Answer:
£7,440
Step-by-step explanation:
We have been given the tax rates as follows:
$0-$11,000 = No tax.
$11,000-$43,000 = 20%.
$43,000-$150,000 = 40%.
Earnings over $150,000 = 45%.
Since last year Carys earned $45,600, so we will have to find the tax paid by her for 11,000-43,000 at rate of 20%, then the tax for amount over 43,000 at the rate of 40%
Therefore, Carys paid an amount of $7,440 in tax.
Carys paid no tax on the first £11,000 of her income. She paid £6,400 in tax on her earnings between £11,000 and £43,000, and £1,040 on her earnings between £43,000 and £45,600. The total tax paid was £7,440.
Explanation:To calculate how much tax Carys paid on her earnings of £45,600, we need to apply the given tax rates to the appropriate segments of her income. Here is the step-by-step working:
She pays no tax on the first £11,000.Earnings between £11,000 and £43,000 are taxed at 20%. To find the tax for this bracket, we subtract £11,000 from £43,000 to get the taxable amount, which is ¤32,000. Then we calculate 20% of ¤32,000, which amounts to £6,400.Earnings above £43,000 up to £150,000 are taxed at 40%. Carys earned ¤2,600 in this bracket (because £45,600 - £43,000 = ¤2,600). The tax on this amount is 40% of ¤2,600, which is £1,040.Since Carys did not earn over £150,000, she does not pay any tax at the 45% rate.We now add the tax from the second and third bullet points to get the total tax that Carys pays: £6,400 + £1,040 = £7,440.
Therefore, Carys paid a total of £7,440 in tax for the last year.
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What is the value of 5^4 over 5^6
One number is 3 more than another. Their sum is -13. Find the numbers
A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A? 50 ≤ x ≤ 58 x ≥ 50 or x ≤ 58 x ≥ 52 or x ≤ 56 52 ≤ x ≤ 56
The inequality that represents the predicted possible percent of votes is 50 ≤ x ≤ 58
The margin of error (E) shows by how much the measured value can differ from the mean value.
Given that the probability of winning the election is 54% and there is a margin of error of 4%, hence:
Let x represent the predicted possible percent of votes.
x = 54% ± 4%
x = (54% - 4%, 54% + 4%)
x = (50%, 58%)
The inequality that represents the predicted possible percent of votes is 50 ≤ x ≤ 58
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The inequality representing the predicted possible percent of votes for candidate A is [tex]\( 50 \leq x \leq 58 \)[/tex].
The predicted possible percent of votes, x, for candidate A considering the margin of error can be represented as follows:
Given:
- Predicted percentage of votes for candidate A = 54%
- Margin of error = ±4%
The predicted range of percentages for candidate A can be expressed as:
[tex]\[ 54\% \pm 4\% \][/tex]
This translates to:
[tex]\[ 54\% - 4\% \leq x \leq 54\% + 4\% \][/tex]
Calculate the lower and upper bounds:
[tex]\[ 50\% \leq x \leq 58\% \][/tex]
Therefore, the inequality that represents the predicted possible percent of votes x for candidate A is [tex]\( \boxed{50 \leq x \leq 58} \)[/tex].
Complete question:- A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A?
50≤ x≤ 58
x≥ 50 or x≤ 58
x≥ 52 or x≤ 56
52≤ x≤ 56
Sterday, a movie theater sold 262 bags of popcorn. a large bag of popcorn costs $3. a small bag of popcorn costs $1. in all, the movie theater made $412 from popcorn sales. write and solve a system of equations to find how many bags of each size of popcorn were sold.
For many hotels, including the Grand Hotel Toplice, the price of a room will fluctuate depending on _____
a.
the time of day
b.
the time of year
c.
the gender of the person
d.
the nationality of the person
Answer:
b.
the time of year
Step-by-step explanation:
The question is to select a suitable option from the given four option to find out the factor that affects the price of room most
a) Time of day is immaterial as hotels charge 24 hours at whatever time they enter.
b) time of year -- this is a correct factor as prices of rooms depend upon demand and demand increases due to seasons, holidays, festivals, etc.
c) the gender of the person is irrelevant in determining the price of the room as equal prices for both genders.
d) nationality of the person cannot differentiate the prices charged
Hence the suitable option is
b.
the time of year
The center of the circle is A( -3,3) and B(1,6) is on the circle. Find the area of the circle in terms of pie
419% of what number is 33.52 ? Find the answer in proportions
To solve the problem, '419% of what number equals 33.52?', one sets up a proportion and solves for the unknown. The calculated result equates to approximately 7.99.
Explanation:This question is asking for the base number where 419% of it equals 33.52.
Proportions play a crucial part in the calculation. Think of percentages as fractions with a denominator of 100. So, 419% can be written as 419/100. Now, let's set up a proportion to find our unknown number:
Let the unknown number be x.Set the proportions as follows: (419/100) / x = 33.52 / 1. This is because 419% of x equals 33.52.Now, cross-multiply and solving for x gives you the equation 419 * 1 = 100 * 33.52.Finally, solving for x gives x = (100 * 33.52) / 419. This results in approximately 7.99.Learn more about Percent Proportions here:https://brainly.com/question/31487888
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Find the average rate of change for f(x) = x2 + 9x + 18 from x = −10 to x = 10.
a.3
b.7
c.9
d.11
The average rate of change of the given function is 9.
