At the moment Mr Finn pays £700 per month in rent.
His landlord has informed that this will increase by 5% for the next two years and by 8% after that.
What will Mr Finn's rent be in three years' time if he stays in his current accommodation?
(4)

With the original price at 25 units , he paid 23 units and d(25) means the price he paid when the original price is 25 units.

Phil works at a department store and gets an employee discount. The price he pays can be modelled by the function d(c) = c - 0.08c , where c is the original price of the item.

Therefore, let's find d(25) and describes what it means.

Hence,

d(c) = c - 0.08c

where

Therefore,

d(25) = 25 - 0.08(25)

d(25) = 25 - 2

d(25) = 23

Therefore, d(25) is the price he paid when the original price is 25 units. Therefore, he paid 23 units

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The probability the card is a diamond or a face card is [tex]\frac{11}{26}[/tex].

Probability refers to the likelihood that any random occurrence will occur. This expression refers to estimating the probability that any specific event will take place. For example, when we throw a coin into the air. Possibility: P(A) = f / N, determines the likelihood that an event will occur. Although probability and ratios are linked, the former dictates the latter. The probability of an occurrence must be known before determining its probability.

When we find the probability, we obtain:

There are 52 cards in a standard deck of cards.As there are four suits, there are 12 face cards, which we identify as the Kings, Queens, and Jacks. There are 13 diamonds total, 3 of which are face cards that have previously been counted. There are thus 10 diamonds without faces.

Out of the 52 cards in the deck, 10 diamonds plus 12 face cards equal 22.

P= [tex]\frac{22}{52}[/tex]= [tex]\frac{11}{26}[/tex].

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The area of the irregular figure to the nearest tenth is 8.12 sq. ft.

Shapes classified as irregular lack both equal sides and equal angles. The entire area occupied by an irregular shape on a two-dimensional plane is referred to as the shape's area. An irregular form can be split into a number of regular shapes, such as triangles, squares, and rectangles, to determine its area. The area of those smaller shapes can then be added to determine the total area.

Given that, the diameter of the semicircle= 2.8 ft.

The radius of the semicircle = 1.4 ft.

The area of the semicircle is:

A = πr² / 2

A = (3.14)(1.4)²/2

A= 3.077 sq. ft

The area of the triangle is given as:

A = 1/2(b)(h)

A = 1/2(2.8)(3.6)

A = 5.04 sq. ft

The area of the irregular figure is:

A = Area of semicircle + area of triangle

A = 3.077 + 5.04

A = 8.117 sq. ft

Hence, the area of the irregular figure to the nearest tenth is 8.12 sq. ft.

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Answer:

  15.8%

Step-by-step explanation:

You want the percentage of world bike production represented by 13.239 million bikes out of a world production of 84 million bikes.

A fraction is converted to a percentage by multiplying it by 100%.

  13.239/84 × 100% ≈ 15.8%

Germany contributed about 15.8% of the world's bike production in 2006.

The derivative of composite functions are listed below:

Case A

Subcase i: y' = 4 · (x³ + 8 · x² - x + 3) · (3 · x² + 16 · x - 1)

Subcase ii: y' = (2 · x - 7)² · [(2 · x + 4) · (2 · x - 7) + 6 · (x² + 4 · x - 2)]

Case B

Subcase i: y' = 5 · (2 · x - 1 / x²) · [(2 · x - 1 / x²) + 2 · x · (2 - 2 / x³)]

Subcase ii: y' = [- (x² + 3 · x - 1) - (2 - x) · (2 · x + 3)] / (x² + 3 · x - 1)²

Chain rule is powerful resource to find the derivative of a composite function, that is, a function of the form:

f ° u (x) = f[u(x)]

And chain rule is now defined:

df[u(x)] / dx = (df / du) · (du / dx)

There are three cases requiring chain rule, now we proceed to determine the derivative for each expression:

Case A

Subcase i

y = (x³ + 8 · x² - x + 3)⁴

y' = 4 · (x³ + 8 · x² - x + 3) · (3 · x² + 16 · x - 1)

Subcase ii

y = (x² + 4 · x - 2) · (2 · x - 7)³

y' = (2 · x + 4) · (2 · x - 7)³ + 6 · (x² + 4 · x - 2) · (2 · x - 7)²

y' = (2 · x - 7)² · [(2 · x + 4) · (2 · x - 7) + 6 · (x² + 4 · x - 2)]

Case B

Subcase i

y = 5 · x · (2 · x - 1 / x²)²

y' = 5 · [(2 · x - 1 / x²)² + 2 · x · (2 · x - 1 / x²) · (2 - 2 / x³)]

y' = 5 · (2 · x - 1 / x²) · [(2 · x - 1 / x²) + 2 · x · (2 - 2 / x³)]

Subcase ii

y = (2 - x) / (x² + 3 · x - 1)

y' = [- (x² + 3 · x - 1) - (2 - x) · (2 · x + 3)] / (x² + 3 · x - 1)²

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Answer:

Step-by-step explanation:

is -2(-12y+5)+4=8(3y+2)-22 a conditional equation an identity or a contradiction

-2(-12y + 5) + 4 - 8(3y - 2) + 22 = 0

24y - 10 + 4 - 24y - 16 + 22 = 0

-6 - 16 + 22

- 22 + 22 = 0

0 = 0   (All real numbers are solutions.)

