5) Margot buys a 5 litre bottle of lemonade for £2.30. She divides it into glasses. She
pours 250ml into each glass. She sells all the glasses at 25p each.
Work out her percentage profit.

The values of the functions are:

a. When x =-4 then f(x) =  -x+4

b. When x = -2 then f(x) =  -x+4

c. When x = -1 then f(x) =  -x+4

d. When x=1/2 then f(x) = 3

e. When x = 2 then f(x) =  2x-5

Given, g(x) = {-x+4 , if x≤-1

                      3 ,   if -1≤x<2

                      2x-5, if x≥2 }

a. when x = -4, f(x) = ?

-4 comes under the condition x≤-1.

therefore, when x=-4 ⇒ f(x) = -x+4

f(-4) = -4+4 = 0

b. when x=-2, f(x)= ?

Again -2 comes under the condition if x≤-1

therefore when x=-2 ⇒ f(x) = -x+4

f(-2) = -2+4 = 2

c. when x=-1, f(x) = ?

-1 comes under the condition if x≤-1

therefore, when x=-1 then f(x) = -x+4

f(-1) = -1+4 = 3

d. when x=1/2 , f(x) = ?

1/2 comes under the condition, if -1≤x<2

therefore, when x=1/2 then f(x) = 3.

e. when x=2, f(x) = ?

2 comes under the condition, if x≥2

therefore, when x=2 then f(x)= 2x-5.

hence we get the required results of the given functions.

Learn more about Functions here:

brainly.com/question/2328150

#SPJ9

Answer:

A person will pay $5.37

Step-by-step explanation:

6.8 pounds of bananas x $0.79 per pound = $5.37.

I hope this helps and have a blessed day! :)

Answer:

D

Step-by-step explanation:

The number of questions is 20; it's the total points that are worth 50 and the question is asking for number of questions

Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

Step-by-step explanation:

What does it mean converse in geometry?

The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."

So, in the figure below, if we can choose n║m, then ∠1≅∠2

Since  n║m , by the corresponding Angles Postulate,

∠1≅∠2.

Therefore, by the definition of congruent angles,

m∠1=m∠2

Since ∠1 and ∠2 form a linear pair, they are supplementary, so

m∠1+m∠2=180°.

Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

Learn about more information https://brainly.in/question/14313548

#SPJ9

The complementary solution is Ус = C₁е¯ + C₂е¯ -6x

Consider the differential equation

=y" + 7y' + 6y = 30...(1)

Rewrite the equation,(D² + 7D + 6)y = 30 where

d /D = dx

Auxiliary equation is,

f(m) = 0

3 m³ +7m+6=0

m² + 6m+m+6=0

m(m+6) +1(m+6) = 0

(m +6)(m + 1) = 0

m = −1, −6 -6

Hence,

The complementary solution is Ус = C₁е¯ + C₂е¯ -6x

To know more about "Differential Equation"

Refer this link:

https://brainly.com/question/14617716

#SPJ4

The correct option is (b) sample size.

In the formula for calculating the standard deviation, the letter n represent  sample size.

What is standard deviation?

Standard deviation is a statistical standard measure in finance that, when applied to an investment's annual rate of return, sheds light on its historical volatility.

Some key features regarding the standard deviation are-

A square root of a value deduced from correlating data points to a population's collective mean is used to calculate standard deviation. The formula is:

Standard Deviation = [tex]\sqrt{\frac{summation n to i=1 (x_{i}-bar x )}{n-1} }[/tex]

Where,

[tex]x_{i}[/tex]= value of the i th point the the given data set.

[tex]barx[/tex]= mean value

n = total number of data points.

Thus, the standard deviation, on the other hand, determines all ambiguity as risk, even when it is in the investor's favor, like above-average returns.

Learn more about Standard Deviation at:

https://brainly.com/question/8511265

#SPJ4

The value of the function f(x) = 2x/(2x + 3).

A function is defined as a relationship between a set of inputs that each have one output.

