The value of the two numbers in b is 15 and 18
How to solve for the numbersTo get the values we would have to set up an equation system
Such that we would have:
the smaller number is given as c
Then the bigger number is given as c + 3
The equation would be
c + c + 3 = 33
then
2c = 33 - 3
2c = 30
From here we would have to divide both sides of the equation by 2
2c / 2 = 30 / 2
c = 15
33 - 15 = 18
Hence the numbers are given as 15 and 18
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Each equation below is a characteristic equation for a recurrence relation. Express the solution to each recurrence relation as a linear combination of terms. Note that you will not know the actual coefficients in the linear combination since you are not given the base cases, so you can use a1, a2, etc.
(a) (x − 1)(x + 2) = 0
(b) (x − 4)(x − 4) = 0
(c) (x − 4)(x − 4)(x + 5) = 0
(d) (x − 4)(x − 4)(x + 5)^4 = 0
The solutions to each recurrence relation can be expressed as a linear combination of terms:
The general solution to the recurrence relation can be written as a1 * 1^n + a2 * (-2)^n.The general solution to the recurrence relation can be written as a1 * 4^n.The general solution to the recurrence relation can be written as a1 * 4^n + a2 * 4^n + a3 * (-5)^n.The general solution to the recurrence relation can be written as a1 * 4^n + a2 * 4^n + a3 * (a root of (x + 5)^4)^n.For (a) The solution to (x - 1)(x + 2) = 0 is
x = 1 and x = -2.For (b) The solution to (x - 4)(x - 4) = 0 is
x = 4.For (c) The solution to (x - 4)(x - 4)(x + 5) = 0 is
x = 4, x = 4, and x = -5.For (d) The solution to (x - 4)(x - 4)(x + 5)^4 = 0 is
x = 4, x = 4, and the 4 roots of (x + 5)^4 = 0.These linear combinations of terms can be used to describe the general solution to each recurrence relation, but the actual coefficients in the linear combination are not given and depend on the base cases of the recurrence relation.
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The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 39 liters, and standard deviation of 5.2 liters.
A) What is the probability that daily production is less than 27.6 liters? Use technology (not tables) to get your probability.
Answer=
(Round your answer to 4 decimal places.)
B) What is the probability that daily production is more than 49.4 liters? Use technology (not tables) to get your probability.
Answer=
(Round your answer to 4 decimal places.)
Warning: Do not use the Z Normal Tables...they may not be accurate enough since WAMAP may look for more accuracy than comes from the table.
a)The probability that daily production is less than 27.6 liters is given by the equation P ( x < 27.6 ) = 0.014179
b) The probability that daily production is more than 49.4 liters is given by the equation P ( x > 49.4 ) = 0.02275
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the probability that daily production is less than 27.6 liters be represented as P
Now , the equation will be
a)
The observed value of x = 27.6 L
The mean of the sample μ = 39 L
The standard deviation of the sample σ = 5.2 L
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 27.6 - 39 ) / 5.2
z = -2.19231
Now ,the p value from the z table is
P ( x < 27.6 ) = 0.014179
And , the probability is P ( x < 27.6 ) = 0.014179 = 1.418 %
Therefore , the probability that daily production is less than 27.6 liters is given by P = 1.418 %
b)
The observed value of x = 49.4 L
The mean of the sample μ = 39 L
The standard deviation of the sample σ = 5.2 L
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 49.4 - 39 ) / 5.2
z = 2
Now ,the p value from the z table is
P ( x < 49.4 ) = 0.97725
P ( x > 49.4 ) = 1 - P( x < 49.4 ) = 0.02275
And , the probability is P ( x > 49.4 ) = 0.02275 = 2.275 %
Therefore , the probability that daily production is more than 49.4 liters is given by P₁ = 2.275 %
Hence , the probabilities are solved
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demonstrating that there is a trade which will leave both players better
off. Suppose:
Amber can produce 24 apples or 48 pears in a day, and
Johnny can produce 8 apples and 32 pears in a day.
They also prefer to spend a half-day producing apples and a half- day
producing pears.
This trade will create a win-win situation for both players, leaving them both better off than they were before.
