The scatterplot contains data points, pairing the age of a child (x) with the child’s weight (y). Using the least-squares regression method, which is the line of best fit?

The net signed area in the above graph can be written as

(x² + 10x - 2√2)dx.

The net signed area can be found by summing the areas of the three parts:

The three being

Hence the area

: 48 + 0 + 8 = 56

We now calculate values:

of c, d, a, and b:

c = 8 - (-2) = 10

d = 3 - 2 = 1

a = 2 + 8 = 10

b = -2√2

It is important to  note that since the area under the x-axis is negative hence the reason value of b is negative.

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The four iterates of the function f(z) = z² + 2 + 2t are:

To find the first four iterates of the function f(z) = z² + 2 + 2t with an initial value of z0 = -1 + 2t, we will substitute the initial value into the function repeatedly.

Substitute z0 into the function:

f(z0) = (-1 + 2t)^2 + 2 + 2t

Simplify the expression:

f(z0) = 1 - 4t + 4t² + 2 + 2t

f(z0) = 4t² - 2t + 3

This is the first iterate of the function.

Substitute the first iterate into the function:

f(f(z0)) = f(4t² - 2t + 3)

Simplify the expression:

f(f(z0)) = (4t² - 2t + 3)² + 2 + 2t

f(f(z0)) = 16t⁴ - 16t² + 40t² - 12t + 14

This is the second iterate of the function.

Repeat the process for the third and fourth iterates:

f(f(f(z0))) = (16t⁴ - 16t³ + 40t² - 12t + 14)² + 2 + 2t

f(f(f(z0))) = 256t⁸ - 512t⁷ + 768t⁶ - 768t⁵ + 560t⁴ - 288t³ + 88t² - 16t + 18

and, f(f(f(f(z0)))) = (256t⁸ - 512t⁷ + 768t⁶ - 768t⁵ + 560t⁴ - 288t³ + 88t² - 16t + 18)² + 2 + 2t

f(f(f(f(z0)))) = 65536t¹⁶ - 262144t¹⁵ + 557056t¹⁴ - 787456t¹³ + 801216t¹² - 623616t¹¹ + 378752t¹⁰ - 185536t⁹ + 72432t⁸ - 21856t⁷ + 4916t⁶ - 800t⁵ + 84t⁴ - 4t³ + 2t² + 2t + 2

These are the first four iterates of the function f(z) = z² + 2 + 2t with the initial value of z0 = -1 + 2t.

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N is rounded to two decimal places so n=7.052/m = 7.052/2.8 2.52.

Take the equation set into consideration:

4x² - my = 10  --- (1)

mx² + ny = 20  --- (2)

When x = 2.1, one of the system's solutions is provided by the problem. Using this knowledge, we can change x in both equations to be 2.1. It results in:

4(2.1)2 my = 10 ---> 17.64 my = 10 ---> my = 7.64 --- (3) m(2.1)² + ny = 20 ---> 4.41m + ny = 20 --- (4)

Ascertaining n's value is necessary.

My = 7.64, as determined by equation (3).

With this number as a replacement in equation (4), we obtain:

4.41m + 7.64 = 20

(Rounded to one decimal place) 4.41m = 12.36 m = 2.8

This value of m is substituted in equation (4) to yield the following results: 2.8(2.1)2 + ny = 20, 12.948 + ny = 20.

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Answer:

what's that

Step-by-step explanation:

The sum or difference that is modeled by the algebra tiles is option D. (-x² + 2x + 3) + (-x² - 2x - 1) = -2x² + 2

Algebra tiles are physical manipulatives used to teach and visualize algebraic concepts. They consist of small, square-shaped tiles that represent different algebraic expressions or values. The tiles come in different colors to represent positive and negative numbers, variables, and constant terms.

Here are the common types of algebra tiles:

1. Unit Tiles: These tiles represent the number one. They are typically square-shaped and are often the base tiles used to build other expressions.

2. Variable Tiles: These tiles represent variables or unknowns. They are usually rectangular in shape and may have different colors to distinguish between different variables.

3. Positive and Negative Tiles: Tiles of different colors, usually red and blue, are used to represent positive and negative values. These tiles can be combined or separated to illustrate operations like addition and subtraction.

4. Area/Rectangle Tiles: These tiles are used to represent quadratic expressions or algebraic expressions involving products or factoring. They are rectangular in shape and can be arranged to model multiplication, factoring, or area representation of polynomials.

Therefore, the type of the algebra tiles in the given question is that of Positive and Negative tiles.

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Answer:

3.33 minutes

Step-by-step explanation:

h = rt - 4.9t^2

In this case, the rocket is launched upward, so the initial velocity (r) is positive 1960 m/s. The rocket will fall to the ground when the height (h) becomes zero.

