Make two questions based on this graph.

Answer:

2x+12

Step-by-step explanation:

2x + 3(x-2) -3(x-6)

distribute

2x+3x-6-3x+18

sort

2x+3x-3x-6+18

add 2x and 3x

5x-3x-6+18

subtract 5x and 3x

2x-6+18

add -6 and 18

2x+12

because we can't add the two the final answer is:

2x+12

The perimeter of the rectangular carpet is 36 yards. (Option A)

To find the perimeter of a rectangular carpet, we need to add the lengths of all four sides. Since the carpet is four times as long as it is wide, we can represent the length as 4w, where w is the width. The width is given as 5 yards. Therefore, the length is 4 times the width, or 4 x 5 = 20 yards. So, the perimeter is (2 x length) + (2 x width) = (2 x 20) + (2 x 5) = 40 + 10 = 50 yards. However, the question asks for the perimeter in terms of the width, which is 5 yards. So, we divide the perimeter by 5 to get 50/5 = 10.

Therefore, the perimeter of the rectangular carpet is 10 times the width, or 10 x 5 = 36 yards.

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Answer:

A

Step-by-step explanation:

Answer:

1-jail for 1 month

2-prombation for 1 month

3-speak to schools

4-solitary confindment for 1 year

5-half life in prison

Step-by-step explanation:

hope this helps!

Answer:

1) jail for a month

2) probation for 10 months

3) speak to schools

4) regular prison for 10

5) lifetime on probation

Step-by-step explanation:

❤️❤️❤️

Step-by-step explanation:

15 . triangle on number 15 is an isoseles because it has two sides that are equal

and also it has two angles that are equal

16. it is a scalene beacause it has no side that is equal furthermore its angles are not the same they are all different

Answer:

Step-by-step explanation:

O points but it’s 1.99

The given expression gives the complex number:

N = 1 + 0i

Here we want to simplify the expression:

N = -4i + (1/4 - 5i) - (-3/4 + 8i) + 17i

Where i is the complex number, now we can just separate the terms with i and the terms without i.

N = -4i + (1/4 - 5i) - (-3/4 + 8i) + 17i

= (1/4 + 3/4) + (-4i - 5i - 8i + 17i)

= ( 1) + (-4 - 5 - 8 + 17)i

=  1  + 0i

That is the complex number that comes out of the given expression.

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Answer:

huh

Step-by-step explanation:

The Giapetto problem is a linear programming problem that involves maximizing profit from producing two types of wooden toys. In response to the questions:

a. The dual of the Giapetto problem can be obtained by interchanging the roles of the variables and constraints. The objective of the dual problem is to minimize the sum of the dual variables (representing the costs) subject to the constraints defined by the coefficients of the original primal problem.

b. To determine the optimal dual solution, we can examine the optimal tableau of the Giapetto problem. The dual solution is obtained by considering the dual variables associated with the constraints. These variables represent the shadow prices or the marginal values of the resources in the primal problem. By analyzing the optimal tableau, we can identify the values of the dual variables and determine the optimal dual solution.

c. In this instance, we can verify that the Dual Theorem holds. The Dual Theorem states that the optimal value of the dual problem is equal to the optimal value of the primal problem. By comparing the optimal solutions obtained in parts (a) and (b), we can confirm whether they are equal. If the optimal values match, it confirms the validity of the Dual Theorem, indicating a duality relationship between the primal and dual problems. The dual of the Giapetto problem involves minimizing costs instead of maximizing profit. By examining the optimal tableau, we can determine the optimal dual solution. Lastly, by comparing the optimal solutions of the primal and dual problems, we can verify the Dual Theorem's validity, which states that the optimal values of both problems are equal, demonstrating their duality relationship.

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Answer:

615.752 square cm

Step-by-step explanation:

          height = h = 7 cm

        radius   = r = 7 cm

Plug in the values of r and h in the formula.

\(\sf \boxed{\text{\bf Surface area of cylinder = $2\pi r(r+h)$}}\)

                                             \(\sf = 2*3.14*7 *(7+7)\\\\= 2*3.14*7*14\\\\= 615.752 \ cm^2\)

Time

2 days =  172, 800 seconds

Formula= Multiply the time value by 86400

             = 86200 X 2

             = 172, 800 seconds

Answer:

Below in bold.

Step-by-step explanation:

a) we need the grestest common factor of  theses values

153 = 3 * 3 * 17

255 =  3 * 5*17

357 = 3 * 7 * 17

The GCF = 3 * 17 = 51.

a) the least possible number of children  is 3.

b) The maximum number is 51 ( as 51 is the GCF of the given values).

c) the least possible number of fruits is when  b)  occurs, that is:

153/51, 255/51 and 357/51

= 3 apples , 5 oranges and 7 pears.

d) the maximum number of fruits is :

153/3, 255/3 and 357/3

= 51 apples , 85 oranges and 119 pears.

Answer:

a) 3 children

b) 51 children

c) 3 apples, 5 oranges and 7 pears

d) 51 apples, 85 oranges and 119 pears

Step-by-step explanation:

lnc - Least possible number of children in group

mnc - maximum possible number of children in group

a - Apples

o - Oranges

p - Pears

a = 153

o = 255

p = 357

a)

To solve this, find the highest divisor for the apples, oranges and pears.

\(a = \frac{153}{51} \)

\(a = 3\)

\(o = \frac{255}{85} \)

\(o = 3\)

\(p = \frac{357}{119} \)

\(p = 3\)

In order for each child to get 51 apples, 85 oranges and 119 pears, there would need to be a minimum of 3 children in the group.

\(lnc \: = 3\)

b)

To solve this, find the lowest divisor for the apples, oranges and pears.

\(a = \frac{153}{3} \)

\(a = 51\)

\(o = \frac{255}{5} \)

\(o = 51\)

\(p = \frac{357}{7} \)

\(p = 51\)

In order for each child to get 3 apples, 5 oranges and 7 pears, there would need to be a maximum of 51 children in the group.

\(mnc = 51\)

c)

In a group of 51, each child will get:

- 3 apples

- 5 oranges

- 7 pears

d)

In a group of 3, each child will get

- 51 apples

- 85 oranges

- 119 pears

Answer:

1025437

Step-by-step explanation:

1000000+25437=1025437

Answer:

1025437

Step-by-step explanation:

hope it helps, please mark as brainliest

The investment problem is modeled by an initial value problem (IVP) where the rate of change of the investment is determined by the initial investment, monthly deposits, and the interest rate.

a) The investment problem can be modeled by an initial value problem where the rate of change of the investment, y(t), is given by the initial investment, monthly deposits, and the interest rate. The IVP can be written as:

dy/dt = 0.09y + 200, y(0) = 500.

b) To solve the IVP, we can use an integrating factor to rewrite the equation in the form dy/dt + P(t)y = Q(t), where P(t) = 0.09 and Q(t) = 200. Solving this linear first-order differential equation, we obtain the solution for y(t).

c) To find the value of the investment after 2 years, we substitute t = 2 into the obtained solution for y(t) and calculate the corresponding value.

d) After 2 years, the monthly deposit increases to $300. To find the value of the investment a year later, we substitute t = 3 into the solution and calculate the value accordingly.

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The disk of convergence is the set of all complex numbers z such that the absolute value of z - 1 is less than the radius of convergence.

The Taylor series of the function f(z) at 1 is given by:

f(z) = f(1) + f'(1)(z - 1) + f''(1)(z - 1)²/2! + f'''(1)(z - 1)³/3! + ...

To find the coefficients of the Taylor series, we need to compute the derivatives of f(z) at 1.

f(z) = 1/z + 1/(z - 2)² + 1/(z - 3)

Taking the derivatives:

f'(z) = -1/z² - 2/(z - 2)³ - 1/(z - 3)²

f''(z) = 2/z³ + 6/(z - 2)⁴ + 2/(z - 3)³

f'''(z) = -6/z⁴ - 24/(z - 2)⁵ - 6/(z - 3)⁴

Evaluating these derivatives at 1:

f(1) = 1/1 + 1/(1 - 2)² + 1/(1 - 3) = 1 - 1 + 1/2 = 1/2

f'(1) = -1/1² - 2/(1 - 2)³ - 1/(1 - 3)² = -1 - 2 + 1/4 = -7/4

f''(1) = 2/1³ + 6/(1 - 2)⁴ + 2/(1 - 3)³ = 2 + 6 + 1/8 = 61/8

f'''(1) = -6/1⁴ - 24/(1 - 2)⁵ - 6/(1 - 3)⁴ = -6 - 24 + 3/16 = -210/16

Plugging these values into the Taylor series formula:

f(z) ≈ 1/2 - (7/4)(z - 1) + (61/8)(z - 1)²/2! - (210/16)(z - 1)³/3! + ...