What is capacity?Capacity in math is the maximum amount that a container or figure can hold. It is typically measured in liters, gallons, or quarts and is determined by the size of the container or figure. Capacity is a measure of volume and is used in a variety of math problems, including those involving capacity conversion, calculating the amount of liquid that can be stored in a container, and determining the amount of material needed to fill a given area.
A trade that will leave both players better off is for Amber to produce all of the apples and Johnny to produce all of the pears. This way, Amber can produce 24 apples in a day and Johnny can produce 32 pears in a day, which is more efficient than if they both tried to produce both items. Amber has a higher capacity for producing apples while Johnny has a higher capacity for producing pears. Therefore, this trade makes the most sense.
The trade will leave both players better off because of the increased efficiency in production. Amber can produce 24 apples in a day and Johnny can produce 32 pears in a day, which is more efficient than if they both tried to produce both items. This means that they will both have more resources to spend on other things. They will also be able to divide their time more evenly between the two tasks, allowing them to be more productive and efficient.
In addition, the trade will also benefit both players in terms of their preferences. Amber will be able to spend a full day producing apples, which she prefers, and Johnny will be able to spend a full day producing pears, which he prefers. This trade will create a win-win situation for both players, leaving them both better off than they were before.
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I don’t understand this question. Can you help me?
Answer:
0.5
Step-by-step explanation:
The two figures are similar
find the linear scale factor of the two figures
=L/l ......... 10/4
=2.5
use the linear scale factor to find the other side
2.5= 5/n
2.5n=5 divide both sides by 2.5
n=0.5
What is the prime factorization of 246?
Step-by-step explanation:
Start by dividing it by a prime number and just go from there. The included pictures will show how :) Because the end result is all prime numbers it is prime factorization.
Which of the answers is equal to sec(x)? *
O 1/cot(x)
O 1/sin(x)
O 1/cos(x)
O 1/csc(x)
The answer choice which is equivalent to sec (x) among the given answer choices is; 1 / cos(x).
Which answer choice is equal to sec (x)?It follows from the task content that the answer choice which is equivalent to sec (x) is to be determined among the given answer choices.
From trigonometric ratios concept, it follows that the inverses of the 3 basic trigonometric ratios are as follows;
1 / sin x = csc (x)
1 / cos x = sec (x)
1 / tan x = cot (x)
On this note, it follows that the answer choice which is equivalent to sec (x) is; 1 / cos x.
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Please help a brothra out
L line
-2
-1
-15.5
-3.5
grph
June says that there should be a decimal
point in the quotient below after the 4.
Is she correct? Use number sense to
explain your answer.
43.94 5.2 = 845
Using the arithmetic operation of division, the value for expression 43.94 ÷ 5.2 is 8.45 where decimal point is before 4 and after 8.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The expression is given as - 43.94 ÷ 5.2
Use the arithmetic operation of division -
43.94 / 5.2
Remove the decimal point by multiplying the numerator and denominator by 100.
(43.94 × 100) / (5.2 × 100)
4394 / 520
Now perform the operation of division -
4394 / 520 = 8.45
June says the decimal point should be after 4.
She is incorrect as the result shows that the decimal point is before 4.
Therefore, June is incorrect in her statement.
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convert to slope intercept form
: x- 2y=-6
Answer:
x-2y =6
x-2y =6
= 6-2y=x=4
You might have noticed that the numbers, or frequencies, on an old radio dial are not evenly spaced. There is, however, some pattern to the placement of these frequencies. You will analyze this data and answer the following questions.
Frequency reading on the radio dial (kilohertz)
distance from the left end of the radio dial (centimeters)
53
1.54
60
2.17
70
2.95
80
3.62
100
4.75
120
5.67
140
6.45
170
7.43
1. a. What is the independent variable and what are its units?
b. What is the dependent variable and what are its units?
2. Make a scatter plot of the data. Describe the data set based on the scatter plot.
b. What do you expect to happen to the distance from the left end of the radio as the frequency gets higher?
c. What do you expect to happen to the distance from the left end of the radio as the frequency gets smaller?
The independent variable is distance from the left end of the radio dial and its unit is centimeters.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
The given coordinate points are (53, 1.54), (60, 2.17), (70, 2.95), (80, 3.62), (100, 4.75)
Here,
1.a) The independent variable is distance from the left end of the radio dial and its unit is centimeters.
b) The dependent variable is frequency and its units is kilohertz.