Answer:

Step-by-step explanation:

To find the zeros of F(x), we need to solve the equation F(x) = 0.

F(x) = x^2(x^2+18x+81)

The expression F(x) can be factored as:

F(x) = x^2(x+9)^2

So, the zeros of F(x) are x = 0 and x = -9, with a multiplicity of 2 for both.

The factor x^2 contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = 0 but does not cross it. The factor (x+9)^2 also contributes to a zero of multiplicity 2, which means that the graph of F(x) touches the x-axis at x = -9 but does not cross it.

To summarize, the zeros and their multiplicities for F(x) are:

x = 0 (multiplicity 2)

x = -9 (multiplicity 2)

Answer:

20000

Step-by-step explanation:

i think this is the right answer i could

Answer:

The net profit would be 26-18=6 dollars per hour.

we need hours such that 8h≥264 =>h≥33 hours

Answer: greater than 6 cm. less than 20 cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

The force exerted by the prism on the floor 245 N.

The physical force applied to an object is referred to as pressure. Per unit area, a perpendicular force is delivered to the surface of the objects. F/A is the fundamental formula for pressure (Force per unit area). Pascals are a unit of pressure (Pa).

Given:

height = 4 m, volume = 28 m³

Pressure = 75 N/m²

Now, Volume of prism = Area of base x height

                              28     = Аrеа х 4

                                Area = 28/4 = 7 m²

Also, Pressure = force / Area

35 = force / 7

Force = 35 x 7

Force = 245 N

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Answer:

Step-by-step explanation:

similar - AA

The ΔBES is similar to ΔGES by AA similarity postulate.

Similar triangles are those triangles, where the angles of the triangles are equal and the sides are proportional.

Given a bigger triangle BEG.

There are two smaller right angled triangles BES and GES.

For ΔBES, ∠BES = 40° and ∠BSE = 90°

For ΔGES, ∠GES = 40° and ∠GSE = 90°

By AA similarity postulate, if two angles of one triangle is equal to two angles of another triangle, then the triangles are similar.

Here, two angles of ΔBES is equal to two angles of ΔGES.

So two triangles are similar.

Hence the two triangles are similar by AA similarity postulate.

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Your question is incomplete. The complete question with the image of the triangle is as given below.

Giving each guest a room in a hotel is impossible if the group size exceeds the number of available rooms, resulting in some individuals having to share a room with someone else or not having a place to stay.

Logical thinking is a type of thinking that involves reasoning based on a set of premises or assumptions to arrive at a conclusion. It is a rational, systematic, and methodical way of thinking that involves analyzing information, identifying patterns, and drawing valid and sound conclusions.

Logical thinking involves using a combination of critical thinking skills, such as analysis, evaluation, and synthesis, to make reasoned judgments. It requires an ability to break down complex problems into smaller, more manageable parts, and to evaluate evidence in a clear and objective manner.

In logical thinking, conclusions are reached through a process of deduction or induction. Deduction involves starting with a general principle or premise and applying it to a specific situation to arrive at a conclusion. Induction, on the other hand, involves starting with specific observations or evidence and using them to make a general conclusion.

Logical thinking is essential in many fields, including science, mathematics, philosophy, and law, among others. It is also important in everyday life, such as when making decisions, solving problems, or evaluating arguments. By using logical thinking, individuals can make informed and reasoned judgments, and arrive at conclusions that are based on evidence and reason, rather than emotion or bias.

The Hotel Cardinality is a mathematical model that assumes that the hotel has an infinite number of rooms. However, in reality, hotels have a limited number of rooms. Therefore, if the group of people is larger than the number of available rooms, it would be impossible to give each person a room. For example, if the hotel has only 10 rooms and the group consists of 15 people, it is not possible to give each person a room. This is because there are more people than the number of available rooms, and some people will have to share a room or be left without a room. Hence, it is not always possible to accommodate all guests in a hotel, especially during peak seasons or when the hotel has limited capacity.

