PLS ANSWER MY QUESTION QUICKLY

PLS ANSWER MY QUESTION QUICKLY

Answers

Answer 1

Answer:

The answer is D.

Step-by-step explanation:

PLS ANSWER MY QUESTION QUICKLY
PLS ANSWER MY QUESTION QUICKLY

Related Questions

What is the equivalent expression to 4(9+3)

Answers

Answer:

4(9+3) = 48

Step-by-step explanation:

To simplify the expression 4(9+3), we need to perform the addition inside the parentheses first and then multiply the result by 4.

9+3 = 12, so we can substitute this into the expression as follows:

4(9+3) = 4(12)

Now we can perform the multiplication:

4(12) = 48

Therefore, the equivalent expression to 4(9+3) is simply 48.

The relation between the time spent walking and the time spent canoeing on a 30 mile
trip if you walk at 4 mph and canoe at 7 mph. Write a constraint equation,
determine two solutions, and graph the equation and mark your solutions.

Answers

The two solutions are (1, 1/7) and (3.36, 1)

Time spent walking and canoeing.

Assume that you spend some time walking (t<sub>w</sub>) and some time canoeing (t<sub>c</sub>) to cover a 30-mile trip. We can use the following formula to relate the time spent walking and canoeing:

distance = speed × time

For the walking part of the trip, the distance covered is (30 - d), where d is the distance covered by canoeing. We know that the walking speed is 4 mph, so we can write:

(30 - d) = 4t<sub>w</sub>

For the canoeing part of the trip, the distance covered is d. We know that the canoeing speed is 7 mph, so we can write:

d = 7t<sub>c</sub>

We also know that the total time spent on the trip is:

t<sub>w</sub> + t<sub>c</sub>

So, the constraint equation is:

t<sub>w</sub> + t<sub>c</sub> = 30/4 + 30/7

Simplifying this equation, we get:

11t<sub>w</sub> - 7t<sub>c</sub> = 30

Now, to determine two solutions, we can arbitrarily assign a value to one of the variables and then solve for the other. Let's assume t<sub>w</sub> = 1, then we get:

11(1) - 7t<sub>c</sub> = 30

7t<sub>c</sub> = 1

t<sub>c</sub> = 1/7

So, one solution is t<sub>w</sub> = 1 and t<sub>c</sub> = 1/7.

Similarly, assuming t<sub>c</sub> = 1, we get:

11t<sub>w</sub> - 7(1) = 30

11t<sub>w</sub> = 37

t<sub>w</sub> = 3.36

So, another solution is t<sub>w</sub> = 3.36 and t<sub>c</sub> = 1.

To graph the equation, we can plot t<sub>w</sub> on the x-axis and t<sub>c</sub> on the y-axis, and then plot the line 11t<sub>w</sub> - 7t<sub>c</sub> = 30. The two solutions will be the points of intersection of the line with the axes.

The two solutions are (1, 1/7) and (3.36, 1).

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In your first semester of college you took 13 credit hours and earned a GPA of 2.13. In your second semester your Gpa of 2.34 was based on 12 credit hours. Your third semester GPA was 3.00 Based on 17 hours. Calculate overall GPA for the three semesters.

Answers

Answer:

below

Step-by-step explanation:

[ 2.13 * 13   +  2.34 * 12  +  3.00 * 17 ] / ( 13 + 12 + 17) = 2.54 GPA

Help Help Help Help Help Help (I don’t need explanation just yes or no)

Answers

Yes,

the equation "y = 2x + 7" represents a proportional relationship.

how can we say that 4:1 and 12:3 are equivalent ratios

Answers

Step-by-step explanation:

This is because when 12 : 3 is simplified it will give you 4 : 1

3 will go into 12 four times and 3 will go into 3 once, leaving 4 : 1

Therefore, 4 : 1 and 12 : 3 are equivalent ratios

The diameter of a circle is 22 feet. What is the circle's area?
Use 3.14 for ​.

Answers

Answer: 3.14 ft

Step-by-step explanation:

★Given,→ Diameter = 2 feet → Circumference = 2/2 = 1 feet

★Now,→Area of a circle = πr²→ = 3.14 × 1 × 1→ = 3.14 feet

Hence , the circumference is 3.14 ft.  

Alan invests $200 at a rate of per year compound interest. After 2 years the value of this investment is $206.46. Show that r²t 200r - 323=0​

Answers

Answer:

unfortunately tdudeyiutddj try Zurich etu

You have a credit card that has a balance of $3589.90 and a credit limit of $5000. How much is the balance over the acceptable debt ratio percentage?

Answers

The balance over the acceptable debt ratio is $1089.90.

What is debt ratio percentage?

A debt ratio calculates a company's leverage by comparing its total debt to its total assets.

Although this ratio varies greatly between industries, capital-intensive enterprises typically have significantly larger debt ratios than other types of businesses.

Divide total debt by total assets to find a company's debt ratio.

A debt ratio of less than 100% signifies a corporation has more assets than debt, and a debt ratio of larger than 1.0 or 100% means the opposite.

According to some sources, the debt ratio is calculated by dividing all obligations by all assets.

Given that, credit card balance = $3,589.90

credit limit = $5,000

Debt Ratio percentage = 50% = 0.50

The balance over is given as

balance = Current Balance - (Credit Limit × 0.50 )

balance = 3589.90 - (5000 × 0.5)

balance = 3589.9 - 2500

balance = 1089.9

Hence, the balance over the acceptable debt ratio is $1089.90.

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The population of a city increases by 0.5% per year. If this year's population is 201,000, what will next year's population be, to the nearest individual?

Answers

Next year's population is 202,005

How to calculate the quantity of next year's population?

The population of a city increases by 0.5% per year

This year's population is 201,000

Next year's population can be calculated as follows

201,000 × 0.5/100

= 201,000 × 0.005+1

= 201,000 × 1.005

= 202,005

Hence next year's population is 202,005

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ind the limit of the function f(x,y) = sin(2(x^2 + y^2)))/2(x^2 + y^2) as (x, y) + (0,0). Assume that polynomials, exponentials, logarithmic, and trigonometric functions are continuous. [Hint: limt 40 sint = 1.) lim (x,y)->(0,0) sin(2(x^²+y^2))/2(x^2+y^2) = ____

Answers

The limit of the given function f(x,y) as (x,y) approaches (0,0) is 0.

What is function ?
Function can be defined in which it relates an input to output.

To find the limit of the given function[tex]f(x,y) = sin(2(x^2 + y^2))/(2(x^2 + y^2))[/tex]as [tex](x,y)[/tex] approaches (0,0), we can use the squeeze theorem.

First, note that [tex]sin(2(x^2 + y^2))[/tex]is bounded between -1 and 1 for all (x,y), since the sine function is bounded between -1 and 1. Therefore, we have:

[tex]-1/(2(x^2 + y^2)) < = sin(2(x^2 + y^2))/(2(x^2 + y^2)) < = 1/(2(x^2 + y^2))[/tex]

Next, we can take the limit as (x,y) approaches (0,0) of both sides of this inequality using the squeeze theorem. The left-hand side approaches 0, and the right-hand side approaches 0 as well. Therefore, by the squeeze theorem, we have:

lim (4/3)π(21.03)³- (4/3)π(20.97)³

Hence, the limit of the given function f(x,y) as (x,y) approaches (0,0) is 0.

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If the value of XYZ Company stock drops from $25 per share to $21 per share, what is the percent of the decrease?​

Answers

The percentage of the decrease in the value of the XYZ Company stock is 16%.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
The decrease in the value of the stock is $25 - $21 = $4.

To find the percent decrease, we need to divide the decrease by the original value and then multiply by 100:

Percent decrease = (Decrease / Original value) x 100

In this case, the original value is $25, so:

Percent decrease = (4 / 25) x 100 = 16%

Therefore, the percentage of the decrease in the value of the XYZ Company stock is 16%.

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write the equation of the line that goes through the point and has the given (4,1); slope=2 Write all final answers in slope-intercept form.

Answers

Answer: y = 2x - 7

Step-by-step explanation:

Slope-intercept form is y=mx+b

m = slopeb = y-intercept

Substitute variables with their given values.

 y = 2x + b

In order to find the y-intercept, or b, we can plug the point provided, (4,1) , into y = 2x + b and solve for b.

 1 = 2(4) + b

 1 = 8 + b

-7 = b

Now we can put the y-intercept into the equation, and get y = 2x - 7 .

One of your friends who is self- employed starters buying, indicional heath Insurance ll years ago at a cost of $579 per quarte.

Answers

Kenny need to buy 4 quarts.

It cost $14.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The mailbox is splitted into two shapes.

One is rectangle and the other is hemisphere.

Length of the rectangle = 2.4 ft

Width of the rectangle = 1.5 ft

Height of the rectangle = 3 ft

Surface area of the given rectangle

                  = 2(lw + wh + lh) – lw

                  = 2(2.4 × 1.5 + 1.5 × 3 + 2.4 × 3) – (2.4 × 1.5)

                  = 2(3.6 + 4.5 + 7.2) – 3.6

                  = 2(15.3) – 3.6

                  = 27

Surface area of the given rectangle = 27 square feet

Radius of the hemisphere = 1.2 ft

Curved surface area of hemisphere

                 = 2*pi*r^2

                  = 9.0432 square feet

Curved surface area of hemisphere = 9.0432 square feet                                      

Total surface area of the mailbox  = 27 + 9.0432

                                                        = 36.0432 square feet

To find how many quarts are needed to cover the mailbox.

1 Quart covers = 10 square feet

36.0432 sq. ft = 36.0432 ÷ 10

                      = 3.60432 quarts

                      ≈ 4 quarts (approximately)

Hence Kenny need to buy 4 quarts.

Cost of 1 quart = $3.50

Cost of 4 quart = 4 × 3.50

                        = 14

Hence it cost $14.

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In the diagram, ABCD - A'B'C'D'. What are the angle measures of A'B'C'D'?

Answers

The measures of the angles are given as A' = 103, B' =100, c' = 80, D' = 77

How to solve for the angles

∠x

125 + ∠x = 180 (angle on a straight line)

∠x = 55 degrees

∠y

∠x + ∠y + 48 = 180 angles in a triangle

55 + ∠y + 48 = 180

∠y = 77 degrees

∠D

∠d = ∠Y vertically opposite

∠a + ∠D = 180

∠A = 180 - 77

= 103 degrees

∠B  + 80 = 180

∠b = 100 degrees

∠c + ∠ b = 180

∠c = 180 - 100

= 80 degrees

hence A' = 103, B' =100, c' = 80, D' = 77

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Regina and Abby both want to buy new shoes for their shoe collection.

Regina only has 500 dollars the shoes she wants is 600 dollars.
Her mom makes her work for 5 hours and she gets 120 dollars per hour.

Abby has 600 dollars and the shoes she wants is $870
Her mom makes her work for 5 hours and gets $320

Is the relationship between hours worked and money proportional? Who would buy their shoes first?

Answers

The relationship between hours worked and money is not proportional.

Regina would be able to buy her shoes first after working an additional 50 minutes.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

To determine if the relationship between hours worked and money is proportional, we need to calculate the hourly rate for each person and see if it is the same.

For Regina, she earned $120 per hour and worked for 5 hours, so she earned a total of 5 x 120 = $600.

This means her hourly rate is $120.

For Abby, she earned $320 for 5 hours of work, so her hourly rate is 320/5 = $64.

Since the hourly rates are different, the relationship between hours worked and money is not proportional.

Now let's see who would be able to buy their shoes first.

Regina needs $100 more to be able to buy her shoes, and she earned $600 from working 5 hours.

Therefore, she can buy the shoes after working for an additional $100/$120 = 0.83 hours, which is approximately 50 minutes.

On the other hand, Abby needs $270 more to buy her shoes, and she earned $320 from working 5 hours.

Therefore, she can buy the shoes after working for an additional $270/$64 = 4.22 hours, which is approximately 4 hours and 13 minutes.

Therefore, Regina would buy her shoes first.

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.
This time, choose the figure that is a cylinder.

Answers

Answer: D.

