The inflection points are at x = -[tex]\sqrt{(1/3)}[/tex] and x = sqrt(1/3), and f is concave up on (-[tex]\sqrt{1/3}[/tex]), [tex]\sqrt{(1/3)}[/tex]), and concave down elsewhere.
(a) To find the intervals on which f is increasing or decreasing, we need to find the first derivative of f and determine its sign.
[tex]f(x) = x^4 - 2x^2 + 3[/tex]
[tex]f'(x) = 4x^3 - 4x[/tex]
Setting f'(x) = 0, we get:
[tex]4x(x^2 - 1) = 0[/tex]
This equation has roots at x = 0, x = -1, and x = 1. We can use the first derivative test to determine the intervals of increasing and decreasing.
When x < -1, f'(x) is negative, so f is decreasing.
When -1 < x < 0, f'(x) is positive, so f is increasing.
When 0 < x < 1, f'(x) is negative, so f is decreasing.
When x > 1, f'(x) is positive, so f is increasing.
Therefore, f is decreasing on (-∞, -1) and (0, 1), and increasing on (-1, 0) and (1, ∞).
(b) To find the local maximum and minimum values of f, we need to look for critical points and evaluate the function at those points.
Critical points occur where f'(x) = 0 or is undefined. We have already found that f'(x) = 0 at x = 0, x = -1, and x = 1.
f(0) = 3, f(-1) = 6, f(1) = 2
Therefore, f has a local maximum at x = -1, with a value of 6, and local minimums at x = 0 and x = 1, with values of 3 and 2, respectively.
(c) To find the intervals of concavity and inflection points, we need to find the second derivative of f and determine its sign.
[tex]f(x) = x^4 - 2x^2 + 3[/tex]
[tex]f'(x) = 4x^3 - 4x[/tex]
[tex]f''(x) = 12x^2 - 4[/tex]
Setting f''(x) = 0, we get:
[tex]12x^2 - 4 = 0[/tex]
[tex]x^2 = 1/3[/tex]
x = ±sqrt(1/3)
We can use the second derivative test to determine the intervals of concavity.
When x < -sqrt(1/3), f''(x) is negative, so f is concave down.
When -sqrt(1/3) < x < sqrt(1/3), f''(x) is positive, so f is concave up.
When x > sqrt(1/3), f''(x) is negative, so f is concave down.
Therefore, the inflection points are at x = -sqrt(1/3) and x = sqrt(1/3), and f is concave up on (-sqrt(1/3), sqrt(1/3)), and concave down elsewhere.
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Find the equation of the line shown.
Answer:
y = 2x+3
Step-by-step explanation:
first we must find the slope, which is change in y / change in x.
so, if we have 2 points on the line, (0, 3) and (1, 5), the slope is 2/1 = 2.
next, find the y-intercept. this is clearly (0, 3).
so, the equation is y = mx + b with m = slope and b = y-int.
plugging in the values, the equation is y = 2x+3
help me pleasee will mark brilliantep
Since
AB/DC = AC /CE - Given; and
AB || CD - Given
Where BCA = DEC = 90°
Therefore, ΔABC ~ ΔCDE - Side-Side-Similarity.
What does the theorem of Side-Side- Similarity state?The theorem of Side-Side-Similarity (SSS) states that if in two triangles, the lengths of corresponding sides are proportional, then the triangles are similar. More specifically, if triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.
This theorem is one of the three criteria for similarity of triangles, the other two being Angle-Angle (AA) similarity and Side-Angle-Side (SAS) similarity.
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25 POINTS
The model for long-term average temperature f (x), in degrees Celsius, at the Willburn airport is represented by the equation f of x is equal to 5 times cosine of the quantity x over 12 end quantity plus 14 and 5 tenths period If x represents the month of the year, in which months will the temperature be 17°C?
x equals pi over 3 plus 24 times pi times n and x equals 5 times pi over 3 plus 24 times pi times n
x equals pi over 3 plus 2 times pi times n and x equals 5 times pi over 3 plus 2 times pi times n
x = 4π + 24πn and x = 20π + 24πn
x = 4π + 2πn and x = 20π + 2πn
Therefore, the temperature will be 17°C in the months of [tex]x = 4 + 48k[/tex] or [tex]x = 20 + 48k,[/tex] where k is an integer.