Given that, a function f(x) = x²+9x+18, we need to find the average rate of change for the function given,
So, the average rate of change = f(b)-f(a) / b-a
Here, a and b are -10 and 10,
So, f(-10) = 100-90+18 = 28
f(10) = 100+90+18 = 208
So, the average rate of change = 208-28 / 10+10
= 180 / 20 = 9
Hence, the average rate of change of the given function is 9.
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Please explain your answer thanks
What is the solution to the system of equation?
-3x-4y-32= -7
2x-6y+2=3
5x-2y+5z=9
Answer:
[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]
Step-by-step explanation:
we are given three equation of variable x, y and z.
-3x-4y-3z= -7 ------------- (1)
2x-6y+z=3 ------------- (2)
5x-2y+5z=9 ------------- (3)
Using elimination method to eliminate z from equation (1) and (2)Make the coefficient of z same in both equation.
Multiply equation (2) by 3
-3x - 4y - 3z = -7
6x - 18y + 3z = 9
Add above equation to eliminate z
3x - 22y = 2 ---------------(4)
Using elimination method to eliminate z from equation (2) and (3)Make the coefficient of z same in both equation.
Multiply equation (2) by -5
-10x + 30y - 5z = -15
5x - 2y + 5z = 9
Add above equation to eliminate z
-5x + 28y = -6 ---------------(5)
Using elimination method to eliminate x from equation (4) and (5)Make the coefficient of x same in both equation.
Multiply equation (4) by 5 and equation (5) by 3
15x - 110y = 10
-15x + 84y = -18
Add above equation to eliminate x
-26y = -8
[tex]y=\dfrac{4}{13}[/tex]
Substitute y into equation (5) to get x
So, [tex]-5x+28(\frac{4}{13})=-6[/tex]
[tex]x=\dfrac{38}{13}[/tex]
Substitute x and y into equation (1)
[tex]-3\cdot \frac{38}{13}-4\cdot \frac{4}{13}-3z=-7[/tex]
[tex]z=-1[/tex]
Solution:
[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]
Help with number 6 and 7! Extra points and brainliest!!
I need this question answered asap! Thank you advance!!
The population in Rochester, New York, was 219,773 people in 2000 and 210,565 people in 2010. By about what percent did the population change? Did the population grow or shrink? Write the percent as a decimal.
Answer:
The population changed by 4.19%. The population shrank.
0.0419.
Step-by-step explanation:
We have been given that the population in Rochester, New York, was 219,773 people in 2000 and 210,565 people in 2010.
[tex]\text{Percent change}=\frac{\text{Final}-\text{Initial}}{\text{Initial}}\times 100[/tex]
[tex]\text{Percent change}=\frac{210,565-219,773}{219,773}\times 100[/tex]
[tex]\text{Percent change}=\frac{-9,208}{219,773}\times 100[/tex]
[tex]\text{Percent change}=-0.04189777\times 100[/tex]
[tex]\text{Percent change}=-4.189777\%[/tex]
[tex]\text{Percent change}\approx-4.19\%[/tex]
Therefore, the population changed by 4.19%.
Since the percent change is negative, therefore, the population decreased or shrank over the given period.
[tex]4.19\%=\frac{4.19}{100}=0.0419[/tex]
How many squares with side length 1/4 inch will fit into 1 square inch?
How many squares with side length 1/4 inch will fit into 1 square inch?
A) 1
B) 16
C) 4
D) 25
The number of squares with side length 1/4 inch that would fit into a 1-square inch is 4
A square to a four-sided quadrilateral that has four equal sides. A square has four right angles. The sum of angles in a square add up to 360 degrees.
Area of a square = length²
Perimeter of a square = 4 x length
In order to determine how many squares would fit into the a 1 inch square, divide the length of the square by the 1/4
Number of squares = 1 ÷ 1 / 4
1 x 4 = 4 squares
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graph and solve the system
Y=-3x+3
Y=2x-7
Suppose that y varies inversely with x. Write an equation for the inverse variation. y = 4 when x = 6
The equation for the inverse variation is y = 24/x.
Explanation:In an inverse variation, the equation can be represented as y = k/x, where k is a constant. To find the equation for the given scenario, we can substitute the values of y = 4 and x = 6 into the equation and solve for k.
4 = k/6
Cross-multiplying, we get k = 24. Therefore, the equation for the inverse variation is y = 24/x.
The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
The value of point R is -2.5 if point R is halfway between the integers on the number line; the answer is -2.5.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
The number line is shown in the picture.
Let the number is R which is halfway between the integers on the number line.
A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
R is between the integers -3 and -2:
R = (-3 + (-2))/2 = -5/2
R = -2.5
Thus, the value of point R is -2.5 if point R is halfway between the integers on the number line; the answer is -2.5.
