what is difference between fraction and rationals

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Answer:

12

Step-by-step explanation:

(2)4 + (1+3)

8 + 4

12

Hey there!

(2)4 + (1 + 3)

= 2(4) + (1 + 3)

= 2(4) + 1 + 3

= 8 + 1 + 3

= 8 + 4

= 12

Therefore, your answer is: 12

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The AFC represents the fixed portion of the total cost, while the difference between ATC and AFC represents the variable cost per unit.

To determine the relationship between average fixed cost (AFC) and average total cost (ATC) at a quantity of output of 1,000 units, we need to understand the formulas for AFC and ATC.

AFC is calculated by dividing total fixed cost (TFC) by the quantity of output (Q). ATC is calculated by dividing total cost (TC) by the quantity of output (Q). Mathematically, we have:

AFC = TFC / Q

ATC = TC / Q

Given that AFC is $8 at a quantity of output of 1,000 units, we can substitute the values into the AFC formula:

$8 = TFC / 1,000

Multiplying both sides of the equation by 1,000, we find:

TFC = $8,000

Now, we are given that ATC is $12 at the same level of output. Substituting the values into the ATC formula, we have:

$12 = TC / 1,000

Multiplying both sides of the equation by 1,000, we find:

TC = $12,000

To summarize:

Total fixed cost (TFC) = $8,000

Total cost (TC) = $12,000

Therefore, it follows that the difference between AFC and ATC lies in the variable cost component. The AFC represents the fixed portion of the total cost, while the difference between ATC and AFC represents the variable cost per unit.

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The union of the sets is E ∪ F = (-∞, 3] or (6, ∞) and the intersection of the sets E ∩ F =  ∅ (null sets) is in interval notation.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have:

E and F are sets of real numbers defined as follows. E={v | v ≤ 3} F={v | v > 6}

E ∪ F = (-∞, 3] or (6, ∞)

E ∩ F =  ∅ (null sets)

Thus, the union of the sets is E ∪ F = (-∞, 3] or (6, ∞) and the intersection of the sets E ∩ F =  ∅ (null sets) is in interval notation.

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Answer:

If a is negative or zero  there are no real solutions

Step-by-step explanation:

y=ax^2-8

Set equal to zero to find the solution

0 =ax^2-8

Add 8 to each side

8 = ax^2

Divide by a  a cannot be zero or we cannot divide by it

8/a = x^2

Take the square root of each side

sqrt(8/a) = sqrt(x^2)

We need 8/a to be positive for it to have real solutions

That means a has to be positive

If a is negative or zero  there are no real solutions

Answer:

10

Step-by-step explanation:

dived them

y in equation 1

-28=3 is false, therefore the system of equations has no solution

There are five whole numbers between 1 and 150 that have exactly 3 different factors. Whole numbers between 1 and 150 with exactly 3 different factors must be the square numbers whose square roots are prime.

To find the complete list begin counting...

skip 1, not prime;

2 is prime and 2 squared is 4;

3 is prime and 3 squared is 9;

skip 4 b/c it is not prime;

5 is prime and 5 squared is 25;

6 not prime;

7 prime and 7 squared is 49;

8 not prime;

10 not prime;

11 prime and squared is 121;

12 is not prime;

13 prime, but squared it is greater than 150.

The complete list is 4, 9, 25, 49, and 121. 4 has 1, 2, 4;

9 has 1, 3, 9;

25 has 1, 5, 25 ;

49 has 1, 7, 49 ;

121 has 1, 11, 121.

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To represent the final price (Px) of the items purchased, we first apply the 30% holiday sale discount and then the 15% off coupon. Let's find the correct function:

1. Apply the 30% holiday sale: Price becomes 0.7x (as 100% - 30% = 70%)
2. Apply the 15% off coupon: Final price becomes 0.85 * 0.7x (as 100% - 15% = 85%)

Now, multiply 0.85 by 0.7, which equals 0.595.

Therefore, the function representing the final price is Px(x) = 0.595x.

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Answer:

$59.80

Step-by-step explanation:

After addressing the issue at hand, we can state that by function Katherine now has 28 quarters.

Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.

here, we have,

Let's represent the unknown quantities with variables.

Let d be the number of dimes Katherine possesses.

Let q represent Katherine's number of quarters.

We can deduce from the problem:

Equation 1: Total dimes and quarters value = $8.60 0.10d + 0.25q = 8.60

Number of quarters = Number of dimes + 12 q = d + 12 Equation 2:

Now we can plug equation 2 into equation 1 to eliminate q and find d:

0.10d + 0.25(d + 12) = 8.60

Katherine now has 16 dimes.

We can use equation 2 to calculate the number of quarters:

q = d + 12 = 16 + 12 = 28

Katherine now has 28 quarters.

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complete question:

Katherine has $8.60 in dimes and quarters. If she has twelve more quarters than dimes, how many dimes does she have? How many quarters does she have?

The function that could represent g(x) is (c) g(x) = f(x) - 5

The figure of the graph that completes the question is added as an attachment

From the attached graph,  we have the equation of the function to be

y = f(x)

Also, the graph of the function f(x) has its intercept to be

y-intercept of f(x) = 3

From the question, we have

y-intercept of g(x) = -2

Subtract the intercepts

Difference = y-intercept of g(x) - y-intercept of f(x)

So, we have

Difference = -2 - 3

Evaluate

Difference = -5

The function g(x) is then represented as

g(x) = f(x) + Difference

So, we have

g(x) = f(x) - 5

Hence, the function g(x) is g(x) = f(x) - 5

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Answer: Isosceles Triangle (if that was what you were looking for)

Step-by-step explanation:

Answer:

12z + 6

z = -1/2

Step-by-step explanation:

y(3z+2)

4(3z+2)-2

(12z + 8) -2

12z + 8 - 2

12z + 6

If going further,

12z = -6

z = -1/2

Answer: x^3+x^2y–4y–4x  = (x-2)(x+2)(x+y)

The value of f(-4) in the function is -87

A function is an equation for which any x that can be put into the equation will produce exactly one output such as y out of the equation. It is represented as y = f(x)

Where x is an independent variable and y is a dependent variable.

In the given question, the function given is;

f(x) = -4x² + 3x - 11

for f(-4), we need to substitute the value of -4 into anywhere we have x.

f(-4) = -4(-4)² + 3(-4) - 11

f(-4) = -64 - 12 - 11

f(-4) = -87

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Answer:

Step-by-step explanation:

2y = -10x - 2

y = -5x - 1

y - 12 = -5(x - 0)

y - 12 = -5x + 0

y = -5x + 12

Answer:

Line A?? im not rlly sure

Step-by-step explanation:

The volume of the solid is (11π/3) cubic units.

We have,

To find the volume of the solid obtained by rotating the region bounded by y = x and y = x^2 about the line x = -3, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is given by:

V = 2π ∫ [a, b] x h(x) dx,

where [a, b] is the interval of integration, x represents the variable of integration, and h(x) represents the height of the shell at each value of x.

In this case, we want to rotate the region bounded by y = x and y = x² about the line x = -3.

Since we are rotating about a vertical line, the height of the shell at each value of x will be given by the difference between the x-coordinate of the curve and the line of rotation:

h(x) = (x - (-3)) = x + 3.

To find the interval of integration, we need to determine the x-values where the two curves intersect.

Setting x = x², we have:

x = x²,

x² - x = 0,

x (x - 1) = 0.

This gives us two intersection points: x = 0 and x = 1.

Therefore, the interval of integration is [0, 1].

Now we can set up the integral to find the volume:

V = 2π ∫ [0, 1] x (x + 3) dx.

Evaluating this integral, we have:

V = 2π ∫ [0, 1] (x² + 3x) dx

= 2π [x³/3 + (3/2)x²] evaluated from 0 to 1

= 2π [(1/3 + 3/2) - (0/3 + 0/2)]

= 2π [(2/6 + 9/6) - 0]

= 2π (11/6)

= (22π/6)

= (11π/3).

Therefore,

The volume of the solid is (11π/3) cubic units.

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Answer:

Step-by-step explanation:

-i= -i

-i^2= 1

-i^3= -i * 1 = -i

-i^4= 1 * (-1)  = -1

-i^5= -i

-i^6= 1

Answer: -1

Step-by-step explanation:

Actually, 0 degrees is not a counterexample for the expression sin(y)*tan(y) = cos(y).

To see why, let's substitute y = 0 degrees into the expression:

sin(y)*tan(y) = cos(y)

sin(0)*tan(0) = cos(0)

0*tan(0) = 1

0 = 1

As we can see, the equation does not hold for y = 0 degrees. However, this does not make 0 degrees a counterexample, because 0 degrees is not in the domain of the tangent function.

The tangent function is undefined at odd multiples of 90 degrees (e.g. 90, 270, etc.), because at those angles the denominator of the tangent function becomes zero. Therefore, we cannot substitute y = 0 degrees into the expression sin(y)*tan(y) = cos(y), because it would result in division by zero.

In summary, 0 degrees is not a counterexample for the expression sin(y)*tan(y) = cos(y), because it is not in the domain of the tangent function.

Answer:

See explanation

Step-by-step explanation:

Here is the complete question:

Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs $3.25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30 before tax. The restaurant only sells pancakes in stacks of 4 pancakes for $5.50 . Let S represent the number of stacks of pancakes that Benjamin buys. What is the largest number of pancakes that Benjamin can afford?

Given:

Cost of chocolate milk = $3.25

Maximum bill that Benjamin wants before tax = $30

Cost of stack of 4 pancakes = $5.50

Let S be the number of stacks of pancakes that Benjamin buys

Solution:

Cost per stack of pancakes = $5.50  

Cost of S number of stacks of pancakes = S*5.50  = 5.50 S

So benjamin will spend money on 1 chocolate milk and S number of stacks of pancakes

Compute the total money spent by Benjamin:

Cost of chocolate milk + cost per stack of pancakes = 3.25 + 5.50 S

Maximum bill that Benjamin wants is $30 So,

The total money should be less than equal to the maximum bill that benjamin wants i.e. less than or equal to 30. So it is represented as:

3.25 + 5.50S ≤ 30  ----- (1)

Now using (1) we can find the largest number of pancakes that  Benjamin can afford :

3.25 + 5.50S ≤ 30

5.50S ≤ 30 - 3.25    

subtract 3.25 from 30

5.50S ≤ 26.75

Divide by 5.50

S ≤ 4.863636

S ≤ 4.86

S≤ 4 approx

Since the restaurant only sells pancakes in stacks of 4 pancakes so,

4 stacks = 4 *4 =  16

So the largest number of pancakes that Benjamin can afford are 16.

If we do not round off the the value stacks then we get:

4.86 stacks = 4.86 *4 =  19.44 pancakes

So the largest number of pancakes that Benjamin can afford are 19

Answer:

what is it asking?

Step-by-step explanation:

if its how many cubes it needs for it to fill up its 9

Answer:

Step-by-step explanation:

Candice = 25mph for 4 hours.

Candice has driven= 25 * 4= 100miles.

Liz =50mph

Liz time to catch up to candice= 50 * 2= 100miles.

Therefore, It would have taken Liz two hours to catch up with Candice

Answer:  # 4.) 9.4

#5.) 10.2 cm  

#6.) 5 inches .

Step-by-step explanation: Assuming that a right triangle is expected, use the Pythagorean Theorem to calculate the third side: a² + b² = c²

\(5^{2}+8^{2}=89\)  Then take the square root of 89. A calculator is handy for most of these!

√89 = 9.433981 .  Round to 9.4

\(2^{2}+10^{2}=104\)

√104 = 10.1980  Round to 10.2 Remember to include the units, cm in the answer.

Memorize this one:

Given side lengths of 3 & 4, the hypotenuse is 5!

3² + 4² = 5²   Called a "Pythagorean Triple"

9 + 16 = 25

The square on the hypotenuse is a perfect square of 5

No calculator necessary, and you are likely to see this ratio in other questions.

