Nick is 64 years younger than Madelyn. 4 years ago, Madelyn's age was 3 times Nick's age. How old is Nick now?

The probability of transitioning from the UU state to the UD state, which is 0.2

a) The state transition diagram for this Discrete time Markov chain can be represented as follows:
``
      0.8        0.2
   UU -------> UU <------- UD
   ^            |          ^
   |            |          |
   |            |          |
   |            V          |
   |          0.4        0.5
   |         DD <------- DU
   |          ^          |
   |          |          |
   |          |          |
   |          |          V
   |         0.35       0.5
   |-------- DD <------- DD
      0.2        0.65
```

Where UU represents the state where the stock price went up for the last two days, UD represents the state where the stock price went up today but not yesterday, DU represents the state where the stock price went up yesterday but not today, and DD represents the state where the stock price went down in the last two days.

b) The transition matrix for this Discrete time Markov chain can be represented as follows:

```
      | UU   UD   DU   DD |
      |-------------------|
  UU  | 0.8  0.2  0.0  0.0 |
  UD  | 0.0  0.0  0.6  0.4 |
  DU  | 0.0  0.5  0.0  0.5 |
  DD  | 0.2  0.0  0.0  0.8 |
```

Where the rows represent the current state and the columns represent the next state. Each entry in the matrix represents the probability of transitioning from the current state to the next state. For example, the entry in the first row and second column represents the probability of transitioning from the UU state to the UD state, which is 0.2.

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The completed statement for the congruence of triangles is ΔXYZ ≅ ΔABC, the correct option is (d).

The Congruence of triangles is a term used in geometry which refers to the equality of shape and size of two triangles. The "Two-triangles" are  congruent if their "corresponding-sides" and angles are equal.

On observing both the triangles, we can say that,

The first triangle is right-angled at "X", and the second triangle is right-angled at "A",

the hypotnuse of first triangle is "ZY" and the hypotnuse of second triangle is "CB",

So, the "vertex X" similar to "vertex A", "vertex Z" similar to "vertex C", and "vertex Y" similar to "vertex B",

Therefore, triangle XYZ is congruent to triangle ABC, Option (d) is correct.

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Answer:

ACB

Step-by-step explanation:

Trust me

To use the elimination method to solve the system of equations 7.4x-y=-255 and 12.1x-y=-233, we need to eliminate one of the variables. We can do this by multiplying one of the equations by a constant to make the coefficients of one of the variables the same, and then subtracting the equations.

1. Multiply the first equation by -1 to make the coefficients of y the same:

-7.4x + y = 255

2. Subtract the second equation from the first equation:

-7.4x + y = 255

-12.1x + y = -233

---------------------

4.7x = 488

3. Solve for x:

x = 488/4.7

x ≈ 103.83

4. Substitute the value of x back into one of the original equations to find y:

7.4(103.83) - y = -255

765.342 - y = -255

y = 765.342 + 255

y ≈ 1020.342

5. Round the solution to the nearest whole number:

x ≈ 104

y ≈ 1020

So the solution to the system of equations is (104, 1020).

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Answer: a. The distribution of X is a binomial distribution with n = 3 and p = 1/4. That is, X ~ Binomial(3, 1/4).

b. The cdf of Y is given by F_Y(y) = P(Y <= y) = P(Y < y) + P(Y = y). Since Y is the middle one of the three points, we can write P(Y < y) as P(X >= 2, Z <= y) where Z is the smallest one of the three points. Similarly, we can write P(Y = y) as P(X = 1, Z = y). Therefore, the cdf of Y is given by:
F_Y(y) = P(X >= 2, Z <= y) + P(X = 1, Z = y)
= P(X >= 2)P(Z <= y) + P(X = 1)P(Z = y)
= (3/64)(y^3) + (9/64)(y^2)(1-y)

c. The pdf of Y is given by the derivative of the cdf with respect to y. That is,
f_Y(y) = dF_Y(y)/dy
= (3/64)(3y^2) + (9/64)(2y)(1-y) + (9/64)(y^2)(-1)
= (9/64)(y^2 - y^3)

Therefore, the pdf of Y is f_Y(y) = (9/64)(y^2 - y^3) for 0 <= y <= 1.

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Both statements are false because the sum of two angles does not equal the sum of their cosines or sines.