0 = 1960t - 4.9t^2

To solve this quadratic equation, we can set it equal to zero and use the quadratic formula:

4.9t^2 - 1960t = 0

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 4.9, b = -1960, and c = 0. Plugging in these values:

t = (-(-1960) ± √((-1960)^2 - 4 * 4.9 * 0)) / (2 * 4.9)

Simplifying further:

t = (1960 ± √(3841600)) / 9.8

t = (1960 ± 1960) / 9.8

t = 1960 / 9.8 = 200

So, the rocket will fall to the ground after 200 seconds. To convert this to minutes, divide by 60:

200 seconds / 60 = 3.33 minutes (approximately)

Therefore, the rocket will fall to the ground after approximately 3.33 minutes.

Answer:

(−∞,∞)

Step-by-step explanation:

Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.

All real numbers

So, the answer is (−∞,∞)

The proof that there is no set X such that P(X) ⊂ X is below

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

There is no set X such that P(X) ⊂ X

The above means that

There is no set X such that the power set of X is a subset of set X

By definition, the power set is the set of all subsets of the a Set which includes the set itself and the null or empty set

Using the above as a guide, we have the following:

Because Y is in X, then by definition of the power set P(X), Y is a subset of X.

However, this is a contradiction because it is not possible for a set to be a proper subset of itself.

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The amount of cars you need to break even is 5.

To determine the number of cars you need to break even, we can set up an equation where the revenue equals the total cost.

Let's denote the number of cars as x.

Revenue = Number of cars × Price per wash

= x × $10

Total cost = Cost per car × Number of cars + One-time cost

= $3x + $35

To break even, the revenue should be equal to the total cost:

x × $10 = $3x + $35

Now, let's solve this equation to find the value of x:

10x = 3x + 35

Subtract 3x from both sides:

10x - 3x = 3x + 35 - 3x

7x = 35

Divide both sides by 7:

x = 35 / 7

x = 5

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(1) The triangles ABC and DEF are not similar

(2) The triangles JKL and JMN are similar by the SAS similarity statement

(3) The triangles ABC and XYZ are similar

(4) The triangles PQR and TSR are similar

(1) Triangle ABC and DEF

The triangles in this figure are

ABC and DEF

These triangles are not similar is because:

The triangles do not have similar corresponding sides i.e. Ratio = 30/24 ≠ Ratio = 24/18

Evaluate

Ratio = 1.25 ≠ Ratio = 1.33

(2) Triangle JKL and JMN

The triangles in this figure are

JKL and JMN

"If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar"

This means that they are similar by the SAS similarity statement

(3) Triangle ABC and XYZ

The triangles in this figure are

ABC and XYZ

These triangles are similar is because:

The triangles have similar corresponding sides i.e. Ratio = 33/22 = 45/30 = 42/28

Evaluate

Ratio = 1.5

(4) Triangle PQR and TSR

The triangles in this figure are

PQR and TSR

These triangles are similar is because:

The triangles have similar corresponding sides i.e. Ratio = 10/5 = 9/4.5

Evaluate

Ratio = 2

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Answer:

c) y=-x^2/4 - 2x - 7

Step-by-step explanation:

Answer:

The cross product of v x u is (-6, 2, 6).

Step-by-step explanation:

so,

   v x u = ( 0 x 4 - 1 x 6 , 1  x 2 - 1 x 4, 1 x 6 - 0 x 2)

   v x u = ( 0 - 6, 2 -4, 6 - 0)

   v x u = ( -6, 2, 6)

Therefore the cross product of u, v is ( -6, 2, 6).

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Answer:

The word or phrase that describes the probability that Ariana will win the raffle if she buys 50 tickets is "likely." Therefore, option (d) is the correct choice.

Since there are 100 tickets in total and Ariana buys 50 of them, her chance of winning the raffle is 50/100 or 1/2, which is equal to 0.5 or 50%. This means that it is more likely than not that she will win the raffle, but it is not guaranteed, as there is still a 50% chance that someone else will win the prize.

The calculated value of x in the circle is 40

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

The circle

From the circle, we have

Center = C

Also, we have

LIne CS bisects the chord RT

Using the above as a guide, we have the following:

RS = ST

Where

ST = 40 and RS = x

So, we have

x = 40

Hence, the value of x is 40

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The number of students who chose comedy movies more than drama movies were 60 students

First, find the number of students who chose comedy :

= 20 % x 1, 200 students

= 0. 20 x 1, 200

= 240 students

Then find the students who chose drama movies ;

= 15 % x 1, 200

= 0. 15 x 1, 200

= 180 students

The number who chose comedy more :

= 240 - 180 students

= 60 students

In conclusion, the number of students who chose comedy more than those who chose drama was 60 students.

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Hello!

13/14 x 26/49

= 13x26/14x49

= 338/686

= 169/343

Answer:

three more couches are needed to increase the truckload to one ton.

