I Need Help!!
Write a rule for this function

The answers for each line are:

a) the slope is  -2

b) The slope is 2/5 and the y-intercept is -2.

c) x = 10/4

d) y = -7x - 2

A linear equation can be written as:

y = a*x + b

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

We know that if the line passes through (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

a) Then the slope of the line that passes through (2, -5) and (-2, 3) is:

a = (3 + 5)/(-2 - 2) = 8/-4 = -2

b) The line is 2x - 5y = 10

Isolating y we will get:

5y = 2x - 10

y = (2/5)*x - 2

The slope is 2/5 and the y-intercept is -2.

c) Here we need to solve:

-4 = (1 + 9)/(0 - x)

-4*-x = 10

x = 10/4

d) if the slope is -7, then we have:

y = -7x + b

And the line also passes through (-1, 5), then:

5 = -7*-1 + b

5 = 7 + b

5 - 7  =b

-2 = b

The line is:

y = -7x - 2

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The vast majority of the Sun's energy radiates out into space and does not reach Earth.

Why does so little of the Sun's energy reach Earth?

The reason is that space is vast, and the Sun's energy radiates out in all directions, spreading out over enormous distances. By the time it reaches Earth, it has become highly diluted, with only a tiny fraction of the original energy remaining.

Factors that reduce the amount of the Sun's energy reaching Earth-

The Sun's energy is produced through nuclear fusion in its core, where hydrogen atoms are fused together to form helium, releasing vast amounts of energy in the process. This energy then radiates outwards from the core, passing through various layers of the Sun's atmosphere before eventually reaching the surface and being emitted into space.

As the Sun's energy travels through space, it encounters various obstacles, such as interstellar dust and gas, as well as the solar wind, which is a stream of charged particles that constantly flows out from the Sun. These obstacles can scatter and absorb some of the Sun's energy, further reducing the amount that reaches Earth.

Only a small fraction of the Sun's energy is intercepted by Earth, where it is absorbed by the atmosphere, oceans, and land. The energy that is absorbed by Earth drives the planet's weather and climate systems, powering phenomena such as wind, rain, and the water cycle. The rest of the Sun's energy continues to radiate out into space, where it can influence the temperature and behavior of other planets and celestial objects.

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Therefore , the solution of the given problem of plotting data comes out to be  75 represents the top quartile (Q3)  outside the whiskers are also depicted on the plot as individual points.

The most popular method for displaying data in a geographical format is to demonstrate the correlation between two additional factors. Digital or hand-drawn sketches are both acceptable. Starting at the starting the spot, move three separate parts upward and then two or more components in the right. The display of the reference system must show the numerals for positions 2, 3, and 4.

Here,

The following details are displayed by the box-and-whisker plot:

The cutoff is somewhere around 35.

=> Around 55 constitutes the bottom quartile (Q1).

=> At around 65, the median (Q2) is.

=> Around 75 represents the top quartile (Q3).

The top number is somewhere around 95.

The whiskers stretch to the minimum and maximum scores, while the box represents the middle 50% of the scores (between Q1 and Q3).

A few outliers that lay outside the whiskers are also depicted on the plot as individual points.

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Answer:

To compare the cost of each option, we need to calculate the cost per flyer.

For the first option, the cost per flyer is:

30 dollars / 100 flyers = 0.3 dollars/flyer

For the second option, the cost per flyer is:

65 dollars / 250 flyers = 0.26 dollars/flyer

Therefore, the second option is cheaper per flyer. However, if you only need 100 flyers, the first option would be more cost-effective.

Step-by-step explanation:

Answer: $65 for 250 flyers is cheaper

Step-by-step explanation:

30 dollars per 100 flyers - 30/100 = 0.30 or 30 cents per flyer

65 dollars per 250 flyers - 65/250 = 0.26 or 26 cents per flyer

Answer:

Probability=number of chances/total possible outcome

P=3/10

we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5. The solution to the compound inequality is u >= 5.

To solve the compound inequality, we need to isolate the variable on one side of the inequality.

For the first inequality, 4u + 5 > 13, we can subtract 5 from both sides to get:
4u > 8

Then, we can divide both sides by 4 to get:
u > 2

For the second inequality, 2u + 6 >= 16, we can subtract 6 from both sides to get:
2u >= 10

Then, we can divide both sides by 2 to get:
u >= 5

Now, we can graph the solution on the number line. The solution will be the intersection of the two inequalities, which is u >= 5.

On the number line, we can draw a closed circle at 5 and shade to the right to indicate that the solution includes 5 and all numbers greater than 5.

The solution to the compound inequality is u >= 5.

