Please answer the question below

The Deposit Fees 15% VAT amount on goods sold at a VAT-inclusive price of R1,500 would be approximately R195.65.

To answer the questions using the provided information, we'll refer to TABLE 2 for the deposit fees.1.2.1 The minimum amount one will pay when making a deposit of notes and coins:

Notes: R2.25 per R100 or part thereof

Coins: R5 per R100 or part thereof

Therefore, the minimum amount one will pay depends on the value of the deposit. For notes, it will be R2.25 per R100 or part thereof, and for coins, it will be R5 per R100 or part thereof.

1.2.2 To determine if Mr Mbhalati's statement is valid, let's calculate the deposit fees for his deposit of notes and coins.

Deposit of notes:

Deposit amount: R1,500

Deposit fee for notes: R2.25 per R100 or part thereof

Calculation:

Deposit fee = (Deposit amount / 100) * Deposit fee per R100

= (1500 / 100) * 2.25

= 33.75

Deposit of coins:

Deposit amount: R500

Deposit fee for coins: R5 per R100 or part thereof

Calculation:

Deposit fee = (Deposit amount / 100) * Deposit fee per R100

= (500 / 100) * 5

= 25

Total deposit fee = Deposit fee for notes + Deposit fee for coins

= 33.75 + 25

= 58.75

Therefore, Mr Mbhalati's statement is not valid. The total deposit fee for his deposit of notes to the value of R1,500 and R500 in coins would be R58.75, not R180.

1.2.3 To calculate the 15% VAT on the amount of goods sold at a VAT-inclusive price:

Amount from the sale of goods: R1,500

Calculation:

VAT amount = (Amount from the sale of goods / (100 + VAT rate)) * VAT rate

= (1500 / (100 + 15)) * 15

= (1500 / 115) * 15

≈ 195.65

Therefore, the Deposit Fees 15% VAT amount on goods sold at a VAT-inclusive price of R1,500 would be approximately R195.65.

1.2.4 One method Mr Mbhalati can use to send money to a person who does not have a bank account is by using a money transfer service like Western Union or MoneyGram. These services allow individuals to send money to recipients who can collect it in cash from designated locations, even if they don't have a bank account.

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The value of the indefinite integral is,

\([\dfrac{1}{5} (x^2 + 44)^{5/2} - 22 (\dfrac{2}{3} )(x^2 + 44)^{3/2} ] + C\)

Where C is the constant of integration.

Now for the indefinite integral \(\int\limits x^3\sqrt {x^2 + 44}dx\), simplify the expression and then apply integration techniques.

Let us assume that;

\(u = x^2 + 44\).

\(du = 2x dx\)

Now, let's rewrite the integral using u:

\(\int\limits x^3\sqrt {x^2 + 44}dx = \int\limits (\dfrac{1}{2} )2x^2 \sqrt {(x^2 + 44} dx\)

\(= \dfrac{1}{2} \int\limits (u - 44) \sqrt {u} du\)

Expanding and simplifying the expression, we have:

\(= \dfrac{1}{2} \int\limits (u^{3/2} - 44 u^{1/2} )du\)

Now integrate each term separately:

\(\dfrac{1}{2} [\dfrac{2}{5} u^{5/2} - 44 (\dfrac{2}{3} )u^{3/2} ] + C\)

\([\dfrac{1}{5} u^{5/2} - 22 (\dfrac{2}{3} )u^{3/2} ] + C\)

Finally, we substitute back \(u = x^2 + 44\);

\([\dfrac{1}{5} (x^2 + 44)^{5/2} - 22 (\dfrac{2}{3} )(x^2 + 44)^{3/2} ] + C\)

So, the indefinite integral is,

\([\dfrac{1}{5} (x^2 + 44)^{5/2} - 22 (\dfrac{2}{3} )(x^2 + 44)^{3/2} ] + C\)

Where C is the constant of integration.

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The complete question is,

Evaluate the indefinite integral. (Use for the constant of integration.) The given indefinite integral is \(\int\limits x^3\sqrt {x^2 + 44}dx\)

The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

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The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

Answer:

y<=-4x-2

Step-by-step explanation:

The impulse response y(n) is y(n) = 3(0.5)^n - 21(0.1)^n, for n >= 0.