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Answer:

C = .25m + 5.45

Step-by-step explanation:

c = (1..05 - .8)m + (16.40 - 10.95)

C = .25m + 5.45

The Luxury car cost  25 cents more per mile and an a higher initial cost of $5.45

Answer:

48

Step-by-step explanation:

2*4*6

The sum of two opposite interior angles of a triangle is equal to the opposite exterior angle of a triangle

Therefore,

( 5x - 101 )° + ( x + 36 )° = ( 9x - 164 )°

5x + x - 106 + 36 = 9x - 164

6x - 65 = 9x - 164

6x - 9x = - 164 + 65

- 3x / - 3 = - 99 / - 3

x = 33

The first interior angle

= ( 5x - 101 )°

= ( 5 ( 33 ) - 101 ) °

= ( 165 - 101 )°

= 64°

The second interior angle

= ( x + 36 )°

= ( 33 + 36 )°

= 69°

The exterior angle

= ( 9x - 164 )°

= ( 9 ( 33 ) - 164 )°

= ( 297 - 164 )°

= 133°

Answer:

Step-by-step explanation:

The expression "X divided by 5 multiplied by 12" can be written as:

( X / 5 ) * 12

To simplify this expression, we can first multiply 12 by X/5, which gives:

( X / 5 ) * 12 = X * (12/5)

So the simplified expression is:

X * (12/5)

or

(12/5)X

which is equivalent to "12/5 times X".

The length of q is approximately is 0.4 cm.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To solve for the length of q in triangle AOPQ, we can use the law of sines, which states:

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.

In triangle AOPQ, we know that:

Side p = 6.3 cm (opposite angle P)

Angle O = 149° (opposite side q)

Angle P = 29° (opposite side p)

Let use angle sum property of triangles to find the measure of angle Q:

Angle Q = 180° - Angle O - Angle P

Angle Q = 180° - 149° - 29°

Angle Q = 2°

Now we can use the law of sines to solve for the length of q:

q/sin Q = p/sin P

q/sin(2°) = 6.3/sin(29°)

q = sin(2°) × (6.3/sin(29°))

q=0.034 × (6.3/0.484)

q = 0.442 cm

Therefore, the length of q is approximately is 0.4 cm.

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The value of the variable(s) in the figure is  60°, explaination is given below.

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that function at those values of the considered variables.

We are given that;

The variables; (5y)⁰,(2x)°,120⁰,1080

Now,

The first two expressions are both equal to 1, because any number raised to the power of 0 is always 1.

The third expression, 120°, is an angle measurement in degrees. In a triangle, the sum of the interior angles is always 180°. So, if we let x and y be the other two angles in the triangle, we have:

x + y + 120° = 180°

Simplifying this equation, we get:

x + y = 60°

Therefore, the answer of the given function will be  60°.

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So the linear model that describes the growth of the organism over the 5 hour period is: y = 6x + 16, where x is the number of hours and y is the weight of the organism in mg.

A linear model is a mathematical equation that describes a linear relationship between two or more variables. In other words, it is a model that assumes that the relationship between the variables can be represented by a straight line. Linear models are commonly used in various fields, including economics, finance, engineering, and science, to analyze and predict the relationship between variables. They are particularly useful when analyzing data that shows a linear trend, or when making predictions based on historical data. Linear models can be simple or multiple, depending on the number of independent variables involved. They can also be adjusted to fit nonlinear data by transforming the variables or using a different model altogether.

Here,

To find a linear model that describes the growth of the organism over time, we need to determine the rate of growth (change in weight per unit time) and the initial weight.

The rate of growth can be found by taking the difference between the final weight and the initial weight and dividing by the time period:

Rate of growth = (final weight - initial weight) / time period

= (46 mg - 16 mg) / 5 hours

= 6 mg/hour

So the organism is growing at a rate of 6 mg per hour.

The initial weight of the organism is given as 16 mg.

Now we can write the equation of the line as:

y = mx + b

where y is the weight of the organism in mg, x is the time in hours, m is the rate of growth in mg/hour, and b is the initial weight in mg.

Substituting the values we found, we get:

y = 6x + 16

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The area of the isosceles trapezoid is 281.25 square cm.

Let's denote the length of the base of the trapezoid as "b".

According to the problem statement, the length of each of the equal sides is one-half the length of the base, which means each equal side has length b/2.

The height of the trapezoid is given as one-fourth the length of the base, so we can write it as h = b/4.

To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

The two parallel sides of length b each contribute b to the perimeter, while the other two sides of length b/2 contribute a total of b to the perimeter.