Here is the graph of the solution on the number line:

    0  1  2  3  4  5  6  7  8  9  10

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Yes, the given ring is commutative.We have that, a commutative ring in abstract algebra is a ring that satisfies a +b = b+a (for a defined operator).

Given: R is a ring such that [tex]$x = x^2$[/tex] for all [tex]$x\in R$[/tex].

To prove: R is a ring commutative.

Proof:

Let [tex]$a$[/tex] and [tex]$b$[/tex] be arbitrary elements in [tex]$R$[/tex].

[tex]$a+b = (a+b)^2 = a^2 + 2ab + b^2$[/tex]

[tex]$b+a = (b+a)^2 = b^2 + 2ab + a^2$[/tex]

Therefore, [tex]$a+b = b+a$[/tex]. Thus, R is a ring commutative.

Q.E.D.

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Answer:

ok divide is easy

Step-by-step explanation:

dividing is not adding or subtracting

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Step-by-step explanation:

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Thank You!

9.63 years are required for $390 to become $660. A charge for borrowing money or other assets is called an interest.

Compound interest simply indicates that the interest paid on a savings account, loan, or investment grows exponentially over time rather than linearly.

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Here, A = Amount,

P = Principal Amount

r = Rate of interest

n = Number of times interest is charged in a year

t = number of years

Given ,Here Principal Amount is $390, the rate of interest is 5.5%(0.055),

the number of times the interest is charged in a year (n=4),

and the final amount is $660,

therefore, number of years will be equal to,

[tex]660 = 390(1 + \frac{0.055}{4} )^{4*t}[/tex]

[tex]\frac{660}{390} = (1.01375)^{4*t}[/tex]

[tex]1.6923 = (1.01375)^{4*t}[/tex]

[tex]log_{1.01375}1.6923 = 4t[/tex]

[tex]4t = 38.5234[/tex]

[tex]t = 9.63[/tex]

Hence, number of years it will take for $390 to become $660 is 9.63 years.

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Answer:

2x-12y

Step-by-step explanation:

This is equivalent to the original fraction--4(1/2x - 3y)

If we were to solve 4(1/2x - 3y), we'd get: 2x-12y.

Meaning, 2x-12y is equivalent to 4(1/2x - 3y).

Answer:

Let's first calculate the number of compounding periods in a year, given that the interest is compounded quarterly:

Number of compounding periods in a year = 4 (since there are 4 quarters in a year)

Next, let's use the formula for compound interest to find the annual interest rate:

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

Where:

A is the balance after t years

P is the principal (initial balance)

r is the annual interest rate (what we are looking for)

n is the number of compounding periods in a year

t is the time in years

We know that P = $1250, A = $1406.08, n = 4, and t = 9/12 years (since the interest is earned for 9 months).

Plugging these values into the formula, we get:

$1406.08 = $1250 (1 + r/4)^(4/3)

Dividing both sides by $1250 and taking the cube root of both sides, we get:

1 + r/4 = (1406.08/1250)^(3/4)

1 + r/4 = 1.038

Subtracting 1 from both sides, we get:

r/4 = 0.038

Multiplying both sides by 4, we get:

r = 0.152

Therefore, the annual interest rate is 15.2%.

Answer:

The 7 screws offer superior tensile strength over the 8 nails. The 7 screws are heavier.

Answer:

  [-4, 2]

Step-by-step explanation:

You want the range of the graph shown.

The range is the vertical extent of the graph. This graph has a minimum at y=-4 and a maximum of y=2. All values between these are represented, so the range is ...

  [-4, 2] . . . . or -4 ≤ y ≤ 2

We can conclude that the equation of the line of best fit is -

ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -

intercept is 1077.04596.

Given is a table as shown in the image.

-6.6

-5.6

-3.6

-1.6

-0.6

0.4

2.4

3.4

5.4

6.4

-4887.5

-3887.5

-2587.5

-1287.5

-637.5

962.5

1762.5

2312.5

3737.5

4512.5

43.56

31.36

12.96

2.56

0.36

0.16

5.76

11.56

29.16

40.96

{SS} : 178.4

32257.5

21770

9315

2060

382.5

385

4230

7862.5

20182.5

28880

{SP} : 127325

Sum of {X} = 66

Sum of {Y} = 57875

Mean {X} = 6.6

Mean {Y} = 5787.5

Sum of squares {SSₓ} = 178.4

Sum of products {SP} = 127325

Regression Equation -

ŷ = bX + a

b = SP/SSₓ = 127325/178.4 = 713.70516

a = MY - bMₓ = 5787.5 - (713.71*6.6) = 1077.04596

ŷ = 713.70516X + 1077.04596

Slope -

{m} = 713.70516

{y} - intercept = 1077.04596

Therefore, we can conclude that the equation of the line of best fit is -

ŷ = 713.70516X + 1077.04596. Also, the slope {m} is 713.70516 and {y} -

intercept is 1077.04596.

