Please help due today

Answer:

The area can be found by multiplying the two terms, and the perimeter by doubling and adding them.

Using this, we find that the area of the rectangle is 60x³, and the perimeter is 10x² + 24x.

Step-by-step explanation:

First let's find the area:

5x² × 12x

= 60x³

Now the perimeter:

2(5x² + 12x)

= 10x² + 24x

Answer:

m = 0 or m = 2

Step-by-step explanation:

m² - 2m = 0

m ( m − 2 ) = 0

m = 0

m − 2 = 0

m = 2

Answer:

£3691 (nearest pound)

Step-by-step explanation:

Consider the rate of compound interest is r and the initial amount of savings is P, hence

\(P \ + \ P \ \times \ r \ = \ P \ (\ 1 \ + \ r \ ) \qquad (Final \ amount \ for \ the \ 1st \ year ) \\ \\ \ P \ (\ 1 \ + \ r \ ) \ + \ P \ (\ 1 \ + \ r \ ) \ \times \ r \ = \\ \ P\ ( \ 1\ + \ r \ ) \ ( \ 1 \ + \ r \ ) \ = \ P \ {( \ 1 \ + \ r \ )}^2 \qquad (Final \ amount \ for \ the \ 2nd \ year) \\ \\ \ P \ {(\ 1 \ + \ r \ )}^2 \ + \ P \ {(\ 1 \ + \ r \ )}^2 \ \times \ r \ = \\ \ P\ {( \ 1\ + \ r \ )}^2 \ ( \ 1 \ + \ r \ ) \ = \ P \ {( \ 1 \ + \ r \ )}^3 \\ \\ (Final \ amount \ for \ the \ 3rd \ year)...\)  

Therefore, the final amount of savings after nth years of compund interest is

\(P \ {( \ 1 \ + \ r \ )}^n\).

Given that 4.2% compound interest was used for the first 4 years to a savings of £2350, thus

\(Final \ amount \ for \ the \ first \ 4 \ years \ = \ 2350 \ {( \ 1 \ + \ \frac{4.2}{100} \ )}^4 \ = \ 2770.36\)

Then, taking the final amount of savings previously into an initial amount for the next 6 years with 4.9% compound interest.

\(2770.36 \ {( \ 1 + \frac{4.9}{100} \ )}^6 \ = \ 3691.40 \ = \ 3691 \ (nearest \ pound)\)

Answer:

187/2

Step-by-step explanation:

On solving the provided question we can say that the equation h(x) = 3x / x^2 +5x +7 => \(h(x^2) =\) \(3x^2 / x^4 + 5x^2 + 7\)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

given h(x) = 3x / x^2 +5x +7

\(h(x^2) =\) \(3x^2 / x^4 + 5x^2 + 7\)

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The best recommendation for the polling firm to follow in the future would be to sample people who have cell phones, in addition to those with landlines.

This approach would help in increasing the diversity of the sample, as relying solely on landline telephones may lead to underrepresentation of certain demographics, such as younger voters who are more likely to use cell phones instead of landlines.

By including both landline and cell phone users, the firm would be able to gather a more accurate and representative sample of the population, which would result in better predictions for the election outcomes.

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The probability that the coin Peter flipped showed heads given that he showed up to the party is 2/3.

Peter tries to avoid going to a party which he was invited to. To justify his absence he flips a coin and if the coin shows heads he goes. Otherwise, he rolls a die to give the party yet another chance. If the die lands on 6 , he goes. Otherwise, he stays home. If Peter ends up being at the party, the probability that the coin he flipped showed Heads is 2/3.

The probability that Peter shows up to the party is found by calculating the probability that the coin shows heads and Peter goes plus the probability that the coin shows tails, the die shows a 6, and Peter goes. We are given that Peter ends up being at the party. Let H be the event that the coin shows heads, T be the event that the coin shows tails, and S be the event that the die shows a 6. We need to find P(H|S'), the probability that the coin showed heads given that Peter showed up to the party. Let us first find P(S|T) and P(S|H).