Statement 53 is false. This is because the sum of two angles does not equal the sum of their cosines. The correct equation for the sum of two angles in terms of their cosines is:

\( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ} \cos 60^{\circ} - \sin 30^{\circ} \sin 60^{\circ} \)

Using this equation, we can calculate the correct value of the cosine of the sum of the two angles:

\( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ} \cos 60^{\circ} - \sin 30^{\circ} \sin 60^{\circ} \)
\( \cos 90^{\circ}=\frac{\sqrt{3}}{2} \cdot \frac{1}{2} - \frac{1}{2} \cdot \frac{\sqrt{3}}{2} \)
\( \cos 90^{\circ}=0 \)

Statement 54 is also false. This is because the sum of two angles does not equal the sum of their sines. The correct equation for the sum of two angles in terms of their sines is:

\( \sin \left(30^{\circ}+60^{\circ}\right)=\sin 30^{\circ} \cos 60^{\circ} + \cos 30^{\circ} \sin 60^{\circ} \)

Using this equation, we can calculate the correct value of the sine of the sum of the two angles:

\( \sin \left(30^{\circ}+60^{\circ}\right)=\sin 30^{\circ} \cos 60^{\circ} + \cos 30^{\circ} \sin 60^{\circ} \)
\( \sin 90^{\circ}=\frac{1}{2} \cdot \frac{1}{2} + \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} \)
\( \sin 90^{\circ}=1 \)

In conclusion, both statements are false because the sum of two angles does not equal the sum of their cosines or sines. The correct equations for the sum of two angles in terms of their cosines and sines are shown above.

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Answer:

It depends on what's given in the problem.

Step-by-step explanation:

There's a few ways to find the hypotenuse of a triangle, but we must have something given to us.

A Few Methods (Most Common to Least Common):

The Pythagorean Theorem. 2 legs of a right triangle are given. You should add the 2 legs together to find the hypotenuse.

[tex]a^2 + b^2 = c^2[/tex]

Sine, or Cosine. This is only used when there's a given angle, and/or at least one given side.

[tex]Sin \ (\theta) = \frac{opposite}{hypotenuse}[/tex]

[tex]Cosin \ (\theta)=\frac{adjacent}{hypotenuse}[/tex]

Rare, but possibly we need to find the area of the triangle. There needs to be at least 1 angle given.

This is the formula we need to find the Hypotenuse:

[tex]Area = \frac{1}{2} \times h^2 (hyp.) \times sin (angle) \times cos(angle)[/tex]

This is a lot to learn. Let me know if you have any questions.

The amount of centiliters in a picoliter is A = 1 x 10⁻¹⁰ cL

In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.

The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.

A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.

Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.

Given data ,

Let the first unit of measurement be represented as A

where A = centiliters

Now , the amount of Liters in a centiliter is

From the unit conversion ,

1 L = 100 cL

And , 1 cL = 10⁻² L

Now , the amount of Liters in a picoliter is

1 L = 10¹² picoliters

And , amount of centiliters in a picoliter is A

where A = 10⁻¹⁰ cL

So , the 1 pL = 10⁻¹⁰ cL

Hence , the unit conversion of liters is solved

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The maximum possible height for the fish tank is 3.37 feet.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

Given that, one cubic foot of water is equivalent to 7.48 gallons.

The capacity of the fish tank is 100 gallons

Now, height = Number of gallons/7.48

= 100/7.48

= 13.37 feet

Therefore, the maximum possible height for the fish tank is 3.37 feet.

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The area of the middle rectangle is 720 square units.

Let's label the areas of the left and right rectangles as A and C, respectively. Let's also label the area of the middle rectangle as B. We know the distance between the first and second rectangles is 18, and the distance between the second and third rectangles is 14.

Using the formula for the area of a rectangle, we can write:

90 = lw

60 = sw

where l and w are the length and width of the left rectangle, and s and w are the length and width of the right rectangle. We want to find the width of the middle rectangle, so we can label it as x:

B = lx

We know the length of the middle rectangle is 32, so we can write:

B = 32x

Now we have three equations and three unknowns. We can use the distances between the rectangles to set up two more equations:

l + s = 18

s + 32 = 14

Simplifying, we get:

l + s = 18

s = -18 + 32 = 14

We can now solve for l and s in terms of x:

l = 18 - s = 18 - 14 = 4

s = 14

Substituting these values into the equations for the areas of the left and right rectangles, we get:

90 = 4w

60 = 14w

Solving for w in each equation, we get:

w = 22.5

Now that we have found the width of the middle rectangle, which is x = 22.5, we can use the formula for the area of a rectangle to find its area:

B = lx = 32(22.5) = 720

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The answer would take Stephanie and Shayna approximately 4.42 hours to clean the attic if they worked together.