2. a) A scatter plot of the data is given below in the attachment.
b) The distance from the left end of the radio as the frequency gets higher is increases.
c) The distance from the left end of the radio as the frequency gets smaller is decreases.
Therefore, the independent variable is distance from the left end of the radio dial and its unit is centimeters.
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An art teacher found that in a bin of markers,1/2 of the caps had been left off the markers. Of these markers,2/4 of them were dried up. Use the model to find what fraction of the markers had the lids left off and were dried up.
Rose's Botanical Garden produced flowers throughout the year. A graph demonstrating how many flowers she produced over a 10-month period is shown:
A graph of a curve with x axis labeled Months and y axis labeled Number of Flowers Produced. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 60 in increments of 10. The curve starts at about 1 comma 22 and goes up to 6 comma 60 at the highest point and ends at about 10 comma 36.
What can be interpreted from the domain of this graph?
The domain represents the total number of flowers produced each month.
The domain represents the total number of flowers produced in 10 months.
The domain represents a 120-month period of flower production.
The domain represents a 10-month period of flower production.
The domain of the graphed function is interpret as follows:
The domain represents a 10-month period of flower production.
How to obtain the domain of the function?The domain of a function is composed by the set containing all the possible input values for the function, hence it is composed by all the values of x assumed by the function.
The input variable, represented by the x-axis, is defined as follows:
Number of Months.
Hence the correct option is given by the fourth option, as x ranges from 0 to 10.
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What is the vertex of the function f(x)=-1/2|x+8|-5
Hello :3
Answer:
(-8,-5)
Hope this helps! :)
See if you can find how many solutions these systems of two linear equations have.
Type 0, 1, or infinite in the answer box.
y=4x - 5
y=3x - 7
Answer:
1
Step-by-step explanation:
The two equations have one solution. This is because when the two equations are graphed, the lines intersect in only one point. Therefore, the system only has one solution.
In the figure below, I || h. Find the values of y and x.
81°
y (6x - 51)
y = 0
X =
The value of the variable x is 99 and y is 22 in the given transversal of parallel lines.
What is transversal?There are several different kinds of lines that can exist in geometry, including parallel, perpendicular, intersecting, and so on. A transversal is a different line that we have in addition to that. A road crossing two or more other roads or a railway crossing several other lines are examples of this. These convey the fundamental concept of a transversal. If two or more other lines in the Euclidean plane are parallel, transversals are crucial in determining this. Learn the definition of a transversal line in this article, along with how it can be used to create angles with both parallel and non-parallel lines. Study additional geometrical ideas here.
Given, I || h
Using the same internal property of transversal
81 + x = 180° (angle sum property)
x = 180 - 81
x = 99°
For (3y + 33), vertical opposite angle rule can be applied so
x = (3y + 33)
3y + 33 = 99°
3y = 99 - 33
3y = 66
y = 66/3
y = 22°
Thus, The value of the variable x is 99 and y is 22 in the given transversal of parallel lines.
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Correct question:
In the figure below, I || h. Find the values of y and x.
The surface area of a prism is 54 square inches. What is the surface area of a similar prism that is smaller by a scale of 1/3? Help!!!
Answer:
18 Square inches
Step-by-step explanation:
Surface Area of original prism: 54 square inches
Surface Area of similar prism:
1/3 x 54
=18 square inches
the studentof class 5 had their sports day on 5th february.If they started parctising 35 days earlier on wich date did the parctice begin?
Answer:
January 2nd
Step-by-step explanation:
subtract 5 from February and 30 from January
a clock loses 10 seconds in every two hours. in how many hours will it take to lose one hour
Answer:
The watch loses 5 seconds per hour. It is 5 minutes slow. 5 minutes is 300 seconds(5 x 60). 300 seconds therefore represents 300/5 hours=60 hours. From Tuesday 10.30 AM backwards 60 hours(2 1/2 days) brings you to 10.30 PM on Sunday evening as the date and time the watch was last set.
Step-by-step explanation:
For the right triangles below, find the values of the side lengths B and C .
Round your answers to the nearest tenth.
For the given right triangles the value of side b is [tex]4\sqrt{3}=6.9[/tex] meanwhile the value of side c is [tex]2.5\sqrt{2} =3.5[/tex].