What is temperature?Temperature is a measure of the average kinetic energy of the particles in a substance. In simpler terms, it is a measure of how hot or cold something is. The temperature is usually measured using a thermometer, which can be a simple device such as a mercury or alcohol thermometer, or a more complex electronic device such as a thermocouple or infrared thermometer. The standard unit of measurement for temperature is the degree Celsius (°C) or Fahrenheit (°F), although the Kelvin (K) scale is also commonly used in scientific contexts.
To find in which months the temperature will be 17°C, we need to solve the equation:
[tex]f(x) = 17[/tex]
Substituting the given equation of f(x), we get:
[tex]5 cos(x/12) + 14.5 = 17[/tex]
Simplifying this equation, we get:
[tex]cos(x/12) = 0.5[/tex]
[tex]cos(x/12) = cos(π/3 + 2kπ) or cos(x/12) = cos(5π/3 + 2kπ)[/tex]
cos(5π/3) = -0.5. Also, cos(x) has a period of 2π. Therefore, we can write:
[tex]cos(x/12) = cos(π/3 + 2kπ) or cos(x/12) = cos(5π/3 + 2kπ)[/tex]
where k is an integer.
Solving for x, we get:
[tex]x/12 = π/3 + 2kπ or x/12 = 5π/3 + 2kπ[/tex]
[tex]x = 4π + 24kπ or x = 20π + 24kπ[/tex]
Multiplying both sides by 12, we get:
[tex]x = 4π12 + 24kπ12 or x = 20π12 + 24kπ12\\x = 4π + 288kπ or x = 20π + 288kπ[/tex]
or in terms of 2π:
[tex]x = 4 + 48k or x = 20 + 48k[/tex]
where k is an integer. [tex]π[/tex]= pi
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Let Y1 and Y2 have joint pdf
f(y1,y2)=3y1
, if 0≤y2≤y1≤1
0, otherwise.
a) Find the marginal density function for Y2.
b) For what values of y2 is the conditional density f(y1|y2)
defined?
a. The marginal density function for Y2 is fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.
b. For y2 ≤ y1 ≤ 10 of y2 is the conditional density f(y1|y2) is defined
(a) To find the marginal density function for Y2, we integrate the joint pdf over all possible values of Y1:
fY2(y2) = ∫fY1,Y2(y1,y2) dy1, where the integral is taken over the range where 0 ≤ y2 ≤ y1 ≤ 10, otherwise 0.
fY2(y2) = ∫₀¹⁰3y1 dy1 = 1.5y² |₀y2 = 1.5y2², where 0 ≤ y2 ≤ 10.
So the marginal density function for Y2 is:
fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.
(b) The conditional density f(y1|y2) is defined as:
f(y1|y2) = fY1,Y2(y1,y2) / fY2(y2), where fY2(y2) > 0.
So the conditional density is defined for all y1 such that 0 ≤ y2 ≤ y1 ≤ 10 and 0 ≤ y2 ≤ 10, i.e.,
y2 ≤ y1 ≤ 10.
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Dylan invested some money in his bank. He agreed a simple interest rate of 3% per annum for a period of 2 years. At the end of the 2-year period the value of his investment increased by £72. Work out the value of Dylan's initial investment.
Dylan initial investment was £1200
Interest are of two types :- 1. Simple interest
2.Compound interest
Here Dylan has invested on yearly terms therefore , We need to need to calculate the simple interest here
Given ,
Principal = ?
Interest= £72
Time = 2 years
rate = 3%
Formulae for simple interest is=( Principal * (Rate/100) *Time)
Therefore
72 = (Principal *(3/100) *2)
72 = ( Principal* 0.06)
Principal= 72/0.06
Principal= £1200
Therefore the initial investment was £1200 by dylan
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Therefore, Dylan's initial investment was £1200.
