please help with this maths question

a)  The sample space for this experiment:

S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }

b) The probability that the expert will correctly identify (by guessing) both of the cans containing water is:  1/6

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Now, According to the information:

Let E1 and E2 represent the empty cans and W1 and W2 be the cans filled with water.  

S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }  

By merely guessing, the events are equally likely. Since there are 6 possible outcomes,  

The probability that the expert will correctly identify (by guessing) both of the cans containing water is:

Since there are 6 possible outcomes,  

probability = 1/6

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The given question is incomplete, complete question is:

According to Webster’s New Collegiate Dictionary, a divining rod is "a forked rod believed to indicate [divine] the presence of water or minerals by dipping downward when held over a vein." To test the claims of a divining rod expert, skeptics bury four cans in the ground, two empty and two filled with water. The expert is led to the four cans and told that two contain water. He uses the divining rod to test each of the four cans and decide which two contain water. a List the sample space for this experiment. b If the divining rod is completely useless for locating water, what is the probability that the expert will correctly identify (by guessing) both of the cans containing water?

The solution of c(r) in 3D spherical coordinates behaves differently  because in 3D, there are radial and angular dimensions.

3D coordinates refers to the system of three-dimensional spatial representation of an object, where each point in 3D space is represented by a set of three values, also known as coordinates. These coordinates are typically written in the form (x, y, z), where x, y, and z represent the values along the three axes of a three-dimensional coordinate system.

3D coordinates are commonly used in computer graphics, engineering, and mathematics to describe the positions and orientations of objects in 3D space. In computer graphics, for example, objects are often represented using 3D coordinates to specify their position, orientation, and size in the virtual world. In engineering and mathematics, 3D coordinates are used to describe the positions of points in three-dimensional space and to perform transformations, such as rotations and translations, on these points.

The 3D coordinate system is a fundamental tool for visualizing, analyzing, and manipulating objects in three-dimensional space, and it provides a powerful way to describe complex 3D shapes, geometric relationships, and physical interactions.

The solution of c(r) in 3D spherical coordinates behaves differently than the solution of c(x) in 1D coordinates because in 3D, there are radial and angular dimensions to consider, which can affect the overall behavior of the solution. Additionally, the spherical coordinates take into account the spherical symmetry of the problem, while the 1D coordinates do not.

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Answer: (−10)=2(+1)

Step-by-step explanation:

Answer:y=-5/3x+26/3

Step-by-step explanation:

2-7/4-1=-5/3

(4,2)

y-2=-5/3(x-4)

y-2=-5/3x+20/3

  +2             +2

y=-5/3x+26/3

[tex]y=-\frac{5}{3}x+\frac{26}{3}[/tex]

It passes through the points

Hi there, here's your answer:

Geometric mean between 2 numbers a and b: [tex]\sqrt{ab}[/tex]

Therefore, the geometric mean between 16 and 64 will be

[tex]\sqrt{16*64}[/tex] = [tex]\sqrt{1024}[/tex] = 32.

Hope it helps!

Please mark as brainliest!

Answer:

126

Step-by-step explanation:

a=9

b=3

we have

15b+a^2

just substitute the value

15*3+9*9

45+81

126

Answer:

126 is your answer!

Step-by-step explanation:

15 x 3=45

9^2=81

45+81=126

The probability of drawing at least 7 clubs in 15 draws from a standard deck of 52 cards is approximately 0.496.

The number of ways to draw 7 or more clubs in 15 draws can be found by using the cumulative distribution function for the binomial distribution. This distribution models the number of successful outcomes (clubs) in n independent trials (card draws), each with the same probability of success (drawing a club). The cumulative distribution function gives the probability of getting a certain number of successful outcomes or fewer.

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Answer:

Both models are exponential

A: $21,573.58

B: $21,589.58

Step-by-step explanation:

A

f(x) = 16,000[tex](1 + .03/4)^{4(10)}[/tex]

f(x) = (16000)[tex]1.0075^{40}[/tex]

f(x) = $21,573.58  Rounded to the nearest cent.