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem. The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) .
The question asks the values of the side lengths b and c. The variables b and c represent one of the sides of the right triangles.
Finding the side b - You should apply the trigonometric ratio sin (Ф). Knowing that: sin (Ф)=[tex]\frac{opposite\ side}{hypotenuse}[/tex] and sin (60)=[tex]\frac{\sqrt{3}}{2}[/tex], you can write:sin (60)=b/8
[tex]\frac{\sqrt{3}}{2}=\frac{b}{8} \\ \\ 2b=8\sqrt{3} \\ \\ b=4\sqrt{3}=6.9[/tex]
Finding the side c - You should apply the trigonometric ratio sin (Ф). Knowing that: sin (Ф)=[tex]\frac{opposite\ side}{hypotenuse}[/tex] and sin (45)=[tex]\frac{\sqrt{2}}{2}[/tex], you can write:
[tex]\frac{\sqrt{2}}{2}=\frac{c}{5} \\ \\ 2c=5\sqrt{2} \\ \\ c=\frac{5}{2} \sqrt{2}\\ \\ c=2.5\sqrt{2}=3.5[/tex]
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Suppose that Y1 and Y2 are independent, standard normal random variables. Find the density function of U = Y1^2 +Y2^2.
The density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]
The density function of [tex]U = Y1^2 +Y2^2[/tex] is given by the formula [tex]f_U(u) = (1/2π)∫_0^∞ f_Y1(y_1)f_Y2(√(u-y_1^2)) dy_1[/tex]. This can be calculated as follows:
Let u ≥ 0, then
[tex]f_U(u) = (1/2π)∫_0^∞ (1/√(2π))e^(-(y_1^2/2))(1/√(2π))e^(-(√(u-y_1^2)^2/2)) dy_1[/tex]
[tex]= (1/2π)∫_0^∞ (1/2π)e^(-u/2) dy_1= (1/2π)e^(-u/2) ∫_0^∞ (1/2π) dy_1= (1/2π)e^(-u/2)[/tex]
Therefore, the density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]
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Which inequality shows the region represented by the
inequality in vertex form?
Oy2(x-50)² +625
O yz-(x +50)² +625
O y2(x +50)² +625
O yz-(x-50)² +625
The appropriate answer to that same previous information is y ≥ -(x-50)² + 25
Why does inequality matter?According to analysts, inequality promotes political dysfunction and slows down economic progress. Because wealthy households typically spend a smaller share of their earnings than do poorer households, concentrated riches lower the amount of demand within the economy. The economy may suffer if low-income families have fewer possibilities.
Assume that the equation is y = a(x-h)² + k
y - a (x-50)² + 625
Put (61,504) in the equation
504 = a(61 - 50)² + 625
504 = a.121+625
121a = -121
a = -1
y = -(x-50)² + 625
Hence, y ≥ - (x-50)² + 625
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A package contains II resistors, 2 of which are defective. If5 are selected, find the probability of getting the following results. Enter your answers as fractions or as decimals rounded to 3 decimal places. 0 defective resistors P (0 defective) = 3/11 I defective resistor P (l defective) = 252/462 2 defective resistors P(2 defective) =
If a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting
a) 0 defective resistors: 0.3164
b) 1 defective resistor: 0.4219
c) 3 defective resistor: 0.0469
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
Probability
First step is to calculate the probability for a defective resistor and non-defective resistor:
Probability=3/12
Probability =0.25
Non-defective resistor:
Probability=(1-0.25)
Probability=0.75
Now let find the probabilities for defective resistors from 0 to 3
P(0)=1(0.75)^4 ×(0.25)^0
P(0)=0.3164
P(1)=4(0.75)^3× (0.25)^1
P(1)=0.4219
P(2)=6(0.75)^2× (0.25)^2
P(2)=0.2109
P(3)=4(0.75)^0×(0.25)^3
P(3)=0.0469
P(4)=1(0.75)^0 × (0.25)^4
P(4)=0.0039
Hence,
a. P(0)=0.3164
b. P(1)=0.4219
c. P(3)=0.0469
Therefore If a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting 0 defective resistors: 0.3164, 1 defective resistor: 0.4219, 3 defective resistor: 0.0469.