Answer:

B

Step-by-step explanation:

They are using square root form which makes a triangle.

Answer:

10x4=40

Step-by-step explanation:

se calcula multiplicado la base por la altura luego de haber multiplicado esto (10 x 4) el resultado es 40

Answer: (x+2)(x+3)

Step-by-step explanation:

Find the multiples of 6 and then see which two numbers adds up to 5

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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The approximate net area bounded by the graph of f and the x-axis on the interval using the midpoint Riemann sum is 0.098π.

b. Calculation of the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n=5: Given that the function f(x) = sin5x:[π/5,2π/5] on the given interval, we have to approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n = 5.

Riemann Sum: Riemann sum is a method of approximating the area under the curve of a function. The area under the curve can be approximated by dividing the area into smaller areas of known shapes. For each of these areas, a function value is computed, and the sum of all these values is the Riemann sum. Approximation using the left Riemann sum: In the left Riemann sum, we use the function value at the left endpoint of each subinterval to determine the area of the rectangle. The left Riemann sum for the given interval is as follows: \($$\begin{aligned} L_5&=\frac{\pi}{5}\left[\sin(\frac{\pi}{5})+\sin(\frac{2\pi}{5})+\sin(\frac{3\pi}{5})+\sin(\frac{4\pi}{5})\right]\\ &=\frac{\pi}{5}\left[0.3090+0.9511+0.5878-0.5878\right]\\ &=0.4704\pi \end{aligned}$$\\\)

Therefore, the approximate net area bounded by the graph of f and the x-axis on the interval using the left Riemann sum is 0.4704π.

Approximation using the right Riemann sum: In the right Riemann sum, we use the function value at the right endpoint of each subinterval to determine the area of the rectangle. The right Riemann sum for the given interval is as follows:\($$\begin{aligned} R_5&=\frac{\pi}{5}\left[\sin(\frac{2\pi}{5})+\sin(\frac{3\pi}{5})+\sin(\frac{4\pi}{5})+\sin(\pi)\right]\\ &=\frac{\pi}{5}\left[0.9511+0.5878-0.5878+0\right]\\ &=0.1902\pi \end{aligned}$$\)

Therefore, the approximate net area bounded by the graph of f and the x-axis on the interval using the right Riemann sum is 0.1902π. Approximation using the midpoint Riemann sum: In the midpoint Riemann sum, we use the function value at the midpoint of each subinterval to determine the area of the rectangle. The midpoint Riemann sum for the given interval is as follows: \($$\begin{aligned} M_5&=\frac{\pi}{5}\left[\sin(\frac{\pi}{5}+\frac{\pi}{10})+\sin(\frac{2\pi}{5}+\frac{\pi}{10})+\sin(\frac{3\pi}{5}+\frac{\pi}{10})+\sin(\frac{4\pi}{5}+\frac{\pi}{10})\right]\\ &=\frac{\pi}{5}\left[0.809+0.588+0.309-0.809\right]\\ &=0.098\pi \end{aligned}$$\).

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Answer:

(x)= 2, 5, 8, 11

Use the formula  

a n  =  a 1  +  d  ( n  −  1 )

to identify the arithmetic sequence.

a n  =  3 n  −  1

f(x)= 5, 11 17, 23

Use the formula  

a n  = a 1  +  d  ( n − 1 )

to identify the arithmetic sequence.

a n  =  6n  −  1

x      f(x)

2      5

5      11

8      17

11      23

Nothing further can be done with this topic. Please check the expression entered or try another topic.

2 ,   5 ,   8 ,   11  

5 ,   11 ,   17 ,   23

Step-by-step explanation:

Write a rule for the linear function in the table.

x;     f(x)

2      8

5     17

5      11

11    23

A; f(x) = x + 5

B;f(x) = x + 1

C;f(x) = 2x + 1

D;f(x) = –2x – 1

If all your solutions are  

A; f(x) = x + 5

B;f(x) = x + 1

C;f(x) = 2x + 1

D;f(x) = –2x – 1

None of the above will work with the data set you have presented.

Answer:

It’s 137.39

Step-by-step explanation: