why are inverse realashinships between operations used to solve twop step inqualites

The characteristics that shows that the graph is a proportional relationship is: D. The line connecting the points passes through the origin.

A graph of a proportional relationship is a straight line that passes through the origin (0, 0) on a coordinate plane, where the points on the line represent pairs of values that are in direct proportion to each other.

From the graph shown above, if we connect the points together, the line will pass through the origin, therefore, the correct answer is: D. The line connecting the points passes through the origin.

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The characteristics that tell you that the graph shows a proportional relationship are: A straight line can be drawn through the points and The line connecting the points passes through the origin. Option B and D are the correct answer.

A proportional relationship is a relationship between two variables where the ratio of their values is constant. This means that if we multiply one of the values by a constant, the other value also gets multiplied by the same constant.

The graph of a proportional relationship is a straight line that passes through the origin. This is because the ratio of the x- and y-values is constant, so the points can be plotted as a straight line.

The ordered pairs all have the same x- and y-values means that the two variables are perfectly correlated. This is not necessary for a proportional relationship, but it is a common characteristic.

The line connecting the points does not need to pass through the origin for the relationship to be proportional. However, if the line does pass through the origin, then the two variables are directly proportional. Option B and D are the correct answer.

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The probability that a statistics teachers do not know the true meaning of life is 46.8%

From the question, we have the following parameters that can be used in our computation:

53.2% of Americans say they believe that statistics teachers know the true meaning of life.

This means that

P(Believe) = 53.2%

For the required probability, we have

P(Not believe) = 1 - P(Believe)

So, we have

P(Not believe) = 1 - 53.2%

Evaluate

P(Not believe) = 46.8%

Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%

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The speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min

The total area or region that is covered by a rectangular prism's six faces is known as its surface area.

Solids called prisms have identical polygon bases and flat parallelogram sides. Prisms come in a variety of shapes, including triangles, squares, rectangles, pentagons, hexagons, and more.

Thus, it can be seen that the speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min

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Answer:

To solve for C in the formula V = CLS, we need to isolate C on one side of the equation.

Starting with the given formula:

V = CLS

Divide both sides of the equation by LS:

V/LS = C

Therefore, the formula for C is:

C = V/LS

No, y=2x+X+1 is not a linear function because it contains a term with an exponent of 1 and a term with an exponent of 0. Linear functions are functions of the form y = mx + b, where m and b are constants, and x is the independent variable. The graph of a linear function is a straight line.

In the given function, the term X is not multiplied by a constant, so it does not have a fixed rate of change. Therefore, the graph of this function is not a straight line. Instead, it is a quadratic function, which has a parabolic graph.

The amount of paint needed for the soup can is 409.77 cm².

Jacque is using an unopened soup can for a school project and wants to paint it.

The can is 10 cm tall and has a diameter of 9 cm. Therefore, the square centimetres of paint required to paint the soup is as follows:

Therefore,

surface area of a cylinder = 2πr(r + h)

where

Therefore,

r = 9 / 2 = 4.5 cm

h = 10 cm

surface area of a cylinder = 2 × 3.14 × 4.5(4.5 + 10)

surface area of a cylinder = 28.26(14.5)

surface area of a cylinder = 409.77 cm²

Therefore,

amount of paint needed = 409.77 cm²

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Answer:

Jasper should use the median to make an inference about the house values in his neighborhood because there is an outlier that affects the mean. The outlier in this case is the house with a value of $2,500,000, which is significantly higher than the other house values in the sample. The mean is sensitive to outliers, which means that the outlier can significantly affect the value of the mean. In contrast, the median is not affected by outliers, which makes it a better measure of central tendency for this data set. Therefore, Jasper should use the median because it is in the center of the data and is not affected by the outlier. Answer: He should use the median because there is an outlier that affects the mean.

Answer:

The answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &;  A & E $150,000 ‘n’ $200,000

Step-by-step explanation:

The outlier is represented as ‘ E ‘ the highest price value and lowest between, $150,000 to $200,000.

