Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. [2 -1 -4 2 6 -3] x = x_2 + X_3 (Type an integer or fraction for each matrix element.)

By applying linear equation concept, it can be concluded that the number of stamps in the 25th month is 990 stamps

Linear equation is equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

y = mx + C where

m = Δy / Δx = slope of the line

C = constant

We have the following data:

Month    Number of stamps

   1                      30

   2                     70

   3                     110

   4                     150

   5                     190

As we look at the attached graph, this data is depicted as a linear graph. Thus we want to find the linear equation.

First, we calculate the m:

m = Δy / Δx

   = (70 - 30) / (2 - 1)

   = 40 / 1

   = 40

To find C, we pick one point, let say point (1,30) and input it into the equation:

 y = mx + C

30 = 40*1 + C

30 = 40 + C

 C = -10

Now we have the linear equation:

y = mx + C

y = 40x - 10

We want to know the number of stamps in the 25th month, so we input this value into the equation:

y = 40x - 10

   = 40*25 - 10

   = 1000 - 10

   = 990

Thus, the number of stamps in the 25th month is 990 stamps.

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The lateral Surface Area of ​​a Cylinder  is is 345  cm²  

What are solids ?

A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

lateral Surface Area of ​​a Cylinder  is :

L= 2 × π × r × h

where, r = base radius,

and h = height of the cylinder

L= 2 × 3.14 × 4.9 × 11.2

=> L=  344.646  cm²

Nearest whole number: 345  cm²

The lateral Surface Area of ​​a Cylinder  is is 345  cm²  

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The total amount when $9500 is invested at 10% simple interest for 5 years is $14, 250

It is important to note that the formula for simple interest is expressed mathematically with the equation;

I = PRT/100

The parameters are given;

From the information given, we have the values of the principal amount, time and the interest rate

Substitute the values, we get;

Simple interest, I = $9500 × 10×5/100

Multiply the values

Simple interest, I = $475, 000/100

Divide the values

Simple interest, I = $4, 750

Thus, the total amount is $14, 250

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How to solve you question!

First, combine multiplied terms into a single fraction.

Like this! (click first file)

sorryyy, i had to do it virtually bc i couldnt find a pencil -.-

then, multiply it by 1.

Like dis! (click second file)

Then, find the common denominator. :>

like dis!!

(obvi, click the third file)

Then, your solution will be dis. (click fourth file.)

Now that we know our solution for the first one, lets do the second one now.

now, if you have the same answers for both, that means, yes, they are equivalent. If no, they are not. If this helped you, please answer my one question of my profile. Thanks!!

Answer:

X=. 1. X=. 2

Step-by-step explanation:

The first story (movie theater) has the equation 6(x+3)= 24. The equation for the juice story is 3(x+6)=24 . The x in the move theater story is the cost of each ticket. The x in the juice story is the amount of juice poured to each friend originally (before the extra 6 ounces). The solution to the movie theater story is 6((1)+3)=24. So x is one is the first story.In the juice story, 3((2)+6)= 24. So x is two. The solution tells me that in the movie theater story that each ticket cost 1 dollar. In the second story, it tells me that 2 ounces of juice where poured to each freind originally. So each freind got a total of 8 ounces of juice.

Step-by-step explanation:

I see only 2 stories and equations.

a.

6(x + 3) = 24

is for the first story (6 show tickets and snacks).

3(x + 6) = 24

is for the second story (juice for 3 friends).

b.

in the first story it is the price of one ticket to the show.

in the second story it is the original amount of juice each friend gets before adding 6 oz.

c. and d.

6(x + 3) = 24

6x + 18 = 24

6x = 6

x = 1

each ticket to the show was $1.

3(x + 6) = 24

3x + 18 = 24

3x = 6

x = 2

each of the 3 friends got first 2 oz of juice, before they each got additional 6 oz. so, ultimately, each friend got 8 oz.

Answer:

We can solve for x by using logarithms.

9^(x + 10) + 3 = 92

9^(x + 10) = 89

Take the log base 9 of both sides:

x + 10 = log9(89)

x = log9(89) - 10

To find the value of log9(89), you can use a logarithm table or calculator.

The solution for x is:

x = log9(89) - 10

The discrete probability distribution of the number of successes in a series of n independent experiments is called the binomial distribution with parameters n and p in probability theory and statistics.

What is the binomial distribution?

The binomial distribution formula aids in determining the likelihood that "x" successes will occur in "n" separate trials of a binomial experiment. Recall that there are two possible outcomes for the statistics probability distribution known as the binomial distribution. The binomial distribution in probability theory has two parameters, n and p. When the probability distribution satisfies the following conditions, it becomes a binomial probability distribution. Each experiment may only yield two results, or results that can be reduced to two results. These results could result in success or failure. There must be a specific number of trails. Each trial's results must be distinct from one another.