To find the impulse response sequence y(n), we can use the Z-transform. First, let's take the Z-transform of both sides of the difference equation

Y(z) - 0.6z^{-1}Y(z) + 0.25z^{-2}Y(z) = X(z) + z^{-1}X(z)

Next, we can rearrange the equation to solve for Y(z)

Y(z) = (X(z) + z^{-1}X(z)) / (1 - 0.6z^{-1} + 0.25z^{-2})

Now, we can substitute X(z) = 8 (the Z-transform of the impulse sequence) and simplify the expression

Y(z) = 8(1 + z^{-1}) / (1 - 0.6z^{-1} + 0.25z^{-2})

We can factor the denominator to get

Y(z) = 8(1 + z^{-1}) / [(1 - 0.5z^{-1})(1 - 0.1z^{-1})]

Now, we can use partial fraction decomposition to write Y(z) as a sum of simpler fractions

Y(z) = A/(1 - 0.5z^{-1}) + B/(1 - 0.1z^{-1})

To find the values of A and B, we can multiply both sides of the equation by the denominators and set z = 0.5 and z = 0.1, respectively

A/(1 - 0.5(0.5)^{-1}) + B/(1 - 0.1(0.5)^{-1}) = 8(1 + (0.5)^{-1}) / [(1 - 0.5(0.5)^{-1})(1 - 0.1(0.5)^{-1})]

A/(1 - 1) + B/(1 - 2) = 8(1 + 2) / [(1 - 1)(1 - 2)]

A - B = -24

A/(1 - 1) + B/(1 - 0.1) = 8(1 + 0.1) / [(1 - 1)(1 - 0.1)]

B - 10A = 72

Solving for A and B, we get

A = 3, B = -21

Therefore, the impulse response sequence y(n) is

y(n) = 3(0.5)^n - 21(0.1)^n, for n >= 0.

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The given question is incomplete, the complete question is:

The difference equation is: y(n) – 0.6y(n-1) + 0.25y(n − 2) = x(n) + x(n-1) Find the impulse response sequence y(n) due to the impulse sequence 8(n)

To determine the theoretical atomic radius of iron with a body-centered cubic (BCC) crystal structure and a cell dimension of 2.86 Å, we will follow these steps:

1. Remember that in a BCC structure, the atoms touch along the body diagonal of the unit cell.
2. The body diagonal length (d) can be found using the formula d = √3 * a, where a is the cell dimension (2.86 Å).
3. In a BCC structure, the body diagonal is equal to 4 times the atomic radius (r), so we can write d = 4r.
4. Combine steps 2 and 3, and solve for the atomic radius (r).

Let's calculate the atomic radius of iron:

1. d = √3 * 2.86 Å ≈ 4.95 Å
2. 4.95 Å = 4r
3. r ≈ 1.24 Å

So, the theoretical atomic radius of iron in a BCC crystal structure with a cell dimension of 2.86 Å is approximately 1.24 Å (Option C).

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Answer:

Lixin is the fastest typist

Step-by-step explanation:

Amirah = 45

Lixin = 46

Shirley = 42

We divide the words by minutes which is basically Unit rate

So we take each person and divide by their words and minutes

\(\frac{words}{minutes}\)

ALWAYS when ur finding unit rate divide the buggest number by the smallest!

The explicit equation of the sequence is an = 3 + (n-1)*6

First term = 3

Second term = 9

A series of numbers in mathematics whose each term is always expressed as a, a+d, a+2d, or a+3d. An arithmetic progression is defined as a + (n-1)d, where a is the first term,d is the common difference of the series and n is the number of terms in the sequence

Any two continuous terms in the arithmetic sequence differ by the same number.

Arithmetic sequence is given by an = a + (n-1)d

So, the common difference = 9-3 = 6

a = 3

Substituting the values in the formula we get:

For nth term: an = 3 + (n-1)*6

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In the given list of conic sections, let's analyze each one and describe its properties.like center's vertices, covertices, directrix, foci and asymptotes

13. The equation (x-1)²/25 + (y-2)²/16 = 1 represents an ellipse centered at (1, 2). The major axis is horizontal with a length of 10 units (2a = 10), and the minor axis is vertical with a length of 8 units (2b = 8). The vertices are located at (1 ± 5, 2), the co-vertices at (1, 2 ± 4), and the foci at (1 ± 3, 2). The directrices and asymptotes are not applicable for ellipses.

14. The equation (x + 2)² + (y - 3)² = 49 represents a circle centered at (-2, 3) with a radius of 7 units. The center is labeled (-2, 3) and the radius is 7.

15. The equation x²/9 - y²/16 = 1 represents a hyperbola centered at the origin. The vertices are located at (±3, 0), the co-vertices at (0, ±4), and the foci at (±5, 0). The asymptotes are y = ±(4/3)x.

16. The equation x² - 9y² + 10x + 54y - 65 = 0 represents a hyperbola. By completing the square, it can be rewritten as (x + 5)²/25 - (y - 3)²/9 = 1. The center is at (-5, 3), the vertices are at (-5 ± 5, 3), the co-vertices are at (-5, 3 ± 3), the foci are at (-5 ± √34, 3), and the asymptotes are y = ±(3/5)(x + 5).

These descriptions provide an overview of the conic sections and their respective properties, including the center, vertices, covertices, foci, directrices, and asymptotes when applicable.