Now, as per the question, the functions are give as;

h(x) = (2x + 3)/x

g(x) = 2/x

And, g(f (x) ) = h(x) =  (2x + 3)/x  ......(equation 1)

To estimate the value of f (x); Substitute x for f(x)

g(f (x) ) = 2/f (x)     ......(equation 2)

Equation (equation 1 and 2).

2/f (x) =  (2x + 3)/x

f (x) = 2x/ (2x + 3)

Thus, the value of the function f (x) = 2x/ (2x + 3).

To know more about the function, here

https://brainly.com/question/25638609

#SPJ4

The correct question is-

The function h (x) = StartFraction 2 (x + 3) Over x EndFraction is a result of the composition (g compose f) (x). If g (x) = StartFraction 2 over x EndFraction, what is f(x)?

Answer:

Step-by-step explanation:

11+(19+6)= (11+19)+6 so it's the associative property

The solution of the expression ( 9y² - 4x )( 9y ² + 4x) will be 81y⁴ - 16x².

Expression in maths is defined as the collection of 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.

Given expression ( 9y² - 4x )( 9y ² + 4x) will be solved as below:-

Use the formula:- ( a + b ) ( a - b ) = a² - b²

a = 9y²

b = 4x

( 9y² - 4x )( 9y ² + 4x ) = ( 9y² )² - ( 4x )²

Therefore, solution of the expression ( 9y² - 4x )( 9y ² + 4x) will be 81y⁴ - 16x².

To know more about an expression follow

https://brainly.com/question/1524138

#SPJ4

Answer:

1647

Step-by-step explanation:

Given the following information:

Length of traffic = 8 miles

Average Length of vehicles on the road :

Cars = 14.5 feets

Trucks = 21 feets

18 Wheeler tractor = 73 Feets

% distribution of the different vehicles :

Cars = 70% = 0.7

Trucks = 20% = 0.2

18 wheeler tractor = 10% = 0.1

Distance between vehicles = 4feets

Number of vehicles stuck in the traffic :

Let number of vehicles = v

Summation of (number of vehicles * length of each vehicle) + distance between each vehicle = Length of traffic

Total distance between each vehicle = 4(v-1)

(0.7v * 14.5) + (0.2v * 21) + (0.1v * 73) + 4(v - 1) = 8 miles

1 mile = 5280

8 miles = (5280 * 8) = 42,240

10.15v + 4.2v + 7.3v + 4v - 4 = 42240

25.65v = 42240 + 4

25.65v = 42244

v =42244 / 25.65

v = 1646.939

v = 1647.

Answer:

-(4/3) is ans by using slope formula

A surveyor asks a friend her opinion and then asks for the names of five friends for obtain additional opinions. This is an example of convenience sampling.

Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.

An elementary illustration of a convenience sampling technique is when businesses hand out their marketing materials and conduct interviews with randomly chosen participants at a mall or on a busy street.

Learn more about sampling on:

https://brainly.com/question/17831271

#SPJ1

The homogeneous linear ODE

[tex]y^{(4)} + y''' + y'' = 0[/tex]

has characteristic equation

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

with a double root at [tex]r=0[/tex] and two complex roots

[tex]r^2 + r + 1 = 0 \implies r = -\dfrac{1 \pm i\,\sqrt3}2[/tex]

Hence the characteristic solution is

[tex]y = C_1 e^{0x} + C_2x e^{0x} + C_3 e^{((-1/2)-i(\sqrt3/2))x} + C_4 e^{((-1/2)+i(\sqrt3/2))x}[/tex]

[tex]y = C_1 + C_2x \\\\ ~~~~~~~~~~ + C_3 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) - i\, \sin\left(\dfrac{\sqrt3}2x\right)\right) \\\\ ~~~~~~~~~~ + C_4 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) + i\,\sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]

[tex]y = C_1 + C_2x + C_3 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_4 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right)[/tex]

Answer:

nothing there

Step-by-step explanation:

Step-by-step explanation:

if you did not leave anything out, all we can do is

T = CB - 6

T + 6 = CB

C = (T + 6)/B

Answer:

x=-10/3

Step-by-step explanation:

(2x+4)=-4(-2x-6)

distribute -4 to (-2x-6) by multiplying 

negative multiplied by a negative is a positive 

8x+24=2x+4

subtract 24 from each side 

8x=2x-20

subtract 2x from each side 6x=-20

divide both sides by 6 

-20/6 

simply to -10/3 or -3 1/3 or -3.3

x=-10/3

hope this helps! if you have any questions please ask!

Answer:

Ok so "X" will ALWAYS be the first number in a ordered pair so in this case 3 WILL be the "X" value 5 will be the "Y" value. "X" is the Horizontal line on the graph you will always start with "X" so you will go over 3 times and up 5  I'm making this complicated but pretty much all you need to know is that "X" is 3

Note: I hope you have a good day and I hoped this helped! :))

The vertical asymptote of the function = ln(x-6) + 5 is option C: x = 6.

The given function is f(x) = ln(x - 6) + 5.

A vertical asymptote is a vertical line that a function approaches but never crosses as it approaches infinity or negative infinity. For a logarithmic function like ln(x), the domain of the function is restricted to positive values only since the natural logarithm is undefined for non-positive arguments.

In the given function, we have f(x) = ln(x - 6) + 5. To find the vertical asymptote, we need to identify the value of x that would make the argument of the natural logarithm equal to zero.

Let's set the argument of the natural logarithm to zero:

x - 6 = 0

Now, solve for x:

x = 6

Thus, the value of x that would make the argument of the natural logarithm zero is x = 6.

So, the correct answer is option C: x = 6.

This means that the vertical asymptote of the function f(x) = ln(x - 6) + 5 is the vertical line x = 6. As x approaches 6 from either side (but never equaling 6), the function's values approach infinity. Similarly, as x approaches negative infinity, the function's values also approach infinity. The function never crosses the vertical line x = 6.

To know more about Function here

https://brainly.com/question/31056852

#SPJ2

The volume required for a 5% solution is 5.7 L, while a 40% solution requires 4.3 L for the experiment.

A percentage is a fraction of a whole represented as a number ranging from 0 and 100.

The equation should be as follows:

If 'x' is the volume of a 40% solution, then the volume of a 5% solution is:

10 L = 40% solution volume + 5% solution volume

10 L = x + 5% volume of solution

10 L - x = 5% solution volume

The volume would then be calculated as follows:

(volume 20% × concentration 20%) = (volume 40% × concentration 40%)           + (volume 5% × concentration 5%)

10 litre × 20% = x litre × 40% + (10- x) litre × 5%

10 L ×  20% = x litre  × 35% + 10 litre × 5%

x litre × 35 = 10 L × 20 - 10 L × 5

                 = 10 L × 15

x litre = 10 L × 15/35

x litre = 4.28 L

x litre = 4.3 L

40% solution volume = 4.3 L

The volume of 5% solution is equal to 10 L - 4.3 L = 5.7 L.

Thus, the volume of 5% solution  requires is 5.7 L and volume of 40% solution required is 4.3 L.

To know more about percentage, here

https://brainly.com/question/24304697

#SPJ9

Answer:

[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]

Step-by-step explanation:

When writing an algebraic fraction as an identity, if its denominator has repeated linear factors, the power of the repeated factor indicates how many times that factor should appear in the partial fractions.

Write out the fraction as an identity:

[tex]\begin{aligned}\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A}{x}+\dfrac{B}{(x+1)}+\dfrac{C}{(x+1)^2}\\\\\implies \dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A(x+1)^2}{x(x+1)^2}+\dfrac{Bx(x+1)}{x(x+1)^2}+\dfrac{Cx}{x(x+1)^2}\\\\\implies 5x^2+20x+16 & \equiv A(x+1)^2+Bx(x+1)+Cx\end{aligned}[/tex]

Calculate the values of A and C using substitution:

[tex]\begin{aligned}\textsf{When }x=0 \implies 16 & =A(1)+B(0)+C(0) \implies A=16\\\\\textsf{When }x=-1 \implies 1 & =A(0)+B(0)+C(-1) \implies C=-1\end{aligned}[/tex]

Substitute the found values of A and C and expand the identity:

[tex]\begin{aligned}\implies 5x^2+20x+16 & \equiv 16(x+1)^2+Bx(x+1)-x\\& \equiv 16x^2+32x+16+Bx^2+Bx-x\\& \equiv (16+B)x^2+(31+B)x+16\\\end{aligned}[/tex]

Compare the coefficients of the x² term to find B:

[tex]x^2 \textsf{ term } \implies 16+B =5\implies B & =-11[/tex]

Replace the found values of A, B and C in the original identity:

[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]

Learn more about partial fractions here:

https://brainly.com/question/27773545

Answer:

e = 40h

After eleven hours, she will earn $440.00

Step-by-step explanation:

Let e = earnings

Let h = hours

e = 40h  She earns 40 for every hours that she tutors.  If she tutors for 11 hours, you would substitute aa for h to calculate her earnings.

e = 40(11)

e = 440

Answer:

Step-by-step explanation:

2x+18=6y

2x=6y−18

(2x)/2=(6y−18)/2

x=3y−9

Answer:

Step-by-step explanation:

2x  +  18+− 18=6y  +  −18

2x  =  6y − 18

2x / 2= 6y −18 / 2

x  =  3y −9

The numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.

It should be noted that even numbers can be divided by 2.

The multiple of 3 in the numbers are 12 and 18 that can be divided by 2 as well.

Therefore, the numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.

Learn more about set on:

brainly.com/question/28365114

#SPJ1

Mr. Drew needs woods of a total length of 32 feet to make the sides of the sandbox.

So,

Therefore, Mr. Drew needs woods of a total length of 32 feet to make the sides of the sandbox.

Know more about squares here:

https://brainly.com/question/25092270

#SPJ4

Answer:

x = - 1 and x = 5

Step-by-step explanation:

the zeros are the values of x where the graph crosses the x- axis

the graph crosses the x- axis at x = - 1 and x = 5 , then the zeros are

x = - 1 and x = 5

Answer:

Step-by-step explanation:

1. a. coordinates of polygon B: (-2, 1), (-4, 1), (-2, 3), (-4, 4)

b. coordinates of polygon C: (-2, -1), (-4, -1), (-2, -3), (-4, -4)

c. coordinates of polygon D: (-2, 1), (-4, 1), (-2, 3), (-4, 4) -> same as polygon B because you after reflecting B to C, they are asking you basically reflect it back to B

2. C (-2, -1)

Answer: b) 9

Step-by-step explanation: if you take 3 * 9 it = 27 take that minus 6 that = 21

Answer:

n = 18

Step-by-step explanation:

The sides in a regular polygon are equal in length.

⇒ BC = CD

If BC = CD then ΔDCB is an isosceles triangle.

As the base angles of an isosceles triangles are equal:

⇒ ∠DBC = ∠BDC = 10°

Interior angles in a triangle sum to 180°.

⇒ ∠DBC  +∠BDC + ∠DCB = 180°

⇒ 10° + 10° + ∠DCB = 180°

⇒ 20° + ∠DCB = 180°

⇒ ∠DCB = 180° - 20°

⇒ ∠DCB = 160°

Therefore, the interior angle of the regular polygon is 160°.

The interior angles of a regular polygon are equal in size.

[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Interior angle of a polygon}\\\\$\dfrac{(n-2) \times 180^{\circ}}{n}$\\\\where $n$ is the number of sides.\\ \end{minipage}}[/tex]

To find the number of sides, equate the formula to the found value of the interior angle and solve for n:

[tex]\begin{aligned}\implies\dfrac{(n-2) \times 180^{\circ}}{n} & =160^{\circ}\\(n-2) \times 180^{\circ} & =n \times 160^{\circ}\\ 180(n-2) & = 160n\\180n-360 & = 160n\\180n & = 160n+360\\180n-160n & = 360\\20n & = 360\\n &= \dfrac{360}{20}\\n & =18\\\end{aligned}[/tex]

Therefore, the regular polygon has 18 sides.