Working alone, it takes Stephanie seven hours to clean an attic. Shayna can clean the same attic in 12 hours. To find how long it would take them if they worked together,

we can use the formula:

1/T = 1/t1 + 1/t2

Where T is the time it takes for both to complete the task together, t1 is the time it takes for the first person to complete the task alone, and t2 is the time it takes for the second person to complete the task alone.

Plugging in the given values, we get:

1/T = 1/7 + 1/12

1/T = 12/84 + 7/84

1/T = 19/84

T = 84/19

T = 4.42 hours

Therefore, it would take Stephanie and Shayna approximately 4.42 hours to clean the attic if they worked together.

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Answer:

y=2500(0.15)^x

y=375^x

Step-by-step explanation:

The constant of proportionality (k) for the data points on this graph is 7.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 7/1 = 14/2 = 21/3 = 28/4 = 35/5

Constant of proportionality, k = 7.

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the above question, we may state that Hence, the surface area rectangular prism has a surface area of 148 square centimeters.

An object's surface area is a measure of how much space it takes up overall. The entire amount of space around a three-dimensional form is its surface area. The total surface area of a three-dimensional form is referred to as its surface area. By summing the areas of each face, one may get the surface area of a cuboid with six rectangular faces. Instead, you may identify the box's dimensions using the following formula: Surface (SA) equals 2lh, 2lw, and 2hw. The total amount of space occupied by the surface of a three-dimensional form is measured as surface area.

Shown above is a rectangular prism. We may apply the formula: to determine the surface area.

2lw + 2lh + 2wh = Surface Area

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

As we look at the image, we can see that it is 6 cm long, 4 cm wide, and 5 cm tall. These values can be used as substitutes in the formula:

Surface Area = (2,6,4,2,6,5,2) (5)

Area of Surface = 48 + 60 + 40

Area of Surface = 148

Hence, the rectangular prism has a surface area of 148 square centimeters.

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Yes, the determinant A = 2 and the matrix A and its determinant do correspond to the area of the parallelogram.

The formula for the area of a parallelogram is A = bh,

where b is the base and h is the height. Since the parallelogram fits within a circle of radius 1, the base of the parallelogram is equal to 2 and the height is equal to 1, so the area of the parallelogram is equal to 2.

This matches the value of the determinant A, which is equal to 2.

Therefore, the determinant A and the matrix A have been calculated correctly to correspond to the area of the parallelogram

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A rational function having the following vertical asymptotes x = -4 and x = 5 and x-intercept (-2, 0) is [tex]f(x) = \frac{x+2}{(x+4)(x-5)}[/tex].

A rational function is a function that can be expressed as the quotient of two polynomials. Vertical asymptotes occur when the denominator of the rational function is equal to zero. An x-intercept occurs when the rational function is equal to zero.

To find a rational function that satisfies the given conditions, we can use the information about the vertical asymptotes and x-intercept to create the function.

The vertical asymptotes occur at x = -4 and x = 5, so the denominator of the rational function must have factors of (x + 4) and (x - 5). The x-intercept occurs at (-2, 0), so the numerator of the rational function must have a factor of (x + 2).

Therefore, one possible rational function that satisfies the given conditions is:

[tex]f(x) = \frac{x+2}{(x+4)(x-5)}[/tex]

This function has vertical asymptotes at x = -4 and x = 5, and an x-intercept at (-2, 0), as required.

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As a result, a new rectangle is created by increasing the breadth by 5 cm, making the οriginal rectangle 12 by 8 cm in size.

A rectangle is a flat, fοur-sided shape that is made by twο sets οf parallel lines at each οf its fοur right angles (angles οf 90 degrees). A rectangle's diagοnals and οppοsing sides have equal lengths and are bisected by its οppοsite sides. The perimeter οf a rectangle is equal tο the sum οf the lengths οf its fοur sides, and its area is calculated by multiplying its length by its breadth. Rectangles are frequently seen in daily living, including οn cοmputer screens, bοοk cοvers, and dοοrs and windοws.

given:

Let L represent the initial rectangle's length in centimetres.

Therefοre, the width οf the initial rectangle can be expressed as L – 4 cm, which is 4 cm less than its length.

The οriginal rectangle's area is equal tο the sum οf its length and breadth, sο:

Area οf the initial parallelοgram is equal tο L(L-4) = L2 - 4L.

The new rectangle's size is specified as 117 cm2, sο:

New rectangle's surface area Equals (L - 3)

(L + 1) = L² - 2L - 3 = 117

When we simplify this sοlutiοn, we οbtain:

L² - 2L - 120 = 0

Using the quadratic fοrmula, we can answer this quadratic equatiοn:

L is equal tο (-b √(b² - 4ac)) / 2a.

