2. Dwayne scored 55 points in the last basketball game, which is 10 points more than his previous personal best. Lebron scored 15 points more than Chris in the
same game. Lebron scored the same number of points as Dwayne’s previous personal best.
Write two algebraic equations, let d represent the number of points Dwayne scored during his previous personal best and c represent the number of Chris’s points.

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Weight of the John increased by 10.71 percent as he is weighing 140 pounds to 155 pounds.

As given in the question,

Original weight of John is equal to 140 pounds

John's changed weight is equal to 155 pounds

155 is greater than 140 pounds

Increase in John's weight.

Change in weight = Increased weight - actual weight

Percent of change in John's increased weight

= [ | change in weight| / Actual weight ] × 100

=  [(155 - 140 ) / 140] × 100

= (15 / 140)× 100

= 10.71%

Therefore, the percent of change in John's weight is increased by 10.71%.

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The value of ∫ (x + 1)/(9x² + 6x + 5) dx by partial fractions is 1/18ln(9x² + 6x + 5) + 1/9 (tan^-1 (3x+1)/2)

Given ∫ (x + 1)/(9x² + 6x + 5) dx

Discriminant of is 9x² + 6x + 5 is

                                 D = 6² - 4 x 9 x 5 = - 144 < 0

So, 9x² + 6x + 5 cannot be factorized in rational factors

Observing that differential of 9x² + 6x + 5, let us split (x + 1)/(9x² + 6x + 5) as (18x + 18)/18(9x² + 6x + 5)

or (18x + 6)/18(9x² + 6x + 5) + (12)/18(9x² + 6x + 5)

So, (x + 1)/(9x² + 6x + 5) = (18x + 6)/18(9x² + 6x + 5) + (12)/18(9x² + 6x + 5)

∫ (x + 1)/(9x² + 6x + 5) dx = ∫ (18x + 6)/18(9x² + 6x + 5) dx + ∫ (12)/18(9x² + 6x + 5) dx

= 1/18∫ (18x + 6)/(9x² + 6x + 5) dx + 2/3∫ 1/(9x² + 6x + 5) dx

Let us integrate the first part and assume u = 9x² + 6x + 5

then, du = (18x + 6) dx

So, 1/18∫ (18x + 6)/(9x² + 6x + 5) dx = 1/18∫ 1/u du

                                                         = 1/18 lnu

                                                         = 1/18ln(9x² + 6x + 5)

For second part, 2/3∫ 1/(9x² + 6x + 5) dx, we will use

                     ∫ dx/(x² + a²) = 1/a tan^-1(x/a) +c

For this converting denominator into the sum of two squares, we get

    2/3∫ 1/(9x² + 6x + 5) dx = 2/27∫ 1 / ((x + 1/3)²+(2/3)²) dx

Let us now substitute u = x + 1/3 and as du = dx

so, 2/27∫ 1 / ((u)²+(2/3)²) dx = 2/27 (3/2 tan^-1 (3u/2))

                                            = 1/9 (tan^-1 (3(x+1/3)/2))

                                            = 1/9 (tan^-1 (3x+1)/2)

Hence,∫ (x + 1)/(9x² + 6x + 5) dx = 1/18ln(9x² + 6x + 5) + 1/9 (tan^-1 (3x+1)/2)

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Answer:

A

Step-by-step explanation:

The solution of the inequality is, x ∈ (- ∞, 5) ∪ (10, ∞)

Where, x represent the number of totts.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

My friend Raw has either no more than 5 toots and more than 10 toots.

Now, Let number of toots = x

Hence, We get;

⇒ x < 5

And, x > 10

Thus, The solution of the inequality is,

⇒ x ∈ (- ∞, 5) ∪ (10, ∞)

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Answer:

It is 25

Step-by-step explanation:

If the equation is 4/5 x n = 20, you will find the answer by dividing because its the opposite of multiplication.

\(20/\frac{4}{5} = 20x5/4=\\24\)

The answer is 25

I hope this helps :3

Answer:

False

Step-by-step explanation:

Horizontal goes from left to right. Therefore, the horizontal axis would be the x-axis because it shows the shifts from left to right. The y-axis would be up and down, which is vertical.

What is Symmetry ?

In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more exact meaning of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling.

A definition of symmetry in mathematics states that whether one shape is moved, rotated, or flipped, it exactly resembles the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the other half exactly matches the first half when you are instructed to cut out a "heart" from a piece of paper. The heart-shaped carving is an illustration of symmetry. Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a shape has been rotated or flipped. There are patterns in it. You may have heard the word "symmetry" quite a bit in modern times.