The probability that Peter goes if the coin shows tails and the die shows a 6 is given by P(S|T) = 1/6

The probability that Peter goes if the coin shows heads and the die does not show a 6 is given by P(S|H) = 1/3

Using Bayes' theorem:

P(H|S') = (P(S'|H) * P(H))/P(S')P(S'|H)

= P(S|H')

= 2/3

P(S') = P(H) * P(S|H) + P(T) * P(S|T)

= 1/2 * 1/3 + 1/2 * 1/6

= 1/4

P(H|S') = (2/3 * 1/2)/(1/4)

= 2/3

Therefore, the probability that the coin Peter flipped showed heads given that he showed up to the party is 2/3.

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The temperature and pH profiles of an enzyme secreted by a bacterium that lives in a mildly alkaline hot spring at temperatures of 70°C or higher can be represented by curves B and D.B and D curves on the graph can represent the temperature and pH profiles of an enzyme secreted by a bacterium that lives in a mildly alkaline hot spring at temperatures of 70°C or higher.

There are two graphs given for the question, which are described below.

Graph 1: This graph shows the temperature and pH of an enzyme's activity.

Temperature is plotted on the y-axis and pH on the x-axis.

The graph has four curves.

Curve A represents an enzyme secreted by a bacterium that lives in the intestines of a cow.

Curve B represents an enzyme secreted by a bacterium that lives in a mildly alkaline hot spring at temperatures of 70°C or higher.

Curve C represents an enzyme secreted by a bacterium that lives in the acidic contents of the human stomach.

Curve D represents an enzyme secreted by a bacterium that lives in the alkaline environment of a deep-sea hydrothermal vent at temperatures of 100°C or higher.

Graph 2: This graph shows the effects of temperature on the activity of three different enzymes. Enzyme A is from a bacterium that lives in the soil at temperatures of 20°C or lower.

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your answer should be three.

~iwa-chan

The rectangle's measurements are 13.2 feet wide by 19.2 feet long, giving it a total area of 253 square feet.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Here,

length of rectangle=l

width=w

l=w+6

area=l*w

253=(w+6)*w

w²+6w-253=0

w=13.2 feet

l=19.2 feet

The dimensions for the rectangle that have area as 253 sq-feet will be 13.2 feet as width and 19.2 feet as length.

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a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.

b) Nyoko cannot find a value of b so that the equation has no solutions.

The equation 1 is given as follows:

6x - 5 + 2x = 4(2x - 1) - 1.

Combining the like terms and applying the distributive property, the simplified equations are given as follows:

8x - 5 = 8x - 4 - 1

8x - 5 = 8x - 5.

As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.

The equation 2 is given as follows:

3x + 7 = bx + 7.

A system of linear equations will have zero solutions when:

As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.

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Answer:

0

Step-by-step explanation:

Combine like terms and everything cancels out

The value of c that makes the two expressions equivalent is -20.74.

Let's start by simplifying the expression 6.1(2x - 3.4). To do this, we use the distributive property of multiplication, which states that a(b + c) = ab + ac. Applying this to our expression, we get:

6.1(2x - 3.4) = 6.1(2x) - 6.1(3.4) = 12.2x - 20.74

Now we can rewrite the equation we want to solve as:

12.2x + c = 12.2x - 20.74

To solve for c, we need to isolate it on one side of the equation. We can do this by subtracting 12.2x from both sides:

c = -20.74

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Answer:

number 3 maybe . sorry if wrong

Answer:

Slope is 20 and y-intercept is 40.

Step-by-step explanation:

First, let's find slope. I'll be using the points (1,60) and (3,100).

\(m=\frac{y2-y1}{x2-x1}=\frac{100-60}{3-1}=\frac{40}{2}=20\)

So the slope is \(m=20\). Now we need to find y-intercept. We can do this by using our slope and a point in the point-slope equation, \(y=mx+b\). I'll use the point (1,60).