Additionally, each trial's likelihood success rate must remain constant.

Using binomial probability formula,

k P(X = k)

0 0.0001

1 0.0020

2 0.0236

3 0.1355

4 0.3899

5 0.4489

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The graph which represents the linear equation y = 1/2 x + 2 is the graph of a line passing through the points (-4, 0) and (0, 2).

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

The slope intercept form of a line is,

y = mx + c,

m : slope and c : y intercept

y intercept is the y coordinate of a point when x coordinate equals 0.

Given linear equation is y = 1/2 x + 2.

m = 1/2 and c = 2

Find the slope and y intercept of each of the line in the options given.

In the first option, we have the point (0, -2).

y intercept of this line = -2, which is not the required y intercept.

In the second option, points given are (-4, 0) and (0, 2).

Since we have the point (0, 2), y intercept = 2

m = (2 - 0) / (0 - -4) = 2 / 4 = 1/2

So the line in the second option is the required line.

Hence the graph of the line represented in the second option is the required line.

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The website is advertising a 46% discount on the jacket, meaning that Farah will pay 46% less than the original price if she decides to buy it now.

A discount is a reduction in the original price of an item, allowing the customer to purchase it for less than the original price.

To calculate the discount mathematically, we can use the following formula:

Discounted price = Original price * (1 - discount percentage)

Let's assume the original price of the jacket is P dollars.

The discount percentage is 46%, which can be written as a decimal 0.46. To find the discounted price, we need to multiply the original price by (1 - discount percentage), which is (1 - 0.46) = 0.54.

So, the discounted price after the 46% saving will be P * 0.54 dollars.

In other words, Farah will pay 0.54 times the original price, P, to buy the jacket with the advertised 46% saving.

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Answer:

[tex] - \frac{8}{7} - ( - \frac{6}{5}) \\ \\ \longrightarrow \: - \frac{8}{7} \: \: + \: \: \frac{6}{5} \\ \\ taking \: LCM \\ \\ \longrightarrow \: \frac{ - 40 + 42}{35} \\ \\ \longrightarrow \: \boxed{ \frac{2}{35} }[/tex]

hope helpful! :-;

The required consumer surplus for the given question is $1000.

The consumer surplus can be calculated by finding the difference between the maximum price the consumers are willing to pay and the actual market price.

Given the demand equation QD = 800 - 100P and the supply equation QS = -100 + 200P, we can find the market equilibrium price and quantity by setting QD = QS and solving for P

800 - 100P = -100 + 200P

900 = 300P

P = 3

So, the market equilibrium price is P = 3, and the market equilibrium quantity is Q = QD = QS = 800 - 100P = 800 - 100 * 3 = 500.

To find the consumer surplus, we need to find the area between the demand curve and the market price. The demand curve can be represented by a linear equation: QD = 800 - 100P. The maximum price the consumers are willing to pay for each quantity can be found by substituting the quantity into the demand equation:

Q = 500: 800 - 100P = 500 => P = 5

So, the maximum price the consumers are willing to pay for Q = 500 is P = 5. The consumer surplus can be found by calculating the area of the triangle between the market price P = 3 and the maximum price P = 5:

Consumer Surplus = 1/2 * (5 - 3) * 500 = 1000

So, the consumer surplus is $1000.

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The probability the stone lands on a black tile is 5/9

This question uses the fundamental counting principle, The fundamental counting principle states that if there are m choices for one event and n choices for another event, then there are m x n total choices for the two events combined.

The total number of outcomes is the product of the number of choices for each event.

Given:

Count the number of black tiles in the arrangement.

There are 5 black tiles.

Count the total number of tiles in the arrangement.

There are 9 total tiles.

Calculate the probability of the stone landing on a black tile.

Probability = (No. of favourable outcomes) / (Total no. of favourable outcomes)

The probability of the stone landing on a black tile is 5/9.

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Answer: 30 ft

Let's assume the original dimension of the carpet was LxW. Now let's have Lin cut a 1 foot wide strip from the length. That gives her a strip that's L feet long. She then cuts a strip from the other side, giving her another strip that L feet long. She then cuts a strip from the width, giving her a 3rd strip that's (W-2) feet long. And finally, she cuts a 4th strip that's also W-2 feet long. So the total length of all those strips is L + L + W - 2 + W - 2 = 2L + 2W - 4 feet long. And since all the strips are 1 foot wide, they cover 2L + 2W - 4 square feet. So: 2L + 2W - 4 = 26 2L + 2W = 30 Now the original perimeter of the carpet is 2L + 2W, therefore the original perimeter is 30 feet.

