\frac{\theta}{360\degree}\times \pi r^2 \)

\( =\frac{60\degree}{360\degree} \times 3.14\times 9^2 \)

\( =\frac{1}{6} \times 3.14\times 81 \)

\( =\frac{1}{6} \times 254.34 \)

\( =42.39\: units^2 \)

Area of sector TRV\( =42.4\:units^2 \)

b)

Length of \( \widehat{VW} \)

\( =\frac{120\degree }{360\degree} \times 2\pi r \)

\( =\frac{2}{3} \times 3.14\times 9 \)

\( =2 \times 3.14\times 3 \)

Length of \( \widehat{VW} \) \( = 18.84\: units \)

\( \overline{TW} =2*RW =2*9 = 18\: units\)

\( \widehat{VW}- \overline{TW}= 18.84-18=0.84\: units\)

\( \widehat{VW}- \overline{TW}= 0.8\: units\)

Answer:

answer is 15 and second one i dont know yet sorry am doing scoo

Step-by-step explanation:

Answer:

10+8+6=24 the ratio of taking the biographies to the science books are: 4:3

Step-by-step explanation:

That is the answer because 10+8+6= total 24 books

ratio of biographies= 24:8=3:1

ratio of science fiction= 24:6= 4:1

hence according axiom 1 ab × Ac= aa × BC

3:1×4:1= 4:3

HOPE THIS HELPSBYOU✌️

Answer:

7083 KM/H

Step-by-step explanation:

17000 / 2.4 = 7083 (Plus some decimals, but rounded up its 7083.)

Answer:

C

Step-by-step explanation:

The domain of the given function is  {–2, 0, 2} while range is {4, 0} so option (C) will be correct.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Given the function,

An arrow goes from negative 2 to 4, 0 to 0, and 2 to 4.

So,

-2 → 4 , 0 → 0 and 2 → 4

Since the domain is a set of input values here input is -2,0 and 2.

So

Domain = {-2,0,2}

And the range is a set of output values here output is 4, 0

So,

Range = {4,0}

Hence "The domain of the given function is  {–2, 0, 2} while range is {4, 0}".

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Asymptote indicates that as time increases, the number of bacteria approaches 0.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Once an antibiotic is given, number of bacteria decreases at a rate of 15% /day.

There were about 15,000 bacteria prior to the treatment.

The line y = 0 is an asymptote of the graph.

The y-intercept is 15,000.

The y-intercept represents the number of bacteria when treatment began.

The asymptote indicates that as time increases, the number of bacteria approaches 0.

Hence, asymptote indicates that as time increases, the number of bacteria approaches 0.

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You can by 24 combinations of items from the store

The given parameters are:

Cups = 3

Bowl = 4

Spoon = 2

The number of combination is:

Combination = Cups * Bowl * Spoon

So, we have:

Combination = 3 * 4 * 2

Evaluate

Combination = 24

Hence, you can by 24 combinations of items from the store

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Answer:

ghjjj

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

5 1/4=21/4, 21/4÷3/4=7

Answer:

15x + 30

Step-by-step explanation:

Step 1:

(15 × x) + (15 × 2)  [∵ a (b + c) = (a × b) + (b × c)]

Step 2:

15x + 30

Hope it helps :)

Please mark my answer as the brainliest

Hi, let me help you out!

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In order to simplify this expression, we should use the Distributive Property:

\(\longrightarrow\tt{a(b+c)=ab+ac}\)

Where a, b, and c can be constants, variables, or both.

Now, simplify:

\(\longrightarrow\tt{15(x+2)}\)

\(\longrightarrow\tt{15x+30}\)

Hence, we conclude that the answer is: \(\tt{15x+30}\).

I hope this helps you! Have an awesome day!

If you need any explanation or clarification, kindly let me know, and I'll comment! :D

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