Write the expression in complete factored form.
5a(b + 1) + 3(b + 1) = please help!

a) Graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380

b) The maximum profit of $5200 achieved.

Selling profit is the profit that a business makes on the sale of its products or services. It is the difference between the selling price and the cost of product.

a) Let x be the number of boards of mahogany sold and y be the number of boards of black walnut sold. Then, the constraints of the problem can be represented by the following system of inequalities:

x ≥ 0 (non-negative constraint)

y ≥ 0 (non-negative constraint)

x ≤ 260 (maximum number of mahogany boards available)

y ≤ 320 (maximum number of black walnut boards available)

x + y ≤ 380 (maximum number of boards that can be sold)

To graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380 on a coordinate plane and shade the feasible region that satisfies all of the constraints. The feasible region is the area that is bounded by these lines and includes the origin (0, 0).

b) The profit function P(x, y) can be defined as follows:

P(x, y) = 20x + 6y

To maximize the profit, we need to find the values of x and y that satisfy all of the constraints and maximize the profit function P(x, y).

One way to do this is to use the corner-point method. We can evaluate the profit function at each of the corners of the feasible region and find the corner that gives the maximum profit.

The corners of the feasible region are (0, 0), (0, 320), (260, 0), and (120, 260).

P(0, 0) = 0

P(0, 320) = 6(320) = 1920

P(260, 0) = 20(260) = 5200

P(120, 260) = 20(120) + 6(260) = 4720

Therefore, the maximum profit of $5200 can be achieved by selling 260 boards of mahogany and 0 boards of black walnut.

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The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.

To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:

A = $4,000.00(1 + 0.045/365)^(365*4)

A = $4,000.00(1.0001234)^1460

A = $4,889.68

The final amount is $4,889.68, which means that the interest earned is:

Interest = $4,889.68 - $4,000.00 = $889.68

We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:

$1.197204 / $1.00 = 1.197204

Interest earned = $889.68 x 1.197204 = $1,064.08

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Answer: 9, 10, and 11

Step-by-step explanation:

If the sum of three consecutive natural numbers is 30, then we can represent the smallest of the three numbers as x. The next two consecutive natural numbers would be x+1 and x+2. Therefore, we can form the equation:

x + (x+1) + (x+2) = 30

Simplifying the left-hand side, we get:

3x + 3 = 30

Subtracting 3 from both sides, we get:

3x = 27

Dividing by 3, we get:

x = 9

Therefore, the three consecutive natural numbers are 9, 10, and 11.

Answer: 0.04

Step-by-step explanation:

In order to get 4% as a decimal, you must divide 4 by 100.

4/100 = 0.04

Thus, the answer to your question is 0.04

Answer:

30,000 grams

Step-by-step explanation:

multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g

Answer:

hi I'm really sorry I can't help

Answer:

Step-by-step explanation:

[tex]\frac{2}{x} -3=\frac{1}{2}[/tex]

      [tex]\frac{2}{x}=\frac{1}{2}+3[/tex]      (-3 both sides)

      [tex]\frac{2}{x}=\frac{7}{2}[/tex]            (added fraction)

      [tex]2=\frac{7x}{2}[/tex]           (×[tex]x[/tex] both sides)

      [tex]4=7x[/tex]           (×2 both sides)

      [tex]x=\frac{4}{7}[/tex]             (÷7 both sides)

Answer:30

Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.

The standard form of a conic section represented by r = 6/(cos x + 3sin x) is  r^2 = 6(x + 3y) and the represented equation is a line.

The equation r = 6/(cos x + 3sin x) is in polar form, where r represents the distance from the origin to a point (x, y) in the plane, and x is the angle that the line connecting the origin to (x, y) makes with the positive x-axis. To determine the standard form of the conic represented by this equation, we need to convert it to Cartesian coordinates.

Using the trigonometric identity cos x = x/r and sin x = y/r, we can rewrite the equation as:

r = 6/(x/r + 3y/r)

Multiplying both sides by r, we get:

r^2 = 6(x + 3y)

This is the standard form of a conic section in Cartesian coordinates, namely an equation of a line. Therefore, the conic represented by the equation r = 6/(cos x + 3sin x) is a line in the Cartesian coordinate system.

