Select all the expressions which are equivalent to three times the sum of six and five. A. 3 x 6 + 5 B. 3(6 + 5) C. 3x5 + 6 D. (6 + 5) + (6 + 5) + (6 + 5) E. 3+ (5 x 6) ​

The requried first term of the sequence is $6.32.

Arithmetic progression is the series of numbers that have common differences between adjacent values

Here,
The amount of money Sally spends on breakfast each week forms an arithmetic sequence.

Let's use the formula for the sum of an arithmetic sequence to find the first term of the sequence. We know that Sally has already spent $31.64, which means that she has made 31.64/4.52 = 7 visits to the breakfast place. So the sum of the first 7 terms of the sequence is:

S₇ = 7/2 * (a₁ + a₇)

We know that a₇ = $4.52, so we can plug this into the formula and simplify

S₇ = 7/2 * (a₁ + 4.52)

a₁ = $6.32

Similarly, all the outcomes can be evaluated,
By the end of the year, Sally will have spent $891.36 on breakfast.

Therefore, the first term of the sequence is $6.32.

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The solution to the system of equations y = 1.5x - 4 and y = -x  is (1.6,-1.6)

The equations are given as: y = 1.5x - 4 & y = -x

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables

Substitute y = -x in the first equation

-x = 1.5x - 4

Collect like terms

-1.5x - x = -4

Any set of values of x1, x2, x2,…xn which simultaneously satisfies the system of linear equations given above is called a solution of the system. If the system of equations has one or more solutions, the equations are called consistent. Also, if the system of equations does not admit any solution, then the equations are called inconsistent.

This gives

-2.5x = -4

Divide both sides by -2.5

x = 1.6

Substitute x = 1.6 in y = -x

y = -1.6

Hence, the solution to the system of equations is (1.6,-1.6).

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Answer:

Reflected over the x axis and translated 4 units left

Step-by-step explanation:

Just took the test and got 5/5 :)

Answer:

Reflected over the X axis

Tanslated 4 units left.

Step-by-step explanation:

Plato 5/5

Answer:

  a) P(IA) = 3/56; P(I) = 3/8

  b) increases

  c) 1/56

  d) less

Step-by-step explanation:

You want various probabilities related to drawing letters from a bag containing the letters G, I, R, V, I, A, I, and N.

The probability of drawing a given letter is the ratio of the number of that letter in the bag to the total number of letters in the bag.

There are 3 letters I in the bag. There is only one of each of the other 5 letters.

P(I) = 3/8

P(A after I) = 1/7

The probability of a sequence of I then A is the product of these probabilities:

  P(IA) = (3/8)(1/7) = 3/56

Before the first I is pulled from the bag, P(A) = 1/8.

After the first I is pulled from the bag, P(A) = 1/7, an increase in the probability.

(You can see that the probability of selecting an A increases after each non-A letter is drawn. Ultimately, after the other 7 letters are drawn, P(A) = 1, as it is the only one left.)

P(I) = 3/8 on the first draw

P(I) = 2/7 after the first I is drawn

P(I) = 1/6 after the second I is drawn

P(III) = (3/8)(2/7)(1/6) = 1/56

P(AI) = (1/8)(3/7) = 3/56

P(II) = (3/8)(2/7) = 6/56 = 3/28

Drawing A then I is less likely than drawing I then I.

Answer:

X= -24

Step-by-step explanation:

1/4x+8 = 0

1/4x = -8

1/4x(4) = -8(4)

X = -24

:)

The mathematical quantity of the instantaneous velocity is a derivative, specifically the derivative of the distance function d(t) with respect to time.

To find the average velocity of the rock from t = 5 to t = 5.1, we need to calculate the change in distance and time over this interval.