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In a group of 59 traders 26 sell gari 8 sell only rice 15 sell only maize 10 sell gari and rice 16 sell rice and maize and 42 sell maize.each trader sell at least one of the three items.find the number if traders who sell
A.gari or maize
B.gari and maize
C.only two food items
The number of vendors selling maize or gari Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. 16 sell wheat and maize, 10 sale gari and rice, 42 sell maize, and 6 sell gari.
How is math used in trading?To assess the trading strategies used by traders to complete a trade transaction, mathematical analysis is employed. Moreover, probability theory is used to evaluate the usefulness of money management strategies.
Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. Ten sell rice and gari, sixteen sell rice and maize, and forty-two sell maize.
Determine the quantity of dealers selling gari of corn using the formula below:
P(G ∪ R ∪ M) = P(G) + P(R) + P(M) - P(G ∩ R) - P(R ∩ M) - P(G ∩ M) + P(G ∩ R ∩ M)
59 = 26 + 8 + 15 - 10 - 16 - P(G ∩ M) + 42
59 - 42 = 49 - 26 - P(G ∩ M)
P(G ∩ M) = - 17 + 23
P(G ∩ M) = 6
Hence, there are 6 dealers selling gari or corn.
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Factor 8y2 + 6y + 1
and check.
The factorization of the given quadratic equation by grouping is (2y + 1) (4y + 1)
Factorization of quadratic equation by grouping.
Factorization is a method of finding factors for any quadratic expression, polynomial, or algebraic expression.
For a polynomial of the form ax^2 + bx + c, rewrite the middle term as a sum of two terms whose product is a×c = 8 × 1 = 8 and whose sum is b = 6.
Given that:
8y² + 6y + 1
8y² + 2y + 4y + 1
Factor out the greatest common factor from each group.
2y(4y + 1) + 1(4y + 1)
(2y + 1) (4y + 1)
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Which number sentence is true?
A. 82 < |-82|
B. |-82| < |-83|
C. |-83| < |83|
D. |82| > |-83|
9. Find b so that the vectors v=5i +2j and w=4i+b are orthogonal.
Answer:
b = -10
Step-by-step explanation:
Two vectors are orthogonal if and only if their dot product is zero. The dot product of v and w is given by:
(v · w) = (5i + 2j) · (4i + bj) = 5 * 4 + 2 * b = 20 + 2b.
For v and w to be orthogonal, we need the dot product to be zero, which means 20 + 2b = 0, so:
2b = -20
b = -10
Therefore, b = -10 makes the vectors v and w orthogonal.
How long will it take for a sum of money to quadruple at 10% compounded annually?
Answer:
Below
Step-by-step explanation:
For compounding annually , the formula would be
4x = x ( 1+ .1)^n x = deposit amount 4x = quadrupled
i = decimal interest (.10) and n = years
you can divide 'x' out of the equation to get :
4 = (1.1)^n solve for 'n' by taking LOG of both sides
log 4 = n log 1.1
log 4/log 1.1 = n = 14.54 years - ~~ 15 years
ACTIVITY 2 Nomusa is a 65-year-old female educator who carned a gross income of R28 500 per month. A monthly deduction of 7,5% was made from her salary and paid into her pension fund. Use the 2019/2020 Income Tax table below to answer the questions that follow. TAX RATES FOR 2019/2020 TAX YEAR (1 March 2019 to 28 February 2020) TAX BRACKET TAXABLE INCOMET RATES OF TAX(R) 195 850 195 851 305 851 555 601 708 311 se 305 850 423 300 $$$ 600 708 310 1 500 000 1 500 001 and above TAX REBATES 2.1 Define the term gross salary. 2.2 Main member First dependant Each additional dependant U102/2023 Test 4 18% of taxable income 35 253 26% of taxable income above 195 850 63 853 +31% of taxable income above 305 850 100 263 + 36% of taxable income above 423 300 147 891 +39% of taxable income above 555 600 207 448 +41% of taxable income above 708 310 532 041 +45% of taxable income above 1 500 000 TAX THRESHOLD R79 000 R122 300 R14 220 R7 794 Primary Secondary (65 and older) Tertiary (75 and older) R2 601 R136 750 MEDICAL TAX CREDIT PER MONTH FOR MEDICAL FUND MEMBERS R310 R310 R209 What is the maximum taxable income for bracket 4 SOURCE: www.ars.g. 2.3 Determine Nomusa's monthly taxable income. 2.4 Identify the tax bracket Nomusa falls in based on his annual taxable income Marks 2.3 Calculate Nomusa's monthly tax in the 2019/2020 tax year. 2.6 Nomusa stated that if she were 10 years younger, she would have paid RS 502.34 monthly tax. Show with calculations whether Nomusa's statement is valid. 2.7 Nomusa is considering joining a medical fund. She plans to include his husband and two grandchildren. Determine the total monthly medical credits she would qualify for if she joined a medical 2.8 Nomusa's brother, who is 45 years old, earned a monthly taxable income of R45 980,17 during the 2019/2020 tax year. He is not a member of any medical scheme. Show, using calculations, that his monthly tax was R11 024,11 TOTAL (5) (3) 1307 Page c,z of 78
Nomusa's statement is not valid because her monthly tax is not equal to R502.34.