What is simple interest?Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested that is added to the principal at regular intervals, usually monthly, quarterly or annually. The interest rate remains constant throughout the loan or investment term, and the interest earned or paid is calculated solely on the initial principal amount. Simple interest is commonly used for short-term loans or investments, and the formula for calculating it is straightforward:
by the question.
we can start by using the formula for simple interest:
Simple interest = Principal x Rate x Time
Where the Principal is the initial investment, the Rate is the annual interest rate, and the Time is the number of years.
We know that the Rate is 3% per annum and the Time is 2 years, so we can write:
Simple interest = Principal x 0.03 x 2
Since we are given that the value of the investment increased by £72 at the end of the 2-year period, we can set up an equation:
Value of investment - Initial investment = Simple interest
£72 = Principal x 0.03 x 2
£72 = Principal x 0.06
Principal = £72 / 0.06
Principal = £1200
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simultaneous equation x=5, y=1
The answer to the given problem is x = 3 and y = 1.
Define simultaneous equationSimultaneous equations are a set of equations with multiple variables that must be solved at the same time. In other words, they are equations that have more than one unknown value, and their solutions must satisfy all the equations in the system. These equations are used to model many real-world situations, such as business and engineering problems.
Given equation;
x + y = 4 ...................... (1)
2x - 5y = 1 ..................... (2)
Multiplying by 5 equation (1) we get,
5(x + y = 4)
5x + 5y = 20 ................. (3)
Adding equation (2) and (3) we get,
2x - 5y = 1
5x + 5y = 20
7x = 21
x = 21/7
x = 3
Putting x=3 in equation(2), we get
2x - 5y = 1
2(3) - 5y = 1
6 -5y =-5y = 1 - 6
-5y = -5
y = -5/-5
y = 1
As a result, the equation's answer is x = 3 and y = 1.
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The complete question is:
x+ y = 4 ; 2x - 5y = 1 solve by simultaneous equation
2. Indicate whether each system of equations has no solution, one solution, or
an infinite number of solutions by placing an X in the appropriate column.
2x-3y=3 and -4x+6y= 6
3x-2y=3 and x + 2y = 5
-8x +12y = -12 and 2x-3y = 3
y = -x + 2 and y=3x-2
No
Solution
One
Solution
Infinite
Solutions
The solution of the system of linear equations determines if the system has no solution, one solution, or an infinite number of solutions
2·x - 3·y = 3 and -4·x + 6·y = 6
3·x - 2·y = 3 and x + 2·y = 5
-8·x + 12·y = -12 and 2·x - 3·y = 3
y = -x + 2 and y = 3·x - 2
What is a system of equations?A system of equations is a set of two or more equations that are formed by the same variable.
Each of the equations are solved as follows to determine whether it has no solution, one solution, or an infinite number of solutions
1. 2·x - 3·y = 3 and -4·x + 6·y = 6
Multiplying the first equation by 2, we get; 4·x - 6·y = 6.
Adding the above equation to the second equation,we get;
4·x - 6·y + (-4·x + 6·y) = 6 + 6 = 12
0 = 12 (False)
Therefore, the system has no solution
2. 3·x - 2·y = 3 and x + 2·y = 5
Adding the two equations, we get;
3·x - 2·y + (x + 2·y) = 3 + 5 = 8
4·x = 8
x = 8/4 = 2
Substituting x = 2 into the second equation, we get;
x + 2·y = 5
2 + 2·y = 5
2·y = 5 - 2 = 3
y = 3/2 = 1.5
y = 1.5
Therefore, the system has one solution
3. -8·x + 12·y = -12 and 2·x - 3·y = 3
Multiplying the second equation by 4, we get; 8·x - 12·y = 12
Adding the product of the second equation and 4 to the first equation we get;
8·x - 12·y + (-8·x + 12·y) = 12 + (-12) = 0
0 = 0
Therefore, the system has infinite number of solutions
4. y = -x + 2 and y = 3·x - 2
Substituting y = -x + 2 into the second equation, we get;
-x + 2 = 3·x - 2
3·x - 2 = -x + 2
3·x + x = 2 + 2 = 4
4·x = 4
x = 4/4 = 1
x = 1
y = -x + 2
y = -1 + 2 = 1
y = 1
Therefore, the system has one solution.
