How much Income Tax would be paid by someone earning £41,000 in a tax year when the basic rate of Income Tax is 20% and the annual tax-free personal allowance is £11,500?

to calculate the total price for car wash services. A base car wash is $10. A dictionary with each additional service and the corresponding cost has been provided. Two additional services can be selected. A '-' signifies an additional service was not selected. Output all selected services, according to the input order, along with the corresponding costs and then the total price for all car wash services.

"""

Python version: 3.6

Python program to calculate the total price for car wash services

"""

# dictionary containing the services as keys and their price as values

services = {'Air freshener' : 1, 'Rain repellent' : 2, 'Tire shine' : 2, 'Wax' : 3, 'Vacuum' : 5}

# variable to store the base car wash price

base_wash = 10

# variable to store the total price

total = 0

# read the 2 services

service_choice1 = input()

service_choice2 = input()

print("ZyCar Wash")

# display the base wash price

print("Base car wash -- ${}".format(base_wash))

total += base_wash # add base_wash to total

# first service read is in services dictionary

if service_choice1 in services:

   total += services[service_choice1] # add the price for the service to total

   # display the service and its price from dictionary

   print("{} -- ${}".format(service_choice1, services[service_choice1]))

# second service read is in services dictionary    

if service_choice2 in services:

   total += services[service_choice2] # add the price for the service to total

   # display the service and its price from dictionary

   print("{} -- ${}".format(service_choice2, services[service_choice2]))

# display the total price  

print("----")

print("Total price: ${}".format(total))    

# end of program

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The total cost of all the 2- liter sodas will be proportional to the number of 2- liter sodas that Sue buys is c = 1.25s

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, Sue is thinking of buying some 2-liters sodas which are on sale for $1.25 each.

Let the number of soda be s.

The total cost will be:

c = 1.25 × s

c = 1.25s

The cost is 1.25s.

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Answer:

She purchased 5 boxes

Step-by-step explanation:

17.40 ÷ 3.48 = 5

It would take approximately 14.1 years (to the nearest tenth of a year) for the mass of the sample of Element X to reach 800 grams.

To determine how long it would take for the mass of the sample of Element X to reach 800 grams, we can use the information provided about its rate of decay.

Given:

Initial mass (M₀) = 1400 grams

Decay rate: The mass decreases by half every 30 years.

To solve this problem, we need to find the time it takes for the mass to decrease from 1400 grams to 800 grams.

Let's set up an equation to represent the decay of the mass:

M(t) = [tex]M\circ * (1/2)^(t/30)[/tex]

Here, M(t) represents the mass at time t in years, M₀ is the initial mass, and t is the time in years.

We need to find the value of t when M(t) = 800 grams:

800 = [tex]1400 * (1/2)^(t/30)[/tex]

To solve for t, we can take the logarithm of both sides of the equation (base 1/2) to isolate t:

[tex]log\base1/2(800/1400) = t/30[/tex]

Using logarithmic properties, we can simplify further:

[tex]log\base1/2(4/7) = t/30[/tex]

Now, we can solve for t by multiplying both sides of the equation by 30:

[tex]t = 30 * log\base1/2(4/7)[/tex]

Using a calculator or logarithmic tables, we find:

t ≈ 14.1 years

Therefore, it would take approximately 14.1 years (to the nearest tenth of a year) for the mass of the sample of Element X to reach 800 grams.

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Answer:

[tex]X=-2\frac{2}{5}[/tex]

Step-by-step explanation:

1/2(x+2)=-1/3(x+3)

1/2x+1=-1/3x-1

           +1/3x

5/6x+1=-1

      -1.  -1

5/6x=-2

/5/6.   /5/6

x=-2*6/5

x=-12/5

x= -2 2/5

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

The slope is determined with two points.

Take the pairs (0, - 9) and (1, - 5).

The slope is:

Answer:

Slope = 4

Step-by-step explanation:

Formula we use,

→ Slope = (y2 - y1)/(x2 - x1)

Then required slope will be,

→ (y2 - y1)/(x2 - x1)

→ (-5 -(-9))/(1 - 0)

→ (-5 + 9)/(1 - 0)

→ 4/1 = 4

Therefore, the slope is 4.

Answer:

=====================

Use identities:

Answer:

[tex]\textsf{11.} \quad 4x^2+ \sqrt{1-16x^2}\sqrt{1-x^2}[/tex]

[tex]\textsf{12.} \quad \dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Double Angle Identity}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Inverse Trigonometric Identities}\\\\$\sin(\cos^{-1}x)=\sqrt{1-x^2}$\\\\$\cos(\sin^{-1}x)=\sqrt{1-x^2}$\\\end{minipage}}[/tex]

Given trigonometric expression:

[tex]\sin ( \sin^{-1} 4x + \cos^{-1} x)[/tex]

Using the Sine Double Angle Identity:

Therefore:

[tex]\begin{aligned}\sin ( \sin^{-1} 4x + \cos^{-1} x)&=\sin(\sin^{-1}4x) \cos (\cos^{-1}x)+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x \cdot x+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x^2+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x^2+ \sqrt{1-(4x)^2}\sqrt{1-x^2}\\&=4x^2+ \sqrt{1-16x^2}\sqrt{1-x^2}\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan Double Angle Identity}\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

Given trigonometric expression:

[tex]\tan(\tan^{-1}1-\tan^{-1}\sqrt{x})[/tex]

Using the Tan Double Angle Identity:

Therefore:

[tex]\begin{aligned}\tan(\tan^{-1}1-\tan^{-1}\sqrt{x})&=\dfrac{\tan (\tan^{-1}1) - \tan (\tan^{-1}\sqrt{x})}{1 + \tan (\tan^{-1}1) \tan (\tan^{-1}\sqrt{x})}\\\\&=\dfrac{1 - \sqrt{x}}{1 + 1 \sqrt{x}}\\\\&=\dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}\\\\\end{aligned}[/tex]

Answer:

The answer is [tex]\frac{4}{13}[/tex].

Step-by-step explanation:

Additive rule:

According to this rule, the probability that events A or B will occur is given by the formula,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Here,

We know that there are 13 spades and 4 queens in a deck of 52 cards. Also, there is only one queen of a spade.

Then,

[tex]\begin{aligned}P(S)&=\frac{13}{52}\\P(Q)&=\frac{4}{52}\\P(S\cap Q)&=\frac{1}{52}\end{aligned}[/tex]

Therefore, the probability that the card you select is a spade or queen is given by,

[tex]\begin{aligned}P(S\cup Q)&=P(S)+P(Q) -P(S\cap Q)\\&=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\\&=\frac{16}{52}\\&=\frac{4}{13}\end{aligned}[/tex]

Therefore, the answer is [tex]\frac{4}{13}[/tex].

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The given function is continuously decreasing for x = (-∝, 1).

Given function,

f(x) = | 4(x - 1) | + 2

⇒ f(x) = |4||x-1| + 2

⇒ f(x) = 4|x - 1| + 2

If x ≥ 1, |x - 1| = x - 1

⇒ f(x) = 4(x - 1) + 2 = 4x - 4 + 2

⇒ f(x) = 4x - 2

On differentiating on both sides:

f'(x) = 4 > 0

⇒ Function is continuously increasing for x ≥ 1.

If x < 1, |x - 1| = -(x - 1) = 1 - x

⇒ f(x) = 4(1 - x) + 2 = 4 - 4x + 2

⇒ f(x) = 6 - 4x

On differentiating on both sides:

f'(x) = -4 > 0

⇒ Function is continuously decreasing for x < 1.

