Ms Grace bought a home theatre system for $4320 including 8%VAT
. Find the original price of the home theatre system before VAT?

Answer:

78 games

Step-by-step explanation:

Think of it this way. Let's name the teams Team 1 through Team 13. Team 1 needs to have 12 games to play each other team. Once those are scheduled, Team 2 needs to have 11 games scheduled to play all the other teams (remember their game against Team 1 was already scheduled). Team 3 needs to have 10 games scheduled to play all the other teams (remember their games against Team 1 and Team 2 have already been scheduled). This patten continues until you schedule a single game between Team 12 and Team 13. So the total number of games that need to be scheduled are:

12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 =  78

I don't know if the concept of triangular numbers has been touched on in your class, but if so, there is a much simpler way to calculate this using the triangular number formula with n = 12. The formula is:

T = (n * (n + 1)) / 2

So in this case:

(12 * (12 + 1)) / 2 = (12 * 13) / 2 = 6 * 13 = 78

The relationship between the variables d and g is given by the equation;

d = 30(14 - g)

We are given that;

She begins the trip with 14 gallons of gas in her car.

The car uses up one gallon of gas every 30 miles.

If g represents the number of gallons of gas she has left in her tank, and d represents the total distance (in miles), then we have the equation;

d = 30(14 - g)

For example, if she uses two gallons, there will be 12 gal left in the tank; g = 12. Thus;

d = 30(14 - 12)

d = 30(2)

d = 60 miles

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Complete question is;

Linda is driving on the highway she begins the trip with 14 gallons of gas in her car. The car uses up one gallon every 30 miles.

Let g represent the number of gallons of gas she has left in her tank, and letd represent the total distance (in miles) she has traveled

Number of pencil packages, n = 5

The total amount spent on art pencils and erasers = $47

The amount of money spent on eraser = $7

The price of 1 package of pencils = $8

Let the number of packages of pencils bought = n

Total amount spent = Amount of eraser + (number of pencil packages x Price of pencil packages)

47 = 7 + (n x 8)

47 = 7 + 8n

47 - 7 = 8n

40 = 8n

40 / 8 = n

5 = n

n = 5

Answer:

Transversal

Step-by-step explanation:

by defination this is a line that intersects other lines

9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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Answer:

106°

Step-by-step explanation:

180-74=106°

Answer:

106

Step-by-step explanation:

supplementary means 2 angles = 180

so..

180-74=106

The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

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The temperature of 30° is within one standard deviation of the mean.

To determine which temperature is within one standard deviation of the mean, we need to consider the range that falls within one standard deviation above and below the mean.

Given that the mean temperature is 24° with a standard deviation of 4°, one standard deviation above the mean would be 24° + 4° = 28°, and one standard deviation below the mean would be 24° - 4° = 20°.

Looking at the temperatures in the chart, we can see that the temperature of 30° is within one standard deviation of the mean. It falls within the range of 28° (one standard deviation above the mean) and 20° (one standard deviation below the mean).

Therefore, the temperature of 30° is within one standard deviation of the mean.

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Answer:

1:72

Step-by-step explanation:

The scale of a drawing is the ratio of the length in the drawing to the real length.

Drawing length: 7 inches

Real length: 42 ft × 12 in. / ft = 504 in.

Scale:

7 in. to 504 in.

Divide both numbers by 7:

1 in. to 72 in.

Scale: 1:72

9514 1404 393

Answer:

  C

Step-by-step explanation:

The vertical asymptote tells you the denominator is zero at x=-1. The only function that has that characteristic is ...

  F(x) = (x +2)/(x +1)

Answer:

(-1, 1)

Step-by-step explanation:

-1 is the opposite of 1, and the point is located in quadrant ll.

Answer:

a^7

Step-by-step explanation:

a^7

Exponents are added when multiplied

Answer: 2

Step-by-step explanation:

Answer:

I think it's 2kg

Step-by-step explanation:

13/5 ÷ 13/10

Reciprocate

13/5 × 10/13

= 26/13

=2kg

Answer:

a111111111111111111111111111111

Step-by-step explanation:

sorry I heeded to do that

The inequality that can be used to determine x, the number of outfits Tamika can purchase is; 539.63+ 52.93x ≤ 800

The given parameters are:

Budget = $800

New bicycle = $482.62

3 bicycle reflectors = $10.84 each

Pair of a bike gloves = $24.49.

New biking outfits = $52.93each.

