Leo flips a fair coin and rolls a fair six-sided dice.
Draw a sample space diagram to show all the possible outcomes.
Work out the probability that he gets an outcome of heads and 4.
Give your answer as a fraction in its simplest form.

For the rectangle shaped drawing, the area of the scale drawing is 31.25  cm².

What exactly is a rectangle?

A rectangle is a four-sided flat form with four right angles on its four sides (90-degree angles). It is a quadrilateral having two pairs of equal-length parallel sides.  A rectangle's perimeter is the total of the lengths of all four sides, and its area is derived by multiplying the rectangle's length and breadth. A square is a specific instance of a rectangle with four equal-length sides.

Now,

To find the perimeter of the scale drawing, we add the lengths of all four sides. Rounded to the nearest half centimeter, the length is 12.5 cm and the width is 2.5 cm, so the perimeter is:

P = 2(12.5 cm) + 2(2.5 cm) = 25 cm + 5 cm = 30 cm

Therefore, the perimeter of the scale drawing is 30 centimeters.

To find the area of the scale drawing, we multiply the length by the width. Rounded to the nearest half centimeter, the length is 12.5 cm and the width is 2.5 cm, so the area is:

A = (12.5 cm) × (2.5 cm) = 31.25 cm²

Therefore, the area of the scale drawing is 31.25 square centimeters.

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Correct Question :-

Central Park is a rectangular park in New York City. A map of Central Park in New York City. The measured length is 12.5 centimeters. The measured width is 2.5 centimeters. Find the perimeter and the area of the scale drawing of Central Park. Round your measurements for the length and the width to the nearest half centimeter to calculate your answers.

We can conclude after answering the provided question that As a result, rectangle the surface area of the trapezoidal prism is 180 to the nearest whole number.

In Euclidean geometry, a rectangle is a triangular prism with four slight angles. It can also be described as a basic rule hexagon or one in which all of the angles are equal. A whole other option for the parallelogram is a straight angle. Four of something like the vertices in a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "vector graphics rectangle" at times. A rectangle is sometimes referred to as a parallelogram due to the equal and parallel sizes of its two sides.

Two trapezoidal faces and four rectangular faces comprise the trapezoidal prism.

To begin, we can use the formula to calculate the area of one of the trapezoidal faces:

Trapezoid area = (1/2) x (sum of parallel sides) x (height)

Area of trapezoidal face = (1/2) x (7 + 10) x 4 = 34

7 x 4 = 28 area of rectangular face

The total area of the rectangular faces is: because there are four rectangular faces

Total rectangular face area = 4 x 28 = 112

Total surface area equals the sum of the areas of trapezoidal and rectangular faces.

Surface area total = 68 + 112 = 180

As a result, the surface area of the trapezoidal prism is 180 to the nearest whole number.

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I remember doing this but I don’t seem to remember

We can start by using the formula for calculating the average:

Average = Total sum / Number of items

Let x be the average weight of the other 3 bags of rice. Then we can set up the following equation:

(2 bags weight + 3 bags weight) / 5 bags = Total weight / Number of bags

Substituting the given values, we get:

(2 x 8.16 kg + 3 bags weight) / 5 bags = 32.4 kg / 5 bags

Simplifying and solving for 3 bags weight, we get:

3 bags weight = (32.4 kg / 5 bags) x 5 - 2 x 8.16 kg

3 bags weight = 16.2 kg - 16.32 kg

3 bags weight = -0.12 kg

This means that the total weight of the other 3 bags is negative, which is not possible. Therefore, we have made an error in our calculations.

We can check our work by solving for the average weight of all 5 bags using the formula:

Average = Total sum / Number of items

Substituting the given values, we get:

Average = 32.4 kg / 5 bags

Average = 6.48 kg per bag

Therefore, the average weight of the other 3 bags of rice is:

Average = (Total weight - 2 x 8.16 kg) / 3 bags

Average = (32.4 kg - 16.32 kg) / 3 bags

Average = 16.08 kg / 3 bags

Average = 5.36 kg per bag

Therefore, the average weight of the other 3 bags of rice is 5.36 kg.