Step-by-step explanation: It's just a cylinder how can you not see

Answer: D. An example of a cylinder is a paper towel roll

A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions?Construct a two-sample z-interval for the difference between population proportions.Answer A: Construct a two-sample z -interval for the difference between population proportions.AConstruct a two-sample z-interval for the difference between sample proportions.Answer B: Construct a two-sample z -interval for the difference between sample proportions.BPerform a z-test for the difference in sample proportions.Answer C: Perform a z -test for the difference in sample proportions.CSubtract the proportions and construct a one-sample z-interval for a single population proportion.Answer D: Subtract the proportions and construct a one-sample z -interval for a single population proportion.DSubtract the proportions and construct a z-interval for a single sample proportion.

Answers

Answer A: Construct a two-sample z-interval for the difference between population proportions.

What is fraction?

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It is written as a/b, where a is called the numerator and b is called the denominator. The numerator represents the number of parts or units being considered, while the denominator represents the total number of parts or units in the whole.

According to given conditions:

The best method for the researcher to use to estimate the true difference between the population proportions would be to:

Answer A: Construct a two-sample z-interval for the difference between population proportions.

This is the most appropriate method for estimating the difference between population proportions, as it takes into account the variability of the sample proportions and provides a confidence interval for the true difference between the two populations. The formula for calculating the two-sample z-interval for the difference between population proportions is:

(p₁−p₂) ± z x √[(p₁(1−p₁))/₁ + (p₂(1−p₂))/₂]

Therefore, Answer A: Construct a two-sample z-interval for the difference between population proportions.

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This problem refers to triangle ABC. If B = 150°, C = 20°, and c = 21 inches, find b. (Round your answer to the nearest whole number.)
b = ? in

Answers

Answer:

Step-by-step explanation:

To solve for b, we can use the law of sines, which states that in any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

Here, we are given B = 150°, C = 20°, and c = 21 inches. We can solve for the remaining angle A by using the fact that the angles of a triangle add up to 180°:

A + B + C = 180°

A = 180° - B - C

A = 180° - 150° - 20°

A = 10°

Now we can use the law of sines to solve for b:

a/sin(A) = b/sin(B)

a = c * sin(A)/sin(C) = 21 * sin(10°)/sin(20°)

b = a * sin(B)/sin(A) = 21 * sin(10°)/sin(20°) * sin(150°)/sin(10°)

b = 21 * sin(150°)/sin(20°)

Using a calculator, we get:

b ≈ 41 inches (rounded to the nearest whole number)

Therefore, the length of side b is approximately 41 inches.

E11.3 (LO 1, 2) (Depreciation Computations—SYD, DDB—Partial Periods) Judds Company purchased a new plant asset on April 1, 2020, at a cost of $711,000. It was estimated to have a service life of 20 years and a salvage value of $60,000. Judds’ accounting period is the calendar year. Instructions a. Compute the depreciation for this asset for 2020 and 2021 using the sum-of-the-years’-digits method. b. Compute the depreciation for this asset for 2020 and 2021 using the double-declining-balance method.

Answers

that in the second year, we use the beginning book value of $639,900

a. Sum-of-the-years’-digits method:

To compute the depreciation using the sum-of-the-years’-digits method, we first need to determine the total number of years of the asset's useful life. We do this by subtracting the salvage value from the cost and dividing by the estimated yearly depreciation.

Cost of asset = $711,000

Salvage value = $60,000

Useful life = 20 years

Yearly depreciation = (Cost - Salvage value) / Useful life

Yearly depreciation = ($711,000 - $60,000) / 20 = $32,550

To calculate the sum-of-the-years’-digits (SYD) for this asset, we add up the digits of the useful life in descending order. For a 20-year useful life, the SYD would be:

SYD = 20 + 19 + 18 + ... + 1 = 210

Using the SYD and the number of remaining years, we can calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = (20/210) x ($711,000 - $60,000) = $64,286

Year 2021:

Depreciation expense = (19/210) x ($711,000 - $60,000) = $60,952

b. Double-declining-balance method:

To compute the depreciation using the double-declining-balance (DDB) method, we first need to determine the asset's straight-line depreciation rate, which is calculated as follows:

Straight-line depreciation rate = 1 / Useful life

Straight-line depreciation rate = 1 / 20 = 0.05

The DDB depreciation rate is twice the straight-line rate, or 0.10. We can then calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset

Depreciation expense = $711,000 x 0.10 = $71,100

Year 2021:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset - Accumulated depreciation from previous years

Accumulated depreciation (2020) = $71,100

Beginning book value (2021) = $711,000 - $71,100 = $639,900

Depreciation expense = $639,900 x 0.10 = $63,990

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Solve for x
2/5(2)^x = 32/5

Answers

Combine = 2 x 2^x/5 =32/5
Rearrange = 2^ 1+x /5 =32/5
Multiply = 5 x 2^x+1/5 = 5 x 32/5
Cancel multiplied terms in denominator= 2^ x+1=32
X +1=5
Subtract 1 from both sides
X+1-1= 5-1
New term= x=5-1=4

X=4

Solve the inequality |3x-2| ≤4

Simplify all fractions as much as possible. Express your answer as an integer or fraction, and not as a decimal. If the answer is a fraction, provide the answer as "a/b". Do not leave spaces between characters.
? ≤ x ≤ ?

Answers

The solution to inequality is -2/3 ≤ x ≤ 2. The value of x lies between -2/3 and 2.

What is inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the expression on the left should be greater or less than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

Given inequality is

|3x-2| ≤ 4

Applying the formula |x| ≤ a → -a ≤ x ≤ a:

-4 ≤ 3x-2 ≤ 4

Add 2 on both sides:

-4 + 2 ≤ 3x-2 + 2 ≤ 4 + 2

-2 ≤ 3x ≤ 6

Divide both sides by 3:

-2/3 ≤ x ≤ 2

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Least Common Denominator

Answers

The required least common denominator for the given expression is  4x³(x + 3). Option C is correct.

What is a rational fraction?

A rational expression is a mathematical expression that is the ratio of two polynomial expressions. That is, a rational expression is formed by dividing one polynomial expression by another polynomial expression.

Here,
The given rational expression,
= 1/x²  - 1/4x² + 12x

In the question, we have been asked to determine the least common denominator for the given rational expression.

Since least common denominator is given expression,
= x² (4x² + 12x)
= 4x³(x + 3)

Thus, the required least common denominator for the given expression is  4x³(x + 3). Option C is correct.

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A 4-yard dumpster cost $95.00 monthly how much would it cost for the year?
Answer options:
A) 190.00
B) 180.00
C) 170.00
D) 160.00

Answers

If a 4-yard dumpster cost $95.00 monthly, the total cost for the year is $1,140.

How is the total cost determined?

The total cost for the year of the dumpster is the product of the multiplication of the monthly cost and 12.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

In any multiplication, there must be the multiplicand (the number being multiplied), the multiplier (the number multiplying the multiplicand), and the product (or the result).

The monthly cost of the 4-yard dumpster = $95.00

1 year = 12 months

The total annual cost = $1,140 ($95 x 12)

Thus, using the multiplication operation, we can find that none of the options is correct as the total annual cost but $1,140.

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Round 317,675 to the nearest ten thousand

Answers

Answer:320000

Step-by-step explanation:

As an oil well is drilled, each new section of drill pipe supports its own weight and that of the pipe and drill bit beneath it. Calculate the stretch in a new 6.00 m length of steel pipe that supports 3.00 km of pipe having a mass of 20.0 kg/m and a 100-kg drill bit. The pipe is equivalent in stiffness to a solid cylinder 5.00 cm in diameter.

Answers

Therefore, the cylinder stretch in the new 6.00 m length of steel pipe is 0.094% of its original length, or about 5.64 mm.

What is a cylinder?

The cylinder, which is frequently a three-dimensional solid, is one of the most primitive curved geometric forms. In simple geometry, it is known as a prismatic with a circular as its basis. The term "cylinder" is also used to refer to an infinitely curved surface in a number of modern domains of geometry and topology. A "cylinder" is a three-dimensional object made up of curved surfaces with round tops and bottoms.