where (a, b, and c) are (1, 2, and -120)

As a result, there are twο οptiοns:

L = 12 οr L = -10

Rectangles cannοt have negative lengths, sο we rule οut the negative sοlutiοn and determine that the initial rectangle's length was 12 cm.

We can determine the breadth by using the fοrmula fοr the width οf the initial rectangle:

Original rectangle's width is equal tο L – 4 (12 – 4), οr 8 centimetres.

As a result, a new rectangle is created by increasing the breadth by 5 cm, making the οriginal rectangle 12 by 8 cm in size.

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Answer:

Step-by-step explanation:

Pls give simple working

Leon will receive ECS250.00 dollars if he exchanges US$100.00 at this bank.

If ECS2.60 is equivalent to US$1.00, then the exchange rate from US dollars to EC dollars is 1:2.60.

To find out how much ECS dollars Leon will receive for US$100.00, we first need to convert US$100.00 to EC dollars using the exchange rate:

US$100.00 * 2.60 = ECS260.00

So, Leon will receive ECS260.00 for US$100.00 before any exchange fees are deducted.

The exchange fee for every US$1.00 exchanged is ECS0.10. Therefore, the exchange fee for US$100.00 will be:

US$100.00 * ECS0.10 = ECS10.00

To find out how much Leon will receive after the exchange fee is deducted, we need to subtract the fee from the initial amount:

ECS260.00 - ECS10.00 = ECS250.00

Therefore, Leon will receive ECS250.00 if he exchanges US$100.00 at this bank.

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The transformations of g(x) as it relates to f(x)=2^(x) are as follows:

- Vertical stretch by a factor of -7
- Horizontal compression by a factor of 10
- Horizontal shift to the right by 3/10
- Vertical shift up by 4

The transformations of g(x) as it relates to the parent function f(x)=2^(x) are:
- A vertical stretch by a factor of -7, since the coefficient of the parent function is -7.
- A horizontal compression by a factor of 10, since the coefficient of x in the exponent is 10.
- A horizontal shift to the right by 3/10, since the term inside the exponent is (10x-3).
- A vertical shift up by 4, since the constant term added to the function is 4.

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The linear equation which would model the temperature at sun rise and the rise in temperature per hour is y = 47 + 2.5x, where y denotes the temperature after 8 hours and x denotes the number of hours passed since sunrise.

It is already given that the temperature after sunrise increases by 2.5 degrees per hour and the temperature after 8 hours of sunrise is 67 degrees. Therefore, if we consider the initial temperature as 'a' and increased temperature as 'b', then a is unknown and b is equal to 2.50.

Now, considering the temperature after 8 hours as y which is equal to 67 and x=8 denote the numbers of hours passed, then the equation would be as follows:

y = a + xb ...(1)

67 = a +8*(2.5)

⇒ a = 47

This represents the temperature at sunrise, that is 47 degrees.

Now putting the value of a in equation (1), we get:

y = 47 + 2.5x

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Raj profited Rs 30,750 from lending and borrowing money.

Raj gained from lending out Rs 65,000 for 3 years at 25% per annum and lost from borrowing Rs 60,000 for 2 years at 15% per annum.

To find out how much he gained or lost, we need to calculate the interest earned from lending and the interest paid from borrowing and then find the difference between them.

Interest earned from lending = Principal x Rate x Time
= Rs 65,000 x 25% x 3
= Rs 48,750

Interest paid from borrowing = Principal x Rate x Time
= Rs 60,000 x 15% x 2
= Rs 18,000

Difference between interest earned and interest paid = Rs 48,750 - Rs 18,000
= Rs 30,750

Therefore, answer is +Rs. 30,750.

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Answer:

here is your answer

Step-by-step explanation:

13x^2y^2 (3x-4)

The final simplified expression is: [tex]6x^(2) - 22x + 9[/tex]

To simplify the given expression, we need to combine like terms. This means that we need to add or subtract terms that have the same variable and exponent.

The given expression is: [tex]12x^(2)+9-8x-6x^(2)-14x[/tex]

First, let's combine the terms with the same variable and exponent:

[tex]12x^(2) - 6x^(2) = 6x^(2)[/tex]

[tex]-8x - 14x = -22x[/tex]

Now, let's substitute these simplified terms back into the expression:

[tex]6x^(2) + 9 - 22x[/tex]

This is the simplified expression. There are no more like terms to combine, so we cannot simplify it further.