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The three-dimensional figure this net will make is a triangular prism and is denoted as option B.

This is defined as a solid figure or an object or shape that has three dimensions such as length, width, and height.

An example is the triangular prism is a polyhedron made up of two triangular bases and three rectangular sides and from the net given above we can deduce that the triangular prism can be formed from it due to the shape and vertices.

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The permutation [[1,2,3,4,5,6],[6,5,4,3,2,1]] can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).



A permutation can be represented as a product of disjoint cycles. A cycle is a sequence of numbers that are permuted in a circular fashion. For example, the cycle (1,2,3) means that 1 is permuted to 2, 2 is permuted to 3, and 3 is permuted to 1.

To write the given permutation as a product of disjoint cycles, we can start with the first number in the first row, 1, and see where it is permuted to in the second row. In this case, 1 is permuted to 6. Then we look at where 6 is permuted to, which is 1, completing the cycle (1,6).

Next, we move on to the next number in the first row that has not been included in a cycle, which is 2. We see that 2 is permuted to 5, and 5 is permuted to 2, completing the cycle (2,5).

Finally, we move on to the next number in the first row that has not been included in a cycle, which is 3. We see that 3 is permuted to 4, and 4 is permuted to 3, completing the cycle (3,4).

Therefore, the given permutation can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).

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The cost of the washer is $265 and the cost of the dryer is $350.

To solve this word problem with two unknowns using a linear equation, we can use the following steps:

So, the cost of the washer is $265 and the cost of the dryer is $350.

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The trigonometric value of angle Cos Z would be = 77°

A trigonometric value is defined as those values that are based on three major trigonometric ratios such as the Sine, Cosine, and Tangent.

According to the rules of trigonometry the following is carried out:

Sine or sin θ = Side opposite to θ / Hypotenuse = XY / XZ

Cosines or cos θ = Adjacent side to θ / Hypotenuse = YZ / XY

Tangent or tan θ =Side opposite to θ / Adjacent side to θ = XY / YZ.

Therefore, the trigonometric value of cos Z = adj/hypo = 9/40 = 0.225

Z = Cos^-1 0.225.

Z = 76.9 = 77°

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Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.

To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:

There were n1 squirrels in the first group.

Second sample's fox count is equal to n2.

Second sample's total number of labelled squirrels is m2.

The following provides the Lincoln-Petersen index:

=> n1 * n2 / m2

Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.

=> n1 * n2 / m2 = 100 * 200 / 20 = 1000

Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.

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The graphs of y = 1/2x - 10 - 3 and y = 1/x are different in shape and behavior, and their only similarity is that they are both continuous functions.

What is a graph ?

Graph can be defined as visual representation of data using ordered pairs.

The graphs of y = 1/2x - 10 - 3 and y = 1/x have different shapes and behaviors.

The graph of y = 1/2x - 10 - 3 is a linear function with a slope of 1/2 and a y-intercept of -13. This means that the graph will have a constant slope of 1/2, and will be downward sloping from left to right. As x increases, y decreases at a steady rate.

On the other hand, the graph of y = 1/x is a non-linear function that is a hyperbola. This means that the graph will be curved and will have two branches, one in the first quadrant and the other in the third quadrant. The graph will approach the x and y-axes but will never touch them. The curve will be symmetric about the line y = x, which means that for every point (x, y) on the graph, there will be a corresponding point (y, x) on the graph.

Therefore, the graphs of y = 1/2x - 10 - 3 and y = 1/x are different in shape and behavior, and their only similarity is that they are both continuous functions.

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The sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.

The sum of the perimeters of the three squares displayed on the computer monitor can be found by first finding the side length of each square, and then multiplying that side length by 4 to find the perimeter of each square. Finally, we add the perimeters of the three squares together to find the sum of the perimeters.

For the first square with an area of 112 cm^2, the side length is √112 cm, or 4√7 cm. The perimeter of this square is 4(4√7 cm) = 16√7 cm.

For the second square with an area of 28 cm^2, the side length is √28 cm, or 2√7 cm. The perimeter of this square is 4(2√7 cm) = 8√7 cm.

For the third square with an area of 63 cm^2, the side length is √63 cm, or 3√7 cm. The perimeter of this square is 4(3√7 cm) = 12√7 cm.

The sum of the perimeters of these three squares is 16√7 cm + 8√7 cm + 12√7 cm = 36√7 cm.