But since ‘ E ‘ is represented highest it is an outlier making ‘ E ;

$150,000 ‘n’ $200,000

So ‘ E ‘ is represented as, $150,000 ‘n’ $200,000

The second option for ‘ 10 points ‘ is He should use the median because there is an outlier that affects the mean, being the ‘ Option C ‘

Thus the answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &;  A & E $150,000 ‘n’ $200,000

Answer:

Step-by-step explanation:

sum of angles in a triangle=180º

90+60x+30x=180

90+90x=180

90(1+x)=180

1+x=2

x=1

angle A=30º

The number of mugs that Maggie made with the left over clay that she had would be = 23 mugs

The total quantity of clay that Maggie bought = 50lbs

The quantity she used for sculpture = 15.6lbs

The quantity of clay she used for mug = 0.84 lbs

The quantity of clay left = 19.28 lbs

If 0.84 = 1 mug

19.28 = X

make X the subject of formula:

X = 19.28/0.84

= 23 mugs

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The image point of (-7, -8) after the sequence of transformations is given as follows:

(-4.5, -4).

The original coordinates are given as follows:

(-7, -8)

The first transformation is a dilation with a scale factor of 1/2, meaning that each coordinate is multiplied by 1/2, hence:

(-3.5, -4).

The second transformation is a translation of one unit left, meaning that one is subtracted from the y-coordinate, thus the image point after the sequence of transformations is given as follows:

(-4.5, -4).

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The plan would be to send 2 group members back to base camp with enough food to sustain them for 5 days, while the remaining 3 members continue to receive 5,600 calories per day from the remaining food supply to complete the journey to the South Pole.

To create a plan for the rest of the trip, we need to consider the total number of days it will take for the group to return to base camp from their current location, and the number of group members who can be taken to the South Pole given the remaining food supply.

Given that the group is missing 28,000 calories, we can calculate the number of days of food that are missing by dividing 28,000 by the daily requirement of 5,600 calories per person. This gives us 5 days of missing food. Therefore, the group has enough food for 5 people to continue to receive 5,600 calories per day for 5 days, but not for all 5 members to continue for the entire trip.

To maximize the number of group members who can continue to the South Pole, we can send two members back to base camp immediately with enough food to sustain them for 5 days (2 people x 5 days x 5,600 calories/day = 56,000 calories). This will leave us with 3 group members who can continue to receive 5,600 calories per day for the remaining journey.

Assuming the trip back to base camp takes the same amount of time as the trip to the current location, we can estimate that the total trip duration will be around 20 days. Therefore, the remaining 3 group members will need a total of 20 days x 3 people x 5,600 calories per day = 336,000 calories.

Given the remaining food supply of 28,000 calories, we have a total of 364,000 calories available (28,000 missing calories + 336,000 required calories). Therefore, the 3 remaining group members can continue to receive their required daily calorie intake and complete the journey to the South Pole.

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Answer:

The answer is Area: 25.5

Step-by-step explanation:

Answer:

Answer is A

Step-by-step explanation:

A) y = -1/2x represents a proportional relationship because the equation can be written in the form y = kx, where k is a constant. In this case, k = -1/2, which means that y is proportional to x with a constant of proportionality of -1/2.

B) y = 2x - 4 does not represent a proportional relationship because the equation cannot be written in the form y = kx. If we try to write it in this form, we get y/x = 2 - 4/x, which means that y/x is not constant. Therefore, y is not proportional to x with a constant of proportionality.

Answer:She is not correct The graph of g grows at a faster rate

than the graph of because 8 greater than 2

Step-by-step explanation:

Using PEMDAS, the exponents are done first.

8^3 = 512

4*2^3 = 32

This works for every number that X can be, 3 was just an example.

By mathematical induction, the given formula holds for all natural numbers n:

S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)

To demonstrate our point, mathematical induction can be employed.

We want to prove that the given formula holds for all natural numbers n:

S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)

Using mathematical induction:

Step 1: Base case (n=1)

S(1) = 6² = 36

12 * 1 * (4 * 1² - 1) = 36

Since S(1) holds true, the base case is proven.

Step 2: Inductive step (Assume it's true for n=k, and show it's true for n=k+1)

Assumption: S(k) = 36 + 324 + 900 + ... + (12k - 6)² = 12k(4k² - 1)

We follow the exhaustive process to prove:

= 12(4k³ + 12k² + 11k + 3)

Since both expressions for S(k+1) are equal, the inductive step is proven.

Thus, by mathematical induction, the given formula holds for all natural numbers n:

S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)

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Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.

To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.

The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).

Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.

However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).

Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.

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Answer:

Step-by-step explanation:

Area and perimeter are both measurements used to describe geometric shapes, but they are fundamentally different concepts and therefore change in different ways.The perimeter of a shape is the distance around the outside of the shape. It is a measure of the total length of the boundaries or sides of the shape. Perimeter depends on the length of each side of the shape, and if one or more sides change in length, the perimeter will change accordingly. For example, if you take a square and double the length of one of its sides, the perimeter will double as well.On the other hand, the area of a shape is the measure of the surface enclosed by the shape. It is a measure of the amount of space inside the shape. The area depends on the length and width of the shape, and if one or both of these dimensions change, the area will change accordingly. For example, if you take a square and double the length of one of its sides, the area will increase by a factor of four.In summary, the perimeter of a shape depends on the length of its sides, while the area of a shape depends on its length and width. Therefore, changes to the length of a side will affect the perimeter, but not necessarily the area, while changes to the length or width will affect the area, but not necessarily the perimeter.

The real solution is 0, and the imaginary solution is 0.5 ±  0.866i.

The solutions of the equation is calculated as follows;

4x(x² - x + 1) = 0

This equation is satisfied when either 4x = 0 or x² - x + 1 = 0.

If 4x = 0, then x = 0 is a solution,

To find the solutions of x² - x + 1 = 0, we will use formula method;

x = [ -(-1) ± √((-1)² - 4(1)(1)) ] / (2(1))

x = [ 1 ± i√3 ] / 2

x = 0.5 ±  0.866i

Thus, the solutions of the cubic equation involves both real and imaginary solution.

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Answer:

larger angle = 63°

Step-by-step explanation:

complementary angles sum to 90°

let x be the smaller angle then larger angle is x + 36 , then

x + x + 36 = 90

2x + 36 = 90 ( subtract 36 from both sides )

2x = 54 ( divide both sides by 2 )

x = 27

Then

larger angle = x + 36 = 27 + 36 = 63°

The possible first mistake Noah made in the evaluation of the sine and cosine of the acute angles of a right triangle is that the acute angles are complementary and are not always congruent. The correct option is the  option (A).

(A) Angles ∠B and ∠C are complementary, not congruent

Complementary angles are angles that when added together are equivalent to 90°

The possible two column table Noah used to attempt to prove that cos(θ) = sin(θ) obtained in a similar proof on the website can be presented as follows;

Statement [tex]{}[/tex]                   Reason

1 m∠B = θ [tex]{}[/tex]                   The acute angles in a right triangle are congruent

2 sin(θ) = AB/BC    [tex]{}[/tex]     Definition of sine

3 cos(m∠B) = AB/BC [tex]{}[/tex] Definition of cosine

4 cos(θ) = AB/BC [tex]{}[/tex]       Substitution

5 cos(θ) = sin(θ) [tex]{}[/tex]         Substitution

Part of the question is; What is the first mistake in Noah's statement used to prove that cos(θ) = sin(θ)

The first mistake is the statement and reason that angle m∠B = θ because all acute angles are congruent.

The acute angles in the right triangle are ∠B and ∠C

The sum of the acute angles in a right triangle is; ∠B + ∠C = 90°

Therefore the acute angles in a right triangle are always complementary, and not always congruent.

The correct option is therefore the option (A)

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The requried, $1000 is invested at 6%, and $7000 is invested at 10%

Let x be the amount invested at 6%, and y be the amount invested at 10%. We know that x + y = $8000 since the total amount invested is $8000.

We also know that the annual interest earned on the 6% investment is 0.06x, and the annual interest earned on the 10% investment is 0.1y. The total annual interest earned is given as $760.

So we have the system of equations:

x + y = 8000 (1)

0.06x + 0.1y = 760 (2)

We can use either substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.06, we get:

0.06x + 0.06y = 480 (3)

0.1y - 0.06y = 0.04y = 280

y = $7000.

Substituting y = $7000 into equation 1, we get:

x + $7000 = $8000

So x = $1000.

Therefore, $1000 is invested at 6%, and $7000 is invested at 10%.

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The two animals are at different stages in their life cycle.  Hence option C: Different stages. The panther is an embryo and the pelican is an infant.

The two creatures are at distinct points of their developmental process. The panther, denoted as Animal 1, is characterized as a cluster of cells undergoing division within its maternal host. This is one that then shows that the panther is at a very early stage of growth, and that it is in embryonic phase.

The pelican, is one that is also known as Animal 2, that has successfully hatched from its egg, telling us the conclusion of its embryonic phase and the start of the post-embryonic phase.

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The explicit formula for the sequence defined by the recursive formula a₁ = 150 and aₙ = -1/5 aₙ₋₁ is aₙ = 150 [tex](-1/5)^{(n-1)[/tex].

To find the explicit formula that represents the sequence defined by the given recursive formula, we need to find a pattern in the sequence and express it using a formula.

The first term in the sequence is a₁ = 150. To find the second term, we use the recursive formula: a₂ = -1/5 a₁ = -1/5(150) = -30. To find the third term, we use the recursive formula again: a₃ = -1/5 a₂ = -1/5(-30) = 6.

We can continue this process to find the fourth term: a₄ = -1/5 a₃ = -1/5(6) = -6/5, and so on.

By observing the pattern, we notice that each term is obtained by multiplying the previous term by -1/5. Therefore, the explicit formula for the sequence can be written as:

aₙ = 150 [tex](-1/5)^{(n-1)[/tex]

This formula gives the value of any term in the sequence based on its position n. It can be used to find any term in the sequence without having to recursively calculate all the previous terms.

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The 8th term of the sequence is 781, 250.

We have geometric sequence 10, 50, 250,...

First term= 10

Common ratio = 50/10 = 5

So, the 8th term of sequence is

= 10 x [tex]r^{8-1[/tex]

= 10 x [tex]r^7[/tex]

= 10 x [tex](5)^7[/tex]

= 10 x 5 x 5 x 5 x 5 x5 x 5 x 5

= 10 x 78125

= 781, 250

Thus, the 8th term of the sequence is 781, 250.

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The steps for the construction are given below:

A new line can be created connecting the points where these two circles intersect using just a simple ruler.

Now that you have succeeded in this task, feel free to experiment and manipulate the astonishing construction you've completed using the same innovative tools.

While this is only an elementary blueprint, there are numerous advanced constructions that can be produced by taking advantage of both GeoGebra and traditional paper/pencil/ruler/compass techniques.

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The value of the median number of eggs laid in a year is,

⇒ 231

We have to given that;

The data table shows the numbers of eggs laid by individual chickens in a year.

Now, We can arrange it into ascending order as;

⇒ 222, 229, 229, 231, 234, 235, 262

Since, There are 7 terms

Hence, Median is,

= (7 + 1)/2

= 4th term

= 231

Thus, The value of the median number of eggs laid in a year is,

⇒ 231

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Answer:

A. 229 is correct

answer D.231 is wrong

Answer:

To find the coordinates for all three possible locations of the fourth vertex, we need to consider the three different ways that a parallelogram can be formed on a 9 by 9 grid.

Method 1: The fourth vertex is directly below the first vertex.

In this case, the coordinates of the fourth vertex are (5, 9), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . X

Method 2: The fourth vertex is directly to the right of the first vertex.

In this case, the coordinates of the fourth vertex are (1, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

X . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Method 3: The fourth vertex is diagonal to the first vertex.

In this case, the coordinates of the fourth vertex are (5, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . X . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Therefore, the coordinates for all three possible locations of the fourth vertex are (5, 9), (1, 5), and (5, 5).

In 2006, the population will reach 109 million.

The correct answer is an option (d)

Here function [tex]f(x)=100(1.0153)^x[/tex] represents the population (in millions) x years after 2000

We need to find the year x when the population will reach 109 million.

i.e., for f(x) = 109, we need to find the value of x.

Consider function f(x),

[tex]f(x)=100(1.0153)^x[/tex]

Substitute f(x) = 109

⇒ [tex]109=100(1.0153)^x[/tex]

⇒ [tex](1.0153)^x=1.09[/tex]

Taking logarithm on both the sides.

⇒ x ln(1.0153) = ln(1.09)

⇒ x = ln(1.09) / ln(1.0153)

⇒ x = 5.675

⇒ x ≈ 6

So, the required year would be,

2000 + 6 = 2006

Therefore, the correct answer is an option (d)

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Answer:

linear

Step-by-step explanation:

have a good day God bless :)

If owner of car paid $780 as annual premium, then the cost of the accident is $26540 more expensive than what car owner paid in premiums, correct option is (d).

The car owner paid a total of $780 per year for 7 years, which means that the total amount paid in premiums is:

⇒ Total premiums paid = $780 × 7 years = $5460,

When the owner caused an accident, the amount of damage claimed by other driver is $32000.

This means that cost of accident was : $32000 - $5460 = $26540 more expensive than what the "owner" had invested in his insurance policy.

Therefore, Option(d) is correct.

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The given question is incomplete, the complete question is

A car owner pays an annual premium of $780 for automobile insurance, including liability coverage of up to $100,000. The car owner pays this for seven years without needing to file a

single claim. Then the car owner causes an accident for which the other driver is claiming $32,000 in damages. How much more expensive were the costs of the accident than what the car owner paid in premiums?

(a) $37,460

(b) $100,000

(c) $5,460

(d) $26,540