In summary, to determine the standard form of a conic represented by an equation given in polar form, we can use trigonometric identities to rewrite it in Cartesian coordinates.

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Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex]  tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.

Accοrding tο the given infοrmatiοn:

The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.

Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].

Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].

In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

Plugging in the values οf a, b, and c, we get:

[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]

Simplifying this expressiοn, we get:

[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

[tex]t = 2 \± 0.632[/tex]

Therefοre, the twο pοssible values οf t are:

t = 2 + 0.632 = 2.632 secοnds

t = 2 - 0.632 = 1.368 secοnds

Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

t = 2 ± 0.632

Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

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Answer: 10.2 cm

Step-by-step explanation:

We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's call the unknown length of the other leg "x". Then we can set up the following equation:

4^2 + x^2 = 11^2

Simplifying this equation, we get:

16 + x^2 = 121

Subtracting 16 from both sides, we get:

x^2 = 105

Taking the square root of both sides, we get:

x = sqrt(105)

x ≈ 10.2 cm (rounded to the nearest tenth)

Therefore, the measure of the other leg is approximately 10.2 cm.

Answer:

n(s) =52. n(f) = 12 n(h) = 13

p (f)= 13/52. p(f)= 12/52

The solution for the other variable, according to the stated statement, is[tex]X = 6^y[/tex] and [tex]y = 21 * 2^X[/tex]

Exponential numbers are represented by an, where an is multiplied by itself n times. An easy example is 8=2³=222. In exponential notation, an is known as the base, whereas n is known as the power, exponent, or index. Scientific notation is an example of an exponential number, with 10 usually typically serving as the base number.

Exponential functions are often employed in the biological sciences to describe the amount of a certain quantity over time, such as population size. Experiment data graphs are often created with time on the x-axis and amount on the y-axis.

a. y = log6(X)

[tex]6^y = X[/tex]

[tex]X = 6^y[/tex]

b. [tex]X = log2(y/21)[/tex]

[tex]2^X = y/21[/tex]

[tex]21 * 2^X = y[/tex]

[tex]y = 21 * 2^X[/tex]

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a. Hence proved that the sum of fractions  [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

b. The value will be 7 for the expression

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

Square rοοt οf a number is a value, which οn multiplicatiοn by itself, gives the οriginal number. The square rοοt is an inverse methοd οf squaring a number. Hence, squares and square rοοts are related cοncepts.

Suppοse x is the square rοοt οf y, then it is represented as x=√y, οr we can express the same equatiοn as x² = y. Here, ‘√’ is the radical symbοl used tο represent the rοοt οf numbers. The pοsitive number, when multiplied by itself, represents the square οf the number. The square rοοt οf the square οf a pοsitive number gives the οriginal number.

Here,

a. [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

Using (a + b)(a - b) = a² - b²

⇒ [tex]${\frac{1 \cdot \sqrt{1}-\sqrt{2}}{\sqrt{1}+\sqrt{2}\cdot \sqrt{1 }-\sqrt{2}}+{\frac{1 \cdot \sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}\cdot \sqrt{1}-\sqrt{2}}}+{\frac{1 \cdot \sqrt{3}-\sqrt{4}}{\sqrt{3}+\sqrt{4}\cdot \sqrt{3}-\sqrt{4}}}$[/tex]

⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{1-2}+{\frac{ \sqrt{2}-\sqrt{3}}{2-3}+{\frac{\sqrt{3}-\sqrt{4}}{3-4}}$[/tex]

⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-\sqrt{4}}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]

⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}}-{\sqrt{3}+2}$[/tex]

⇒ [tex]$ -1+2}$[/tex]

⇒ 1

a. Hence proved that the sum of fractions  [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

B. This will be done with the same process,

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}} \cdot \cdot \cdot -{\sqrt{63}+8}$[/tex]

There, will be same roots of every number until - 8

So,

⇒ [tex]$ -1+8}$[/tex]

= 7

b. The value will be 7 for the expression

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

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Answer:The prices of the adult movie tickets and the child movie tickets are $15 and $5 respectively.

Given that, the Jones family spent $45 on movie tickets for 2 adults and 3 children.

Step-by-step explanation:What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let cost of adult tickets be x and the cost of children tickets be c.

The Jones family spent $45 on movie tickets for 2 adults and 3 children.

2a+3c=45 ------(I)

The Smith family spent $40 for 2 adults and 2 children.

2a+2c=40

a+c=20 ------(II)

From equation (II), we have a=20-c

Substitute a=20-c in equation (I), we get

2(20-c)+3c=45

⇒ 40-2c+3c=45

⇒ c=$5

Put c=5 in equation (II), we get

a+5=20

⇒ a=$15

If the set of expressions represents measures of the sides of a triangle x, 4, 6 , the range of possible measures of x is 2 < x < 10.

To determine the range of possible measures of X if the set of expressions represents measures of the sides of a triangle x, 4, 6, we need to use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Mathematically, this can be expressed as:

x + 4 > 6

x + 6 > 4

4 + 6 > x

Simplifying these inequalities, we get:

x > 2

x > -2

x < 10

The first two inequalities indicate that x must be greater than 2, since the sum of any two sides of a triangle must be greater than the third side. The third inequality indicates that x must be less than 10, since the longest side of a triangle cannot be greater than the sum of the other two sides.

This means that x can take any value between 2 and 10, but not including 2 or 10, in order for the set of expressions to represent the measures of the sides of a triangle.

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The z-score for the 25th percentile of a standard normal distribution is approximately -0.625. Here option A is the correct answer.

To find the z-score for the 25th percentile of a standard normal distribution, we need to use a standard normal distribution table or calculator. The 25th percentile corresponds to a cumulative area under the standard normal curve of 0.25.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative area of 0.25 is about -0.68. This means that approximately 25% of the area under the standard normal curve lies to the left of -0.625.

So, among the given options, the correct answer is Option A, -0.625, Option D, -0.50, which is also incorrect. Option E, 0.00, is definitely incorrect because the 25th percentile is to the left of the mean.

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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, 2).

In Geometry, a reflection over or across the y-axis is represented and modeled by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate (y-axis) while the sign of the x-coordinate (x-axis) would change from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (-3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)

Lastly, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).

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Answer:

105 degrees

Step-by-step explanation:

sum of angles in triangle is 180 degrees

11x-5+6x+5+x = 180

simplify this to get 18x=180

180/18 = 10 = x

plug in 10 for x

11(10) - 5

110-5

105

the area of her entire bedroom is 176 feet².

A rectangle is a parallelogram with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equivalent. A square is a rectangle with four equal edges.

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Area of first rectangle = length * breadth= 10*8=80 feet²

Area of second rectangle = length * breadth= 12*8 = 96 feet²

Total area of bedroom= 80+96= 176 feet²

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216 cm2 is the size of the rectangle border.

the translation of the question is

A painting including its frame is 25 cm long and 10 cm wide, what is the area of ​​the frame if it is 4 cm wide?

What is a rectangle's area?

When the dimensions of a rectangle with length and width are multiplied, the area of the rectangle is determined as follows:

A = lw.

The total area is therefore given by:

A = 25 x 10 = 250 cm².

The white region's size is shown by:

A = (25 - 2 x 4) x (10 - 2 x 4) is equal to 17x 2 and 34 cm2.

Hence, the border's area is as follows:

216 cm2 = 250 cm2 - 34 cm2.

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First, re-read the problem until you understand it and can put it into your own words.  I re-wrote it like this:  "Find the area of a rectangle by first finding the length (L) and the width (W)."   [note that I added "find L and W," but that is how I'm going to solve the problem;  I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).

Translate the problem:

 "The length of a rectangle is 3 ft longer than its width"      means

         L                             =    3             +         W                 (eq1)

 "the perimeter of the rectangle is 30 ft"     means

            P                                = 50                      (eq2)

So, now the math is easy, just find L and W so we can compute the area:

     P = 50 = 2L + 2W                         (eq3; from eq2 and the formula for P)

          50 = 2(3+W)  +  2W              (use eq1 to substitute for L)

          50 = 6 + 2W   + 2W              (distribute)

           50 = 6 + 4W                       (collect terms)

            44 = 4W                        (subtract 6 from both sides)

            11 ft = W                        (divide both sides by 4)

Use the easiest equation (either eq1 or else eq3) to find L:

          L = 3 + W        (eq1)

          L = 3 + 11

         L = 14 ft

What is the area (A)?

          A = L*W

          A = (14 ft) x (11 ft)

          A = 154 sq ft

Therefore, the initial value of the function is $1,852 and the rate of change is $12.18 per shirt. The initial value represents the cost of the shirts before any were purchased,

In mathematics, a function is a rule that assigns to each element in a set called the domain, a unique element in another set called the range. In other words, a function is a mathematical object that takes an input and produces a specific output, according to a specific set of rules or operations.

by the question.

et the initial value be represented by a and the rate of change by r.

The given information can be represented by the following equation:

a + 150r = 1,852

Since the flat-rate shipping cost is $25, the cost of the 150 shirts alone would be:

a + 150r - 25 = 1,827

The initial value, a, represents the cost of the shirts before any shirts were purchased. In this case, it would be the cost of the shirts if no shirts were purchased plus the flat-rate shipping cost of $25.

So, a = 1,827 + 25 = 1,852.

The rate of change, r, represents the increase in cost for each additional shirt purchased. In this case, it would be the cost of one shirt.

So, r = (1,852 - 25)/150 = 12.18.

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Answer:

mn(4m - 7n)

Step-by-step explanation:

➠ 4m^2n-7mn^2

➠ 2^2 x m^2n - 7mn^2

➠ mn([tex](\frac{2^2*m^2n}{mn} -\frac{7mn^2}{mn} )[/tex]

➠ mn([tex]2^2*m^{2-1}-(7n^{2-1}))[/tex]

➠ mn(4m - 7n)

Answer:

668.376

Step-by-step explanation:

Please hit brainliest if this was helpful!

To simplify 650 – 0.394 + 18.77, we can first add 650 and 18.77 since they're both whole numbers:

650 + 18.77 = 668.77

Then, we can subtract 0.394 from 668.77:668.77 - 0.394 = 668.376

Therefore, 650 – 0.394 + 18.77 simplifies to 668.376.

Answer: If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.

Step-by-step explanation:

I hope that this helped! :)

The nearest hundredth, we get:

C ≈ 12.56 feet.

Circle circumference (or perimeter) = 2R

where R denotes the circle's radius. 3.14 is the approximate (up to two decimal points) value of the mathematical constant. Again, Pi () is a special mathematical constant that represents the circumference to diameter ratio of any circle.

The circumference of a circle is calculated as follows:

C = 2πr

where C is the circumference, (pi) is a constant close to 3.14, and r is the radius of the circle.

When the given values are substituted, the following results are obtained:

C = 2(3.14)(2) \s= 12.56

We get the following when we round to the nearest hundredth:

C ≈ 12.56 feet.

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We cannot construct an interval using the normal approximation of survival rate between control and treatment groups because the samples must be random, independent, and their sample sizes must be sufficiently large.

The normal approximation is valid when the sample sizes are large enough to ensure that the sampling distribution of the mean of the variable is approximately normal.

The central limit theorem applies to the distribution of the sample mean when the sample size is large enough, according to the normal approximation.

As a result, the mean difference between the two groups must have a normal distribution. The normal distribution may not be an accurate representation of the underlying distribution of the difference between the two population means in the absence of this requirement, causing the confidence interval to be inaccurate. It will lead to incorrect inferences about the difference in the survival rates of the two groups.

The confidence interval constructed despite this problem will lead to incorrect inferences about the difference in the survival rates of the two groups. This would make it difficult to draw any conclusions based on the findings of this experiment.

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Answer:

18+m=24, 6

Step-by-step explanation:

You will get the first part by understanding that 24 is the whole and 18 is the part. Part + the other part, m, is the whole. You will then solve this by isolating the variable m, and subtracting 18 on both sides of the equation. Since 24-18=6, that is the final answer.

The discount percentage is different, the amount that Lisa pays will also be different.

The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.

We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.

Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:

Discounted price = Regular price minus discount amount

Normal price x Discount percentage = Discount amount

Discount rate = 1/3 = 33.33% (rounded to two decimal places)

Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)

Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)

As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.

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Lisa uses her railcard to buy a ticket.

She gets off the normal price of the ticket.

The normal price of the ticket is £24.90

Work out how much Lisa pays for the ticket.