\(y=mx+b\\60=20(1)+b\\60=20+b\\b=40\)

I hope this helps!

Answer:

7 ft

Step-by-step explanation:

7 x 7 x 7 = 343

Step-by-step explanation:

✧ \( \underline{ \underline{ \large{ \tt{G\: I \: V \: E \: N}}} }: \)

✧ \( \underline{ \underline{ \large{ \tt{T \: O \: \: F \: I\:N\: D}}}} : \)

✧ \( \underline{ \underline{ \large{ \tt{ S \: O \: L \: U \: T \: I\: O \: N}}} }: \)

☪ \( \boxed{ \large{ \text{Volume \: of \: a \: cube }= \sf {l}^{3} }}\)

⇾\( \large{ \sf{343 = {l}^{ 3}}} \)

⇾\( \large{ \sf{ {l}^{ 3} = 343}}\)

⇾\( \large{ \sf{l = \sqrt[3]{343} }}\)

⇾\( \large{ \sf{l = \sqrt[3]{7 \times 7 \times 7}}} \)

⇾\( \large{ \sf{l = \boxed{ \sf{7 \: ft}}}}\)

\( \huge{ \boxed{ \boxed{ \large{ \text{OUR \: FINAL \:ANSWER }: \boxed{ \underline{ \bold{ \sf{7 \: ft}}}}}}}}\)

⭒Hope I helped ! ⭒

Have a wonderful day / night ! ♡

Let me know if you have any questions regarding my answer ! ツ

⋆ \( \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}\) !! ✎

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

The answer is C. (4x+12)+8x=180

Answer:

C

Step-by-step explanation:

alt. interior angles are congruent, so don't worry about y

also, because of alt. int. angles, we know that (4x+12)+8x=180

we can solve it by grouping like terms to get x=14

The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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Answer:

41/333

Step-by-step explanation:

it is unclear what you mean.

I assume the recurring decimal is

0.123123123123...

with the recurring sequence being 123.

I will base my answer on that assumption.

0.123 would be easy, right ?

that would be

123/1000

but what would be

123/999 ?

the same as

123/1000

but it leaves 123 additional remaining compared to 123/1000.

that adds 0.000123 with an additional 123 remainder. and so on for all eternity.

that is why

123/1000

creates simply 0.123, but

123/999

creates

0.123123123123123...

so, the answer is

123/999 = 41/333

FYI

the length of the recurring sequence defines how many 9s to use in the denominator. and we use the recurring sequence as numerator

if the length is 1, we use one 9.

like 2/9 = 0.222222...

if the length is 2, we use two 9s.

like 34/99 =0.3434343434...

and if the length is 3 (like in our assume case), we use three 9s.

like in 123/999 = 0.123123123123123...

and so on.

There are six possible ways a person can choose two balls at random from an urn containing five balls numbered 1, 2, 2, 6, and 6.

To understand how to calculate the number of combinations, let's break it down into two parts: selecting the first ball, and then selecting the second ball. Since there are five balls in the urn, the first ball can be chosen in five possible ways. Then, when selecting the second ball, the number of possible selections is reduced to four because one ball has already been selected. This can be expressed mathematically as: n(A)=5x4.

To calculate the total number of combinations, we then multiply the two numbers: 5x4=20. This result is then divided by two because the order of selection does not matter. As a result, 20/2=10, which means that there are ten possible combinations when choosing two balls at random from the urn. In conclusion, if an urn contains five balls numbered 1, 2, 2, 6, and 6, there are six possible ways a person can choose two balls at random. This can be expressed mathematically as n(A)=6 or n(A)=5x4/2.

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The sum of the areas of the two segments defined by the chords AB and CD in the circle is 18π - 36.