Here,

The total weight supported by the new 6.00 m length of pipe is the weight of the pipe and drill bit beneath it, which is:

W = (20.0 kg/m)(3.00 km) + 100 kg

W = 60,100 kg

The equivalent diameter of the solid cylinder is 5.00 cm, or 0.05 m, so its radius is 0.025 m. The cross-sectional area of the steel pipe is therefore:

A = πr^2 = π(0.025 m)^2 = 0.0019635 m^2

The modulus of elasticity for steel is typically around 200 GPa (gigapascals), or 200,000,000 N/m^2. Using the formula for the stretch of a rod under tension, which is:

ΔL/L = F/(AE)

ΔL/L = (Wg)/(AE)

where g is the acceleration due to gravity (9.81 m/s^2).

Substituting the values we have calculated, we get:

ΔL/L = [(60,100 kg)(9.81 m/s^2)]/[(0.0019635 m^2)(200,000,000 N/m^2)]

ΔL/L = 0.0009397 or 0.094%

Therefore, the stretch in the new 6.00 m length of steel pipe is 0.094% of its original length, or about 5.64 mm.

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read in the values for a tic tac toe game and evaluate whether x or o won the game. the first number in the files represents the number of data sets to follow. each data set will contain a 9 letter string. each 9 letter string contains a complete tic tac toe game.

Answers

To evaluate whether x or o won the tic tac toe game, we need to check for the three possible winning conditions:
- A horizontal row of three x's or o's
- A vertical column of three x's or o's
- A diagonal of three x's or o's

Here's the step-by-step process:

1. Read in the first number from the file, which represents the number of data sets to follow.
2. For each data set, read in the 9 letter string representing the tic tac toe game.
3. Check for the three winning conditions by comparing the values in the string.
4. If any of the winning conditions are met, return the winning player (x or o).
5. If none of the winning conditions are met, return "No winner".

Here's the code in Python:

```
# Read in the first number from the file
num_data_sets = int(input())

# Loop through each data set
for i in range(num_data_sets):
 # Read in the 9 letter string
 game = input()

 # Check for the three winning conditions
 if (game[0] == game[1] == game[2]) or (game[3] == game[4] == game[5]) or (game[6] == game[7] == game[8]) or (game[0] == game[3] == game[6]) or (game[1] == game[4] == game[7]) or (game[2] == game[5] == game[8]) or (game[0] == game[4] == game[8]) or (game[2] == game[4] == game[6]):
   # If any of the winning conditions are met, return the winning player
   print(game[0])
 else:
   # If none of the winning conditions are met, return "No winner"
   print("No winner")

```

This code will read in the values for a tic tac toe game and evaluate whether x or o won the game.

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How do you solve this

Answers

Answer:

Step-by-step explanation:

1st you solve the triangle by L x W then round it by x 10, hope this helps!

A right triangle has a base, b
, that is 6
inches. The area of the triangle, with h
representing the height, is given by the expression

Answers

The height of the triangle is h = 2A/6.

What is height?

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).


To find the height of a right triangle given the base, we can use the area formula A = 1/2bh. Rearranging this equation gives us the height: h = 2A/b. In this case, the base is 6 inches and the area is given as A. Therefore, the height of the triangle is h = 2A/6.

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Veston 20 This scatter plot shows the relationship between the age and the average emails per day. The line of best fit is shown on the graph. a. The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of b. b= (Enter your estimate to the nearest whole number.) b. Enter the approximate slope of the estimated line of best fit in the second box. slope=24 (Enter your estimate to the nearest tenth.) Average Emails per Day 40 30 20 10 0 0 Emails per Day by Age 12 24 36 48 60 Age 72​

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Answer:

Error refresh.

Step-by-step explanatithanksforfreepointlolon:

Answer:

a. The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of b.

b. Approximately 8.

b. Enter the approximate slope of the estimated line of best fit in the second box. slope=24 (Enter your estimate to the nearest tenth.)

Approximately 2.4.

State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for the equation y'=(ycot(2t))/(t^2+y^2+1)

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We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

Where in the ty-plane the hypotheses of the existence and uniqueness theorem are satisfied

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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