The disk of convergence of this Taylor series is the set of complex numbers z for which the series converges.

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(a) We have shown that there exists an element b ∈ B that is an upper bound for A.

(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.

(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.

Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).

Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.

(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.

Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.

This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.

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Answer: False

Step-by-step explanation:

4 x 10^6 = 4000,000

400,000 is 4 x 10^5

Answer:

False

Step-by-step explanation:

10^6=1,000,000   ==> 10^6 has 6 zeros after the '1', making 10^6=1 million.

4*10^6=4,000,000, not 400,000

We must conclude that there are infinitely many primes of the form 3k + 2, where k is a non-negative integer.

To adapt the proof:

We can use a similar contradiction argument.

Suppose that there are only finitely many primes of the form 3k + 2, say p1, p2, ..., pn.

Let N = 3p1p2...pn + 2. Note that N is of the form 3k + 2 for some non-negative integer k.

Now, let's consider the prime factorization of N. Either N is prime and of the form 3k + 2, in which case we have found a new prime of the desired form, contradicting our assumption that there are only finitely many such primes. Or, N is composite and has a prime factorization consisting only of primes of the form 3k + 1 (since any prime of the form 3k + 2 would divide N). But this implies that N itself is of the form 3k + 1.

Now, let's consider the number M = 3N + 2. M is also of the form 3k + 2, and so must have a prime factorization consisting only of primes of the form 3k + 1. But since N is of the form 3k + 1, we have

M = 3(3p1p2...pn + 1) + 2 = 9p1p2...pn + 5. This means that M has a prime factorization consisting of primes of the form 3k + 2, which contradicts our assumption that there are only finitely many such primes.

Therefore, we must conclude that there are infinitely many primes of the form 3k + 2, where k is a non-negative integer.

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Answer:

It's 25

Step-by-step explanation:

It's asking for distance between the two numbers

Answer:25

Step-by-step explanation:

Answer:

No there not the same

Step-by-step explanation:

There are not equivalents to each other the answer would be 2:1

The radius of the container is then r = 1 in. and the height is h = 12.15 in.

The volume of a right circular cylinder is given by the formula V = πr^2h, where r is the radius, h is the height, and π is a constant approximately equal to 3.14. We are given that V = 38 in.3, so we can write the equation 38 = πr²h. To minimize the amount of metal used, we want to minimize either the radius or the height (since the volume is fixed). Since h is squared in the formula, it is more effective to minimize the radius.

If we let r = 1, then the equation becomes 38 = π(1)²h, or 38 = πh. Solving for h, we get h = 38/π ≈ 12.15.

Thus, the radius of the container is then r = 1 in. and the height is h = 12.15 in.

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Answer:

6.

1 table seats 5 students

2 tables seat 8 students

3 tables seat 11 students

4 tables seat 14 students

5 tables seat 17 student

Each new tables allows 3 more students to have a seat.

7.

Each additional table does not have seats for 5 students because the side of it is pressed against another table, so a student cannot sit there.

The probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.875.

To solve this problem, we can calculate the complementary probability that it takes more than 3 attempts to make a satisfactory item and then subtract that from 1.

Let's first calculate the probability that it takes more than 3 attempts:

1. First attempt: unsatisfactory (0.5)
2. Second attempt: unsatisfactory (0.5)
3. Third attempt: unsatisfactory (0.5)

The probability that all three attempts are unsatisfactory is (0.5) * (0.5) * (0.5) = 0.125.

Now, we'll find the complementary probability by subtracting the probability of more than 3 attempts from 1:

1 - 0.125 = 0.875

So, the probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.875.

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Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants.

The sampling method described in the scenario is called systematic sampling.

Systematic sampling involves selecting every nth element from a population after randomly selecting a starting point. In this case, the store manager randomly chooses a shopper entering the store as the starting point and then proceeds to interview every 20th person after that initial selection.

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants. By ensuring a regular interval between selections, systematic sampling provides a representative sample from the population.

However, it's important to note that systematic sampling can introduce a form of bias if there is any periodicity or pattern in the population. For example, if the store experiences a peak in customer traffic during specific time periods, the systematic sampling method might overrepresent or underrepresent certain groups of shoppers.