5.36kg.

I hope my answer helped you.

RobertOnBrainly

Answer:

The first step is to calculate the area of the circle pool:

- The diameter of the pool is 16 ft, which means the radius is 8 ft (half of the diameter).

- The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

- Plugging in the values, we get A = π(8 ft)^2 = 64π sq ft.

The total area of the yard is 25 ft x 60 ft = 1500 sq ft. To find out how many square feet of the yard will be grass, we need to subtract the area of the pool from the total area of the yard:

- Grass area = Total area - Pool area = 1500 sq ft - 64π sq ft ≈ 1304.43 sq ft.

Therefore, about 1304.43 square feet of their yard will be grass, to two decimal places.

Answer:

  40 seconds

Step-by-step explanation:

You have a Ferris wheel such that the height of a rider is modeled by d=30sin(πt/20)+15, and you want to know the time it takes for one revolution.

The sine function has a period of 2π. The value of the function when the argument is 2π is the same as when it is zero. The period is the time difference between those argument values. Since the argument is 0 when t=0, we only need to find the value of t that makes the argument 2π:

  2π = πt/20

  40 = t . . . . . . . multiply by 20/π

The Ferris wheel makes one revolution in 40 seconds.

The fixed fee of $6 covers the cost of the vehicle, and the fee of $4 per person covers the cost of maintaining the park facilities and services.

In mathematics, a function is a rule that assigns a unique output for each input in a specified set. It is often denoted by an equation or formula, and it describes the relationship between the inputs (independent variables) and the outputs (dependent variables). The set of all possible inputs is called the domain, and the set of all possible outputs is called the range. Functions are used in many areas of mathematics, as well as in science, engineering, and other fields to model real-world phenomena and to solve problems.

Here,

1. To estimate how much a bus containing 30 people would be charged, we can look for a pattern in the given examples. We notice that the fee increases as the number of people in the vehicle increases. Also, the fee for a car containing 2 people is $14, which can be seen as a fixed fee. Therefore, we can assume that the fee for a vehicle containing n people is of the form f(n) = a + bn, where a is the fixed fee and b is the fee per person. Using the information given, we can set up two equations:

f(2) = 14, which gives a + 2b = 14

f(4) = 20, which gives a + 4b = 20

Solving these equations, we get a = 6 and b = 4. Therefore, the rule for the entrance fee is f(n) = 6 + 4n. Substituting n = 30, we get f(30) = $126.

2. To estimate how many people a bus contains if it is charged $122, we can use the same rule that we derived in part 1: f(n) = 6 + 4n. Setting f(n) = 122, we get 6 + 4n = 122, which gives n = 29. Therefore, we can estimate that the bus contains 29 people.

3. Based on the given examples and our analysis in parts 1 and 2, we can infer that the state park uses a linear rule to decide the entrance fee for a vehicle. Specifically, the rule is f(n) = 6 + 4n, where n is the number of people in the vehicle.

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the total number of days spent in Bolivia by Audrey is 7days.

Audrey spent two weeks in Brazil

that mean

the total number of days spent in Brazil by Audrey = 2x7

= 14 days

This is twice as many days as she spent in Bolivia.

2m = 14

m = 14/2

m = 7

so, the total number of days spent in Bolivia by Audrey = 7days

The term "week" most commonly refers to any span of seven continuous days. The term "week" is also frequently used to describe the seven-day period that runs from Sunday through Saturday (though in some places this may be different, with the week considered to begin on Monday, for example)

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Answer: 8

Step-by-step explanation:

First we must set up the equation.

Jake adds 5 to the number then he multiplies it by 2.

2(x+5)

This is equal to the same number times 5 minus 14.