The solution is (-5,0), the interval in which the function is increasing.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

In case when you tracking the finger across the line, at which there is an increase or decrease in y axis so this is we called intervals. Moreover, the interval notation is also necessary as it depicts the beginning and ending points. In this, the first number denotes the minimum number while the second number denotes the maximum number

For Decreasing:

(-8,-5)

(4,8)

For Increasing:

(-5,0)

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Answer:400

Step-by-step explanation:

The height of the arch at a distance of 7.5 m from the center is 7m

It's important to keep in mind that a parabola has the usual form of y = a(x - h)2 + k, where (h, k) denotes the vertex and a determines the shape and vertical orientation. x and y are (100, 0) in. You are then provided with the parabola's equation.

What height of the arch, as measured from a point on the water 40 meters from the center of the arch, would sustain a bridge over a river?

The arch is 200 meters wide at water level and 80 meters tall at its tallest point

The peak of the arch might serve as the vertex and be located at position y0 on the y-axis if we wish to plot this on a graph or represent it in an equation

The equation of the parabolic arch is

x² = - 4ay

Lets take x and y for first case as (14, 30)

⇒ 14² = - 4a(30)

⇒ a = −49/30

Now we have a so lets put the formula for another variable to find height

Here, y = 7.5

​x² = - 4ay

⇒ ​x² - 4(-49/30)(7.5)

x = 7

Thus, The height of the arch at a distance of 7.5 m from the center is 7m.

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The  term could be put in the blank to create a fully simplified polynomial written in standard form is  x²y².

option A.

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

From the given polynomial equation 8x³y² ------ + 3xy² - 4y³

Here the power of x decreases by 1, so the the power of x of the next term will x²y².

Thus, the complete polynomial equation would be 8x³y² - x²y² + 3xy² - 4y³

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Answer: 1. No, because figure 1 is 5 squares and figure 2 is 6 squares

Step-by-step explanation:

As a result, the function [tex]f(x)=-2x^5+3x^3[/tex] has values of 405 for f(3) and 88 for f(-2) when x is substituted for 3 and 2, respectively.

Statistics and their variations, equations but also associated structures, shapes as well as their locations and potential locations, are all topics covered in algebra. The interaction between a collection of inputs, each of which has an associated output, is referred to as a "function." An relationship between inputs and outputs, where each input yields a single, distinct outcome, is called a function. For each function, a region and a minimal area, or scope, are designated. The letter f is frequently used to represent functions (x). X is the input. The four basic kinds of functions that are offered are on actions, one-to-one operations, many-to-one functions, within functions, and on functions.

given

[tex]f(x)=-2x^5+3x^3f(3) = -2(3)^5 + 3(3)^3[/tex]

= -486 + 81

= 405

ii)[tex]f(x)=-2x^5+3x^3f(-2) = -2(-2)^5 + 3(-2)^3[/tex]

= -64 - 24

= - 88

As a result, the function [tex]f(x)=-2x^5+3x^3[/tex]has values of 405 for f(3) and 88 for f(-2) when x is substituted for 3 and 2, respectively.

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The equation  models the problem is 54

The given parameters that will help us to determine the number are

During the first weekend of December, 43 pine trees were sold. The farm sold 97 trees in all that weekend.

There are two kinds of trees

Tir and Pine.  On the farm and in the weekend as 97 trees were sold with 43 pine tress.

Let f represent fir trees

This implies that f+43 = 97

⇒f= 97-43

f=54 tress

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To solve the equation 5x^2 - x - 5 = 0, you can use the quadratic formula.

First, rearrange the equation to have 0 on the right side:

5x^2 - x - 5 = 0

Next, use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 5, b = -1, and c = -5.

Plug in the values:

x = (-(-1) ± √((-1)^2 - 4 * 5 * -5)) / 2 * 5

x = (1 ± √(1 + 100)) / 10

x = (1 ± √101) / 10

So the two solutions are:

x = (1 + √101) / 10

x = (1 - √101) / 10

--The question is incomplete, answering to the question below--

"How to solve 5x^2-x = 5?"

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She will travel a distance of 62.8 feet × 5 revolutions = 314 feet.

Calculate the circle of the carousel (the distance around the outside) and multiply it by the number of revolutions to determine how far Sierra will move after five rotations.

The following equation can be used to determine the carousel's circumference:

Circumference = 2πr

Where "radius" refers to the carousel's radius and "" is an irrational integer roughly equivalent to 3.14. (in this case, 10 feet).

Substitute the values in the above equation, we get

Circumference = 2 × 3.14 × 10 feet

Circumference = 62.8 feet

Since Sierra will make five revolutions, she will travel a distance

= 62.8 feet × 5 revolutions = 314 feet.

Remember that this is only an estimate because the precise distance may have varied slightly depending on the carousel's speed and Sierra's position on it, among other things.

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The probability that all red balls will be selected is 0.0083.

The total number of ways to select 6 balls from the jar is 12C6, which is equal to 495. The number of ways to select only red balls is 4C6, which is equal to 1. So, the probability of selecting all red balls is 1/495 = 0.0083. This means that only a small chance of selecting all red balls exists among all possible selections of 6 balls.

Probability is a mathematical concept that provides a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain to occur.

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Answer:

The ratio of the population of Japan to the population of Brazil is 1.30 x 108 : 1.95 x 108, which can be simplified to 13:19. Therefore, x = 6.

Step-by-step explanation:

The gallons of water used column should have four entries: 0, 20, 40, andTo plot the point, you need to plot the values from the table on a graph.

Time (minutes): 0, 2, 4, 6

Gallons of Water Used: 0, 20, 40, 60

Plot: (0, 0), (2, 20), (4, 40), (6, 60)

To complete the table, you need to fill in the time (minutes) and gallons of water used columns.

The time column should have four entries: 0, 2, 4, and 6.

The gallons of water used column should have four entries: 0, 20, 40, andTo plot the point, you need to plot the values from the table on a graph.

The point (0, 0) represents 0 minutes and 0 gallons of water used.

The point (2, 20) represents 2 minutes and 20 gallons of water used.

The point (4, 40) represents 4 minutes and 40 gallons of water used.

The point (6, 60) represents 6 minutes and 60 gallons of water used.

The complete question is :

A shower used 60 gallons of water in 6 minutes. Complete the table and plot the point.

Time (minutes): 0, 2, 4, 6

Gallons of Water Used: 0, 20, 40, 60

Plot: (0, 0), (2, 20), (4, 40), (6, 60)

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To find C the Pythagorean formula is used which would be = 7.6

The formula for the Pythagorean theorem is given as follows:

c² = a²+b²

where;

a = 7

b = 3

C = ?

c² = 7²+3²

c² = 49+ 9

c² = 58

C= √ 58

C = 7.6

Therefore, when the Pythagorean formula is being used, the value of the missing side of the triangle = 7.6.

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The hypotenuse of the right triangle is:

C = 7.6

On the image we can see a right triangle where C is the hypotenuse of said triangle.

Remember the Pithagorean's theorem, it says that if A and B are the two legs of the right triangle, then C can be written as:

C = √(A² + B²)

Here we can see that:

A = 3

B = 7

Replacing that we will get:

C = √(3² + 7²) =7.6

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A frequency table is a simple tabular representation of the number of times a particular value or range of values appears in a data set.

It lists the values in one column and the corresponding frequencies in another column. For example, if we have data on the heights of a group of people, a frequency table could list the heights (in cm) in one column and the number of people with that height in the other column.

A frequency distribution is a graphical representation of the same information as a frequency table. It shows the number of occurrences of values in a data set by grouping the values into classes or intervals, and then plotting the frequency of each class or interval. For example, a histogram is a type of frequency distribution where the data is divided into equal-width intervals and the height of each bar represents the frequency of the data that falls within that interval.

A frequency table can be used for both qualitative and quantitative data, whereas a frequency distribution can only be used for quantitative data. This is because the classes or intervals used in a frequency distribution require a numerical representation of the data, which is not possible for qualitative data.

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The measure of ∠K is 72°.

To find the measure of ∠K in ΔJKL, we can use the Law of Cosines. The formula is:

cos C = (a^2 + b^2 - c^2) / 2ab where C is the angle opposite the side of length c.

In this case,

Plugging in the values, we get:

cos C = (720^2 + 640^2 - 520^2) / 2 * 720 * 640

cos C = 0.4756

Finally, to find the measure of ∠K, we use the inverse cosine function:

∠K = cos^-1 (0.4756)

∠K = 72.22°

Rounding to the nearest degree, ∠K = 72°.

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The complete question is:

In ΔJKL, j = 520 inches, k = 730 inches, and l=640 inches. Find the measure of ∠K to the nearest degree.

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Alfred sold 98 + the minimum required tickets, so the total number of tickets he sold is 98 + the minimum required.

1. Alfred reported that he raised 98 dollars more than the minimum required.

2. To get the total number of tickets he sold, we will need to add the 98 dollars more than the minimum required to the minimum required amount.

3. Therefore, the total number of tickets Alfred sold is 98 + the minimum required.

Alfred sold 98 + the minimum required tickets, so the total number of tickets he sold is 98 + the minimum required.

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