To minimize this potential bias, the store manager could randomly select the starting point for the systematic sampling at different times of the day or on different days of the week. This would help ensure a more representative sample and reduce the impact of any inherent patterns or periodicities in customer behavior.

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The equation that models the situation with d, the price in dollars, of one dozen bagels is given by option C. `2d = 17.98`.

Emma spent $17.98 on 2 dozen bagels. The equation that models the situation with d, the price in dollars, of one dozen bagels is given by option C. `2d = 17.98`.What are dozen bagels?A dozen bagels are 12 bagels. If Emma bought 2 dozen bagels, it means she bought 24 bagels. If you want to know the cost of one bagel, you can divide the total cost by the number of bagels she bought. So the cost of one bagel can be given by the equation;`Total cost of bagels / number of bagels bought = cost per bagel`Let us now use the given options to see which one of them represents the above equation.A. 17.98d = 2Here, we have the total cost multiplied by the cost per bagel which doesn't make sense.B. 17.98 + d = 2We can see that this equation does not have any terms to represent the number of bagels bought, it only has the total cost and the cost per dozen bagels.D. 2 + d = 17.98We can see that this equation does not have any terms to represent the total cost or the number of bagels bought. Hence it cannot represent the given situation.C. 2d = 17.98Here, we have the number of bagels multiplied by the cost per bagel to give us the total cost, which is what we need. Therefore the equation that models the situation with d, the price in dollars, of one dozen bagels is given by option C. `2d = 17.98`.

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Answer:

$72.5

Step-by-step explanation:

4 hours of babysitting = $29.00

Therefore $29.00 divided by 4 is 1 Hour of babysitting which is $7.25

To find 10 hours we multiply $7.25 by 10 = $72.5

So Erin would make $72.5 babysitting for 10 Hours.

We can conclude that the system represented by the given Gauss-Jordan elimination has infinitely many solutions, and the values of the variables can be expressed in terms of a free variable x4.

The Gauss-Jordan elimination is a method used to solve a system of linear equations. The final step of the method is to transform the augmented matrix of the system into reduced row echelon form, which allows for easy identification of the solution(s) of the system.

In the given final step of the Gauss-Jordan elimination, the augmented matrix of the system is represented as:

11 0 0 51

0  1 0 21

0  0 1 -3

0  0 0  0

The augmented matrix is in reduced row echelon form, where the leading coefficients of each row are all equal to 1, and there are no other non-zero elements in the same columns as the leading coefficients. The last row of the matrix corresponds to the equation 0 = 0, which represents an identity that does not provide any new information about the system.

The system represented by this matrix is:

11x1 + 51x4 = 0

x2 + 21x4 = 0

x3 - 3x4 = 0

We can see that the third row of the matrix corresponds to an equation of the form 0x1 + 0x2 + 0x3 + 0x4 = 0, which indicates that the variable x4 is a free variable. This means that the system has infinitely many solutions, and the value of x4 can be chosen arbitrarily.

The values of x1, x2, and x3 can be expressed in terms of x4 using the equations given by the first three rows of the matrix. For example, we can solve for x1 as follows:

11x1 + 51x4 = 0

x1 = -51/11 x4

Similarly, we can solve for x2 and x3:

x2 = -21 x4

x3 = 3 x4

Therefore, the general solution of the system is:

x1 = -51/11 x4

x2 = -21 x4

x3 = 3 x4

x4 is a free variable

In summary, we can conclude that the system represented by the given Gauss-Jordan elimination has infinitely many solutions, and the values of the variables can be expressed in terms of a free variable x4.

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Answer: 26

Step-by-step explanation:

Two Angles are Complementary when they add up to 90 degrees (a Right Angle). Then

∠A + ∠B = 90

∠A =90- ∠B

∠A  = 26

Answer:

The measure of \(\angle A\):

\(\angle A = 26\textdegree\)

Step-by-step explanation:

Since both \(\angle A\) and \(\angle B\) are complementary (Which they both add up to 90°), and you want to find the measure of

Measure of \(\angle A\): unknown

Measure of \(\angle B\): 64°

Finding the measure of \(\angle A\):

\(90 - 64 = 26\)

\(\angle A = 26\textdegree\)

So, the measure for \(\angle A\) is \(26\textdegree\).

Answer:

I'm pretty sure the answer is C

Step-by-step explanation: