15) Eileen has a piece of paper that is 30 cm long and 20 cm wide.
She cuts out the shaded triangle as shown on the diagram.
What is the area of the triangle?
20 cm
30 cm
Not drawn to scale​

The increase in weekly wages for both the man and the boy is Rs. 40.

Let's assume that the increase in wages for both the man and the boy is x.

After the increase, the man's weekly wage will be Rs. 80 + x and the boy's weekly wage will be Rs. 35 + x.

We know that the man's wage after the increase is 8/5 of the boy's wage after the increase. Mathematically,

80 + x = (8/5)(35 + x)

Simplifying this equation, we get:

80 + x = 56 + (8/5)x

Multiplying both sides by 5, we get:

400 + 5x = 280 + 8x

Subtracting 5x from both sides, we get:

400 = 280 + 3x

Subtracting 280 from both sides, we get:

120 = 3x

Dividing both sides by 3, we get:

x = 40

Therefore, the increase in wages is Rs. 40.

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To create a list of 10 random numbers ranging from 1 to 1000, you can use the `random` module in Python. Here's an example of how you can generate the list:

```python
import random

def create_random_list():
   random_list = []
   for _ in range(10):
       random_number = random.randint(1, 1000)
       random_list.append(random_number)
   return random_list

numbers = create_random_list()
print(numbers)
```

This code will generate a list of 10 random numbers between 1 and 1000 and store it in the variable `numbers`.

Next, let's design a function that accepts this list and uses recursion to find the biggest value and its index number. Here's an example:

```python
def find_biggest(numbers, index=0, max_num=float('-inf'), max_index=0):
   if index == len(numbers):
       return max_num, max_index
   if numbers[index] > max_num:
       max_num = numbers[index]
       max_index = index
   return find_biggest(numbers, index + 1, max_num, max_index)

biggest_num, biggest_index = find_biggest(numbers)
print("The biggest value in the list is:", biggest_num)
print("Its index number is:", biggest_index)
```

In this function, we start by initializing `max_num` and `max_index` as negative infinity and 0, respectively. Then, we use a recursive approach to compare each element in the list with the current `max_num`. If we find a number that is greater than `max_num`, we update `max_num` and `max_index` accordingly.

The base case for the recursion is when we reach the end of the list (`index == len(numbers)`), at which point we return the final `max_num` and `max_index`.

Finally, we call the `find_biggest` function with the `numbers` list, and the function will return the biggest value in the list and its index number. We can then print these values to verify the result.

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Answer:

34 hours

Step-by-step explanation:

358-35=323

323/9.50= 34

Answer:

40

Step-by-step explanation:

14/35 = f/100

35f = 14 x 100

f = 14 x 100 /35

f = 40

Answer:

40

Step-by-step explanation:

Well, 35% of 40 is 14, but I'm not confident on what it wants when it suggests to answer as a numeric expression. But, if it means in it's unadulterated, unsimplified, primitive nature, then sure, let me list the work below.

14/.35

There.

He rented the pressure washer for 4 hours, given that the total bill was $86.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = total number of hours he rented the pressure washer

The total bill, which was $86, includes the flat fee of $50 plus $9 per hour of use.

Hence, the equation will be 50 + 9x = 86.

Solve for x.

50 + 9x = 86

9x = 86 - 50

9x = 36

x = 4

total number of hours he rented the pressure washer = 4

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Answer:

22

Step-by-step explanation:  babab

Answer:

(-2,8)

Step-by-step explanation:

Slope m = (y2-y1)/(x2-x1)

Line 1: m = (0 - 6)/(2 - -1) = -6/3 = -2

y = mx+ b => y = -2x + b => 0 = -2(2) + b => 0 = -4 + b => b = 4

y = -2x + 4

Line 2: m = (9 - 5)/(-1 - -5) = 4/4 = 1

y = mx + b => y = x + b => 9 = -1 + b => b = 10

y = x + 10

When the 2 line intersects, they will same the same (x,y)

so line 1 = line 2

-2x + 4 = x + 10

-2x - x = 10 - 4

-3x = 6

x = -2

y = -2x + 4 = -2(-2) + 4 = 8

so the lines intersect at (-2,8)

Scenario y describes evolution by natural selection. I know this because it involves heritable variation and fitness. In this scenario, the hominins with less dense hair had a trait that was heritable within the population, and they were able to maintain a cooler body temperature and be more successful in obtaining food.

As a result, over time, the hominin populations evolved to have less body hair. This process of natural selection involves the traits that are passed on through genetics that lead to survival and reproductive success. The individuals with advantageous traits are more likely to survive and pass on those traits to their offspring. In contrast, scenario x describes the evolution of individuals who became adapted to the environment due to a mutation that increased their survival chances. However, it does not involve heritable variation or the process of natural selection.

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Answer:

It’s M and N

Step-by-step explanation:

they both add up to make 180 degrees. sorry for the late answer and ur welcome :)

Answer:

No, it doesn't include them.

Step-by-step explanation:

In statistics intervals, the lower limit is the least value in the class limit while the upper limit is the highest value in the class interval.

For example, an interval of a class limit of 20 - 30,the lower limit is 20 while the upper limit is 30.

Thus,the lower limit doesn't include the numbers in the interval or the upper limit.

Answer:

roughly 8.58

Step-by-step explanation:

long division I hope this helps bye !!! have a great day!!! :D

You would need to prepare approximately 1.05 milliliters of 2% lidocaine solution for a child weighing 21 kg.

To determine the number of milliliters of 2% lidocaine to prepare for a child weighing 21 kg, we need to calculate the appropriate dose based on their weight and the concentration of the solution.

The dose of lidocaine is given as 1 mg/kg.

Therefore, for a child weighing 21 kg, the dose would be:

Dose = 1 mg/kg x 21 kg = 21 mg

The concentration of the lidocaine solution is 2%. This means that for every 100 ml of the solution, there are 2 grams (2000 mg) of lidocaine.

Now we can calculate the volume of the solution needed to administer the dose:

Volume = (Dose ÷ Concentration) x 100

Volume = (21 mg ÷ 2000 mg) x 100 = 1.05 ml

Therefore, you would need to prepare approximately 1.05 milliliters of 2% lidocaine solution for a child weighing 21 kg.

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The rate of change of volume is 418.6  inch³/s .

Rate of increase of radius with time is ( dr/dt ) = 5

rate of decrease of height with time is (dh/dt ) = -3

volume of a cone is given by (V) =  \(\frac{1}{3} \pi r^{2}h\)

Now the rate of change of volume  with respect to time is given by dV/dt

∴ dV/dt = d( \(\frac{1}{3} \pi r^{2}h\)) / dt

dV/dt =  \(\frac{1}{3} \pi (2rh\frac{dr}{dt} + r^{2}\frac{dh}{dt} )\)

value of radius and height when volume is changing are :

r = 20 inches

h = 40 inches

dV/dt = \(\frac{1}{3} \pi (\) 2×20×40 ×5 - \(20^{2}\)×3 )

dV/dt = \(\frac{1}{3} \pi\)(1600 - 1200)

dV/dt = (400/3) 3.14

dV/dt = 418.66 inch³/s

So the rate of change of the volume is 418.66 inch³/s.

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The ratio of the area of the triangle to the area of the square is \(\frac{1}{4}\).

State the formula for the triangle's area?

The formula for the area of a triangle can be calculated using the base and height of the triangle. The general formula is:

Area = \(\frac{(base\ *\ height) }{2}\)

In this formula, the base refers to the length of any side of the triangle, and the height refers to the perpendicular distance from the base to the opposite vertex.

Let's assume the square has side length s. Since the given points are the midpoints of two sides, they divide each side into two equal segments, each with length \(\frac{s}{2}\).

We can construct a triangle by connecting these two points and one of the vertices of the square. This triangle will have a base of length s and a height of \(\frac{s}{2}\).

The area of a triangle is given by the formula:

Area = \(\frac{(base\ *\ height) }{2}\)

Substituting the values, we have:

\(Area of traingle=\frac{(s\ *\frac{s}{2}) }{2}\\=\frac{(\frac{s^2}{2})}{2}\\=\frac{s^2}{4}\)

The area of the square is given by the formula:

Area of square =\(s^2\)

Now, we can calculate the ratio of the area of the triangle to the area of the square:

\(Ratio =\frac{ (Area of triangle)}{ (Area of square)} \\=\frac{(\frac{s^2}{ 4})}{s^2} \\\\= \frac{s^2 }{4 * s^2}\\\\=\frac{1}{4}\)

Therefore, the ratio of the area of the triangle to the area of the square is \(\frac{1}{4}\), expressed as a common fraction.

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To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.

To increase usability in a spreadsheet, you can utilize the following techniques:

1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.

2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.

3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.

4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.

5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.

6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.

7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.

By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.

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Answer:

-9/7

Step-by-step explanation:

Distribute

2x + 8 = -5x - 1

Get variables on left; constants on right

2x + 5x = -1 -8

Gather like terms and do the math

7x = -9

x = -9/7

The errors that may have occurred in the student's measurements are random errors. These types of errors can arise from various sources, such as slight variations in measurement techniques or environmental factors.

Since the measured values are slightly different, it suggests that random errors affected the measurements rather than systematic errors, which would result in consistently incorrect measurements.

To minimize the impact of random errors during data analysis, the student can calculate the average of the three measured values. The average value can serve as the best estimate of the true value of the mass of the rock. Additionally, the student can calculate the standard deviation of the measured values to determine the precision of the measurements. The smaller the standard deviation, the more precise the measurements.

The student can further minimize random errors by taking multiple measurements and averaging them to obtain a more accurate value. Additionally, using a digital balance instead of an analog one may reduce random errors as digital balances have greater precision and accuracy.

It is also important for the student to use proper measurement techniques such as ensuring that the balance is calibrated and zeroed correctly before each measurement. The student should also avoid applying excessive force on the balance and ensure that the rock is stable and level during measurement.

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Answer:

The answer is 17. if you look at the table in the column 5-10, that's 4 people,, plus the column 10-15, which is 7 plus the number of people in the column 15-20 which is 6. add them up and you get 17

Linear Equation and It's Application in Real Life

In the given problem, it is an application of linear equation and solving word problem about mathematical operation. It is a combination of general mathematics and algebra.

In word problem about time and work, the equation is 1/x + 1/y + 1/z + ... = 1/t, where

x is the amount of time consume by first person

y is the amount of time consume by second person

z is the amount of time consume by third person

t is the amount of time they consume working together.  

In this case, to solve for the amount of work that Rizal can finish the school project alone.

1/x + 1/y + 1/z + ... = 1/t

It can be derived as 1/x = 1/t - (1/y + 1/z + ... ), where x is the amount of work done by Joseph, and y for Maria.

Given

Joseph can finish the chores in 2 hours

Maria can finish the same chores in 4 hours.

Create  mathematical equation using the given formula for work problem.

1/x + 1/y = 1/t, where x = 2 hours, and y = 4 hours

½ + ¼ = 1/t, solve for t

The LCD of 2, 4 and t is 4t, the new equation will be

4t(1/2) + 4t(1/4) = 4t(1/t)

2t + t = 4

3t = 4

t = 4/3

t = 1 1/3 hours

Final Answer

1 1/3 hours to complete the task when they work together.  

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The rate at which Ms. Sanchez's students can write lines of code can be expressed as 12 lines of code per hour. This means that, on average, each student is able to write 12 lines of code within a one-hour time period.

The rate at which Ms. Sanchez's students can write lines of code can be calculated as follows:
In 20 minutes, each student can write an average of 4 lines of code.
To find the rate per hour, we need to convert the time from minutes to hours. Since there are 60 minutes in an hour, we divide the number of minutes by 60:
20 minutes ÷ 60 minutes/hour = 1/3 hour

Now, we can calculate the rate per hour by multiplying the rate per 20 minutes by the number of 20-minute intervals in an hour:
4 lines of code/20 minutes × 3 intervals/hour = 12 lines of code/hour

Therefore, the rate at which each of Ms. Sanchez's students can write lines of code is 12 lines of code per hour.

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Answer: x = 7

Step-by-step explanation:

First, we will plug 4 in for y. Then, to solve we will isolate the variable "x" in the equation.

