Which of the following rational functions is graphed below?

Salut/Hello!

Step-by-step explanation:
/ - fraction line
Ben's probability to pass is 0,8
to make it simpler for you to understand I'm going to use percentages.

We can transform 0,8 in a fraction so 8/10 and amplify it by 10 so 80/100
so the percentage showing that Ben will pass is 80% to find out the percentage that Ben will fail we subtract 80% from 100% which results in 20%

so the probability that Ben will fail is 0,2
and Tom's probability to fail is 0,3


To find out the answer to b) we need to understand how we calculate it.

Take as an example a dice. A dice has 6 faces and you need 1 side to get out of jail (let's say you need a 6). Your probability to get that side is 1/6

But what if you have two dice and you need both to be 6? Well in that case it'll be 1/6 x 1/6 which is 1/36

So, to find out the probability of both passing, we have to do 8/10 x 7/10 which is 56/100 and it's equal to 0,56. And you might wonder why the probability both will pass seems bigger than their probability to pass. Well 0,8 actually can mean 0,800000... and so on but it's easier to just let it as 0,8

For c) the probability that only one will pass is: 0.12

We first need to find the probability both fail
100% - 56% = 44%

and we subtract 44% from 56% which is equal to 12% or 0.12


I hope it was helpful! :]

Rearranging the equation and solving for dy/dx, we have:

dy/dx = (2 - 3x^2y^2) / (12y^2 + 2x^3y)

The slope of the tangent at (3, 2) is -17/51.

(a) To find dy/dx, we differentiate the implicit relation 4y^3 + x^3y^2 - 2x + 22 = 0 with respect to x.

Differentiating term by term, we get:

12y^2(dy/dx) + 3x^2y^2 + 2x^3y(dy/dx) - 2 + 0 = 0

Rearranging the equation and solving for dy/dx, we have:

dy/dx = (2 - 3x^2y^2) / (12y^2 + 2x^3y)

(b) To find the slope of the tangent at (3, 2), we substitute x = 3 and y = 2 into the expression we obtained in part (a).

dy/dx = (2 - 3(3)^2(2)^2) / (12(2)^2 + 2(3)^3(2))

Simplifying the expression, we get:

dy/dx = (2 - 36) / (48 + 54)

dy/dx = -34 / 102

Simplifying further, we have:

dy/dx = -17 / 51

know more about slope of the tangent here:

https://brainly.com/question/32393818

#SPJ11

The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

for more such questions on probability visit:

https://brainly.com/question/251701

#SPJ8

The old mileage is 10,000 miles and the new mileage is 25 miles per gallon (MPG).

To calculate the old and new mileage, we need to know the old and new miles per gallon (MPG) values.

Let's assume that the old mileage is 25 miles per gallon (MPG) and the new mileage is 30 miles per gallon (MPG).

To calculate the old mileage:

Old mileage = Distance traveled / Gasoline used

Given that you originally used 400 gallons of gasoline per year, we can calculate the distance traveled using the old mileage:

Distance traveled = Old mileage * Gasoline used

Distance traveled = 25 MPG * 400 gallons

Old mileage = 10,000 miles

To calculate the new mileage:

New mileage = Distance traveled / Gasoline used

Since the distance traveled remains the same, we can use the same value of 10,000 miles for the distance traveled. Let's calculate the new mileage using the new MPG value:

New mileage = 10,000 miles / Gasoline used

Assuming the same amount of gasoline used (400 gallons per year), we can calculate the new mileage:

New mileage = 10,000 miles / 400 gallons

New mileage = 25 miles per gallon (MPG)

Therefore, the old mileage is 10,000 miles and the new mileage is 25 miles per gallon (MPG).

Learn more about mileage from

https://brainly.com/question/29806974

#SPJ11

Answer:6

1/3

Step-by-step explanation:

Using binary search to find the key 60 in the given list, the elements compared in order are: 38, 76, 60.

1. We start by comparing the key (60) to the middle element of the list, which is 38. Since 60 is greater than 38, we know that the key must be in the second half of the list.
2. Next, we compare the key to the middle element of the second half of the list, which is 76. Since 60 is less than 76, we know that the key must be in the first half of the second half of the list.
3. We then compare the key to the middle element of the first half of the second half of the list, which is 50. Since 60 is greater than 50, we know that the key must be in the second half of the first half of the second half of the list.
4. Next, we compare the key to the middle element of the second half of the first half of the second half of the list, which is 72. Since 60 is less than 72, we know that the key must be in the first half of the second half of the first half of the second half of the list.
5. Finally, we compare the key to the middle element of the first half of the second half of the first half of the second half of the list, which is 60. Since 60 is equal to 60, we have found the position of the key in the list.


To know more about binary search visit :-

https://brainly.com/question/15178888

#SPJ11

Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

know more about multiply here;

https://brainly.com/question/30875464

#SPJ11

Answer: it is an  octagonal prism

Answer:

It's a hexagonal prism

Answer:

y = 12

Step-by-step explanation:

We'll use the form of an equation of a straight line of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are told the slope, m, is -2.

That leads to:  y = -2x + b

y = -2x + b

B, the y-intercept, can be found by using the given point (3,28) in the equation (it falls on the line, so must be a valid solution to the equation.  Use the given x and y in the equation and solve for b:

            y = -2x + b

           28  = -2*(3) + b

           28  = -6 + b

b = 34

The equation is y = -2x + 34

Use this to find y when x = 11:

  y = -2(11) + 34

  y = -22 + 34

  y = 12

y is 12 when x is 11

     See the attached graph.

Answer:

I think n is -25 but im not sure

Step-by-step explanation:

We can write that the values of a, b, and c in the given expression are 13/4, -7/4, and 7, respectively. Given expression is(2,-1,c) + (a,b,1) -3 (2,a,4) = (-3,1,2c)

Expanding left hand side of the above equation, we get2 - 6 - 4a = -3 => - 4a = -3 - 2 + 6 = 13b - a - 4 = 1 => a - b = 5c - 12 = 2c => c = 7

Hence, the values of a, b and c are 13/4, -7/4 and 7 respectively.

let's understand the given expression and how we have solved it.

The given equation has three terms, where each term is represented by a coordinate point, i.e., (2, -1, c), (a, b, 1), and (2, a, 4).

We are supposed to calculate the values of a, b, and c in the equation.
We are given the result of the equation, i.e., (-3, 1, 2c).

To find out the value of a, we used the first two terms of the equation and subtracted three times the third term of the equation from the result.

Once we equated the equation, we solved the equation using linear equation methods.

We have found that a = 13/4, b = -7/4, and c = 7.

To learn more about coordinate point, refer:-

https://brainly.com/question/16679833

#SPJ11

AnswerProbability = the number of wanted outcomes/the number of possible outcomes

The probability of drawing a green marble is  

number of green marbles/ total number of marbles in the bag

7/16

If you replace the marble each time, each time your chance of drawing green is 7/16.  If this is done 3 times, the probability is

(7/16)(7/16)(7/16) = 0.084

For not replacing green, there is no impact on the first draw, the probability of getting green on the first draw is still 7/16. If you do not replace, this means that there are no longer 16 marbles in the bag for the second draw, there are now 15.  And since you already drew one green one, there are no longer 7 green ones, there are now 6.  So probability for green on the second draw is 6/15.  If you draw a 3rd time and there isn't replacement,  there are no longer 15 marbles in the bag for the second draw, there are now 14. And since you already drew one green one, there are no longer 6 green ones, there are now 5. So probability for green on the third draw is 5/14.  Combining the 3 draws together:

(7/16)(6/15)(5/14) = 0.063

The probability of drawing 3 with replacement is higher than without.:

Answer:

just use Pythagoras theorem ....

The equation of direct variation for this scenario is: y = 7x

In direct variation, the relationship between two variables can be expressed as y = kx, where k is a constant.

Therefore, the equation of direct variation for this scenario is:

y = 7x

This equation represents that the number of campers (y) is directly proportional to the number of counselors (x), with a constant ratio of 7.

Learn more about equation at https://brainly.com/question/29174899

#SPJ1

B5 + C9 = 164

Split the numbers.

B0 +C0 +14 = 164.

B0 + C0 = 150

B + C = 15

B cannot be 1, 2, 3, 4, or 5 because that forces C to be a two digit number and C only represents 1 digit.

B cannot be 6 or 9 because they are present.

B can only be 7 or 8. C can also be 7 or 8.

Therefore, B = 7  and C = 8, OR B = 8 and C = 7.

The highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

In mathematics, a base is the number of digits or distinct symbols used to represent numbers in a positional numeral system. For example, in the decimal system (which we commonly use), the base is 10 because we use 10 distinct digits from 0 to 9.

Now, let's consider the number 1000. In order to find the lowest base in which this could be a valid number, we need to break down 1000 into its constituent digits. Since 1000 has 4 digits, we can represent it as:

1000 = 1 x base^3 + 0 x base^2 + 0 x base^1 + 0 x base^0

where base is the number system we are using. Now, we need to find the lowest value of base that makes this equation valid.

We can see that if we set base = 2, then the equation becomes:

1000 = 1 x 2^9 + 0 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0

Here, we have used the binary system, which has a base of 2. As we can see, the highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

To know more about Number visit:

https://brainly.com/question/3589540

#SPJ11

Zane set out to create a table that would demonstrate equivalent ratios for x and y, but after completing it, he noticed an error.

As per the question given,  

Determined to correct the mistake and provide accurate information, he took a closer look at each row and column of the table to identify the incorrect number.

Using his problem-solving skills, Zane was able to pinpoint the incorrect number and replace it with the correct one, ensuring that the table accurately represented the equivalent ratios for x and y. With this correction, Zane could rest easy knowing that he had provided reliable information for others to use and reference.

As the saying goes, "to err is human," but Zane's dedication to accuracy and attention to detail ensured that his mistake did not go unnoticed, and he was able to take the necessary steps to correct it.

For such more questions on Ratio

https://brainly.com/question/12024093

#SPJ4

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

Learn more about exponents here:

https://brainly.com/question/5497425

#SPJ1

Answer:

5(4) - 6 + 5(4) - 6

Step-by-step explanation:

k(x) = 5x - 6

(k+k)(x) = 5x - 6 + 5x - 6

(k+k)(4) = 5(4) - 6 + 5(4) - 6

=> Option D is correct

Hope this helps!

The expression is equivalent to (k+k) (4) will be 5(4) - 6 + 5(4) - 6. The correct option is B.

Expression in maths is defined as the collection of the 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.

The expression will be solved as below:-

k(x) = 5x - 6

(k+k)(x) = 5x - 6 + 5x - 6

(k+k)(4) = 5(4) - 6 + 5(4) - 6

Therefore, the expression is equivalent to (k+k) (4) will be 5(4) - 6 + 5(4) - 6. The correct option is B.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ6

The value of x, considering the proportional relationship in this problem, is given as follows:

\(x = 0.77 \times 10^{-46}\)

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The proportional relationship for this problem is given as follows:

1u - \(6.02 \times 10^{23}\)

x u - \(4.65 \times 10^{-23}\)

Applying cross multiplication, the value of x is given as follows:

\(x = \frac{4.65 \times 10^{-23}}{6.02 \times 10^{23}}\)

\(x = 0.77 \times 10^{-46}\)

A similar problem, also featuring proportional relationships, is presented at https://brainly.com/question/7723640

#SPJ1

Answer:im not sure what u mean

Step-by-step explanation:

Answer:

7. 45, 60, 75

8. id k sorry

9. 40, 135, 165

10. 15, 20

To solve this problem, we need to find the x-values where the curve intersects the x-axis, which occurs when y=0.
0=x²-2kx ,We can factor out an x: 0=x(x-2k) .So the x-intercepts are at x=0 and x=2k.

To find the value of k, we need to follow these steps:

Step 1: Find the points of intersection between the curve y = x^2 - 2kx and the x-axis.
To do this, set y = 0:
0 = x^2 - 2kx
x(x - 2k) = 0

This means that the curve intersects the x-axis at x = 0 and x = 2k.

Step 2: Determine the limits of integration.
Since we are looking for the region in the fourth quadrant, we will have limits 0 and 2k for our integration.

Step 3: Calculate the area using integration.
Area = ∫[0 to 2k] (x^2 - 2kx) dx

Step 4: Solve the integral.
Area = [1/3x^3 - kx^2] evaluated from 0 to 2k
Area = (1/3(2k)^3 - k(2k)^2) - (1/3(0)^3 - k(0)^2)
Area = (8k^3/3 - 4k^3)

Step 5: Set the area equal to 36 and solve for k.
36 = 8k^3/3 - 4k^3
36 = (8k^3 - 12k^3)/3
36 = -4k^3/3

Now, multiply both sides by 3 and divide by -4:
-108/-4 = k^3
27 = k^3

Take the cube root of both sides:
k = 3

The value of k is 3 (Option b).

To learn more about intercepts : brainly.com/question/14180189

#SPJ11

Answer:

The answer is 77 degrees

Answer:

40cm²

Step-by-step explanation:

A=b×h

A=10cm×4cm

A=4O²/40cm²

  x - 4y = 4

-3x - 4y = 12

Subtract the first equation from the second

  x - 4y = 4

-4x      = 12

Divide the second equation by (-4)

  x - 4y = 4

  x      =  -3

Subtract the second equation from the first

   - 4y  =  7

  x      =  -3          

Divide the first equation by (-4)    

       y  =  -7/4

  x      =  -3        

The equation is c = -5f + 35. f is the independent variable while c is the dependent variable

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

The variable f(number of friends) is the independent variable (input value) while c(number of carrots) is the dependent variable (output value)

From table, using pairs (1, 30) and (2, 25):

c - 30 = [(25 - 30)/(2 - 1)](f - 1)

c - 30 = -5(f - 1)

c = -5f + 35

The equation is c = -5f + 35

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The expression for profit, P(x), is P(x) = 204x + 3x + 2x - 1 - (3x² + 2x + 3).

The profit, P(x), is defined as the difference between the revenue, R(x), and the cost, C(x). Given R(x) = 2043x + 2x - 1 and C(3)x² + 2x + 3, we can substitute these expressions into the profit formula.

Substituting R(x) and C(x) into the profit formula, we have P(x) = (2043x + 2x - 1) - ((3x² + 2x + 3).

Simplifying this expression, we can distribute the negative sign to the terms within the parentheses:

P(x) = 2043x + 2x - 1 - 3x² - 2x - 3.

Combining like terms, we have P(x) = -3x² + (2043x + 2x - 2x) - (1 + 3).

Simplifying further, we get P(x) = -3x² + 2043x - 4.

Therefore, the expression for profit, P(x), is P(x) = -3x² + 2043x - 4.

Learn more about revenue here : brainly.com/question/27325673

#SPJ11