Conrad Savings Bank has a $50 overdraft fee. On Friday, Mr. McQuire deposited his paycheck of $332 for a total
account balance of $750. The next morning, his wife wrote a check for $1,183.15 for a new refrigerator and stove.
The check cleared the bank by the end of the day. What is the current balance in the McQuire's account?

Answer: We can set up the equation 21 stickers/pack + 24 stickers/pack + x stickers/pack = 15 stickers.

We can solve this equation to find that x, the number of stickers in each pack, is equal to 6 stickers/pack. Answer: 6

Answer: 20

Step-by-step explanation:

24 + 21 = 45

45 + 15 = 60

60 / 3 = 20

Answer:

$8 per person

Step-by-step explanation:

32 divided by 4 is 8

32 : 4 = 8 : 1

With all this information, and reading our question carefully, we can decipher the following:

9(n-3) = 3 + (9n + 3n)

9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)

9n - 27 = 3 + 12n       (Step 2. Combine like terms; 9n + 3n = 12n)

-9n                  -9n    (Step 3. Subtract 9n from both sides to isolate the variable)

______________

  -27 = 3 + 3n            

     -3      -3               (Step 4. Subtract 3 from both sides)

________________

-30 =       3n                        

 -----         ----

  3            3              (Step 5. Divide 3 from both sides)

________________

 -10 = n

Therefore, n = -10

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Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

What is differentiation?

In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.

Main body:

by using product rule;

Let = u = x² + 4x + 6

⇒ du/dx = 2x + 4 .

Now y = u⁵

⇒ dy/dx = 5u⁴ .

dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)

= 5 * (x² + 4x + 6)⁴ * (2x + 4)

= 5(2x + 4) * (x² + 4x + 6)⁴

hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

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Error Analysis 1:(x-3)/(x+7)

Error Analysis 2:(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

Error analysis is a procedure that is usually used to identify the cause of the issue when pupils continually make mistakes. The method entails going over a student's work and looking for patterns of misinterpretation. Mathematical errors can occur for a variety of reasons and can be factual, procedural, or conceptual. The study of the kind and quantity of mistake, or uncertainty, that might be present in the solution to a problem is known as error analysis in mathematics. This issue is particularly common in practical disciplines like statistics and numerical analysis. The teacher can examine a student's errors on a worksheet, test, or progress monitoring tool to do an error analysis for mathematics. In order to grade each problem, the teacher should mark each wrong digit in the student's response, starting from the RIGHT, going to the LEFT for addition, subtraction, and multiplication problems.

Error Analysis 1:

(x²-x-6)/(x²+9x+14)

=(x-3)(x+2)/(x+2)(x+7)

=(x-3)/(x+7)

Error Analysis 2:

(x²-6x-27)/(2x²+2x)÷(x²+14x+45)/(x²)

=(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

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Answer:

Step-by-step explanation:

To find the percentage increase in the dog's weight, you can use the following formula:

percentage increase = (final value - initial value) / initial value x 100%

In this case, the initial value is 40 pounds and the final value is 48 pounds, so the percentage increase is:

percentage increase = (48 - 40) / 40 x 100% = 8 / 40 x 100% = 20%

Therefore, the dog's weight increased by 20%.

The supplement of BIE equals the supplement of GMD is a false assertion if lines BG and CF are parallel.

Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the total of angle 130° and angle 50° is 180°, hence they are supplementary angles.

Lines BG and CF are parallel, as shown in the figure.

If BIE = X, then its supplement of BIE will be 180 - X;

similarly, if GMD = Y, then its supplement of GMD will be 180 - Y.

Since BG and CF are parallel, the supplements of BIE and GMD are interior angles on the same side ( as shown in figure)

and for parallel line the interior angle on the same side is 180

so 180 - X and 180 -Y there sum should be 180

They cannot be equal

line BG and CF are parallel, then the supplement of BIE = the supplement of GMD are not equal.

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Graph (C) which has points (0, 400) and (16, 0) represent the solution to the given situation of Rashawn.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Graphs and charts are useful visual aids because they make information accessible and quick to understand.

Therefore, it is not unexpected that print and electronic media frequently use graphs.

When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.

So, Rashawn consumed 25 pages of his book daily till it was finished. There were 400 pages in his book.

400 / 25 = 16 days is the estimated number of days he needs to finish the book.

He will have 400 pages finished in 0 days and 0 pages in 16 days.

As a result, the situation is represented by a graph with a line segment in the first quadrant.

Days are shown on the x-axis, and Pages left are listed on the y-axis.

The line segment's ends are (0, 400) and (16, 0).

Therefore, graph (C) which has points (0, 400) and (16, 0) represent the solution of the given situation of Rashawn.

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Complete question:
Rashawn read 25 pages of his book each day until he finished the book. His book was 400 pages long.

Which sketch represents this situation?

a) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 400 end ordered pair and begin ordered pair 25 comma 0 end ordered pair.

b) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 16 end ordered pair and begin ordered pair 400 comma 0 end ordered pair.

c) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 400 end ordered pair and begin ordered pair 16 commas 0 ends ordered pair.

d) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y-axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 25 ends ordered pair and begin ordered pair 400 commas 0 ends ordered pair.

The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.

What are domain and range?

The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

From the given question, and the above definition of domain and range,

the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value

Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.

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c is the answer. jdjsisiao

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

What is the property of slopes of parallel lines and perpendicular lines?

If two lines are given and they are parallel to each other then the slopes are equal and for perpendicular lines, the product of their slopes is equal to -1.

(7) The line AB is passing through the points (-1, 5/2) and (3/2, -1/2).

   Slope = y2 - y2/x2 - x1

              = (-1/2 - 5/2)/(3/2-(-1))

              = -6/5

   As line AB and line CD are parallel in nature so the slope of line CD is also -6/5.

(8) The line AB is passing through the points (1/2, 1) and (5/2, 5/2).

    Slope = y2 - y2/x2 - x1

              = (5/2 - 1)/(5/2-1/2)

              =3/2/2

             = 3/4

    Line CD is passing through points (1, 1) and (2, 3).

    Slope = y2 - y2/x2 - x1

              = (3 - 1)/(2-1)

              =2/2

             = 1

  As the product of their slopes is not equal to -1.

  So lines are neither parallel nor perpendicular.

(9) Slope of AB can be computed as (-2, 1) and (-5, 5)

     Slope = 5 - 1/-5 + 2

                = 4/-3.

  The slope of line passing through the point P = -4/3 as we have to draw the parallel line.

 Point P = (-1, 3)

Equation of the line :

      y - 3 = -4/3(x + 1)

    3y +9 = -4x - 4

   3y = -4x - 13

Now we can draw the line

(10) Slope of line AB = -4/3

    So the slope of the line passing through point P should be 3/4 in order to be perpendicular to line AB.

     Equation of the line passing through point P:

       y - 3 = 3/4(x - (-1))

       y - 3 = 3/4(x+1)

Hence,

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

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The value of p is 0.16. So the option b is correct.

A local entrepreneur takes a random sample of 100 people.

Of the urban participants, 22 buy a real tree.

Of the rural participants, 28 buy a real tree.

Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree.

Let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree.

We have to find the p-value

p1 = X1/N1

p1 = 28/100

p1 = 0.28

p2 = X2/N2

p2 = 22/100

p2 = 0.22

p = (X1 + X2)/(N1 + N2)

p = (28+22)/(100+100)

p = 0.25

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: p1 = p2

Alternate Hypothesis, Ha: p1 > p2

Test statistic

z = (p1 - p2)/√(p*(1-p)*(1/N1 + 1/N2))

z = (0.28-0.22)/√(0.25*(1-0.25)*(1/100 + 1/100))

z = 0.9798

P-value Approach

P-value = 0.16

Hence, the option A is correct. 0.16 is the p-value.