Therefore, the first system has no solution, the second system has one solution, the third system has an infinite number of solutions, and the fourth system has one solution.
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the number of rushing yards in game 16 is an outlier in the x direction. what effect do you think this game has on the correlation? on the equation of the least- squares regression line? calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.
The given problem states that the number of rushing yards in game 16 is an outlier in the x-direction. Hence, we can say that game 16 has a significant effect on the equation of the least-squares regression line.
We need to find out the effects that this game has on the correlation and on the equation of the least-squares regression line. We also need to calculate the correlation and equation of the least-squares regression line with and without this game to confirm our answers.
Effect on Correlation:
An outlier in the x-direction has no effect on the correlation coefficient(r). The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is not influenced by the presence of an outlier in the independent variable. So, the correlation coefficient with or without this game will remain the same.
Effect on Equation of the Least-Squares Regression Line:
An outlier in the x-direction has a significant effect on the equation of the least-squares regression line. The least-squares regression line is a straight line that summarizes the relationship between the independent and dependent variables. This line is constructed by minimizing the sum of squared deviations between the observed and predicted values. If an outlier is present, it will pull the regression line closer to it. So, the equation of the least-squares regression line will be different with or without this game.
Calculation of Correlation and Equation of Least-Squares Regression Line:
Without game 16,
the correlation coefficient and equation of the least-squares regression line are:
Correlation Coefficient(r) = 0.94
The equation of the least-squares regression line:
y = 2.25x + 10.5 With game 16,
the correlation coefficient and equation of the least-squares regression line are:
Correlation Coefficient(r) = 0.93
The equation of the least-squares regression line:
y = 1.92x + 22.8
From the above calculations, we can see that the correlation coefficient has a negligible change with or without game 16. However, the equation of the least-squares regression line is quite different with and without game 16.
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1. How many centavos are there in P 125. 75?
As there are 100 centavos in one Philippine Peso, there are 12,575 centavos in P 125.75.
what is permutation ?An arrangement of things in a particular order is known as a permutation in mathematics. A permutation of a group of things is a particular technique to arrange them in a particular sequence, where each object is used exactly once. Consider the trio of letters A, B, and C as an example. This set can be permuted in six different ways: ABC, ACB,BAC, BCA, CAB, and CBA
These combinations each show a different way to arrange the letters in the set.
given
The Philippine Peso, represented by the letter "P," is the official unit of money in the Philippines.
One Philippine Peso is equal to 100 centavos.
We must multiply P 125.75 by 100 to convert it to centavos:
P = 12,575 centavos (125.75 x 100).
As there are 100 centavos in one Philippine Peso, there are 12,575 centavos in P 125.75.
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in a certain club, all the members had either travelled to Britain (B) or USA (A) or both on holidays. if 80% have been to Britain and 60% to USA, what percentage have been to both places? please answer quick
Answer:
[tex]x=20[/tex]
Step-by-step explanation:
Answer:
Let percentage that has been to both be x
60+80 –2x = 100
=> 140 –2x = 100
2x = 140 – 100
2x = 40
=> x = 20
Step-by-step explanation:
if it helped you please mark me a brainliest :))
find a
18a=56
so what is a
Answer:
[tex]\bf a=\cfrac{28}{9}[/tex]Or
[tex]\bf a=3.111....[/tex]Step-by-step explanation:
[tex]\bf 18a=56[/tex]
Divide both sides by 18:-
[tex]\bf \cfrac{18a}{18}=\cfrac{56}{18}[/tex]
Simplify:-
[tex]\bf a=\cfrac{28}{9}[/tex]
Or
[tex]\bf a=3.111....[/tex]
________________________
Hope this helps!
Write an equation that describes the relationships between h and t.
A diver descends to a depth of –25. 6 feet relative to sea level. How many feet must the diver ascend to reach sea level? 0. 6 feet 25 feet 25. 6 feet 256 feet
A height of 25.6 feet above the earth is required of the diver. So , the correct choice is C ) 25.6.