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Answer:

Step-by-step explanation:

quit

Answer:

D.  8

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}\dfrac{1}{3}x+\dfrac{1}{4}y=1\\\\2x-4y=-30\end{cases}[/tex]

Multiply the first equation by -6:

[tex]\implies -6 \cdot \dfrac{1}{3}x+-6 \cdot \dfrac{1}{4}y=-6 \cdot 1[/tex]

[tex]\implies -2x-\dfrac{3}{2}y=-6[/tex]

Add this to the second equation to eliminate x:

[tex]\begin{array}{rrcccl}&2x &- &3y& = &-30\\\phantom{\dfrac12}+ &(-2x& - &\frac{3}{2}y &= &\;\;-6)\\\cline{2-6} \phantom{\dfrac12}&0&-&\frac{9}{2}y&=&-36\\ \cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies -\dfrac{9}{2}y=-36[/tex]

[tex]\implies \dfrac{9}{2}y=36[/tex]

[tex]\implies 9y=72[/tex]

[tex]\implies y=\dfrac{72}{9}[/tex]

[tex]\implies y=8[/tex]

1. When Alice shrank, the height will be 12.05cm.

2. When she grew 10 times, the height will be 1205cm.

1. Since Alice's actual height was 120.5 cm and she shrank to 1/10 of her height, the height will be:

= 1/10 × 120.5

= 12.05 cm

2. If Alice grew to 10 times her normal size, the height will be:

= 120.5 × 10

= 1205cm

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The instance in question was chosen at random assignment.

Given statement;

Participants should be selected by chance for an experimental or control group so each has an equal probability of being assigned to any of the groups.

The given case is done by Random assignment.

In Mathematical experiments, random assignment refers to the use of chance processes to ensure that each participant has an equal chance of being assigned to any particular group. Participants in studies are divided into several groups at random, such as the experimental group or the treatment group.

It is known as random assignment.

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The largest length each square can be in order to have the least amount of waste from the fabric will be 34.5.

It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.

It is given that, Jordan and her grandma are creating a quilt as a result. To make their quilt, they will cut square pieces of cloth. They have already bought three fabric lengths. 30 inches, 48 inches, and 60 inches are the lengths.

The total length of the fabric is,

=30+48+60

=138 inches

The perimeter of a square is,

P = 4a

138 = 4a

a=138/4

a=34.5 inches

Thus, the largest length each square can be in order to have the least amount of waste from the fabric will be 34.5.

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The value of cos 2θ will be;

⇒ cos 2θ = 7/25

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The sides of triangle are 3 , 5, 4

Now,

Since, In a triangle;

cos 2θ = 2cos²θ - 1   .....(i)

And, cos θ = Base / Hypotenuse

Substitute all the values, we get;

cos θ = Base / Hypotenuse

cos θ = 4 / 5

Substitute above value in equation (i), we get;

cos 2θ = 2cos²θ - 1  

cos 2θ = 2(4/5)² - 1  

cos 2θ = 32/25 - 1

cos 2θ = 7/25

Thus, The value of cos 2θ will be;

⇒ cos 2θ = 7/25

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From the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.

As given in the question,

Quantity of 60% solution in making 50% solution is = 7 gallons

Let us consider y gallons be the quantity of 35% solution to make 50% solution.

Quantity used to make 50% solution is (7 + y)

Required equation is:

(y × 35%) + (7× 60%) = (7+y) 50%

⇒(35y/100) + (420/100) = (350 + 50y)/100

⇒35y + 420 = 350 + 50y

⇒50y - 35y = 420 -350

⇒15y = 70

⇒y = 4.666..

⇒y = 4.7 gallons ( approximately)

Therefore, from the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.

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The required equation of a parabola expressed in vertex form is f(x) = (x + 2)² - 1.

The equation of a parabola expressed in vertex form is

y = a(x - h)² + k

Where a is a multiplier and (h, k) are the coordinates of the vertex

The expression is given in the question as

f(x) = x² + 4x + 3

To complete the perfect square:

We have to add/subtract ( half the coefficient of the x- term )² to x² - 4x

f(x) = x² + 2(2)x + 4 - 4 + 3

f(x) = (x + 2)² - 1

Thus, the required equation of a parabola expressed in vertex form is f(x) = (x + 2)² - 1.

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Answer:

A: $7.50 per cap

Step-by-step explanation:

IM BACCCCKKKKK XD

we use the slope formula of y2-y1/x2-x1

37.5-22.5/5-3

15/2

7.5

So he gets $7.50 per cap

Hopes this helps please mark brainliest

Answer: He gets $7.50 per cap.

Step-by-step explanation:

If at 3 caps he got $22.50, we'll need to divide $22.50 by 3 to get the cost for a single cap.

$22.50/3 = $7.50

This means that he gets $7.50 per cap.

The x value that more contradictory to h0 than 117.2 is the value less than 117.2 and p-value is 0.0465 and the conclusion is we reject h0.

μ = mean = 120

x = 117.2

σ = standard deviation = 10

n = random sample = 36

Lets take the z test,

z = [tex]\frac{x-\mu }{\sigma / \sqrt{n}}[/tex]

= [tex]\frac{117.2 - 120}{10/\sqrt{36}}[/tex]

= [tex]\frac{-2.8}{1.667}[/tex]

= -1.68

From the test, we know test is left tailed and the rejection area is negative. So, the less x than 117.2 the more contradictory to h0.

For p-value use z-score table and we get 0.0465. Because the p-value is less than the appropriate α, which is 0.1, it can be concluded that h0 is rejected.

Thus, the less x value than 117.2 the more contradictory to h0 and we rejected h0 because p-value is lower than appropriate α.

Your question is incomplete, but most probably your full question was (image attached)

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The  end behavior of function is positive non decreasing.

A function is a relationship between a set of inputs and a set of allowable outputs in mathematics. The feature of functions is that each input corresponds to exactly one output. For example, in the function f(x)=x², any x input will result in only one output.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.

Given function f(x) = 5/4x²

as the function is square of x hence we can clearly see function is positive

Hence end behavior of function is positive non decreasing.

The complete question is : What is the end behavior of the function f(x)=5/4x2?

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The margin of error is approximately 0.3

To answer the question, we must figure out what margin of error corresponds to a 90% confidence level. The definition of the margin of error used to create confidence intervals for the population mean is as follows;

Mean = μ = 20.6

Standard deviation = σ = 2.7

Number of students = n = 225

the result of the sample mean's standard error and the accompanying z-score. The formula used to compute the sample mean's standard error is;

⇒  σ / √n

The z-score associated with a 90% confidence level:

From the given table z-score is 1.645

Therefore, the margin of error;

σ / √n * 1.645 = 2.7/√225 * 1.645

                      = 0.296

Hence, the margin of error is approximately 0.3

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Answer:

Approximately 0.3 of an error is allowed.

Given data in question

Confidentialevel=90%

Mean = μ = 20.6

2.7 as the standard deviation

N = 225 students are enrolled.

the outcome of the standard error of the sample mean and the corresponding z-score. The formula used to determine the standard error of the sample mean is;

⇒ σ / √n

The z-score for a 90% degree of confidence is:

Z-score for the provided table is 1.645.

Consequently, the error margin;

σ / √n * 1.645 = 2.7/√225 * 1.645

= 0.296

Consequently, the margin of error is roughly 0.3.

The compression work if the final state is 500 kpa will be 44.32KJ

Step-by-step explanation:

The stated circumstance is;

P₁= 1.0 MPa

T₁ = 250°C

M=0.6 Kg

v₂=0.4v₁

v₁=0.30661 m/sec

P₂=1 Mpa

T₂=250°C

repairs made to the piston;

 W= mP(V2-V1),

W= 0.6*1,000(0.232-0.30661)

W= -44.32\J

illustrates the compression work using (- ve)

Since there is pressure in the final condition, the compression work is 44.32. (KJ)

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Convenience sampling is not a type of statistical sampling.

What is statistical sampling?

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study.

If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

Main body:

Simple random sample:

Each individual and group of individuals have the same chance of being selected for the sample. To obtain a basic random sample, one needs technology, random number generators, or some other type of chance mechanism.

stratified Random sample :

The population is first divided into sections. There are some people from each group in the overall sample. Each group's participants are chosen at random.

Cluster sampling:

Grouping the population first, a cluster random sample is taken. Every member of some of the groups makes up the overall sample. The selection of the groups is random.

Hence Convenience sampling is not a type of statistical sampling.

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The car is about a year old if it depreciates exponentially at a rate of 9% per year 0.62

In order to know how old the car is, we will use the depreciation formula expressed below:

[tex]P_{t}=P_{0}e^{rt}[/tex]

[tex]P_t[/tex] is the final price = 16000

[tex]P_0[/tex]  is the initial price = 28000

Given the rate of 0.09

Substitute the given parameters into the formula to get the time "t"

[tex]16000 = 28000e^{0.09t}[/tex]

[tex]\frac{16000}{28000} = e^{0.09t}[/tex]

t=0.5714/0.9139

This shows that the car is about a year old if it depreciates exponentially at a rate of 9% per year

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The distance covered by bicycle is 1.885 km.

What is distnace?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.

Given:  A bicycle wheel with radius 30cm made 1000 revolutions.

We have to find the total distance covered by bicycle.

First to find the circumference of the bicycle wheel.

Circumference = 2πr

where, r is the radius.

Here r = 30.

So,

Circumference = 2 x π x 30 = 60π

Now to find the total distance,

D = circumference x number of revolutions.

D = 60π x 1000

D = 188,495.5592 cm

D = 188,495.5592 /1000 km

D = 1.88 km

Therefore, the distance covered by bicycle is, 1.885 km.

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Answer: -6

Step-by-step explanation:

Answer:

5 + (1/x)

Step-by-step explanation:

(3x - 4x + 2) - (7x - 10x - 8x)

3x - 4x + 2 - 7x + 10x + 8x

(3x - 4x - 7x + 10x + 8x) = 10x

10x + 2

  10x + 2     10x        2               1

  ---------- = ------- + ------- = 5 + ------

      2x          2x        2x              x

I hope this helps!

Answer: 3

Step-by-step explanation:

Answer:(4 x 103) x (2 x 107) = ( 4 x 2 ) x ( 103 + 7 ) = 8 x 10 10.

Step-by-step explanation:

The obtained expression after subtracting  8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Is given expression is, Subtract 8x¹⁰ from x² - 2x.

In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.

=8x¹⁰-x²+2x

=8(x²)⁵-x²+2x

=x²(8x⁴-1)+2x

Thus, the obtained expression after subtracting  8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.

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The factors of the given expression are [tex]\frac{(x-1)^{2}}{x^{\frac{3}{2} }}[/tex]  .

In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftovers. We may employ a variety of techniques, including the division method and the multiplication method, to determine the factors of a given integer. When we need to split anything into equal rows and columns, compare prices, exchange money, and other real-world scenarios, we employ factors.

The given expression is [tex]x^{\frac{-3}{2}} -2x^{\frac{-1}{2} }+ x^{\frac{1}{2} }[/tex]

Apply the exponential rule [tex]a^{b+c}= a^{b}a^{c}[/tex], so we can write

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

Factor out the common term [tex]x^{\frac{-1}{2} }[/tex]

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

Apply the exponential rule [tex]a^{b+c}= a^{b}a^{c}[/tex],

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

Factor out the common term [tex]x^{\frac{-3}{2} }[/tex]

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

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

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

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Answer:

10 meters

Step-by-step explanation:

Use the pythagorean theorem. 'c' represents the length of the hypotenuse of a right triangle.

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]6^{2} +8^{2} = 100\\[/tex]

[tex]c^{2} =100\\c=10[/tex]

Take the sq rt of 100 which is 10

Answer:

10 meters

Step-by-step explanation:

hypotenuse = √(6² + 8²)

hypotenuse = √(36 + 64)

hypotenuse = √100

hypotenuse = 10 m