(A)

Any two indices will do i!=j Paul's time and the time of the ith runner are equally distributed and independent, hence according to the Symmetry, p (Ai) = p(Aj)= 1/2. Consider the intersection of Ai and Aj. Thus, Paul is outpaced by both runners I and j. There are 6 possible permutations of their times because they are i.id, with Paul being the slowest. P(Ai intersection Aj) hence equals 1/3.

But now wе have that P(Ai intersection Aj)= 1/3 != 1/4 = P(Ai)P(Aj)

thus, events They are not autonomous, Ai and Aj. However, they are only somewhat independent given Paul's timing. Paul can be removed from the narrative if such is the case. Then, only these two runners are left. Events As a result of their independent and equal distribution of times, Aj and AI are independent.

(B)

Define Ij as the random variable indication that indicates whether or not the jth runner is superior to Paul. via means of symmetry. We know p(Ij = 1)=1/2.

We determine that 

E(N) = E(I1+I2 +.......In) 

= nE(i1) 

=nP(I1-1) 

=n/2

using the linearity of expectation.

(C)

Paul's estimated time of completion is t The probability that each runner will finish ahead of Paul is P (time of rumer I t) = F. (t)

By using part (a), we can determine that other runners' times are independent of Paull's time, and that the number of runners who finish faster than Paul has a binomial distribution with the parameters n and F. To come to the conclusion that N/T= t Binom (n, F(t)) and if we choose T at random, N/T Binom (n, F(T)),

(D)

Let's figure out Var (N)

Var (N)=F(Var (N/T)) + Var(E(N/T))

= E(n F(T) (1- F(T)) + Var(on F(T))

according to Eve's Law.

Here, we can use the uniform distribution's universality to produce

F(T) ~Unif (0, 1) = U

Hence symmetry, which states that U I-U, leads to

Var(N) = nE(U2) + n2 var (U)

=n/3 + n2/12,

where E(U2)=1/3

Var(U)=1/12.

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The complex nature of bureaucracies, combined with factors

such as autonomy, information asymmetry, and institutional resistance, makes it challenging to control them fully.

Combination of legislative oversight, executive control, judicial review, administrative procedures, and public participation

The bureaucracy can be controlled through various means, including,

Legislative Oversight,

The legislature, such as a parliament or congress, can exercise control over the bureaucracy through oversight mechanisms.

This includes holding hearings, conducting investigations, and reviewing agency budgets.

By closely monitoring bureaucratic actions and decision-making processes, the legislature can ensure accountability and transparency.

Executive Control,

The executive branch, which includes the president or prime minister.

Has the power to control the bureaucracy through appointments, policy directives, and administrative orders.

The executive sets the agenda and priorities for the bureaucracy, establishes goals, and monitors performance.

Judicial Review,

The judiciary plays a crucial role in controlling the bureaucracy through the power of judicial review.

Courts can examine bureaucratic actions and determine whether they comply with the law and constitution.

Judicial review acts as a check on excessive bureaucratic power and ensures adherence to legal principles.

Administrative Procedures:,

Implementing standardized administrative procedures and regulations can help control the bureaucracy.

These procedures define the decision-making processes, establish checks and balances, and provide guidelines for accountability.

Rules and regulations can prevent bureaucratic abuse and ensure consistency.

Public Participation and Feedback,

Engaging the public in the decision-making process and seeking their feedback can be an effective way to control the bureaucracy.

By involving citizens, civil society organizations, and interest groups, the bureaucracy can be held accountable to the people it serves.

Despite these control mechanisms, controlling the bureaucracy can be challenging due to several reasons,

Bureaucratic Autonomy,

Bureaucracies often have a degree of independence and discretion in implementing policies and carrying out their functions.

This autonomy can make it difficult for external actors to influence or control their actions.

Complexity and Size,

Bureaucracies are often complex and large organizations with multiple layers and departments.

Managing and controlling such complex systems can be a daunting task.

And it becomes challenging to ensure consistent control throughout the organization.

Information Asymmetry,

Bureaucracies possess specialized knowledge and expertise in their respective domains.

Which can create information imbalances between bureaucrats and external actors.

This information asymmetry can limit effective control and oversight by external actors who may lack the necessary expertise or information.

Institutional Resistance,

Bureaucracies develop their own organizational cultures, norms, and interests over time.

These institutional factors can lead to resistance to external control and influence.

Bureaucrats may seek to protect their autonomy, power, or resources, making it difficult to implement changes or reforms.

Political Interests and Influence,

Bureaucracies can be subject to political pressure and influence, both from within the government and external actors.

Political considerations and interests may sometimes override effective control mechanisms.

Leading to the manipulation of bureaucracy for partisan or personal gains.

Lack of Resources and Expertise,

Controlling the bureaucracy requires adequate resources, technical expertise, and capacity-building efforts.

Insufficient resources or a lack of expertise among external control mechanisms can hinder effective control over the bureaucracy.

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Answer:

Step-by-step explanation:

Let's find and use the intercepts.  They speed up graphing of lines.

y-intercept:  In y = 6 – 2x, let x = 0.  Then y = 6, and the y-intercept is (0, 6).

x-intercept:  In y = 6 – 2x, let y = 0.  Then 2x = 6, and x = 3.  The x-intercept is therefore (3, 0).

Plot these two points and then draw a line through both.

The only true statement is

To begin converting the equation to standard form, abate 36 from both sides.

To dissect the given circle equation x² + 2 + 4x - 64 - 36 = 0, let's go through the handed statements one by one

1. To begin converting the equation to standard form, abate 36 from both sides.

This statement is true.

By abating 36 from both sides, the equation becomes x² + 2x + 4x -100 = 0.

2. To complete the forecourt for the × terms, add 4 to both sides.

This statement isn't true.

Adding 4 to both sides would not complete the forecourt for the x terms. In this equation, we do not need to complete the square since the x terms are formerly in standard form.

3. The center of the circle is at(- 2, 3).

This statement isn't true.

The equation x² + 2x + 4x -100 = 0 isn't in the form( x- h)² + ( y- k)² = r², which represents the equation of a circle centered at the point( h, k). thus, we can not determine the center of the circle from this equation.

4. The center of the circle is at( 4,-6).

This statement isn't true. As explained in statement 3, we can not determine the center of the circle from the given equation.

5. The compass of the circle is 6 units.

This statement isn't true. The compass of the circle can not be determined from the given equation.

6. The compass of the circle is 49 units.

This statement isn't true. The compass of the circle can not be determined from the given equation.

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Answer:

=

Step-by-step explanation:

Answer:

=

Step-by-step explanation:

the square root of 169 is 13

The regression estimate for how much he parties is 6.4.

Using the data, the regression line can be computed using any spreadsheet program. The regression line for this data will be in the format of y = ax + b where y is the dependent variable (drinking), x is the independent variable (partying hours), a is the slope, and b is the y-intercept.

To fill in the blanks, calculate the slope and intercept of the regression line. The formula for the slope of the regression line is given by:

Slope (a) = [(nΣxy) - (ΣxΣy)] / [(nΣx²) - (Σx)²]
where n is the number of data points, Σx and Σy are the sums of the x and y values, respectively, and Σxy is the sum of the product of x and y for each data point.

Similarly, the formula for the y-intercept is given by:
b = (Σy - aΣx) / n
Substituting the given data into the formulas, we get:
Slope (a) = [(6 × 638) - (21 × 6)] / [(6 × 91) - 6²] = 0.89
Intercept (b) = (21 - (0.89 × 91)) / 6 = 2.54

Therefore, the regression line is given by:
y = 0.89x + 2.54.

The regression estimate for how much the students reported drinking is given by the y value, while the regression estimate for how much they reported partying is given by the x value.

Using the last line of the table, where the number of drinks one student reported having per week is 8, the regression estimate for how much he parties is calculated by:
x = (8 - 2.54) / 0.89 = 6.4 (approx)

Therefore, the regression estimate is 6.4.

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Answer:

Should he take the new position?

He shouldn't not take the new position

Why or why not?

This is because he makes a lot more at his old job than his new position

Step-by-step explanation:

Please find attached to this answer, Marcus worksheet at for a week at the coffee shop

For his first job

Marcus works at a coffee shop. He earns $10.25 each hour.

Let the number of hour is = x

The equation is given as:

$10.25x

For a week

October 11, He worked from 5:45 - 12.00pm = 6 hours 15 mins = $61.5

For his

October 12, He worked from 5:45 - 1:00pm = 7 hours 15 mins = 71.75

October. 13

3. Marcus was offered a position which pays a salary of $150 every week and a 25 cent commission for each ice cream cone he sell.

Let the number of ice cream sells be equal to x

25cent = $0.25

$150 + $0.25× x

$150 + $0.25x

Marcus sells an average of 125 ice cream cones each week.

The amount Marcus makes in his new position in 1 week =

$150 + $0.25 × 125

= $150 + $31.25

= $181.25

Compare this to how much he made for a week at his current job.

Marcy makes more at his old job than his new position.

Should he take the new position?

He shouldn't not take the new position

Why or why not?

This is because he makes a lot more at his old job than his new position

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

here we go~

\(\qquad \sf  \dashrightarrow \: 4x {}^{2} - 25y {}^{2} \)

[ identity : a² - b² = (a + b)(a - b) ]

\(\qquad \sf  \dashrightarrow \: (2x) {}^{2} - (5y) {}^{2} \)

\(\qquad \sf  \dashrightarrow \: (2x + 5y)(2x - 5y)\)

The greater number is 20

Answer:m= 83 degrees

Step-by-step explanation: the sum of all three corners will always add up to 180 so adding 31 and 66 together is 97 an then 180-97 is 83.brainliest?

To check if a number is self-describing, we need to count the number of times each digit appears in the number and compare it to the digit itself

Let's break this down further using mathematical terms. Let's assume that we have a positive integer n with N digits. We can represent this integer as:

\(n = d(N-1)\times10^{N-1} + d(N-2)\times10^{N-2} + ... + d(1)\times10 + d(0)\)

where d(i) represents the digit in the i-th position of the integer n. For example, in the number

21200, d(0) = 0, d(1) = 0, d(2) = 2, d(3) = 1, and d(4) = 2.

To check if the number n is self-describing, we need to count the number of times each digit appears in the number. We can do this by iterating over each digit in the number and counting the number of times it appears. We can represent the count of digit i as c(i).

Once we have the counts for each digit, we can compare them to their respective digit in the number. If c(i) equals d(i) for all i from 0 to N-1, then the number n is a self-describing number.

In conclusion, a self-describing number is a positive integer where each digit in the number is equal to the number of times that digit appears in the number. .

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The distance between the rock and the surface is 827.20 cm.

Given data,

There is a robot on Mars' surface. 13.33 degrees of depression can be seen between a camera in the robot and a boulder on the surface of Mars. 196.0 cm is how high the camera is from the ground.

How far is the rock from the camera?

From the given data,

tan c = AB/BC

tan 13.33° = 196/BC

BC = 196/tan 13.33°

BC = 827.20 cm

Hence, the distance between the rock and the surface is 827.20 cm.

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Answer:

19.4

Step-by-step explanation:

In a right triangle, the tangent of an angle is defined as the quotient between the length of the side opposite to the angle and the length of the side adjacent to the angle.

Nevertheless, that is only true when the triangle is a right triangle. If BCA is a right angle, then all the reasoning is correct. But we cannot assume that BCA is a right angle unless it is given or there is a way to prove it.

Therefore, the mistake resides in assuming that the triangle is a right triangle without prior proof.

The solution to the system of equations graphed below is,

⇒ (0, 1)

Since, We have to given that;

Two system of equations are,

⇒ g (x) = 3x + 2

⇒ f (x) = |x - 1| + 1

Here, The graph of both system of equation are shown in graph.

We know that;

In a graph, the solution of system of equation are represented by a intersection point of both graph.

Here, In the graph of system of equation,

Intersection point is,

⇒ (0, 1)

Hence, The solution to the system of equations graphed below is,

⇒ (0, 1)

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okay so since the area is 22cm^2 , you will need to simplify it.

Which you will get 22*22 and the total would be 484. Which u will divide by 4 ( Square) to get each of the side your looking for.

So your answer is... 121

The difference in salary options for the month of February would be $9,875.

In Option #1, you would earn $100 per week plus 7.5% commission on sales. In Option #2, you would earn a fixed salary of $350 per week, with no commission. To calculate the difference in salary options for the month of February, we need to calculate the earnings for each option and then subtract Option #2 from Option #1.

In Option #1, the commission on sales would be 7.5% of $145,000, which is $10,875. The weekly earnings would be $100 per week. Since there are four weeks in February, the total earnings for Option #1 would be $100 * 4 + $10,875 = $11,275.

In Option #2, the weekly earnings would be a fixed $350 per week. So, the total earnings for Option #2 in February would be $350 * 4 = $1,400.

To find the difference in salary options, we subtract the earnings of Option #2 from Option #1: $11,275 - $1,400 = $9,875.

Therefore, the difference in salary options for the month of February would be $9,875.


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Answer is 41

Hope it help you