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Answer: the number is -16

Step-by-step explanation: if you add 17 to -49, you will get -32. you do this because it is 17 less than NOT more than. that would be called inverse operations. then, you divide that number by 2 to get -16. again, you use inverse operations because you are going backwards to try and find the number.

Answer: -16

Step-by-step explanation: So, to solve, we should write an equation. It should look like this:

2x - 17 = -49

So, using inverse operations, we would add 17 to - 49, which is -32, then divide that by 2, which would be -16. I hope this helped!

P.S. our new equation would look like 2(16) - 17 = -49

32-17 = 49

32 + -17 = 49

49 = 49

It checks out.

Answer:

There is 1/32 pound food for each fish

Step-by-step explanation:

24 fish = 3/4 pound food

1 fish = (3/4)/24 pound food = 1/32 pound food

(Problem solved by using unitary method)

Economies of scale occur when average cost declines with an increase in output. This occurs up to output level Q1.

Diseconomies of scale occur when average cost increases with an increase in output. This begins at output level Q3.

The phenomenon known as economies of scale occurs when the size or magnitude of the production generated by a business increases while the average cost per unit of output decreases.

The Long Run Average Cost Curve demonstrates how a firm's average expenses change over time. The shift from point A to point B illustrates how the cost per unit decreases as the curve slopes down. Because of economies of scale, the average cost grows less proportionally to output over the downward sloping region of the curve.

Minimum efficient scale is the level of output where economies of scale have been fully exploited.

A competitive firm produces at the minimum point of ATC in the long run and thus achieves productive efficiency.

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a) The amounts that the team needs to sell is given as follows:

b) The advantage and disadvantage is given as follows:

The amounts needed are found applying the proportion, considering the costs and the number of candles.

A package of 5 candles for $18, hence the number of candles needed to earn $1404, in packages, is given as follows:

5 candles - $18

n candles - $1404

Applying cross multiplication, we have that:

18n = 5 x 1404

n = 5 x 1404/18

n = 390 candles.

With a single candle, the number of candles is calculated as follows:

1404/4 = 351 candles.

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The required equivalent expression is given as 5(w - 3).

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
An equivalent expression of any expression is given as the simplifying the expression using various operations such as factors.
So,
Given expression,
=  5w - 15
As in the expression 5 is a common term between 5w and 15.
Take 5 commons and put the rest of the expression in the parenthesis.
= 5(w - 3)

Thus, the required expression is 5(w - 3).

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The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.

Given that,

Give the equation for the parabola's axis of symmetry by sketching the graph of each quadratic function using its vertex and intercepts.

We have to determine the function domain and range using the graph is f(x) = (x-1)²+2

We know that,

Its vertex A quadratic function's form is provided by

f(x) = a(x-h)²+k

So, (h,k) is the vertex of the parabola

Take

f(x) = (x-1)²+2

(1,2) is the vertex of the parabola.

Therefore, The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.

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Answer:

I was willing to pay $20 more for the toy than I actually paid.

Step-by-step explanation:

Let us take the maximum bid be y

So,

(y × 60) ÷ 100 = 30

60y/100 = 30

60y/100 × 100 = 30 × 100

60y = 3000

60y/60 = 3000/60

y = 50

60% of $50 is $30

So,

50 - 30 = 20

Thus, I was willing to pay $20 more for the toy than I actually paid.

Answer: 84 bells

Step-by-step explanation:

12 + 9x8

84

Answer:

125+25n

Step-by-step explanation:

We are given that

Heather opens a bank account with=$125

Each week she deposited money  into her account=$25

We have to find the explicit rule for the amount of money that has Heather after n weeks.

