How do you prove that between any two irrationals there is a rational number and vice versa?

Answer: 1) (0, -3) & 2) (0,0)

Step-by-step explanation:

A plumber worked 3. 5 hours for AED 1,075 in total. He added AED 200 for supplies to the customer's bill hourly rate of the plumber is AED 364.29.

How much is charged, paid, or earned for each hour worked?

Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.

We must first deduct the price of the materials from the plumber's overall profits in order to get his hourly rate:

Income equals AED 1,075 plus AED 200, or AED 1,275.

After that, we may split his total income by the quantity of hours he put in:

Hourly fee is calculated as follows: AED 1,275 / 3.5 hours of work.

Hourly rate is 364.29 AED.

The plumber's hourly charge is therefore AED 364.29.

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Answer:

0.32958 kilometers per minute

Step-by-step explanation:

Distance covered = 26.219 miles

Step 1: Convert this distance to kilometers using the conversion( 1mi = 1.609  km)

==> 26.219 miles = 26.219 miles x 1.609 km/mile = 42.186371 km

This distance was covered in 128 minutes

Step 2: To find the speed in km/min, divide 42.186371 by 128
= 42.186371/128

= 0.32958 kilometers per minute
------------------------------------------------------------------------------------
We could also solve this problem using the following alternative technique
Step 1 Determine speed in miles/minute = 26.219/128 = 0.2048 m per min

Step 2: Multiply by conversion factor 1.609:
0.2048 x 1.609 = 0.32958 kilometers per minute

Answer: 1/6 of an hour

Step-by-step explanation: multiply the numerator and denominator by 3 of 1/2 and 1/3 to get 3/6 and 2/6. There is 1/6 more

The system of equations has a unique solution. The solution of the system of equations is (-3,4).

What is the system of equations?

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

Given equations are

y = x + 7   ......(i)

y = -7/3x - 3   ......(ii)

Putting x = 0 in equations (i) and (ii):

y = 0 + 7

y = 7

y = -7/3 × 0 - 3

y = -3

Putting x = 3 in equations (i) and (ii):

y = 3 + 7

y =10

y = -7/3 × 3 - 3

y = -10

Putting x = -3 in equations (i) and (ii):

y = -3 + 7

y = 4

y = -7/3 × (-3) - 3

y = 4

The points in equation (i) are (0,7), (3,10), (-3,4)

The points in equation (ii) are (0,-4), (3,-10), (-3,4)

Plot the points and join the points:

The intersection of the equation is (-3,4).

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The six trigonometric functions of the angle θ for the given point (-4, -1) are sin θ = -1/5, cos θ = -4/5, tan θ = 1/4, cot θ = -4, sec θ = -5/4, and csc θ = -5.

The six trigonometric functions of an angle θ are sine (sin θ), cosine (cos θ), tangent (tan θ), cotangent (cot θ), secant (sec θ), and cosecant (csc θ). These functions can be used to calculate the coordinates of a point on the terminal side of θ when the angle and one coordinate are known.

For example, if you know the angle θ and one coordinate (in this case, -4) of a point on the terminal side of θ, you can use the six trigonometric functions to calculate the remaining coordinate. In this case, the point is (-4, -1). The sine of θ is equal to the y-coordinate (-1) divided by the hypotenuse (distance from the origin). Therefore, sin θ = -1/5. The cosine of θ is equal to the x-coordinate (-4) divided by the hypotenuse. Therefore, cos θ = -4/5. The tangent of θ is equal to the y-coordinate (-1) divided by the x-coordinate (-4). Therefore, tanθ = -1/-4 = 1/4. The cotangent of θ is equal to the x-coordinate (-4) divided by the y-coordinate (-1). Therefore, cot θ = -4/-1 = -4. The secant of θ is equal to the hypotenuse (distance from the origin) divided by the x-coordinate (-4). Therefore, sec θ = 5/-4 = -5/4. The cosecant of θ is equal to the hypotenuse divided by the y-coordinate (-1). Therefore, csc θ = 5/-1 = -5.So, the six trigonometric functions of the angle θ for the given point (-4, -1) are sin θ = -1/5, cos θ = -4/5, tan θ = 1/4, cot θ = -4, sec θ = -5/4, and csc θ = -5.

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[tex] \frac{1}{8} < \frac{3}{4} [/tex]

The equation 2 and 3 would not present linear functions.

What is linear function?

A linear function is one in which the maximum power of the variables is one.

A linear function is a function that has the form f(x) = mx + b, where m and b are constants. In other words, a linear function is a straight line when plotted on a graph.

Out of the given relationships, the following do not represent a linear function:

2) The ant population for a colony that begins with 5 ants and doubles in number every two weeks.

This relationship is not linear because the rate of change (the number of ants per unit time) is not constant. The number of ants increases exponentially, which results in a curve rather than a straight line when plotted on a graph.

3) A history student's grade on a test that begins at 100 but decreases by 4 points for each question answered incorrectly.

This relationship is not linear because the rate of change (the decrease in points per incorrect question) is not constant. The decrease in points results in a curve rather than a straight line when plotted on a graph.

The other two relationships do represent linear functions.

Therefore, The equation 2 and 3 would not present linear functions.

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Without any data, we cannot determine the variance and standard deviation for the number of patients arriving at a hospital with flu-like symptoms between 12:00pm and 12:20pm.

To determine the variance and standard deviation for the number of patients arriving at a hospital with flu-like symptoms between 12:00pm and 12:20pm, we would need to know some data about the number of patients arriving during this time period. Without this data, we cannot calculate the variance and standard deviation.

If we were given a sample of data for the number of patients arriving during this time period, we could calculate the sample variance and sample standard deviation using the following formulas:

Sample variance = [(Σx²) - (Σx)² / n] / (n - 1)

Sample standard deviation = √(sample variance)

where Σx² is the sum of the squares of the deviations from the mean, Σx is the sum of the deviations from the mean, n is the sample size.

Alternatively, if we were given the mean number of patients arriving during this time period and the population variance, we could use the following formula to calculate the population standard deviation:

Population standard deviation = √(population variance)

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Some of the similarities between sales tax and hotel tax include the following:

B) Both must be paid in advance when you make a hotel reservation.

C) Both are based on a percentage of the original cost.

Taxation can be defined as the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.

The types of tax.

In Economics, there are different types of tax that are levied on individuals or business firms by the government and these include the following:

Hotel tax

Sales tax

Property tax

Income tax

we can reasonably infer and logically deduce that both sales tax and hotel tax must be paid in advance when making a hotel reservation in the United States of America.

Hence, Some of the similarities between sales tax and hotel tax include the following:

B) Both must be paid in advance when you make a hotel reservation.

C) Both are based on a percentage of the original cost.

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The complete question is given below:

What are some similarities between sales tax and hotel tax? Select all that apply. Multiple select question. cross out A) Both are an additional amount one must pay. cross out B) Both must be paid in advance when you make a hotel reservation. cross out C) Both are based on a percentage of the original cost. cross out D) Both the sales tax and the hotel tax are equal when you stay in a hotel. cross out E) Both represent a guest fee that hotels charge their customers.

Answer:

y+3=-3/4(x+4)

Step-by-step explanation:

the formula is

y-y1=m(x-x1)

y1 is -4 and x1 is -3 and m is slope

when the x or y is a negitive it then is added

The proportion EF/DF = BC/AC is true. Hence, option A is the accurate answer to this question.

We are given that the two triangles ΔABC and ΔDEF are similar.

According to the definition of a similar triangle, we know that the ratio of the corresponding sides is proportional and the corresponding angles are always congruent.

Since ΔABC and ΔDEF are similar, this implies that -

∠A corresponds to ∠D,

∠B corresponds to ∠E, and

∠C corresponds to ∠F.

Thus we can say -

EF/DF = BC/AC

AB/DF = DE/AC

AB/EF = DE/BC

Only option A satisfies the condition. Hence, the proportion EF/DF = BC/AC is true.

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The complete question is -

The triangle abc and triangle def are similar. Which proportion must be true?

It will take approximately 12.96 minutes for the oven to reach a temperature of at least 375 degrees.

What is Approximation?
Approximation is the act of estimating or finding a value that is close to the true or exact value, but not necessarily identical to it. In other words, an approximation is a rough calculation or an educated guess that is used when the exact value is not known or is too difficult to calculate. Approximations are commonly used in mathematics, science, engineering, and many other fields where exact values are often difficult to obtain or not required. The level of accuracy of an approximation depends on the method used and the degree of precision needed for the particular situation.

Let's use the information given to find the rate of temperature increase per minute.

Between the first two data points, the temperature increased by 3 degrees in 1 minute. Between the next two data points, the temperature increased by (112.5 - 3) = 109.5 degrees in (5 - 1) = 4 minutes. So the rate of temperature increase is (109.5/4) = 27.375 degrees per minute.

To find out how long it will take the oven to reach 375 degrees, we can use the formula:

time = (final temperature - initial temperature) / rate of temperature increase

In this case, the initial temperature is 3 degrees and the final temperature is 375 degrees. Substituting these values and the rate of temperature increase we calculated earlier, we get:

time = (375 - 3) / 27.375 = 12.96 minutes (rounded to two decimal places)

So it will take approximately 12.96 minutes for the oven to reach a temperature of at least 375 degrees.

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Answer:

D. 8/11

Step-by-step explanation:

why ?

the sum of the probabilities of all possible outcomes of an experiment must always be 1.

because there always has to be an outcome - one of the many possibilities.

the reality has to be part of this list of possibilities, and so, their total sum is 1 : the sure event.

the probability of A is 1/11.

of B is 1/11.

of C is 1/11.

A + B + C + D = 1

1/11 + 1/11 + 1/11 + D = 1

3/11 + D = 1

D = 1 - 3/11 = 11/11 - 3/11 = 8/11

Rudy has 3003 different ways to choose 6 toppings from a menu of 14 toppings if each topping can only be chosen once.

The number of ways to choose 6 toppings from a menu of 14 toppings where each topping can only be chosen once is 14!/(14-6)! = 14!/(8!) = 3003. This is because for the first topping, Rudy has 14 options, for the second topping he has 13 options, for the third topping he has 12 options, and so on. To calculate the total number of combinations, we use the formula n!/(n-r)! where n is the number of items and r is the number of items to choose. This formula gives us the number of ways to choose r items from a set of n items without regard to order, which is the number of combinations.

The formula for combinations is given by n!/(n-r)! where n is the number of items and r is the number of items to choose. Here, n = 14 (the number of toppings on the menu) and r = 6 (the number of toppings Rudy wants to choose). So, the number of combinations is 14!/(14-6)! = 14!/(8!).

The factorial (!) is the product of all positive integers up to that number. For example, 4! = 4 x 3 x 2 x 1 = 24.

So, 14! = 14 x 13 x 12 x ... x 2 x 1 = 87178291199, and 8! = 8 x 7 x 6 x ... x 2 x 1 = 40320.

Now, to calculate the number of combinations, we divide 14! by 8!: 14!/(8!) = 87178291199/40320 = 3003.

Therefore, Rudy has 3003 different ways to choose 6 toppings from a menu of 14 toppings if each topping can only be chosen once.

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The probability that the actress will need to attend more than 5 try-outs is approximately 0.478.

Since the outcomes of each try-out are independent,

As per the given information,

Number of try-out is 0.15

probability means the possibilities.

We can model the number of try-outs needed to get an offer as a geometric random variable with the probability of success p = 0.15.

Let X be the number of tryouts needed to get an offer.

Then, X follows a geometric distribution with parameter p=0.15, and the probability of needing to attend more than 5 try-outs is:

[tex]P(X > 5) &= 1 - P(X \leq 5)[/tex]

=[tex]1 - \sum_{k=1}^{5} P(X=k)[/tex]

= 1 [tex]- \sum_{k=1}^{5} P(X=k)[/tex]

= [tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]

=[tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]

=  0.478

Hence the number of possibility required to attend more than 5 try-outs is approximately 0.478.

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The population of the frogs will be double after 4 years when the current number of frogs were 100 and the annual rate of increment is 22%.

In the given question,

the current population of frogs are: 100

Annual rate of increase in population of frogs = 22%

Population required = double the current population = 2 x 100

                                                                                        = 200

Using the compound interest formula for amount, we can calculate the number of years in which the population of the frogs will be double:

Amount = principal ((1 + r%)^n) ,

here we will consider the amount to be population required, principal will be the current population, r is the annual rate of increment, and n is the time in years.

200 = 100 ((1 + 0.22) ^ n)

⇒ 200/100 = (1.22)^n

⇒ 2 = (1.22) ^ n

We plug digits in place of n and check for the closest result as 2.

We observe that (1.22)^4 = 2.2153 ≈ 2

Hence, we can say that the population of the frogs will be double after 4 years.

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The translation of a function and coordinates are given below..

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The following functions:

y = x²

y = 2x

The transformation is:

Translate two units to the left.

So,

y = (x - 2)²

y = 2(x - 2)

Translation 5 units up.

y = x² + 5

y = 2x + 5

The following coordinates:

Translate 2 units to the right.

(1, 4) = (1 + 2, 4) = (3, 4)

(5, 8) = (5 + 2, 8) = (7, 8)

Translation 5 units down.

(1, 4) = (1, 4 - 5) = (1, -1)

(5, 8) = (5, 8 - 5) = (5, 3)

Thus,

The translation of a function and coordinates are given above.

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Answer:

16 students are taking Physics and 12 are taking calculus

Step-by-step explanation:

40×40%=16 students taking Physics

40×30%=12 students taking calculus

16+12=28

40-28=12 students are taking both

If Armer Brown used and equal number of each bag then there will be 21 bags.

What is algebraic expression?

When we use numbers and words to solve a mathematical problem, we are using algebraic expressions.

Let's say that Armer Brown used x bags holding 20 oranges, y bags holding 10 oranges, and z bags holding 5 oranges. We know that he harvested 245 oranges, so we can write an equation:

20x + 10y + 5z = 245

We also know that he used an equal number of each bag, so we can write another equation:

x = y = z

We can use the second equation to substitute y and z with x:

20x + 10x + 5x = 245

Simplifying this equation, we get:

35x = 245

Dividing both sides by 35, we get:

x = 7

So he used 7 bags holding 20 oranges, 7 bags holding 10 oranges, and 7 bags holding 5 oranges.

In total, he used: 7 + 7 + 7 = 21 bags.

Therefore, There will be 21 bags.

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Answer:

38 yards of ribbon

Step-by-step explanation:

23.92 +.16x = 30

30-23.92 = 6.08

.16x =6.08

6.08/.16 = x

x =38 yards

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ m(t)=800(1.08)^t \qquad \begin{cases} t_1=2\\ t_2=4 \end{cases}\implies \cfrac{m(4)-m(2)}{4 - 2} \\\\\\ \cfrac{800(1.08)^4~~ - ~~800(1.08)^2}{2} ~~ \approx ~~ \cfrac{1088.39-933.12}{2}~~ \approx ~~\text{\LARGE 78} ~~ \frac{\$}{year}[/tex]

The value of the expression  5c−3d+11 is 22 when c is 7 and d is 8.

An expression is combination of variables, numbers and operators.

The given expression is 5c−3d+11

Five c minus three times of d plus eleven.

c and d are the variables in the expression

Given that value of c is seven and value of d is eight

c=7 and d=8

Now we have to find the value of the expression when c is 7 and d is 8

Plug in the value of c and d in expression.

5(7)-3(8)+11

Five times seven is 35 and three times of eight is 24, we get

35-24+11

22

Hence, the value of the expression  5c−3d+11 is 22 when c is 7 and d is 8.

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Complete question is given below,

5c−3d+115, find the value of expression when c=7 and d=8

The cost of the fourth book is 3500. To find the cost of the fourth book, we used the formula Average Price = Total Cost / Number of Items and calculated the cost to be 3500.

Formula: Average Price = Total Cost / Number of Items.Calculation: Since Kofi bought 4 books at an average price of 2500, the total cost of the 4 books must be 4 x 2500 = 10000. Since the total cost of 3 books was 6500, the cost of the fourth book must be 10000 - 6500 = 3500.In conclusion, the cost of the fourth book is 3500. To find the cost of the fourth book, we used the formula Average Price = Total Cost / Number of Items and calculated the cost to be 3500.

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The sample is approximately 50,000 years old, as the amount of Carbon-14 in it is lower than that of a contemporary sample.

1) Calculate the ratio of Carbon-14 in the sample compared to a contemporary sample.

Ratio = (60/100) = 0.6

2) Calculate the number of half-lives since the sample was alive.

Number of half-lives = ln(0.6) / ln(0.5) = 0.69897

3) Calculate the age of the sample.

Age of sample = (0.69897 x 5730) = 4020 years

60% of the Carbon-14 identified in a sample taken from a waste site close to the Strait of Magellan was present in the sample from the trash deposit. We must first determine the sample's carbon-14 ratio in relation to a more recent sample in order to determine the sample's age. This ratio is equivalent to the sample's 60% carbon-14 content, or 0.6, when divided by 100. The number of half-lives since the sample has been alive may then be determined by taking the natural log of the ratio and dividing it by the natural log of 0.5, which is 0.69897. By dividing the quantity of half-lives by the 5730-year half-life of carbon-14, we may finally determine the sample's age.

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1) The area of the first figure is 99 square units, 2) Total area = Area of rectangle + Area of triangle = 30 + 6 = 36 square units, 3) Total area = Area of rectangle + Area of triangle = 13.5 + 10.5 = 24 square units.

i) The first figure is a trapezium with height 9 units, bottom base 9 units and top base 13 units.
To find the area of the trapezium, we can use the formula:
Area of trapezium = h/2[a + b]
where h is the height, a and b are the lengths of the parallel sides.
Substituting the given values, we get:
Area = 9/2[13 + 9] = (9 x 22)/2 = 99 square units
Therefore, the area of the first figure is 99 square units.

ii) The second figure is composed of a rectangle with sides 6 and 5 units and a right-angled triangle with base 3 and height 4 units.
To find the area of the rectangle, we can use the formula:
Area of rectangle = length x breadth
Substituting the given values, we get:
Area of rectangle = 6 x 5 = 30 square units
To find the area of the right-angled triangle, we can use the formula:
Area of right-angled triangle = 1/2 x base x height
Substituting the given values, we get:
Area of right-angled triangle = 1/2 x 3 x 4 = 6 square units
Therefore, the total area of the second figure is:
Total area = Area of rectangle + Area of triangle
= 30 + 6 = 36 square units

iii) The third figure is made up of a rectangle with length 9 and breadth 1.5 units and a right-angled triangle with base 6 (9-3) and height 3.5 (5-1.5) units.
To find the area of the rectangle, we can use the formula:
Area of rectangle = length x breadth
Substituting the given values, we get:
Area of rectangle = 9 x 1.5 = 13.5 square units
To find the area of the right-angled triangle, we can use the formula:
Area of right-angled triangle = 1/2 x base x height
Substituting the given values, we get:
Area of right-angled triangle = 1/2 x 6 x 3.5 = 10.5 square units
Therefore, the total area of the third figure is:
Total area = Area of rectangle + Area of triangle
= 13.5 + 10.5 = 24 square units
Thus, the areas of all three figures have been determined.

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Complete question is in the image provided.

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[tex] \: [/tex]

hope it helps! :)

━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer:

[tex] \sf \: n = - 3[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of n.

The equation is,

→ 2 - 2n = 3n + 17

Then the value of n will be,

→ 2 - 2n = 3n + 17

→ 2 - 17 = 3n + 2n

→ -15 = 5n

→ 5n = -15

→ n = -15 ÷ 5

→ [ n = -3 ]

Hence, the value of n is -3.

Most profitable investment option for retirement depends on your individual circumstances, such as your risk tolerance, time horizon, and investment goals. It's essential to consult with a financial advisor who can help you create a personalized retirement plan that meets your specific needs and goals.

Retirement planning is crucial to ensure that you have enough money to live comfortably during your golden years. The amount of money you will need in retirement depends on several factors, including your lifestyle, health, and expected lifespan.

However, a general rule of thumb is that you should aim to have saved 10-12 times your current annual income by the time you retire. Assuming a retirement age of 67, if you earn $50,000 per year, you would need to have saved between $500,000 and $600,000 by the time you retire. This amount may vary depending on your specific circumstances, such as your expected retirement lifestyle, expected lifespan, and anticipated expenses.

When it comes to investment options for retirement, there are several options that can be financially beneficial. Some of the most profitable investment options for retirement include:

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