  Given:

8x – 2y = 48

  Plug in the y value of 4:

8x – 2(4) = 48

  Multiply -2 times 4:

8x – 8 = 48

  Add 8 to both sides of the equation:

8x = 56

  Divide both sides of the equation by 8:

x = 7

Answer:

x=7

Step-by-step explanation:

8x – 2y = 48

Let y=4

8x -2(4) = 48

8x - 8 = 48

Add 8 to each side

8x-8+8= 48+8

8x = 56

Divide by 8

8x/8 = 56/8

x = 7

Answer:

Step-by-step explanation:

no, because -5+3=-2 This is the same as 3-5=-2.

Based on the total number of pages in the textbook, and the total thickness, the average thickness per page is 0.0047 cm.

The average thickness per page of the textbook can be found by the formula:

= Total thickness of textbook / Number of pages

Solving gives:

= 3.86 / 820

= 0.0047 cm

In conclusion, the average thickness per page is 0.00470 cm.

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The solution to the equation using quadratic formula is n= -1±√11

A formula that provides the solution to a quadratic issue is the quadratic formula in elementary algebra. Other approaches to solving quadratic equations outside the quadratic formula comprise factoring, solving the square, graphing, and others.

Given expression= 2 + 13n = 9n + 20

Rearranging the equation we get

= 2n²+13n-9n-20=0

= 2n²+4n-20 =0

Taking out the common factor 2, we get

= 2 (n²+2n-10) = 0

Dividing both side with same factor 2, we get

= n²+2n-10 = 0

Use the quadratic formula:

n= \(\frac{-b +/- \sqrt{b^{2} -4ac} }{2a}\)

In the given expression n²+2n-10 = 0, a=1, b=2, c=-10

Therefore, n= \(\frac{-2 +/- \sqrt{2^{2} -4*1(-10)} }{2*1}\)

After evaluating the exponents, multiplying the numbers, adding the numbers, evaluating the square root and final multiplication we get:

n= \(\frac{-2 +/- 2\sqrt{11}}{2}\)

Separating the equations and rearranging them we get:

n= -1+√11

n= -1-√11

The solution to the equation using quadratic formula is n= -1±√11

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A dot plot that corresponds to the values in the table include the following: dot plot B.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the values contained in the table, the high school students' essays score on a scale of 0 to 10 should be plotted on a dot plot as follows:

An essay score of 3 would have 1 dot.

An essay score of 4 would have 1 dot.

An essay score of 5 would have 2 dots.

An essay score of 6 would have 5 dots.

An essay score of 7 would have 4 dots.

An essay score of 8 would have 7 dots.

An essay score of 9 would have 3 dots.

An essay score of 10 would have 2 dots.

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Answer:

C

Step-by-step explanation:

For Youfang, the time spent running is equal to 15 times the week

The time taken to complete 5 questions is (option b) 22 minutes, 30 seconds

Given,

The number of questions = 2

Time taken to complete 2 questions = 9 minutes

Now,

The number of questions = 5

We have to find the time taken to complete 5 questions:

We can consider ratio here:

That is,

Number of questions : Time taken to complete

So,

2 : 9 and 5 : x

Lets equate:

2 : 9 = 5 : x

That is,

2x = 5 × 9

Now, divide 2 on both sides:

2x/2 = (5 × 9) / 2

Here,

x = 45/2

Then,

x = 22.5

Converting this into minutes, we get 22 minutes, 30 seconds.

That is,

The time taken to complete 5 questions is (option b) 22 minutes, 30 seconds

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The monthly interest rate on Jada's student loans is 0.308%.

To find the monthly interest rate, we convert the annual interest rate of 3.73% to a monthly rate using the formula (1 + Annual Interest Rate)^(1/12) - 1.

Plugging in the values, we get (1 + 0.0373)^(1/12) - 1, which simplifies to approximately 0.003083, or 0.3083% when rounded to the nearest thousandth of a percent.

To calculate the monthly interest rate on Jada's student loans, we first need to convert the annual interest rate to a monthly rate.

The formula to convert an annual interest rate to a monthly rate is:

Monthly Interest Rate = (1 + Annual Interest Rate)^(1/12) - 1

In this case, the annual interest rate is 3.73%. Let's calculate the monthly interest rate:

Monthly Interest Rate = (1 + 0.0373)^(1/12) - 1

Using a calculator, we can find that the monthly interest rate is approximately 0.003083, or 0.3083%.

Rounding to the nearest thousandth of a percent, the monthly interest rate on Jada's student loans is 0.308%.

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