What do you mean by medical fund?A medical fund is a type of financial arrangement that individuals, families, or organizations set up to pay for medical expenses. The purpose of a medical fund is to help cover the cost of medical treatments, procedures, or medications that may not be covered by insurance. There are different types of medical funds, including personal savings accounts, health savings accounts (HSAs), flexible spending accounts (FSAs), and crowdfunding platforms that allow people to raise money for medical expenses. These funds can be used to pay for a variety of medical expenses, including doctor visits, surgeries, prescription drugs, and medical equipment. The goal of a medical fund is to provide individuals and families with a source of financial support for medical expenses, and to help reduce the financial burden associated with medical care.
Gross salary is the total amount of money earned by an individual before any deductions or taxes have been taken out.
2.3 Nomusa's monthly taxable income can be determined as follows: Gross salary = R28 500; 7.5% pension deduction = R28 500 x 7.5% = R2,137.5; Monthly taxable income = Gross salary - pension deduction = R28 500 - R2,137.5 = R26,362.5
2.4 Based on Nomusa's annual taxable income of R26,362.5 x 12 = R316,350, she falls in tax bracket 4, with a taxable income between R305,850 and R423,300.
2.5 Nomusa's monthly tax can be calculated as follows: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R316,350 - R195,850) = 26% x R120,500 = R31,230; Total tax = R35,253 + R31,230 = R66,483; Monthly tax = Total tax ÷ 12 = R66,483 ÷ 12 = R5,540.25.
2.6 To determine whether Nomusa's statement is valid, we would have to calculate her monthly tax if she were 10 years younger, and compare it to the stated amount of R502.34: If she were 10 years younger, she would not be eligible for the secondary tax threshold, so her monthly tax would be the same as calculated in 2.5: R5,540.25. This amount is not equal to R502.34, so Nomusa's statement is not valid.
2.7 If Nomusa joins a medical fund and includes her husband and two grandchildren, she would qualify for the following monthly medical credits: For herself: R310; For her husband: R310; For each grandchild: R209; Total monthly medical credit = R310 + R310 + 2 x R209 = R936.
2.8 To calculate Nomusa's brother's monthly tax, we can use the same process as in 2.5: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R45,980.17 - R195,850) = 26% x (R26,129.17) = R6,792.19; Total tax = R35,253 + R6,792.19 = R42,045.19; Monthly tax = Total tax ÷ 12 = R42,045.19 ÷ 12 = R3,503.77, which is approximately R11,024.11.
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Emma was given $16.09 for washing her neighbor's car. She now has $20.23. Let m equal the amount of money she had before washing the car. Choose the equation to solve the problem.
Answer: m = 20.23 - 16.09
Step-by-step explanation:
A case of vegetable costs $10.68. He can spend at most $50 for this project. what is the maximum amount of cases of vegetables he can buy
Answer:
4
Step-by-step explanation:
The maximum number of cases of vegetables that he can buy can be calculated by dividing the maximum budget of $50 by the cost of a single case of vegetables, which is $10.68:
$50 ÷ $10.68 = 4.67 cases
Since you can't buy fractional cases, the maximum number of cases he can buy would be 4. Round down to the nearest whole number, the maximum number of cases he can buy is 4.