Let the number of new biking outfits be x So, we have;

New bicycle + 3 . price of bicycle reflectors + Pair of a bike gloves + New biking outfits <= Budget

This gives;

482.62 + 3( 10.84) + 24.49+ 52.93x ≤ 800

This gives;

539.63+ 52.93x ≤ 800

Solve the inequality;

52.93x ≤ 260.37

Divide by 52.93

x ≤  4.91

Hence, the inequality is 539.63+ 52.93x ≤ 800

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Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

Answer:16x16

Step-by-step explanation:

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The point on the ellipsoid where the tangent plane is perpendicular to the line with parametric equations x = 2 - 4t, y = 1 + 8t, and z = 3 - 2t is (-3/2, 1/2, 3/2).

The gradient of the ellipsoid is given by (2x, 8y, 2z). At the point (x₀, y₀, z₀) on the ellipsoid, the gradient is (2x₀, 8y₀, 2z₀).

The line with parametric equations x = 2 - 4t, y = 1 + 8t, and z = 3 - 2t has a direction vector of (-4, 8, -2).

For the tangent plane at the point (x₀, y₀, z₀) to be perpendicular to the line, the normal vector of the plane must be parallel to the direction vector of the line. Thus, we have:

(2x₀, 8y₀, 2z₀) · (-4, 8, -2) = 0

-8x₀ + 64y₀ - 4z₀ = 0.

Also, the point (x₀, y₀, ₀) lies on the ellipsoid, so we have:

x₀² + 4y₀² + z₀² = 9.

We solve the system of equations to find the values of x₀, y₀, and z₀:

x₀ = -3/2, y₀ = 1/2, ₀ = 3/2.

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Answer:

x ≈ 0.843913

Step-by-step explanation:

1) 2π × 3x = 7x + 10

2) 6πx = 7x + 10

3) 6πx - 7x = 10

4) ( 6π - 7)x = 10

5) x =10/6π - 7 0R x ≈ 0.843913

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

the probability is 0.0750

Step-by-step explanation:

The computation of the probability is shown below;

The mean of x is

= 1.5 ÷ √79

= 0.1688

Now the probability is

= P(Z < -0.3 ÷ 0.1688) + P(\bar{x} > 0.3 ÷ 0.1688)

= P(Z < -1.78) + P(Z > 1.78)

= P(Z < -1.78) + 1 - P(Z < 1.78

= 0.0375 + 1 - 0.9625

= 0.0750

hence, the probability is 0.0750

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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In the first case the solution comes to be equal to 4.75% and in second one it is equal to 1.73

What is Standard Deviation ?

The standard deviation is a metric that reveals the degree of variation (such as spread, dispersion, and spread) from the mean. The standard deviation represents a "average" departure from the mean. Because it uses the original units of measurement from the data set, it is a well-liked measure of variability. Similar to variance, there is little variation when data points are close to the mean, but there is much variation when data points are widely scattered from the mean. The amount of departure from the average is determined by standard deviation. The most common measurement of dispersion, the standard deviation, is based on all values. Therefore, a change in even one value has an impact on the standard deviation's value. It is independent of origin but not of scale. It is also useful in certain advanced statistical problems.

Given that,

μ = 1.5

σ = 0.18

a. P ( X>1.8 ) = 1 - P(X<1.8) = 1 - P ( X-μ / σ < 1.8 - 1.5 / 0.18 )

  = 1 - P (Z<1.67)

  = 1 - 0.9525

  = 0.0475

Which is approximately equal to 4.75%

b. P (X > x) = 0.10

  = P (X < x) = 1 - 0.10 = 0.90

      x - 1.5 / 0.18 = 1.28

     x = 1.7304

which is approximately equal to 1.73.

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Answer:

Ur answer is in attachment

Step-by-step explanation:

please mark me as brainliest

The probability that a student has both box and a console is 1/6 and the P(B/A) = 0.378

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here, the number of students with both video games is 30 thus

The probability that a student has both box and a console is 30/180=1/6

And the conditional probability P(B/A) is = 1/6/0.44

                                                                    = 0.378

Hence, The probability that a student has both box and a console is 1/6, and the P(B/A) = 0.378

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Answer:

ok so 90 is 40 more dollars then 50 and there is 4 25 cents in each dollars so

4*40=160

so she would have to drive 161 miles to save money

Hope This Helps!!!

The maximum volume of the cylinder is approximately 1257 cubic centimeters.

The volume V of a right circular cylinder with radius r and height h is given by:

V = πr²h

Substituting the given expressions for the radius and height of the cylinder, we get:

V = πx²(800/πx - x)

Simplifying the expression, we get:

V = 800x - πx³

To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

dV/dx = 800 - 3πx² = 0

3πx² = 800

x² = 800/3π

x ≈ 6.43

Substituting this value of x back into the expression for V, we get:

V ≈ 1257

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