Therefore, the sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.

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The technology formula for the given function is B. (x^2 − 8)/(x^2 + 8).

We can use technology, such as a graphing calculator or an online math solver, to evaluate the function for the given values of x. Here are the steps to do so:

1. Enter the technology formula (x^2 − 8)/(x^2 + 8) into the calculator or solver.

2. Enter the values of x one at a time and evaluate the function for each value.

3. Round all answers to four decimal places.

Here are the results:

h(0.5) = 0.9310
h(1.5) = 0.6765
h(2.5) = 0.5161
h(3.5) = 0.4196
h(4.5) = 0.3548
h(5.5) = 0.3103
h(6.5) = 0.2778
h(7.5) = 0.2533
h(8.5) = 0.2346
h(9.5) = 0.2199
h(10.5) = 0.2081

Therefore, the function evaluated at the given values of x is as follows:

h(0.5) = 0.9310
h(1.5) = 0.6765
h(2.5) = 0.5161
h(3.5) = 0.4196
h(4.5) = 0.3548
h(5.5) = 0.3103
h(6.5) = 0.2778
h(7.5) = 0.2533
h(8.5) = 0.2346
h(9.5) = 0.2199
h(10.5) = 0.2081

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The multiplication sentence will be: Volume = Length × Width × Height.

Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).

To calculate the volume of a rectangular prism, you can use the multiplication sentence: Volume = Length × Width × Height. Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).

For example, if the length of the rectangular prism is 5 cm, the width is 3 cm, and the height is 2 cm, the multiplication sentence would be:

Volume = 5 cm × 3 cm × 2 cm

The volume of this rectangular prism would be 30 cm^3.

In general, the multiplication sentence to calculate the volume of a rectangular prism is:

Volume = Length × Width × Height

Make sure to include the units (cm) in your multiplication sentence in order to get the correct answer in cubic centimeters (cm^3).

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The coordinates of R′ for the dilation centered at P with scale factor 0.5 are R' (-1, -0.5).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 0.5 centered at the point P (-3, -3) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate R, we have;

Coordinate R = (1, 2)  →  (0.5(1 - (-3)) + (-3), 0.5(2 - (-3)) + (-3))

Coordinate R = (1, 2)  →  (0.5(1 + 3) - 3, 0.5(2 + 3) - 3)

Coordinate R = (1, 2)  →  (0.5(4) - 3, 0.5(5) - 3)

Coordinate R' = (1, 2)  →  (-1, -0.5)

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Answer:

5x - 3

Step-by-step explanation:

Given:

A Number and multiply it by 2.

To Find:

to write it algebraically

Solution:

Let the number that was asked to think to be x.

Then it is multiplied by 2 which becomes 2x.

Now the number is multiplied by 5.

So, x multiplied by 5 will become 5x.

Then, 5x is subtracted from 3.

So, we can write it as 5x - 3

Therefore, it can be written as 5x - 3 algebraically.

We can expect 2 black horses out of a sample of 15 horses from the stable.

To determine how likely something is gonna occur, use probability. The event is typically stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty.

To solve it, we need to use the information provided about the proportion of different horse colors in the stable to estimate the number of black horses we would expect to find in a sample of 15 horses.

According to the information provided, there are 3+19+1+4+3= 30 horses in the stable, and 4 of them are black. Therefore, the proportion of black horses in the stable is:

4/30 = 0.1333...

So, if we were to randomly select 15 horses from the stable, we would expect approximately 13.33% of them to be black. To find the expected number of black horses in a sample of 15 horses, we can multiply the proportion by the sample size:

0.1333... x 15 = 1.999...

Rounding to the nearest whole number, we can expect 2 black horses out of a sample of 15 horses from the stable.

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To find the percent of the original amount of Carbon-14 in the bone remains when found in 1968, we can use the following formula:
A = A0 * (1/2)^(t/h)
Where A is the final amount of Carbon-14, A0 is the original amount of Carbon-14, t is the time elapsed, and h is the half-life of Carbon-14.

Plugging in the given values, we get:
A = A0 * (1/2)^(12600/5730)
Simplifying the exponent, we get:
A = A0 * (1/2)^2.199
Using a calculator, we find that (1/2)^2.199 is approximately 0.153, so:
A = A0 * 0.153
This means that the final amount of Carbon-14 is 15.3% of the original amount of Carbon-14. Therefore, the percent of the original amount of Carbon-14 in the bone remains when found in 1968 is 15.3%.

As for the second part of the question, Sarah Anzick was a member of the team that did DNA sequencing on the remains in 2014. This allowed for further analysis and understanding of the remains and their significance in terms of human history and evolution.

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