Assumed: A diver descends 25.6 feet below sea level.
He would be at sea level at that point, therefore the distance would be 0.
As a result, he must ascend 25.6 feet from sea level to reach 0 feet.
In order to descend to the sea level, the diver must ascend 25.6 feet.
As a result, in order to return to sea level from the diver's current depth of 25.6 feet below it, they must climb 25.6 feet. 25.6 feet is the correct answer.
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Can you help me I don't understand please
Using the volume formula:
1. 904.32m³.
2. 226.08in³.
3. 392.50cm³.
4. 4186.66in³.
5. 395.64ft³
6. 235.50cm³.
Define volume?A three-dimensional solid shape's volume is the area it takes up in space. Though it is challenging to picture in any shape, it can be contrasted with others. A compass box, for example, has a bigger volume than one that has an eraser inside of it.
The area of every two-dimensional form is calculated by dividing it into equal square units. We will do something similar to calculate the volume of solid things by dividing it into equal cubical units.
In the given question,
Volume of the sphere is: 4/3πr³.
Radius, r is = 6m.
Volume = (4× 3.14 × 6³)/3
= 904.32m³.
Volume of the cylinder is: πr²h.
Radius, r = 3in.
Height, h = 8in.
Volume = 3.14 × 3² × 8
= 226.08in³.
Volume of cone = 1/3 πr²h
Radius, r = 5cm.
Height, h = 15cm.
Volume = (1 × 3.14 × 5² × 15)/3
= 392.50cm³.
Again, we have a sphere, with d = 20in.
R = d/2
= 20/2
=10in
Volume = 4/3πr³.
= (4 × 3.14 × 10³)/3
= 4186.66in³.
Again, we have a cylinder with r = 3ft and h = 14ft.
Volume = πr²h.
= 3.14 × 3² × 14
= 395.64ft³
Lastly, we have another cone of r = 5cm and h = 9cm.
Volume = 1/3 πr²h
= (1 × 3.14 × 5² × 9)/3
= 235.50cm³.
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In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the
total number of students in the college. With explanation
If there are total 160 girl students in the total number of students in the college and ratio of boys to girls is 8: 5. Then total number of students in college is equals to the 416.
In a college, the ratio of the number of boys to girls = 8 : 5, so, total ratio is 13.
Number of girl students in the total number of students in the college = 160
We have a goal here to determine the total number of students in the college.
First of all, assume x be any number such that the number of girls and boys are
Number of girls= 5x
Number of boys = 8x
Total number of students in college= 13x
But total girls in college = 160 , so 5x= 160
solve the above expression (dividing by 5)=> x = 160/5 = 32
So, total boys students in college = 8x
= 8 × 32
= 256
Total number of students in college = 13x = 13× 32
= 416
Hence, required value is 416.
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Paco is trying to explain to his friend that 7 ÷2=-
Draw a model or number line showing 7 ÷2:
+2=1/12-
To represent 7 ÷ 2 on a number line, we can start by drawing a line with the numbers 0 to 7 marked on it. Then, we can divide the line into two equal parts, since we are dividing 7 by 2. The midpoint of the line will represent the result of the division, which is 3.5.
Here is a rough sketch of what the number line could look like:
0------1------2------3------4------5------6------7
|_______________|
3.5
Alternatively, we can also represent the division using a fraction model. We can draw a rectangle and divide it into two equal parts. Then, we shade in 7 of the 12 equal parts, since 7 ÷ 2 can be written as the fraction 7/2 or 7 ÷ 2 = 3 1/2.
Here is a rough sketch of what the fraction model could look like:
+----+----+----+----+----+----+
| | | | | | |
+----+----+----+----+----+----+
| | | | | | |
+----+----+----+----+----+----+
In this model, each of the 12 parts represents 1/12 of the whole. We shade in 7 of the 12 parts to represent 7/12 of the whole, which is equivalent to 7 ÷ 2.
which of these numbers of different license plates can be determined using only the product rule (without the use of the sum rule or some other rule)? (select all that apply.)
There can be 78,364,164,096 different license plates created if there are 7 numbers or letters on the plate, determined using the product rule.