2(x+5)=5x-14

Distribute.

2x+10=5x-14

Add 14 to both sides.

2x+24=5x

Subtract 2x from both sides.

24=3x.

Divide both sides by 3.

8=x

Answer:

Jake thinks of the number 8.

Hope this helps!

Step-by-step explanation:

Turn the paragraph-given information into an equation:

Adds 5 = x + 5 and then multiplies the result by 2 = ( x + 5 ) * 2

5 times the number = x * 5 then take away 14 = ( x * 5 ) - 14

The same as means :

2 * ( x + 5 ) = ( x * 5 ) - 14

2x + 10 = ( 5x ) - 14

2x + 10 = 5x - 14

2x ( - 2x ) + 10 ( + 14 ) = 5x ( - 2x ) - 14 ( + 14 )

24 = 3x

8 = x

x = 8

If you plug 8 into the two equations, you will find both equations equal 26.

Given data in the problem is,

—-> 43 litre bucket of dye per 1 roll

-—> In feet, it is 1067 feet long

If 4 buckets of dye, can it dye 5 rolls of fabric

The factory has 172 liters of dye available.

Liters is a unit of volume in the International System of Units (SI). It is commonly used to measure the volume of liquids, gases, and solids that can be poured or contained in a container. One liter is equivalent to 1000 cubic centimeters (cc) or milliliters (ml), and it is roughly equal to 1.057 quarts or 0.264 gallons.

In the given question,

First, we need to find out how much dye is needed for one roll of fabric. We know that 43 liters of dye are needed for 1 roll of fabric that is 1,067 feet long.

Therefore, we can say that:

1 roll of fabric = 43 liters

To find out how much dye is needed for 5 rolls of fabric, we can multiply both sides of this equation by 5:

5 rolls of fabric = 5 × 43 liters

1,067 feet = 215 liters

1,067 feet

So, 5 rolls of fabric would require 215 liters of dye.

Next, we need to check if the 4 buckets of dye are enough to dye 5 rolls of fabric. Each bucket contains 43 liters of dye, so 4 buckets would contain:

4 buckets of dye = 4 × 43 liters

= 172 liters

Therefore, the factory has 172 liters of dye available.

Since 215 liters of dye are required for 5 rolls of fabric, and the factory has only 172 liters of dye available, it cannot dye 5 rolls of fabric with the given amount of dye.

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A sufficient estimator is the distributions of exponential.The correct answer to this question is (c) exponential.

An estimator is a rule or procedure that is used to determine an estimate of a parameter based on observed data. A statistic is used to estimate a parameter, and it is computed from the observed data. An estimator is a random variable that computes a statistic from the data.

The following distributions have a sufficient estimator:

Poisson Distribution with parameters λ and x is a Poisson distribution.

The rate of the occurrence is λ.

Exponential Distribution with parameters λ and x is an exponential distribution.

The mean waiting time is 1/λ.

Bernoulli The Bernoulli distribution is not sufficient for an estimator, but the binomial distribution, which generalizes the Bernoulli distribution, is. In the context of the binomial distribution, p is a parameter Exponential

The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, such as the amount of time until the next vehicle arrives at a traffic intersection or the amount of time a particular component lasts in a manufacturing process.

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Answer:x=7

Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    5*x-2+x-(9+3*x+10)=0

Step by step solution :

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  3x - 21  =   3 • (x - 7)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true:

2.1      Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    x-7 = 0

Add  7  to both sides of the equation :

                     x = 7

One solution was found :

x = 7

let me give you a cheesy answer, hmm the exponent on the compound interest is 4t, the years is "t", and the number pegged to it is the "compounding period", in this case is 4, so that means the compounding period is 4, so the account compounds 4 times a year, so is a quarterly period.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$200\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\\ t=years \end{cases} \\\\\\ ~\hfill A=200(1.10)^{4t}~\hfill[/tex]

The law of large numbers says that as a company insures more and more workers chosen at random, the average costs get closer to $439. So, the answer is option B.

As a company insures more and more workers chosen at random, the average cost gets closer to $439.

The law of large numbers states that as the sample size increases, the sample mean gets closer to the population mean. In this case, the population mean is the mean worker's compensation claim cost of $439 per insured worker.

As the company insures more and more workers chosen at random, the sample size increases, and the sample mean of the worker's compensation claim cost will converge to the population mean of $439.

The law of large numbers does not guarantee that an insurance company can get an average workers' compensation cost lower than the mean by insuring a large number of people. The option B is correct.

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--The given question is incomplete, the complete question is given below

"Medical care and compensation costs for workers injured on the job vary a lot and are strongly skewed as a whole. The National Academy of Social Insurance reports that the mean worker's compensation claim cost in a year is = $439 per insured μworker, with standard deviation = $20,000. The law of large numbers says that σ(choose the correct option)

A) an insurance company can get an average workers’ compensation cost lower than the mean by insuring a large number of people.

B) as a company insures more and more workers chosen at random, the average costs gets closer to $439"--

The value of the constant c such that the function f(x) = cx³ is a probability density function is 4.

The given function is f(x) = cx³, where 0 < x < 1. We know that a function f(x) is said to be a probability density function on the interval [a, b] if it satisfies the following conditions: 1. f(x) ≥ 0 for all x ∈ [a, b].2. ∫f(x)dx = 1 over the interval [a, b]. Given that 0 < x < 1, the limits of integration are from 0 to 1.

Now, integrating the given function, we get: ∫₀¹ cx³ dx= [c/4 x⁴]₀¹= c/4 × 1⁴ - c/4 × 0⁴= c/4

Therefore, for the given function to be a probability density function, the value of c should be such that∫₀¹ cx³ dx = 1⇒ c/4 = 1⇒ c = 4

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A financial investment broker earns 4% on each customer dollar invested. If the broker invests $50,000, the commission on the investment is $2,000.

The commission earned by the broker on the investment will be equal to 4% of the total investment amount.

So, the commission earned by the broker on investing $50,000 will be:

Commission = 4% of $50,000

Commission = (4/100) x $50,000

Commission = 4 x  $500

Commission = $2,000

Therefore, the commission earned by the broker on investing $50,000 will be $2,000.

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Answer:

a) y = -2.812x + 97.554

b) the correlation coefficient is about -0.97, which is a strong linear fit.

Step-by-step explanation:

you need a graphing calculator for linear regression, but desmos works fine :)

plugging in all the values into a table and letting the calculator do the work :D (attatched image)

the equation: y = -2.812x + 97.554

next, (also in the screenshot) the r-value, or the correlation coefficient, is about -0.97, and we want this to be as close to 1 or -1 as possible to get a perfect linear regression.

this is pretty close to -1, so i'd say that the linear fit is strong :)

Answer:

Q and R

Step-by-step explanation:

735.24563 is the the sphere's volume V.

What does sphere refer to?

The shape and symmetry of a sphere are both round. All of its surface points are equally spaced from the centre, making it a three-dimensional solid. On the basis of its radius, it has a surface area and a volume.

                             There are no faces, corners, or edges on it. the collection of all locations in three dimensions that are the same distance from a specific point (the centre) is known as the radius, or the outcome of rotating a circle around one of its diameters. The elements and characteristics of a sphere are comparable to those of a circle.

 D = 11.2  

 r = 11.2/2  = 5.6

 the sphere's volume  = 4/3 πr³

                                   = 4/3 * 3.14  * (5.6)³

                                  = 735.24563

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Answer: Using the absolute value function, linear functions and translations, we have that:

9. Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

10. The equation is f(x) = -5x + 100.

11. The correct option is: The slope of f(x) is greater than the slope of g(x).

12. h(-5) = 10.

13. The equation is f(x) = 2x + 5.

14. The graph of y = f(x) will shift right 9 units.

Step-by-step explanation:

The full scope of her survey or the methodology she used to collect her data.

According to Kierra's survey results, it seems that the number of females attending summer camp is slightly higher than the number of males. To complete the table for her survey results, we can use the following information:
- In the "Gender" column, we can write "Male" and "Female" to represent the two categories Kierra surveyed.
- In the "Number of Participants" column, we can fill in the values that Kierra collected from her neighborhood.

For example, if she surveyed 100 people and found that 40 of them were males attending summer camp, we can write "40" in the row for "Male" under the "Number of Participants" column.
- We can then add up the values in each row to find the total number of participants in each category. For example, if Kierra found that 60 females attended summer camp, we can write "60" in the row for "Female" under the "Total" column.
| Gender | Number of Participants | Total |
|--------|----------------------|-------|
| Male   | 40                   | 100   |
| Female | 60                   | 100   |
It's important to note that this is only a small part of Kierra's survey results, and we don't know the full scope of her survey or the methodology she used to collect her data.

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There are 36 options, and 6 of them match.

The idea of probability describes the possibility of an event happening.

We frequently have to make forecasts about the future in real life.

We may or may not be aware of the outcome of an event.

When this happens, we declare that there is a chance the event will take place.

In summary, probability has a wide range of fantastic applications in entertainment, business, and this recently expanding branch of artificial intelligence.

The probability formula can be used to determine the likelihood of an event by only dividing the favorable number of possibilities by the entire number of p-ossible outcomes.

According to our question-

Die 1  |  Die 2   | Same?

____________________

   1      |    1       |    YES

   1      |     2      |    N

   1      |     3      |    N

   1      |     4      |    N

   1      |     5      |    N

   1      |    6       |    N

   2      |    1       |    N

   2      |    2       |    YES

   2      |   3        |    N

Hence, There are 36 options, and 6 of them match.

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The best description of the roots of the equation [tex]x^2 - 4x + 4 = 0[/tex]  is that it has two equal or identical real roots.

Identical real roots are solutions to a quadratic equation in which both roots have the same value. In other words, if a quadratic equation has identical real roots, it means that there is only one solution to the equation, and that solution is repeated twice.

To use the discriminant to describe the roots of equation [tex]x^2 - 4x + 4 = 0[/tex] we need to first identify the coefficients of the quadratic equation:

[tex]a = 1\\b = -4\\c = 4[/tex]

The discriminant is given by the expression [tex]b^2 - 4ac[/tex].  Substituting the values of a, b, and c, we get:

[tex]b^2 - 4ac\\ = (-4)^2 - 4(1)(4)\\ = 16 - 16 = 0[/tex]

Since the discriminant is equal to zero, this tells us that the quadratic equation has two equal roots. In other words, the equation has a single root with a multiplicity of two.

The best description of the roots of equation x^2 - 4x + 4 = 0 is that it has two equal or identical real roots.

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Therefore, each bus can hold 22 students if there were 12 students per van.

In mathematics, an equation is a statement that asserts the equality of two expressions. Equations typically contain one or more variables, which are symbols that can represent different values. Solving an equation means finding the value or values of the variable(s) that make the equation true.

Here,

a) Let V be the number of vans and B be the number of buses. We know that there were 8 vans and 12 buses, so we can write:

V + B = 20 (the total number of vehicles)

We also know that there were 360 students in total. If we assume that each van can hold 12 students, and each bus can hold some number of students, we can write:

12V + bB = 360 (the total number of students)

where b is the number of students that each bus can hold.

b) We can use the equation we derived in part a) and substitute V = 8 to solve for B:

V + B = 20

8 + B = 20

B = 12

So there were 12 buses in total. We can then use the equation 12V + bB = 360 and substitute V = 8 and B = 12 to solve for b:

12V + bB = 360

12(8) + b(12) = 360

96 + 12b = 360

12b = 264

b = 22

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Answer:

Step-by-step explanation:

60$. (((150 * 40 and divide by 100)))

Step-by-step explanation:

She used    40%  of $150  :

40%  *  $150   =   .40 * 150  =  $ 60  for the   pup-a-roo.