The final simplified expression is: [tex]6x^(2) - 22x + 9[/tex]

Answer: [tex]6x^(2) - 22x + 9[/tex]

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Answer:

15m,20m,25m

Step-by-step explanation:

15 cm, 20cm and 25cm follows the same pattern as the 3-4-5 pattern of the Pythagorean triplet. The Pythagorean triplet holds true.

a) Measure of fourth angle of quadrilateral diamond is equals to the 120°.

b) The measures of other two angles

of rhombus are equal to the 30° and 110°.

A polygon is a flat or plane figure that is described by a finite number of straight line segments ( not curves) connected to form a closed figure. The bounded plane region is known as a polygon. The finite line segments of a polygon are called its edges or sides. We have a round center cut diamond.

a) Three angles of the quadrilateral are of measure 60°, 70°, 110°. Let the fourth angle of quadrilateral be 'x degrees'. As we know, the Sum of all interior angles of a quadrilateral = 360°

=> 60° +70° + 110° + x = 360°

=> 240° + x = 360°

=> x = 360° - 240°

=>x = 120°

b) We have measure of two angles of the rhombus are 30°, 110°. Let the measure of other two angles be 'a degrees' and ' b degree'. As we know, tge Opposite angles of rhombus are equal

⇒ a = 30°

⇒ b = 110°

Hence, required measure of angles are 30° and 110°.

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Complete question:

2. Brilliance measures the amount of light that passes into the diamond and reflects out from its internal surfaces. A round center cut diamond is shown.

a) Outline one irregular quadrilateral in the diamond. The measure of three of the

angles of one of the irregular quadrilateral facets of the diamond are 60°, 70°,and 110°. What is the measure of the fourth angle? Explain your reasoning.

b) Outline one rhombus in the diamond. The measure of two of the angles of one of the rhombus facets of the diamond are 30° and 150°. What are the measures of the other two angles? Explain your reasoning.

Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.

What is equation of a straight line?

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

After 2 months, Javier has saved a total of $920. Therefore, we can write the following equation:

2m = 920

Simplifying this equation, we get:

m = 460

This means that Javier is saving $460 each month.

After 4 months, Javier has saved a total of $1030. Using the same logic as before, we can write:

4m = 1030

Simplifying this equation, we get:

m = 257.5

This means that Javier is saving $257.5 each month.

To model the relationship between the amount of money Javier has saved and the number of months he has saved for, we can use the equation of a straight line:

y = mx + b

where y is the amount of money saved, x is the number of months, m is the monthly savings rate, and b is the starting amount saved.

Using the values we found earlier, we can write two equations:

y = 460x + b (for the first two months)

y = 257.5x + b (for the first four months)

To find the value of b, we can substitute the values of x and y for one of the points:

920 = 460(2) + b

Simplifying, we get:

b = 0

So the final equation that models the relationship between the amount of money Javier has saved and the number of months he has saved for is:

y = 460x (for the first two months)

y = 257.5x (for the first four months)

This means that Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.

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Answer:

Step-by-step explanation:

Let [tex]x[/tex] be number of $1 bills.

Let [tex]y[/tex] be the number of $5 bills.

So we get:

[tex]x+y=60[/tex]       [tex](1)[/tex]

[tex]x+5y=150[/tex]   [tex](2)[/tex]

Then we solve these simultaneously:

[tex](2)-(1)[/tex]  gives

[tex]4y=90[/tex]  ⇒ [tex]y=22.5[/tex]

Substitute [tex]y=22.5[/tex] into [tex](1)[/tex] gives:

[tex]x+22.5=60[/tex]  ⇒  [tex]x=37.5[/tex]

So there appears to be no solution to this question as you cannot have half bills.

Phillip's net loss after adding 15 pencils to his collection and giving away 30 pencils is 15 pencils.

A term is composed of one mathematical expression. A single variable (a letter), a single integer (positive or negative), or a number of variables that have been multiplied but never added or subtracted are all examples of single variables. There is a number in front of certain words that are variables. A word or phrase is preceded by a coefficient.

To calculate Phillip's net gain or loss, we need to subtract the number of pencils he gave away from the number he added to his collection.

Let's use the variable "x" to represent the number of pencils Phillip had before he added 15 pencils to his collection.

Then the expression for the total number of pencils Phillip has after giving away 30 pencils would be:

x + 15 - 30

Simplifying this expression, we get:

x - 15

Therefore, x - 15 is the required expression.

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Answer:

First we would shrink by a factor of 3

Then translate 6 units on the x axis

Then reflect across x=6