Change in distance = d(5.1) - d(5) = (35(5.1) - 5\((5.1)^{2}\)) - (35(5) - 5\((5)^{2}\)) ≈ -24.5 m

Change in time = 5.1 - 5 = 0.1 s

Average velocity = (change in distance) / (change in time) ≈ -245 m/s

To find the equation for the average velocity from 5 seconds to t seconds, we need to use the formula for average velocity:

average velocity = (d(t) - d(5)) / (t - 5)

Taking the limit of this expression as t approaches 5 gives us the instantaneous velocity at t = 5:

instantaneous velocity = lim (t→5) [(d(t) - d(5)) / (t - 5)]

Using the given function for d(t), we can evaluate this limit as:

instantaneous velocity = lim (t→5) [(35t - 5\(t^{2}\) - 35(5) + 5\((5)^{2}\) / (t - 5)] = -50 m/s

Since the instantaneous velocity is negative, the rock is going down at t = 5. We can tell this because the velocity is the rate of change of distance with respect to time, and the negative sign indicates that the distance is decreasing with time.

The mathematical quantity of the instantaneous velocity is a derivative, specifically the derivative of the distance function d(t) with respect to time.

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The scale where the Sun is represented by an exercise ball and Jupiter is represented by a golf ball, Earth would be approximately 126,750 km in size.

To determine the size of Earth on the scale where the Sun is represented by an exercise ball (75.0 cm) and Jupiter is represented by a golf ball (4.3 cm), we need to calculate the proportional size of Earth.

The diameter of the Sun (represented by the exercise ball) is 75.0 cm, and the diameter of Jupiter (represented by the golf ball) is 4.3 cm. We can use the ratio of these diameters to find the proportional size of Earth.

Let's calculate it:

Proportional size of Earth = (Diameter of Earth / Diameter of Jupiter) × Diameter of the Sun

Proportional size of Earth = (Diameter of Earth / 4.3 cm) × 75.0 cm

To find the diameter of Earth on this scale, we need to determine the ratio of Earth's diameter to Jupiter's diameter and then multiply it by the diameter of the Sun:

Proportional size of Earth = (12,742 km / 139,820 km) × 1,391,000 km

Calculating this expression:

Proportional size of Earth = (0.09108) × 1,391,000 km

Proportional size of Earth ≈ 126,750 km

Therefore, on the scale where the Sun is represented by an exercise ball and Jupiter is represented by a golf ball, Earth would be approximately 126,750 km in size.

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Step-by-step explanation:

From the original question, we can rewrite this as:

An airplane company is determining the difference in selling price if rows of first-class seats are added to a new design. The total selling price for one new row is f(r) = 4,000r. Each row in first class eliminates a pair of rows of economy seats. The total price for each pair of removed rows is e(r) = 1,800r. Which is d(r), the profit or loss for adding r rows of first class seats?

f(r) = 4000r

e(r) = 1800r

d(r) = ? (profit or loss)

Assuming we had added a row of first class seats,

+ f(r) = 4000r

But we had to remove a pair or rows from the economy seats,

- e(r) = 1800r

Translating these into one equation:

d(r) = f(r) - e(r) = 4000r - 1800r = 2200r

Therefore, OPTION A.) d(r) = 2200r

The value of d(r) will be 2200r. The correct option is A.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Assuming we had added a row of first-class seats,

+ f(r) = 4000r

But we had to remove a pair or rows from the economy seats,

- e(r) = 1800r

Translating these into one equation:

d(r) = f(r) - e(r) = 4000r - 1800r = 2200r

Therefore, the value of d(r) will be 2200r. The correct option is A.

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Answer:

15x+20y+5z

Step-by-step explanation:

Trust me.

The probability is 0.46 of no student having the answer to more than one question.

So, the probability formula is:

P(E) = Favourable events/Total events

We know that in total there are 15 students (Total events).

Students can not answer more than 1 question:
8 - 1 = 7 (Favourable events)

Now, calculate the probability:

P(E) = Favourable events/Total events

P(E) = 7/15

P(E) = 0.46

Therefore, the probability is 0.46 of no student having the answer to more than one question.