To find the sum of the areas of the two segments defined by the chords AB and CD in a circle, we need to calculate the areas of each segment separately and then add them together.

First, let's determine the radius of the circle. Since we are given the lengths of the chords AB and CD, we can use the following formula:

r = (1/2) * AB * CD / sqrt((AB/2)^2 + r^2)

We know that AB = 8 and CD = 6, so let's substitute those values into the formula: r = (1/2) * 8 * 6 / sqrt((8/2)^2 + r^2)

r = 24 / sqrt(16 + r^2)

To solve this equation for r, we can square both sides:

r^2 = (24 / sqrt(16 + r^2))^2

r^2 = 576 / 16

r = 6

Now that we have the radius of the circle, we can calculate the angles subtended by the arcs AB and CD. We are given that the total scale of the two arcs is 180 degrees, so each arc subtends an angle of 180 degrees / 2 = 90 degrees.

To find the area of each segment, we can use the formula:

Segment Area = (θ/360) * π * r^2 - (1/2) * r^2 * sin(θ)

For the segment defined by the chord AB: θ = 90 degrees

Segment Area_AB = (90/360) * π * (6^2) - (1/2) * (6^2) * sin(90)

Segment Area_AB = 9π - 18

For the segment defined by the chord CD: θ = 90 degrees

Segment Area_CD = (90/360) * π * (6^2) - (1/2) * (6^2) * sin(90)

Segment Area_CD = 9π - 18

Now we can find the sum of the areas of the two segments:

Sum of Segments Area = Segment Area_AB + Segment Area_CD

Sum of Segments Area = (9π - 18) + (9π - 18)

Sum of Segments Area = 18π - 36. Therefore, the sum of the areas of the two segments is 18π - 36.

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Answer:

14

Step-by-step explanation:

A fully loaded truck weighs 10 3/5 tons

After unloading the truck weighed 3 2/3 tons

Therefore the weight of the load can be calculated as follows

= 10 3/5 - 3 2/3

= 53/5 - 11/3

= 265-55/15

= 210/15

= 14

Hence the weight of the load 14

The work done by the force field F over the counterclockwise movement along the circle is 0.

To find the work done by the force field F(x, y) = (x, 2y^2) as an object moves counterclockwise about the circle (x - 2)^2 + y^2 = 1, we need to evaluate the line integral of F dot dr along the curve of the circle.

First, let's parameterize the circle. We can use the parameterization:

x = 2 + cos(t)

y = sin(t)

where t ranges from 0 to 2π to trace the circle counterclockwise once.

Next, we need to calculate dr, the differential displacement vector along the curve:

dr = dx i + dy j

= (-sin(t)) dt i + cos(t) dt j

Now, we can calculate F dot dr:

F dot dr = (x, 2y^2) dot (dx i + dy j)

= (2 + cos(t), 2sin^2(t)) dot (-sin(t) dt i + cos(t) dt j)

= (2 + cos(t))(-sin(t)) dt + 2sin^2(t) cos(t) dt

= -2sin(t) - cos(t)sin(t) dt + 2sin^2(t) cos(t) dt

= -2sin(t) - sin(t)cos(t) dt + 2sin^2(t) cos(t) dt

= -2sin(t) - sin(t)cos(t) + 2sin^2(t) cos(t) dt

To find the work done, we integrate F dot dr over the parameter t from 0 to 2π:

Work = ∫[0, 2π] (-2sin(t) - sin(t)cos(t) + 2sin^2(t) cos(t)) dt

Integrating term by term, we have:

Work = ∫[0, 2π] -2sin(t) dt - ∫[0, 2π] sin(t)cos(t) dt + ∫[0, 2π] 2sin^2(t) cos(t) dt

The integral of -2sin(t) is 2cos(t), and the integral of sin(t)cos(t) is -cos^2(t)/2. For the last integral, we can use the identity sin^2(t) = (1 - cos(2t))/2:

Work = [2cos(t)]∣[0, 2π] - [-cos^2(t)/2]∣[0, 2π] + 2∫[0, 2π] (1 - cos(2t))/2 * cos(t) dt

= [2cos(t)]∣[0, 2π] + [cos^2(t)/2]∣[0, 2π] + ∫[0, 2π] (cos(t) - cos(2t)cos(t))/2 dt

= [2cos(t)]∣[0, 2π] + [cos^2(t)/2]∣[0, 2π] + [sin(t) - (1/2)sin(2t)]∣[0, 2π]

Evaluating this expression, we get:

Work = [2cos(2π) - 2cos(0)] + [cos^2(2π)/2 - cos^2(0)/2] + [sin(2π) - (1/2)sin(4π)] - [sin(0) - (1/2)sin(0)]

Since cos(2π) = cos(0) = 1, cos^2(2π) = cos^2(0) = 1, and sin(2π) = sin(0) = 0, we can simplify the expression further:

Work = [2 - 2] + [1/2 - 1/2] + [0 - 0] - [0 - 0]

= 0

Therefore, the work done by the force field F over the counterclockwise movement along the circle is 0.

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Answer:

It is A

Step-by-step explanation:

Because 18 to 14 is subtracting 4 and then it goes 14 to 10 which is another 4. Hope you ace the quiz or test or whatever your doing hope it helps.

Option A

It's an arithmetic sequence

Rule is

\(\\ \rm\hookrightarrow a_n=a+(n-1)d\)

\(\\ \rm\hookrightarrow a_n=18+(n-1)4\)

Answer:

see below

Step-by-step explanation:

MNO  maps to M'N'O'

That means M corresponds to M'

N corresponds to N'

O corresponds to O'

Answer:

i did not learn that i am grade 6

Step-by-step explanation:

u know i am 12

umm maybe mno is m'n'o

The standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

To calculate the standard deviation of the sampling distribution of sample means, we need to use the formula for the standard deviation of a sample mean. This formula states that the standard deviation of the sampling distribution (σ) is equal to the standard deviation of the population (σ) divided by the square root of the sample size (n).

Given that the population standard deviation (σ) is 5.9 pounds and the sample size (n) is 72, we can plug these values into the formula:

Standard Deviation of the Sampling Distribution (σ) = σ / √n

σ = 5.9 pounds

n = 72

Substituting these values, we get:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / √72

To find the standard deviation of the sampling distribution, we need to evaluate the square root of 72. Using a calculator or mathematical software, we find that √72 is approximately 8.49.

Now, let's calculate the standard deviation of the sampling distribution:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / 8.49 ≈ 0.695 pounds (rounded to two decimal places)

Therefore, the standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

This value represents the average amount of variation or dispersion in the means of different samples taken from the population. It indicates how much the sample means are likely to deviate from the population mean.

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Answer:

Step-by-step explanation:

I'm assuming that strange looking thing is a 9, so begin by multiplying both sides by that denominator to get:

\(x-9=\sqrt{x}+3\) then subtract 3 from both sides to get

\(x-12=\sqrt{x}\) and then square both sides to get

\(x^2-24x+144=x\) and get everything on one side to solve for x by factoring:

\(x^2-25x+144=0\) and factor that however it is you have learned to factor second-degree polynomials to get that

x = 16 and x = 9. We have to check for extraneous solutions because anytime you manipulate an equation, as we did by squaring both sides, you run the risk of these solutions that actually don't work when you plug them back into the original equation. Let's try 16 first:

\(\frac{16-9}{\sqrt{16}+3 }=1\)  If 16 is a solution, then this statement will be mathematically true.

\(\frac{7}{4+3}=1\)  and   \(\frac{7}{7}=1\) so 16 works. Let's try 9:

\(\frac{9-9}{\sqrt{9}+3 }=1\)  We know that one doesn't work, because 9-9 = 0 and 0 over anything = 0, not 1.

x = 16 is the only solution.