After solving the given equation we find out that the value of x = -2, y = 6.

To solve for x and y, we can use the method of elimination, also known as the addition method. The idea is to add the two equations together in a way that eliminates one of the variables. In this case, we can add the two equations as follows:

(4x + y) + (3x - y) = -2 + (-12)

Combining like terms, we get:

7x = -14

Dividing both sides by 7, we get:

x = -2

Now that we know x, we can substitute this value into either of the original equations to solve for y. Let's use the first equation:

4x + y = -2

Substituting x = -2, we get:

4(-2) + y = -2

Simplifying, we get:

-8 + y = -2

Adding 8 to both sides, we get:

y = 6

Therefore, the solution to the system of equations is:

x = -2, y = 6.

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The dot plot for the given data is given below with Title Number of hours students watched Netflix in a month. The mode is 21, median is 29.5, mean is 26.92, range is 16.

A dot plot is a simple and effective way to display data graphically. It is a type of chart that uses dots to represent values and shows the distribution of a dataset.

Mode is a statistical term that refers to the value that appears most frequently. In the given data, 21 occurs most frequently, hence the mode is 21.

To find the median first arrange the data in ascending or descending order

18, 18, 21, 21, 21, 22, 29, 30, 31, 32, 33, 33, 34, 34

Hence, the number of observations in the data set are 14, therefore the median is the average of 7th and 8th observation is the arranged data set.

Median = (29 + 30)/2 = 59/2 = 29.5

Mean is the ratio of sum of all observations to the total number of observations.

Mean = (18 + 18 + 21 + 21 + 21 + 22 + 29 + 30 + 31 + 32 + 33 + 33 + 34 + 34)/14 = 26.92

Range is the difference between the highest and lowest number in the data set.

Range = 34 - 18 = 16

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The total area of the rectangle and square joined together is 27 cm².

First, let's find the area of the rectangle. The formula for the area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width.

In this case, the length of the rectangle is 6 cm and the width is equal to the length of the square, which is also 3 cm. So, the area of the rectangle is:

A = 6 cm x 3 cm

A = 18 cm^2

Now let's find the area of the square. The formula for the area of a square is A = s^2, where A is the area and s is the length of a side.

In this case, the length of the side of the square is also 3 cm. So, the area of the square is:

A = 3 cm x 3 cm

A = 9 cm^2

To find the total area of the rectangle and square joined together, we simply add the two areas together:

Total area = area of rectangle + area of square

Total area = 18 cm^2 + 9 cm^2

Total area = 27 cm^2

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Let's call the speed of the wind "w". When the airship is flying with the wind, its effective speed is 50 + w km/hour. When the airship is flying against the wind, its effective speed is 50 - w km/hour.

Using the formula distance = rate x time, we can write two equations for the round trip:

150 = (50 + w)(t1)

150 = (50 - w)(t2)

where t1 is the time the airship took to fly with the wind and t2 is the time it took to fly against the wind.

We also know that the total round trip took 6 hours and 15 minutes, or 6.25 hours:

t1 + t2 = 6.25

Now we can solve for w. Let's rearrange the second equation to solve for t2:

t2 = 150 / (50 - w)

Substitute this expression for t2 into the third equation:

t1 + 150 / (50 - w) = 6.25

Solve for t1:

t1 = 6.25 - 150 / (50 - w)

Now substitute this expression for t1 into the first equation:

150 = (50 + w)(6.25 - 150 / (50 - w))

Simplify and solve for w:

w = 25 km/hour

Therefore, the speed of the wind is 25 km/hour.