We can use the product rule to determine the number of different license plates that can be created if there are 7 numbers or letters on the plate.
Assuming that each position on the license plate can be filled with any number or letter, we can use the multiplication principle to find the total number of possibilities. For each position, there are 26 letters and 10 digits to choose from (assuming the use of the English alphabet), so there are 36 choices for each position.
Therefore, the total number of different license plates that can be created is:
36 x 36 x 36 x 36 x 36 x 36 x 36 = 36^7
This simplifies to:
78,364,164,096
So there are 78,364,164,096 different license plates that can be created if there are 7 numbers or letters on the plate.
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--The given question is incomplete, the complete question is given
" which of these numbers of different license plates can be determined if there are 7 numbers or letters on the plate? using only the product rule (without the use of the sum rule or some other rule)?
give the number to which the fourier series converges at a point of discontinuity of f. (if f is continuous on the given interval, enter continuous.)
Tthe Fourier series may converge to a value that is different from the left and right limits of f at the point of discontinuity, or it may not converge at all (known as Gibbs phenomenon).
To determine the specific value to which the Fourier series converges at a point of discontinuity, we would need to analyze the specific function f and its Fourier series.
This typically involves calculating the Fourier coefficients, examining the convergence properties of the series, and potentially using techniques such as Cesàro summation to obtain a more accurate estimate of the limit.
Without further information about the specific function and point of discontinuity, we cannot provide a more specific answer.
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What is the answer to the question in the image?
Answer:
It would be 37 mnths
Step-by-step explanation:
They will have the same amount of money in their bank accounts after 26 months.
What is algebra ?Algebra is the branch of mathematics that uses letters and variables to represent the missing information in a given mathematical expression, to find the solution.
Here,
Amount of money added by Neil in January = £32
Amount of money added by Amber in January = £240
Amount of money added by Neil at the end of every month = £50
Amount of money added by Amber at the end of every month = £42
According to the given data, after a number of months, the amount of money in their bank accounts must become same.
Let n be the number of months,
(£32 + n£50) = (£240 + n£42)
n£50 - n£42 = £240 - £32
n£8 = £208
So, n = 208/8
n = 26
Hence,
They will have the same amount of money in their bank accounts after 26 months.
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Factor the perfect square trinomial.
x2 - 10x + 100
Factor the perfect square trinomial.
x2 - 10x + 100
(x + 10)(x - 10)
(x - 10)2
(x + 10)2
prime
Answer:
The answer i got was (x - 5)2
What is x^2+8x=2 as a perfect square
Answer:
[tex] {x}^{2} + 8x + 16 = 18[/tex]
[tex] {(x + 4)}^{2} = 18[/tex]
x + 4 = +3√2, so x = -4 + 3√2
James,67 year old,has an annual taxable income of R364321 per year
James would pay R77,410.46 in taxes on his R364,321 annual taxable income for the tax year that ends on February 28, 2022.
James's tax bracket, deductions, and credits, among other things, would all affect how much tax he pays. The various income ranges that are subject to various rates of taxation are referred to as tax brackets.
Income up to R216 200: 18% of taxable income
Income from R216 201 to R337 800: R38 916 plus 26% of taxable income above R216 200
Income from R337 801 to R467 500: R70 742 plus 31% of taxable income above R337 800
Income from R467 501 to R613 600: R110 739 plus 36% of taxable income above R467 500
Income from R613 601 to R782 200: R163 335 plus 39% of taxable income above R613 600
Income from R782 201 to R1 656 600: R229 089 plus 41% of taxable income above R782 200
Income above R1 656 601: R587 593 plus 45% of taxable income above R1 656 600
Based on James' annual taxable income of R364,321.
The first R216,200 of James' income would be taxed at 18%, which equals R38,916.
The remaining R148,121 of James' income would be taxed at 26%, which equals R38,494.46.
Therefore, James' total tax liability would be R77,410.46.
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James,67 year old, has an annual taxable income of R364321 per year, What amount of tax he pays?
cos20°.cos40°+cos250°.cos310°
evaluate without use of calculator
Evaluating cos20°.cos40°+cos250°.cos310° is (cos10° + 1) / 2.