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No because 2(4)+4\(\neq\)15

Why?

Now calculate sum

Hence its false

The fact that the sum can be approximated by an integral. we can approximate the sum as the area under the curve y=√x from x=1 to x=10000. This can be written as: ∫1^10000 √x dx

Using integration rules, we can evaluate this integral to get:
(2/3) * (10000^(3/2) - 1^(3/2))
This evaluates to approximately 66663.33. Therefore, an estimate for the sum ∑ i=1 to 10000 √i is 66663.33.

In mathematics, integrals are continuous combinations of numbers used to calculate areas, volumes, and their dimensions. Integration, which is the process of calculating compounds, is one of the two main operations of computation, [a] the other being derivative. Integration was designed as a way to solve math and physics problems like finding the area under a curve or determining velocity. Today, integration is widely used in many fields of science.

To estimate the sum of ∑ from i=1 to 10000 of √i using an integral, we'll approximate the sum with the integral of the function f(x) = √x from 1 to 10000.

The integral can be written as:

∫(from 1 to 10000) √x dx

To solve this integral, we first find the antiderivative of √x:

Antiderivative of √x = (2/3)x^(3/2)

Now, we'll evaluate the antiderivative at limits 1 and 10000:

(2/3)(10000^(3/2)) - (2/3)(1^(3/2))

(2/3)(100000000) - (2/3)

= (200000000/3) - (2/3)

= 199999998/3

Thus, the integral estimate of the sum from i=1 to 10000 of √i is approximately 199999998/3.

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Answer:

see below

Step-by-step explanation:

A

Add the students who passed french, german, both

add 17+19+11 = 47

Subtract this from 55 to get b

b = 55-47 =8

b =8

B

P( passed french and german)

    = number that passed french and german / total

    = 19/55

P( french or german) =

  = number that passed french or german / total

    = (17+11)/55 =28/55

Answer:

point form is: (-7,2)

equation form is: x = -7, y = 2

Step-by-step explanation:

add the equations in order to solve for the first variable. plug this value into the other equations in order to solve for the remaining variables

pls mark as brainliest lol

A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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The pigeonhole principle shows that in any set of six classes, there must be at least two classes that meet on the same day because there are only five weekdays for each class to meet on.

This principle states that if there are more items than the number of spaces available to place them in, at least two items must occupy the same space. In this case, there are six classes and only five weekdays available for each class to meet on. Therefore, at least two classes must meet on the same day.

Correct answer: b. The pigeonhole principle shows that in any set of six classes, there must be at least two classes that meet on the same day because there are only five weekdays for each class to meet on.

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Mr. Knapp initially had 61 stamps.

Given that Mr. Knapp had some stamps,

if he gave 7 stamps to each of his children, now he would have 5 stamps left.  

If he gave 8 stamps to each child, he would need 3 more stamps in order for the children to have an equal number of stamps.  

We need to find that how many stamps did Mr. Knapp had.

Let's solve the problem step by step.

Let's assume Mr. Knapp has "x" stamps initially.

According to the first condition, if he gave 7 stamps to each of his children, he would have 5 stamps left.

This can be expressed as:

x - 7c = 5,

where "c" represents the number of children.

According to the second condition, if he gave 8 stamps to each child, he would need 3 more stamps in order for the children to have an equal number of stamps.

This can be expressed as:

x - 8c = -3.

We now have a system of two equations with two variables:

x - 7c = 5,

x - 8c = -3.

Let's use the elimination method to eliminate "x" from the equations:

(x - 7c) - (x - 8c) = 5 - (-3),

x - 7c - x + 8c = 5 + 3,

c = 8.

Now that we know the value of "c" is 8, we can substitute it back into either of the original equations to find the value of "x."

Let's substitute it into the first equation:

x - 7(8) = 5,

x - 56 = 5,

x = 5 + 56,

x = 61.

Therefore, Mr. Knapp initially had 61 stamps.

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The charges for a week in which Charlene's facility did 35 oil changes and tuned 5 four-cylinder engines, and 7 six-cylinder will be $2313.25.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that charges per oil change are $33.95, charges for a four-cylinder engine $72.50, charges for a six-cylinder engine $82.50, and, charges for an eight-cylinder engine $92.50.

The total charges will be calculated as below:-

No oil changes done by Charlene = 35

price of 5 - four-cylinder engines = 5 × 72.50

= 362.50                                .....(1)

Price of 7 - six cylinder engines = 7 × 82.50

= 577.50                                ........(2)

Price of 2 - eight-cylinder engines = 2 × 92.50

= 185                                       ...........(3)

Now, adding (1), (2),(3)

= 362.50 + 577.50 + 185

= 1125                                        ...........(4)

Total charges for oil = 33.95 × 35

= 1188.25                                  ..........(5)

Add equations (4) and (5) to get the total charges.