Answer:

x =  16

Step-by-step explanation:

\(\frac{x-9}{\sqrt{x}+3}=1\)

Cross multiply,

x - 9 = √x + 3

Subtract 3 from both sides

x - 9 - 3 = √x

x - 12 = √x

Square both sides

(x -12)² = (√x)²

x² - 2 * x*12 + 12² = x

x² - 24x + 144 = x

x² - 24x + 144 - x = 0

x² - 25x + 144 = 0

Sum = -25

Product = 144

Factors = -9 , -16            {(-9)+(-16) = -25  & (-)*(-16) = 144}

x² - 25x + 144 = 0

x² - 16x - 9x + (-9)*(-16) = 0

x(x - 16) - 9(x - 16) = 0

(x - 16) (x - 9) = 0

x - 16 = 0     ; x - 9 = 0

x = 16          ; x = 9

x = 9 is  an extraneous solution.

When we plug in 9 in the LHS of the equation,

LHS = \(\frac{9-9}{\sqrt{9}+3}\)

       \(= \frac{0}{3+3}\)

        = 0 ≠ RHS

So, x = 16 is the only  solution

The greatest common factor also known as the HCF for D = 2², E = 1, H = 5, N = 3, A = 16, O = 27, T = 2, G = 10, S = 7, I = 11, R = 46, M = 6, and L = 8.

The given numbers are expressed as products of their prime factors and then we collect the factor(s) which are common.

Given that W = 9 is the HCF for the numbers 9 and 8, we shall calculate for the other numbers by first expressing them as products of their prime factors as follows:

For 8 and 20

8 = 2×2×2

20 = 2×2×5

HCF = 2×2 = 2²

For 8 and 17

8 = 1×2×2×2

17 = 1×17

HCF = 1

For 35 and 15

35 = 5×7

15 = 3×5

HCF = 5

For 15 and 9

15 = 3×5

9 = 3×3

HCF = 3

For 16 and 80

16 = 2×2×2×2

80 = 2×2×2×2×5

HCF = 2×2×2×2 = 16

For 81 and 27

81 = 3×3×3×3

27 = 3×3×3

HCF = 3³ = 27

For 82 and 4

82 = 2×41

4 = 2×2

HCF = 2

For 100 and 10

100 = 2×2×5×5

10 = 2×5

HCF = 2×5 =10

For 28 and 7

28 = 2×2×7

7 = 7

HCF = 7

For 55 and 66

55 = 5×11

66 = 2×3×11

HCF = 11

For 92 and 46

92 = 2×2×23

46 = 2×23

HCF = 2×23 =46

For 18 and 24

18 = 2×3×3

24 = 2×2×2×3

HCF = 2×3 = 6

For 32 and 55

32 = 2×2×2×2×2

56 = 2×2×2×7

HCF = 2³ = 8

Therefore, expressing the numbers as product of their prime factors has made it easy to determine their HCFs as D = 2², E = 1, H = 5, N = 3, A = 16, O = 27, T = 2, G = 10, S = 7, I = 11, R = 46, M = 6, and L = 8.

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The amount paid for 2 hours at the internet cafe is P^(50.00), and the amount paid for 6 hours is P^(120.00).

a. For 2 hours:

The first four hours are charged at P^(25.00) per hour, so for 2 hours, the charge would be 2 * P^(25.00) = P^(50.00).

b. For 6 hours:

The first four hours are charged at P^(25.00) per hour, which totals to 4 * P^(25.00) = P^(100.00). For the remaining 2 hours, the extra charge of P^(15.00) per hour is applied. Thus, the extra charge for 2 hours is 2 * P^(15.00) = P^(30.00). Adding this to the base charge, the total amount paid for 6 hours is P^(100.00) + P^(30.00) = P^(130.00).

Therefore, the amount paid for 2 hours is P^(50.00), and the amount paid for 6 hours is P^(130.00).

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