B

f(x) = 16000[tex](1+ .03/12)^{12(10)}[/tex]

f(x) = (16000)[tex]1.0025^{120}[/tex]

f(x) = $21,589.66 Rounded to the nearest cent

Answer:

∠ BCA = 75°

Step-by-step explanation:

∠ ABC = 90° ( angle in a semicircle )

then the 2 remaining angles in Δ ABC = 90° , that is

∠ BAC + ∠ BCA = 90° ( ∠ BCA = 5 × ∠ BAC )

∠ BAC + 5 ∠ BAC = 90°

6 ∠ BAC = 90° ( divide both sides by 6 )

∠ BAC = 15°

Then

∠ BCA = 90° - 15° = 75°

Answer:

Step-by-step explanation: y=22.5

The number of bagels when you buy for $50 will be 120 bagels.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A shop sells bagels for $5 per dozen.

Let 'x' be the number of bagels and 'y' be the total cost. Then the equation is given as,

y / x = 5 / 12

12y = 5x

The number of bagels when you buy for $50 will be given as,

12(50) = 5x

600 = 5x

5x = 600

x = 120

The number of bagels when you buy for $50 will be 120 bagels.

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Answer:

12/8 = 1.5 °C per hour

Step-by-step explanation:

basically write the change over time in a formula, calculate it and find the answer, using the answer u can say that:

over the course of 8 hrs, the temperature has been reducing by a rate of 1.5°C/hr. (link it to the context as well)

The cost to ride 5.25 miles in a taxi is, $5.63.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The equation represents the cost y (in dollars) of riding in a taxi x miles is,

⇒ y = 0.5x + 3

Hence, The cost to ride 5.25 miles in a taxi is,

⇒ y = 0.5x + 3

Substitute x = 5.25 in above equation,

⇒ y = 0.5 × 5.25 + 3

⇒ y = 2.63 + 3

⇒ y = $5.63

Thus, The cost to ride 5.25 miles in a taxi is, $5.63.

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Answer:

Step-by-step explanation:

a. The equation of the line that describes the relationship between distance and time for Car X can be found by using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we can use the formula: m = (change in y) / (change in x) = (distance traveled) / (time elapsed) = 174 miles / 3 hours = 58 miles per hour.

Since the car starts at time x = 0 and has traveled 174 miles at time x = 3, the y-intercept (b) can be found by setting x = 0 and solving for y: y = 58x + b, and y = 174 when x = 3, so b = 174 - 58(3) = -160.

Putting it all together, we get the equation: y = 58x - 160.

b. The graph that represents the relationship between distance and time for Car X is a line that passes through the point (0, -160) and has a slope of 58. This line represents the linear relationship between the distance traveled and the time elapsed for Car X.

The y-intercept of -160 represents the distance traveled when time is equal to 0. The slope of 58 represents the rate of change of the distance traveled with respect to time. This means that for every hour that passes, Car X travels 58 miles.

Evaluating multiple companies before making an investment decision helps to make informed decisions, diversify your portfolio, and maximize returns.

It is critical to consider multiple companies before investing because:

Diversification reduces the risk of loss because the performance of one company does not determine the overall performance of your portfolio.

Opportunity Cost: Comparing and selecting the best investment options allows you to avoid missing out on potential higher returns by evaluating multiple companies.

Due Diligence: Investing in a company necessitates extensive research and due diligence. When you look at multiple companies, you can compare financial statements, management, products, and other factors that can affect stock performance.

Finally, evaluating multiple companies prior to making an investment decision allows you to make informed decisions, diversify your portfolio, and maximize returns.

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Answer:

B. A radioactive compound decays at a rate of 19% per hour.

Step-by-step explanation:

We can eliminate C. (A town's population grows at a rate of 9.2% every year.) and D. (Money invested in a savings account grows at an annual rate of 4.2%.) since both of the options show growth, not decay. That leaves us with A. and B. The problem speaks of exponential, not linear, so B. would be the answer. If they asked for the linear decline or decay, A. would be the answer.

The contexts that represents exponential decline or decay is A radioactive compound decays at a rate of 19% per hour.

Exponential Decay is a reduction or decrease in the value of the quantity compared to the value of the previous quantity. Examples of phenomena that are classified as decay are a decrease in the price of goods and the decay of radioactive substances.

Based on the question above, option C and Option D Both options increase, It shows no decrease, so it can be ruled out.

While option B: the problem is exponential rather than linear.

If ask about linear decay, the answer is A.  

A.  radioactive compound decays at a rate of 19% per hour.

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The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equations are given below.

y = - 2x + 17           ...1

y = x - 7                 ...2

From equations 1 and 2, then we have

x - 7 = - 2x + 17

3x = 24

x = 8

Then the value of 'y' is given as,

y = 8 - 7

y = 1

The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.

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The equivalent expression 36x + 12 is the same as 24x - 48. Because the statement is identical to itself, the label 24x - 48 fits it.

This equation denotes the result of multiplying 24 by x and then subtracting 48.

The phrase is referred to as "36x + 12" since it is a duplicate of itself. This formula denotes the result of multiplying 36 by x and then adding 12.

The formulations in the two scenarios cannot be compared since they use different coefficients for x and different constant terms. The word "neither" does not apply to either phrase because they are both equal to one another.

Therefore, 36x + 12 is equal to the formula 24x - 48.

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You must pay $2,089.90 at the end of the month to bring the balance to the acceptable debt ratio percentage.

From the question, we have the following parameters that can be used in our computation:

Balance = $3589.90

Credit limit = $5000

To determine the acceptable debt ratio percentage, we make use of 30% minimum credit utilization rate.

So, the acceptable balance on the credit card is:

Balance = $5,000 * 30% = $1,500.

Since the current balance is $3,589.90, we have

Payment = $3,589.90 - $1,500

Payment = $2089.9

So, you must pay $2,089.90

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Answer:

Step-by-step explanation:

Since ∠S and ∠Y are complementary, we have:

∠S + ∠Y = 90°

We also know that:

m∠S = 2(m∠Y) − 30°

Substituting the second equation into the first equation, we get:

2(m∠Y) − 30° + ∠Y = 90°

Combining like terms:

3(m∠Y) = 120°

Dividing both sides by 3:

m∠Y = 40°

Therefore, m∠Y is 40 degrees.

A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

A function is a mathematical concept that assigns a unique output value for each input value.

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

To model the world population data, we can use a mathematical function to fit the data points. A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

To find the expected world population in 2017, we would need to estimate the polynomial regression model using the data points provided and then evaluate the model at the year 2017.

Research shows that the actual world population in 2017 was approximately 7.5 billion, which is higher than our estimated value based on the limited data points provided. This highlights the importance of considering additional factors and data when making predictions about the world population.

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The complete question is

The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be 2.23 x 10 ⁻¹⁵ kilotons.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a small country emits 115,000 kilotons of carbon dioxide per year. in a recent global agreement, the country agreed to cut its carbon emissions by 1.6% per year for the next 11 years.

The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be calculated as:-

Amount = 115000 x ( 0.016)¹¹

Amount = 2.23 x 10 ⁻¹⁵ kilotons.

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Answer:

Second choice:

[tex]\mbox{\large y = \sqrt{wz}}[/tex]

Step-by-step explanation:

Consider the right triangle ABC

By the Pythagorean theorem,

AB² = BC² + AC²

BC = x, AC = (w + x) and AB = v

Plug in above values
(w + z)² = v² + x²    (1)

In right triangle BCD,
BC² = BD² + CD²

Plugging in values we get
x² = w² + y²  (2)

In right triangle ABD
AB² = BD² + AD²
v² = y² + z²  (3)

Plug in values of x² from eq (2) and v² from eq 3 into equation (1) to get

(w + z)² = y² + z²  +w² + y²  

Left side (w + z)² = w² + 2wz + z²

==>  w² + 2wz + z² = y² + z²  +w² + y²  

w² and z² cancel out since they are on both sides of the equation with same sign

=> 2wz = y²+y²

2wz = 2y²

Divide by 2:

wz = y²

Switch sides:

y² = wz

[tex]\mbox{\large y = \sqrt{wz}}[/tex]

Answer:

14

Step-by-step explanation:

formula

SQURED A+B=C

10+b =18

100+b=324

100-100 324-100

=224

squre root of 224

is 14

Answer:

(-1,1)

Step-by-step explanation:

1.  Rearrange either equation to isolate one of the variables.   Lets use 6x - y = -7 :

6x - y = -7

-y = -7 - 6x

y = 7+6x

2.  Now use this definition of x in the second equation:

5x + y = -4

5x + (7+6x) = -4

11x  = -11

 x = -1

3.  Now use x = -1 in either equation to find y:

   6x - y = -7

  6 (-1) - y = -7

-y = -1

y = 1

The solution is  (-1,1)

See the attached graph.

The rectangle measures 6 centimetres in width and 18 centimetres in length.

The rectangle's length is two millimetres longer than its width. As a result, the length (L) is equal to 3(W) + 2, where W is the rectangle's width. Additionally, we are aware that the rectangle (A) has a 33 square centimetre area. In order to find W, we can apply the formula A = L x W. 33 = 3W2 + 2W because it is (3(W) + 2) x W. The quadratic equation can be used to find W, which equals 6. This indicates that the rectangle has a width of 6 centimetres and a length of 3(6)+2=18 cm.

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The required equation in a system of equations that has a solution (4, −1) is given as y = -1/4x.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Let's assume that the equation passing through the origin and (4, -1)

The equation is given as,

(y₂ - y₁) /  (x₂ - x₁)

y - y₁ = (y₂ - y₁) /  (x₂ - x₁) (x - x₁)
y - 0 = -1 - 0 / 4 - 0 [x - 0]
y = -1/4x

Thus, the required other equation in a system of equations has a solution (4, −1) is given as y = -1/4x.

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The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05  and the number of miles is 13.

Here we will use the linear equation concept to solve the problem. Since we don't know the number of miles represent it with a variable 'x' and form a Linear equation according to the given condition in the problem. Now solve the resultant equation for the value of variable 'x'  

Here we have  

The taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. the total fare was $33.05, not including the tip.    

Let 'x' be the number of miles in the taxi ride

Total cost to travel 'x' mile = 3.80 + 2.25(x)  

From the given data, the total fare was $33.05

=> 3.80 + 2.25(x) = 33.05

=> 2.25x = 33.05 - 3.80

=> 2.25x = 29.25

=> x = 29.25/2.25

=> x = 13

Therefore,

The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05  and the number of miles is 13.

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The infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.

The infinite series for ax/a+x can be represented as a geometric series. The first five terms can be expressed as:

[tex]Term 1: ax/(a+x)\\Term 2: (ax)^2/(a+x)^2\\Term 3: (ax)^3/(a+x)^3\\Term 4: (ax)^4/(a+x)^4\\Term 5: (ax)^5/(a+x)^5[/tex]

The infinite series can be expressed using summation notation as:

[tex]∑_(n=1)^∞ (ax)^n / (a+x)^n[/tex]

Using the formula for a geometric series, the sum of the infinite series can be calculated as:

[tex]S = ax/(a+x) * 1/(1-ax/(a+x)) \\ = ax/(a+x) * (a+x)/(a-ax) \\ = ax/(a-ax) \\ = a/a-x[/tex]

Therefore, the infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.

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The value of x, given the parallel lines and the angles involved, can be found to be 12. 3 .

The angles on the parallel lines are drawn such that 11 x and 45 degrees are supplementary angles .

This means that they add up to 180 degrees .

The value of x can therefore be found to be :

11 x + 45 = 180

11 x = 180 - 45

11 x = 135

x = 135 / 11

x = 12. 3

In conclusion, the value of x is 12. 3 .

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