= 1125 + 1188.25

= 2313.25

Therefore, the total charges will be $2313.25.

The complete question is given below:-

Charlene operates an oil change and tune-up service. she charges $33.95 per oil change. a tune-up is $72.50 for a four-cylinder engine, $82.50 for a six-cylinder engine, and $92.50 for an eight-cylinder engine. what are the charges for a week in which Charlene's facility did 35 oil changes and tuned 5 four-cylinder engines, and 7 six-cylinder?

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The unit rate, which is a constant between the ratio of two numbers that vary concurrently, can also be used to refer to the slope. Slope follows the same rule.

As long as the rise/run along the line remains constant, the slope between any two places on a straight line will always be the same.

A linear relationship grows or shrinks at a constant rate of change, similar to a proportional relationship. This is known as the constant of proportionality in a relationship. It can also be referred to as the slope or unit rate in a linear connection. The slope of a line said to be its steepness.

Like the proportionality constant, the slope shows how quickly an amount is rising or falling. The only difference between the slope and the constant of proportionality is that the relationship need not begin at 0. Mathematicians frequently substitute the term slope or unit rate for the proportionality constant.

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Answer:

x - 10 = 0

Step-by-step explanation:

Vertical line passing through this point should be perpendicular to x - axis and parallel to y - axis, and this point should be in Quadrant IV.

In this case,

y = 0

x = 10

Therefore,

the equation is

x - 10 = 0

Marguerite drew a net of a polyhedron that has one square face and four triangular faces. We can conclude that Marguerite drew a net for a square pyramid.

From the information given in the problem, we know that Marguerite's net has one square face and four triangular faces. This means that the polyhedron that the net represents must have five faces in total. We can use the number of faces, along with the fact that the faces are either triangles or squares, to determine which polyhedron it is.

A triangular prism has two triangular faces and three rectangular faces. Therefore, it is not possible that Marguerite drew a net for a triangular prism.

A triangular pyramid has one triangular face and three triangular faces. Therefore, it is not possible that Marguerite drew a net for a triangular pyramid.

A square pyramid has one square face and four triangular faces. Since this is the only option with one square face and four triangular faces, it must be the polyhedron that Marguerite drew a net for.

A rectangular prism has six faces, and none of them are triangles. Therefore, it is not possible that Marguerite drew a net for a rectangular prism.

Therefore, we can conclude that Marguerite drew a net for a square pyramid.

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The total number of times that the coin was flipped would be 10 times. Option D.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable." Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.

In order to prove that the number of flips that was done by the families 10, we would have to solve for the probability of heads using total of 10 and 4 as the total for the Rodriguez.

4 / 10 * 100

= 40%

Hence the other family flipped the coin 60 percent of the time. Such that 10 - 4 = 6

6 + 4 = 10

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The optimal strategy is to pick door 1 and stay - this will give you a 50 percentage chance of winning the car.

The optimal strategy to win the game show is to pick door 1 initially and stay. This is because door 1 has the car 50% of the time, which is the highest chance of any of the three doors. If you switch to a different door, then you would have a 40% chance of winning if you switched to door 2, and a 10% chance of winning if you switched to door 3. Since door 1 has the highest chance of having the car, it is the optimal choice to initially select door 1 and stay. By doing so, you have a 50% chance of winning the car.

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Answer:

Step-by-step explanation:

Step one:

given data

the cost of the laptop= $800

initial payment= $200

monthly payment = $60

let the number of months be x

the expression for the situation is the function for the equation of line

y=mx+c

Step two:

the expression for the situation is

800=200+60x

solve for x

800-200=60x

400=60x

divide both sides by 60

x=400/60

x=6.7

Approximately 7 months

Answer:

\(32 \frac{2}{3 }miles- - - - 3 \frac{1}{ 2} minutes \\ \frac{98}{3} miles - - - - \frac{7}{2} minutes \\ \frac{2}{7} \times \frac{98}{3} miles - - - - 1minute \\ 60 \times \frac{2}{7} \times \frac{98}{3} miles - - - - 1 \: hour \\ 560 \: miles - - - - 1hour\)

The correct descriptions about the burial site of the Qin Emperor are that the faces on the soldiers are all alike, and it contains almost 8,000 terracotta soldiers.

Among the given descriptions, the following are true about the burial site of the Qin Emperor:

The faces on the soldiers are all alike.

It contains almost 8,000 terracotta soldiers.

The other two descriptions are not accurate:

It does not fill a two-square-mile site. The actual size of the site is around 22 square miles (56 square kilometers).

It did not take 11 years to build. The construction of the Terracotta Army and the overall mausoleum complex spanned several decades.

Therefore, the correct descriptions are:

The faces on the soldiers are all alike.

It contains almost 8,000 terracotta soldiers.

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