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Answer:

Step-by-step explanation:

They tell you that x is the number of shirts, then say that the number of shirts is equal to 5. So just plug it in

y = 2.5*5

y = 12.50$

Answer:

C (12.50)

Step-by-step explanation:

2.50 x 5 = 12.5

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The probability that fewer than 60 adults will work from home will be 2%.    

we have to use the Normal probability distribution to find the probability

In a normal distribution with mean μ, SD σ, z-score Z of a measure X  is given by

Z = (X-μ)/ σ

here,

15% adults work from home , So  p= 0.15

                                                       n = 500

∴  μ = np = 500(0.15) = 75

σ  = \(\sqrt{np(1-p)}\)

σ = 7.98

Now we have  selected adults(60) less than n (500)

So using the continuity correction , the probability is P(X< 60 - 0.5)

                                                                            = P( X< 59.5)

which is the p-value of Z when X = 59.5

∴ Z = (X-μ)/ σ

Z  =  (59.5 - 75)/7.98

Z =   - 1.98

so the p-value is 0.02

0.02 = 2% probability that fewer than 60 adults will work from home.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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For a two tailed hypothesis evaluating a Pearson correlation, the null hypothesis  states that :

The population correlation is zero.

Null hypothesis:

H0 : ρ = 0

Alternative hypothesis:

Ha : ρ ≠ 0

Thus,

The population correlation is zero.

What does the term "null hypothesis" mean?

The null hypothesis is a common statistical theory that asserts that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

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The cost of a taxi ride that is m miles long can be represented by the equation: Cost of ride, m miles = $2 + $1.50m

To calculate the cost of a taxi ride for 9 miles, we need to consider the fixed pickup cost of $2 and the additional cost per mile driven, which is $1.50.

For the 9-mile ride, the additional cost would be:

Additional Cost = $1.50 per mile × 9 miles = $13.50

Adding the pickup cost and the additional cost gives us the total cost of the ride:

Total Cost = Pickup Cost + Additional Cost = $2 + $13.50 = $15.50

Therefore, the cost of the taxi ride for 9 miles would be $15.50.

For a taxi ride that is m miles long, we can use the same formula. The additional cost would be:

Additional Cost = $1.50 per mile × m miles = $1.50m

The total cost of the ride would then be:

Total Cost = Pickup Cost + Additional Cost = $2 + $1.50m

This formula allows us to calculate the cost of the taxi ride for any given number of miles, represented by the variable m.

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Answer:

1056

Step-by-step explanation:

The computation of the area of the rectangle is shown below;

But for that first we have to compute the area of square which is

As we see in the diagram that there are 9 square sides

i.e 1,4,7,8,9,10,14,15 & 18

And, as we know that

Area of Square  is

\(= Side^2\)

\(1^2 = 1\)

\(4^2 = 16\)

\(7^2 = 49\)

\(8^2 = 64\)

\(9^2 = 81\)

\(10^2 =100\)

\(14^2 = 196\)

\(15^2 = 225\)

\(18^2 = 324\)

So, the Total Area is

= 1 + 16 + 49 + 64 + 81 + 100 + 196 + 225 + 324

= 1056

Area of rectangle = 1056  

So, it can come from

\(1056 = 33 \times 32\)

As the area of rectangle is

\(= length \times width\)

Answer:

what is this pls isit a question

Answer:

254 inches squared

Step-by-step explanation:

Hi there!

\(A=\pi r^2\) where r is the radius of the circle

The radius is equal to half the diameter. Given that the diameter is 18 inches, we know that the radius of the circular plate is 9 inches. Plug this into the equation:

\(A=\pi (9)^2\\A=81\pi \\A=254\)

Therefore, the area of the plate is approximately 254 inches squared.

If this is not an answer choice, the question may have been asking for the radius of the circle rather than the area.

I hope this helps!