Therefore, we can write:

Perimeter = 2b + 2(b/2) = 3b

We know that the perimeter of the trapezoid is 45 cm, so we can set up an equation:

3b = 45

Solving for b, we get:

b = 15

Now we can use the formula for the area of a trapezoid to find the area of this isosceles trapezoid. The formula is:

Area = (1/2)h(b1 + b2)

where h is the height, b1 and b2 are the lengths of the two parallel sides. In this case, b1 and b2 are both equal to b (since it's an isosceles trapezoid), and h = b/4.

Substituting these values, we get:

Area = (1/2)(b/4)(b + b) = (1/2)(b/4)(2b) = b^2/8

Substituting b = 15, we get:

Area = 15^2/8 = 281.25 sq cm

Therefore, the area of the isosceles trapezoid is 281.25 square cm.

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In an isosceles trapezoid, the length of the equal sides is one-half the length of the base, while the height is one-fourth the length of the base. If the perimeter of the trapezoid is 45 cm.

Find the areae

Answer:

y= -6x+5

y= 2x+(-5)

Step-by-step explanation:

This is the equation of the line in point-slope form.
y - 5 = (-5/4)(x + 6)

The equation in slope-intercept form is y = (-5/4)x - 5/4.

And So the equation in standard form is 5x + 4y = -5.

The 90% confidence interval for the mean number of books people read is (-16, 38.6).

To construct a 90% confidence interval for the mean number of books people read, we first need to find the critical value (z*) that corresponds to a 90% confidence level. This can be found using a z-table or calculator. The critical value for a 90% confidence level is 1.645.

Next, we need to calculate the margin of error (ME) using the formula ME = z* x SE, where SE is the standard error. In this case, SE = 16.6 books, so ME = 1.645 x 16.6 = 27.3 books.

Finally, we can construct the 90% confidence interval by adding and subtracting the margin of error from the sample mean (x overbar). The confidence interval is:

(x overbar - ME, x overbar + ME) = (11.3 - 27.3, 11.3 + 27.3) = (-16, 38.6)

This means that we are 90% confident that the true mean number of books people read is between -16 and 38.6 books.

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Statements B , D and E are True.

Statements A and C are False.

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

A. Prism A and C have the same volume. - False

The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.

B. Prism B has a greater volume than Prism C. - True

The volume of Prism B is 8 x 4 x 3 = 96 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.

C. Prism B has the least volume. - False

The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, which is greater than the volume of Prism B.

D. The volume of Prism A is 120 cubic centimeters. - True

As calculated above, the volume of Prism A is 120 cubic cm.

E. The volume of Prism C is less than the volume of Prism A. - True

As calculated above, the volume of Prism C is 105 cubic cm, which is less than the volume of Prism A.

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Answer:

No solution

Step-by-step explanation:

We are given the following equation and asked to solve for x

[tex]\dfrac{\left(x+2\right)}{2x-2}=\dfrac{1}{2}[/tex]

[tex]\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\dfrac{a}{b}=\dfrac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot[/tex]

[tex]\left(x+2\right)\cdot \:2=\left(2x-2\right)\cdot \:1[/tex]

[tex]\mathrm{Simplify}2x + 2 = 2x - 2\\\\\textrm{Subtract\;$2x$\;both\;sides}:\\-2 = 2[/tex]

Since the sides are not equal this indicates there is no solution to this system.

Thus, the value of x is 1.

The description that will be used to break this problem is D description of a midpoint.

By description, a midpoint is a point on a line member that divides it into two equal corridor. thus, Y is the midpoint of XZ, which means that XY is equal in length to YZ.

Using the Member Addition hypothetical( A), we can write

XZ = XY YZ

Substituting the values given in the problem, we get

x- 2 = XY 2x 2

Simplifying this equation, we get

x- 2 = XY 2x 2

4x = 4

x = 1

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The length of side x is approximately 9.05 cm.

What is law of sines ?

The Law of Sines, also known as the Sine Rule, is a formula used to find unknown angles or sides of a triangle, given some combination of angle and side measurements. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Mathematically, the Law of Sines can be expressed as follows:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides, respectively.

Given by the question:

To find x, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Let's use the sine function to find the length of side AB:

sin A / AB = sin C / BC

sin 45 / x = sin 40 / 12

Rearranging and solving for x:

x = sin 45 * 12 / sin 40

x ≈ 9.05 cm

Therefore, the length of side x is approximately 9.05 cm.

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The missing side of the prism measures 56 units.

Here we can see that the front face is a triangle with a base of 8 units and a height of 15 units. And x is the length perpendicular to that face, then the volume of the prism is:

V = (15)*(8)*x/2

We know that V = 3,360 cubic units, then:

3,360  = (15)*(8)*x/2

3,360 = 60*x

3,360/60 = x

56 = x

The missing side measures 56 units.

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