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Fran graphs the equations y = 2x2 – 2 and y = –0.5x + 4. Her graph is shown below.
Which value is an approximate solution of 2x2 – 2 = –0.5x + 4?
Answer:
A
Step-by-step explanation:
I just took the test
Write the ratio as a fraction in simplest form. 213213 feet : 412412 feet the ratio as a fraction in simplest form is .
What is the sum of the geometric sequence 1, 3, 9, … if there are 10 terms?
Answer: 29524
Step-by-step explanation:
Given geometric sequence : 1, 3, 9, …........................
First term of G.P. [tex]a = 1[/tex]
Second term of G.P.[tex]a_2=3[/tex]
Common ratio =[tex]r=\frac{a_2}{a}=\frac{3}{1}=3[/tex]
We know that the sum of the geometric sequence with n terms is given by :-
[tex]S=\frac{a(r^n-1)}{r-1}[/tex] for |r|>1
Substitute a = 1 , r =3 and n=10 , we get
[tex]S=\frac{1(3^(10)-1)}{3-1}\\\\=\frac{59049-1}{2}\\\\=-\frac{59048}{2}\\\\\Rightrrow\ S=29524[/tex]
What is the largest rectangular area that can be enclosed with 400 feet of fencing?
An angle measuring 22 degrees is bisected what is the measure of he angle that are formed?
i will give brianliest
Lars bought 3 jars of marbles. Each jar has 42 marbles, of which 13 are red. Lars can use the calculation below to find the total number of red marbles.
3×(13×42)
How can Lars simplify the calculation using only the associative property of multiplication?
a1/3 b 3 c 42 d (3×13) e (13×42)
Answer:
3 times 1/3
Step-by-step explanation:
in parallelogram ABCD, angle D is a right angle. determine whether the parallelogram is a rectangle. If so, by what property
Which property of multiplication is used to rename 5/6 to 10/12?
The property of scaling or multiplying by a fraction is used to rename 5/6 to 10/12.
Explanation:The property of multiplication used to rename 5/6 to 10/12 is the property of scaling or multiplying by a fraction. To rename a fraction, you can multiply both the numerator and denominator by the same number. In this case, we can multiply both 5 and 6 by 2 to get 10 and 12 respectively. Therefore, 5/6 = 10/12.
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PLEASSEEE HELPPP
Daisy's friend calls her and asks her to meet at the park in exactly 40 minutes. Which method should Daisy use to most accurately determine when 40 minutes have passed?
A. Daisy should use a stopwatch with minutes and seconds.
B. Daisy should count the minutes in her head after she receives the call.
C. Daisy should use an hourglass and flip it over every time the sand runs out.
D. Daisy should look at a clock that shows hours and minutes only.
A rectangle has an area of 98 square inches. the length of the rectangle is double the width of the rectangle. find the dimensions of the rectangle
The midpoint of EF is M (4,10) one endpoint is E (2,6). Find the coordinates of the of the other endpoints F.
6,14
6,17
10,17
14,8
By applying this formula and solving for the unknown coordinates, the coordinates of endpoint F are determined to be (6, 14).
The student is asking to find the coordinates of the other endpoint F of a line segment EF given that the midpoint M is (4,10) and one endpoint E is (2,6). To find the coordinates of F, we can use the midpoint formula which states that the midpoint's coordinates are the averages of the endpoints' coordinates:
Midpoint Formula
Mx = (Ex + Fx) / 2
My = (Ey + Fy) / 2
Knowing the coordinates of endpoint E (2, 6) and midpoint M (4, 10), we can set up two equations to solve for the coordinates of F.
Finding Fx
4 = (2 + Fx) / 2
=> Fx = 4 * 2 - 2
=> Fx = 6
Finding Fy
10 = (6 + Fy) / 2
=> Fy = 10 * 2 - 6
=> Fy = 14
Therefore, the coordinates of the other endpoint F are (6, 14).
PLEASE PLEASE HELP IM LITERALLY CRYING.
Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down.
What is the equation for g(x)?
Enter your answer in the box.
g(x)= ????
Answer:
g(x) = 32x-7
Step-by-step explanation:
A vertical stretch is shown in an equation by multiplying the equation by a factor greater than 1. Since we are stretching by a factor of 4, we multiply the equation by 4:
g(x) = 4(8x) = 32x
A vertical translation is performed by subtracting a value from a function. To translate the function 7 units down, we will subtract 7 from the equation:
g(x) = 32x-7
The equation for g(x) = 32x - 7.
Given that,
Let f(x) = 8x,The graph of f(x) should be transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down.Based on the above information, the calculation is as follows:
g(x) = 4(8x)
= 32x
Now here we subtract 7 from the equation.
So, it is g(x) = 32x-7
Therefore we can conclude that the equation for g(x) = 32x - 7.
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Which is a rational function?
A. y=sqrt x-3
B. y=5
C. y=x^2-3x+5
D. y=x-5/x
Find an expression in terms of n for the number of grey tiles in pattern n?