Step-by-step explanation:

First, let's calculate the weight of the five couches:

5 couches * 250 pounds/couch = 1250 poundsSince one ton is equal to 2000 pounds, we can subtract the weight of the couches from one ton to find out how much additional weight is needed:

2000 pounds - 1250 pounds = 750 poundsEach couch weighs 250 pounds, so we can divide the additional weight needed by the weight of each couch to determine how many more couches are needed:

750 pounds / 250 pounds/couch = 3 couches Therefore, three more couches are needed to increase the truckload to one ton.

Answer:

region I

Step-by-step explanation:

Based on the description given, the regions that represent A ∩ B' ∩ C' are:

Region I: Items only in group A, not in B or C. (A intersection not B intersection not C)

These regions fulfill the condition of being in group A (A) and not in group B (B') and not in group C (C') simultaneously.

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The correct option is b, the solutions of the quadratic equation are x = ±2

Here we want to solve the following quadratic equation:

3x² = 12

To solve this, we need to isolate the variable, so let's start by dividing both sides by 3, then we will get:

x² = 12/3

x² = 4

Now we can apply the square root in both sides:

√x² = ±√4

x = ±2

These are the two solutions, then the correct option is b.

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The measure of angle B is given as follows:

m < B = 60º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For the angle B, we have that:

Hence we apply the cosine ratio to obtain the measure of angle B as follows:

cos(B) = (x/2)/x

cos(B) = 1/2

B = arccos(1/2)

B = 60º.

The triangle is given by the image presented at the end of the answer.

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The two areas where buckeyes and monarchs have the same proportion are areas A and B.

Based on the information given, we can determine the two areas where the number of buckeye butterflies and the number of monarch butterflies are in the same proportion.

Comparing the data in the table, we can see that the ratio of buckeye butterflies to monarch butterflies is consistent in areas A and B.

In area A, there are 15 buckeye butterflies and 27 monarch butterflies, which simplifies to a ratio of 5:9.

In area B, there are 27 buckeye butterflies and 48 monarch butterflies, which also simplifies to a ratio of 5:9.

Therefore, the two areas where buckeyes and monarchs have the same proportion are areas A and B.

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The price for which the designer will sell the maximum number of shirts is given as follows:

$11.

As the amount sold is modeled by a concave down quadratic function, the price for which the designer will sell the maximum number of shirts is given by the x-coordinate of the vertex of the quadratic function.

The function in the context of this problem is given as follows:

S(x) = -4x² + 88x - 160.

The coefficients are given as follows:

a = -4, b = 88, c = -160.

Hence the x-coordinate of the vertex is obtained applying it's formula as follows:

x = -b/2a

x = -88/-8

x = 11. -> price of $11.

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Answer: 484cm

Step-by-step explanation:

Every side of a square has equal lengths.

88/4 = 22

A = LW

   = 22 x 22

   = 484cm

The triangles ABC and CDE are similar

The width AB of the river is 172.73 ft

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

The triangles ABC and CDE

The above triangles have corresponding angles and they also have similar side lengths

This means that the triangles are similar

Here, we have the following ratio

AB : 100 = 38 : 22

So, we have

AB/100 = 38/22

This gives

AB = 100 * 38/22

Evaluate

AB = 172.73

Hence, the width AB of the river is 172.73 ft

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The length of the radius of the given circle whose central angle has been given would be = 7cm.

To calculate the radius of the given circle, the formula that should be used will be given below as follows:

Length of arc = 2πr×∅/360

Length of arc = 14cm

∅ = 115°

14 = 2×3.14×r ×115/360

make R the subject of formula;

r = 14/2.006

= 6.9

= 7cm

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Hello !

student's number / total students

9)

288/360 = 0,8

⇒ it's C

10)

90/360 = 0,25

⇒ it's B

Have a good day!

Answer:

1. Group B

2. Group A

3. The median.

Answer:

1. Group B has the lowest age range out of both groups. Group B has at least 18 students under 16 and Group A has ages from 5 through 30.

2. Group A has more of a variability of ages because it is more scrambled than Group B. Group B had more students that had ages that were all close to each other.

3. I think it's best to use the median because it measures the age above which is found. If we use the mean, it will only be calculated by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Here are the completed tables for each sequence:

Sequence 1 Sequence 2 Ordered Pair

5                    15                   (5, 15)

6                        14               (6, 14)

7                        13             (7, 13)

8                    12                 (8, 12)

9                   11                (9, 11)

The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x.

The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x. This means that the two sequences are increasing at the same rate.

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The number of terminates are 2,384.78.

An exponential function can be used to illustrate the daily growth of termites.

If "t" represents the number of days, then "N" represents the number of termites.

⇒ N = [tex]1600(1 + 0.042)^{t}[/tex]

Where 0.042 is the decimal form of 4.2%.

Using this formula,

It can be  calculate the number of termites after any number of days t.

For example,

After 10 days, the number of termites would be:

⇒ N = [tex]1600(1 + 0.042)^{10}[/tex]

⇒ N = [tex]1600(1.042)^{10}[/tex]

⇒ N ≈ 2,384.78 termites

Hence,

⇒ N =  2,384.78 termites

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