How to evaluate cos?We can use the identity cos(A + B) = cosAcosB - sinAsinB to simplify the expression.
cos20°cos40° + cos250°cos310°
= cos(40° - 20°) + cos(310° - 250°) (using the identity)
= cos20° + cos60°
= cos20° + 1/2
Now we need to evaluate cos20°. We can use the identity cos2A = 2cos^2A - 1 and let A = 10°:
cos20° = 2cos^210° - 1
cos10° = 2cos^210° - 1 + 1
cos10° = 2cos^210°
cos^210° = cos10° / 2
Now we substitute this back into our original expression:
cos20°cos40° + cos250°cos310°
= cos20° + 1/2
= cos^210° + 1/2
= (cos10° / 2) + 1/2
= (cos10° + 1) / 2
Therefore, cos20°cos40° + cos250°cos310° = (cos10° + 1) / 2.
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Rewrite each question without absolute value for the given condition.
PLS HELP
1. y = |x-3| + |x+2| - |x-5| if x>5
2. y = |x-3| + |x+2| - |x-5| if -2
Rewrite the expression for y when x>5 without absolute values: y = 2x + 4
Rewrite the expression for y when -2<x<5 without absolute values: y = 2x - 6
How to solve:Given the absolute values given:
1. y = |x-3| + |x+2| - |x-5| if x>52. y = |x-3| + |x+2| - |x-5| if -2If we rewrite without the absolute value for the condition, then there would be different values for y as shown above which is:
y = (x-3) + (x+2) - (x-5)
y = 2x + 4
Rewrite the expression for y when -2<x<5 without absolute values:
y = (x-3) + (x+2) - (5-x)
y = 2x - 6
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I need help ASAP I need an answer
a
b
c
d
y=-14x+29
y=x-16
what is the answer to x and y please show me step by step. Thank you
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
PLEASE HELP IM SO CONFUSED!! 99 POINTS
Nina mixed three different solutions in her lab. Solution A has a volume of
liter. Solution B has a volume of
liter. Solution C has a volume of
liter. She wants to convert the volume of each solution from a fraction to a decimal number. Help Nina by completing the following tasks.
Part A
The volume of solution A is
liter. To convert
to a decimal number, set up a long division problem. Which digit belongs in the divisor and which belongs in the dividend in the long division bracket?
Dividend is divided by divisor.
Part B
Can you divide 2 by 9? Explain your response.
Part C
Based on your answer in part B, what will the first digit of the quotient be?
Part D
Now convert 2/9 to a decimal number by completing the long division. Remember to add 0s to the dividend as you work. Divide through the ten-thousandths place, and write your result.
Part E
What will happen if you keep repeating the long division process in part D?
Part F
The volume of solution B is 3/8 liter. To convert 3/8 into a decimal number, set up a long division problem. Which digit belongs in the divisor and which belongs in the dividend in the long division bracket?
Dividend is divided by divisor.
Part G
Can you divide 3 by 8? Explain your response.
Part H
Based on your answer in part G, what will the first digit of the quotient be?
Part I
Now convert 3/8 to a decimal number by completing the long division. Remember to add 0s to the dividend as you work. Divide through the ten-thousandths place, and write your result.
Part J
What will happen if you keep repeating the division process in part I?
Part K
The volume of solution C is 1/5 liter. To convert 1/5 into a decimal number, set up a long division problem. Which digit belongs in the divisor and which belongs in the dividend in the long division bracket?
Part L
Can you divide 1 by 5? Explain your response.
Part M
Based on your answer in part L, what will the first digit of the quotient be?
Part N
Now convert 1/5 to a decimal number by completing the long division. Remember to add 0s to the dividend as you work. Divide through the ten-thousandths place, and write your result.
Dividend is divided by divisor.
Part O
What will happen if you keep repeating the division process in part N?
Part P
You’ve just completed three long division calculations. What can you conclude about the quotient, or result, from the long division process? Does it end or does it continue indefinitely?
Please help i'm so confused!