Heather has money after 1 week=125+25=$150

Heather has money after 2 week=125+2(25)=$175

Heather has money after 3 weeks=125+3(25)=$200

Heather has money after n weeks=125+25(n)

Hence, the explicit rule for the amount of money that has Heather after n weeks is given by

125+25n

(x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

as the polynomial with rational coefficients that has zeros x=2 and x=3i

(x-2) and (x-3i) are factors of third-degree polynomial.

so ,

⇒(x-2)(x-3i)

solving (x-3i)

x = 3i

squaring both sides,

x² = -9

so , (x²+9) is a factor.

hence , (x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

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Observing the provided equation, We can't solve these equations using substitution method or any other methods because these lines are parallel and never intersect each other.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

x=4-8y

3x+24=12

Taking first equation and rearranging it we get,

x+8y=4

multiply this with 3, we get 3x+24y=12 which are identical in nature. Which shows these two lines are parallel in nature. We can't solve them because parallel lines never intersect.

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Observing the provided equation, We can't solve these equations using substitution method or any other methods because these lines are parallel and never intersect each other.

What do you mean by equations?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

What is a substitution method?

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

x=4-8y

3x+24=12

Taking first equation and rearranging it we get,

x+8y=4

multiply this with 3, we get 3x+24y=12 which are identical in nature. Which shows these two lines are parallel in nature. We can't solve them because parallel lines never intersect.

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Answer:

y = -1/2x - 2

Step-by-step explanation:

y = mx+b, m = -1/2, and b (the y-intercept) is -2.

The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity

A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graph, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.

We are given the function;

g(x) = 2(x + 4)²/(x² - 16)

Simplifying the denominator gives;

(x² - 16) = (x + 4)(x - 4)

Thus, our function is;

g(x) = 2(x + 4)²/[(x + 4)(x - 4)]

(x + 4 ) will cancel out to give;

g(x) = 2(x + 4)/(x - 4)

Vertical asymptote:

Point in which the denominator is 0, so:

(x - 4) = 0

x = 4

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Ф {0, [3√3/2(3√3-π)]}

The poster above has good diagrams ; so , I will just go through the calculations .

The region of integration is with in the circle x ^2+y^2=2y but outside the circle   x^2+y^2=1.

I would convert to polar . With polar , we have  x^2+y^2=r^2 ,x=rcosФ and        y=rsinФ
We thus have the first circle becomes x^2+y^2=2y ⇒r^2=2rsinФ Divide through by r,  and you get r=2sinФ(1).  
This is the upper circle in the previous posters diagrams .

The other equation of a circle becomes :
x^2 + y^2 =  1  ⇒ r^2 = 1 ⇒ r =  1   (2)      
These two curves intersect at :
r= 2sinФ =1 ⇒     sinФ=1/2  ⇒Ф= [tex]\alpha[/tex]/6 or 5[tex]\pi[/tex]/6    
From the previous poster's diagrams , we can see that there is as much mass on either side of the positive. y axis or
Ф=[tex]\pi[/tex]/2 axis in polar ; so , the X  coordinate of the center of mass is zero  
X=0 We can also see from his diagrams that the mass and moment of mass is symmetrical about the Ф=[tex]\pi[/tex]/2
we only need to integrate from Ф=[tex]\pi[/tex]/6 to Ф=[tex]\pi[/tex]/2  ( the answers from to are the same and double )
The differential of area in polar coordinates is
d A=rdrdФ  They say the area mass density is inversely proportional to the distance from the origin .

This can be written as : p=k/r. We can thus say the differential of mass is
d M=PDA=

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The proof that  Δ SVW ≅ Δ UTW is given by ASA congruence criterion.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

The symbol of congruence is’ ≅’.

Given:W is the midpoint of SU

⇒ SW = WUTU ⊥ SU and SU ⊥ SV

To prove:Δ SVW ≅ Δ UTW

Proof:In Δ SVW and Δ UTWSW = UW (given)

∠S ≅ ∠U (given)

∠ SVW ≅ ∠ UTW (vertically opposite angle)

Therefore, Δ SVW ≅ Δ UTW (by ASA congruence criterion)

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