Answer:

72 ounces of fruit snacks were eaten

Step-by-step explanation:

Because,

20(fruit snacks) * 6(ounces)= 120(ounces)

12(ounces) - 48(ounces) =72 (ounces eaten)

:)

Answer:

0

Step-by-step explanation:

Since you didn't attach an image of the graph I'll have to do this the hard way.

x + 2y = 2  (1)

2x + 4y = -8 (2)

x + 2y = -4 (Divide equation (2) by 2)

0 = 6 (Subtract the third equation from the first)

Since 0 is not equal to 6 the answer is No Solutions.

Answer:

no solutions

Step-by-step explanation:

x+2y=2

2x+4y=−8​

Multiply the first equation by -2

-2x -4y = -4

Add this to the second equation

-2x-4y = -4

2x +4y = -8

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

0x+0y = -12

0 = -12

This is never true so there are no solutions

Answer:

Step-by-step explanation:

Its the last two and the first one

The woman at the dinner party consumed 24 fluid ounces of wine containing approximately 4.8 standard drinks assuming the wine had an alcohol content of 12%. She exceeded the recommended limit for moderate drinking on that day.

Assuming each glass of wine contained 8 fluid ounces, the woman consumed a total of 24 fluid ounces of wine throughout the evening.

To determine the number of standard drinks ingested, we need to know the alcohol content of the wine. In the United States, a standard drink is defined as containing 0.6 fluid ounces or 14 grams of pure alcohol.

Assuming the wine had an alcohol content of 12% (which is a typical percentage for table wine), we can calculate the number of standard drinks ingested by using the following formula:

Number of standard drinks = (Volume of alcohol consumed in ounces x % alcohol by volume) / (0.6 ounces of alcohol per standard drink)

Number of standard drinks = (24 fl oz x 0.12) / 0.6 fl oz

Number of standard drinks = 4.8

Therefore, the woman consumed approximately 4.8 standard drinks.

To determine if she drank alcohol in moderation, we need to consider the recommended limits for moderate drinking. According to the National Institute on Alcohol Abuse and Alcoholism, moderate drinking is defined as up to one drink per day for women.

Since the woman consumed 4.8 standard drinks in one evening, she exceeded the recommended limit for moderate drinking for that day.

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We need to roll the die at least 5 times to ensure that the probability is at least 2/3 that at least one 2 will appear.

To calculate the probability of rolling a 2 on a fair six-sided die, we first need to know the probability of rolling any number on a single roll, which is 1/6.

Since each roll of the die is independent of the previous roll, we can use the formula for the probability of independent events occurring together to find the probability of rolling a 2 at least once in a certain number of rolls.

Let's call the probability of rolling a 2 at least once in n rolls "P(n)". We can find P(n) using the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. So, the probability of not rolling a 2 in n rolls is (5/6)^n, since there are 5 possible outcomes (1, 3, 4, 5, or 6) on each roll that is not 2. Therefore, we can write:

P(n) = 1 - (5/6)^n

We want to find the minimum number of rolls needed to ensure that P(n) is at least 2/3, or 0.667. In other words, we want to find the smallest value of n that satisfies the inequality:

P(n) ≥ 2/3

Substituting the formula for P(n), we get:

1 - (5/6)^n ≥ 2/3

By multiplying both sides by -1 and rearranging, we get:

(5/6)^n ≤ 1/3

Taking the natural logarithm of both sides, we get:

n ln(5/6) ≤ ln(1/3)

Dividing both sides by ln(5/6), we get:

n ≥ ln(1/3) / ln(5/6)

Using a calculator, we find that:

n ≥ 4.81

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Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips. This is because the more times a coin is flipped, the more accurate the experimental probability is likely to be.

An experiment is a type of scientific study in which a researcher manipulates variables in order to observe the effects on a particular outcome. Experiments are used to determine cause and effect relationships between variables, as well as to explore and test hypotheses. Experiments can be conducted in the laboratory or in the field, and involve the use of scientific equipment and techniques to observe, measure, and record data. Experiments are an important tool for scientists to gain knowledge and understanding of the natural world, and to discover new ways to solve problems.

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