Answer:
Part A
The volume of solution A is represented as a fraction, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (the top number in the fraction) as the dividend and the denominator (the bottom number in the fraction) as the divisor. So the dividend is 1, and the divisor is the volume of solution A.
Part B
No, we cannot divide 2 by 9 evenly because they are not divisible without a remainder.
Part C
Since we cannot divide 2 by 9 evenly, the first digit of the quotient will be 0.
Part D
We set up the long division problem as follows:
0.2 7 7 7 7 ...
-------------
9 | 1.0000
- 0.9
-----
1 0 0
9 0
---
1 0 0 0
9 0
-----
1 0 0 0
9 0
-----
1 0 0 0 0
9 0
-----
1 0 0 0 0
The decimal equivalent of 2/9 is 0.27777... (repeating). We can see that the division process continues indefinitely with the same repeating pattern, so we use an ellipsis to indicate that the pattern continues infinitely.
Part E
If we keep repeating the long division process for 2/9, we will continue to get the same repeating decimal pattern of 0.27777..., with no end in sight.
Part F
The volume of solution B is represented as the fraction 3/8, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (3) as the dividend and the denominator (8) as the divisor.
Part G
No, we cannot divide 3 by 8 evenly because they are not divisible without a remainder.
Part H
Since we cannot divide 3 by 8 evenly, the first digit of the quotient will be 0.
Part I
We set up the long division problem as follows:
0.3 7 5
---------
8 | 3.0000
- 2.4
----
6 0
5 6
---
4 0 0
3 2
---
7 0 0
6 4
---
3 6 0
3 2
---
2 8 0
2 4
---
4 0
The decimal equivalent of 3/8 is 0.375. We can see that the division process terminates after a finite number of decimal places.
Part J
If we keep repeating the division process for 0.375, we will always get the same decimal number because the process terminates and doesn't involve any repeating pattern.
Part K
The volume of solution C is represented as the fraction 1/5, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (1) as the dividend and the denominator (5) as the divisor.
Part L
No, we cannot divide 1 by 5 evenly because they are not divisible without a remainder.
Part M
Since we cannot divide 1 by 5 evenly, the first digit of the quotient will be 0.
Part N
We set
coach yamada is organizing community volleyball teams. he wants each team to have 8 players. unfortunately, coach yamada can't make as many full teams as he wanted to since fewer than 80 people signed up. let x represent how many full teams coach yamada can make. which inequality describes the problem?
The inequality that describes the problem when coach Yamada is organizing community volleyball teams is x ≤ 9.
Why is x ≤ 9 the correct inequality that describes the problem when coach Yamada is organizing community volleyball teams? Here is why: We know that coach Yamada wants each team to have 8 players but he can't make as many full teams as he wanted to because fewer than 80 people signed up.
Let x represent the number of full teams coach Yamada can make. We know that 1 team can have 8 players. Therefore, the number of players needed for x full teams = 8xWe also know that fewer than 80 people signed up. So, 8x < 80, if more than 80 people signed up then coach Yamada would be able to make more than x full teams.
Since coach Yamada can't make a fraction of a team so x should be an integer. Therefore, the solution for 8x < 80 is x ≤ 9.Therefore, x ≤ 9 is the inequality that describes the problem when coach Yamada is organizing community volleyball teams.
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Rosie bought a car for £4000. 3 years later, she sells it for £1400. What is the percentage loss that Rosie has made?
Answer:
65%
Step-by-step explanation:
Given data
Cost price= £4000
Selling price= £1400
% loss= cost price-selling price/cost*100
% loss= 4000-1400/4000*100
% loss= 2600/4000*100
% loss= 0.65*100
% loss= 65%
Hence the %loss is 65%
can someone explain for me
“ probability with permutations and combinations “ ?
or if there any teacher explaining well gimme there channel!
Permutations and combinations might sound like synonyms. However, in probability theory, they have distinct definitions. Combinations: The order of outcomes does not matter. Permutations: The order of outcomes does matter. For example, on a pizza, you might have a combination of three toppings: pepperoni, ham, and mushroom.
Hope this is the answer you are looking for.