(a) Bob wants to open a new fastfood shop. He estimates he needs to spend at least $100,000 on renovation and buying commercial kitchen appliances. The average running cost per customer (for food, staff salary, etc.) is $7. Each customer spends $15 on average.

(i) If the number of customers is n, write down the cost function and revenue function as functions of n.

(ii) Determine the minimum number of customers for the business to breakeven.

(iii) Bob has to borrow $100,000 from a bank with interest rate of 3% p.a. with interest payable monthly. If Bob does not repay a single cent, how much does Bob owe the bank after 3 years?

Answer: -9

2 to the power of 0 = 1 then all you have to do is plug in the numbers and simplify

Answer:

-9

Step-by-step explanation:

Well you just subsitute it all and solve from there

s^0= 2^0

p^-2= -3^-2

Anything squared to the power of 0 is 1

so its already 1/smth

the second part is just 3^-2 first which is 1/9 then the negative sign which is -1/9

If a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1, the final formula for the cubic polynomial is f(x) = x³ - 3x² + 12x - 6.

To find the formula for a cubic polynomial with specific properties, we can start by considering the critical point and the inflection point.

Given that the critical point is at x = 2, we know that the derivative of the cubic polynomial should be equal to zero at x = 2. This means that the slope of the polynomial at x = 2 is zero. Taking the derivative of the cubic polynomial, we have:

f'(x) = 3ax² + 2bx + c.

Setting this equal to zero and substituting x = 2, we get:

3a(2)² + 2b(2) + c = 0.

12a + 4b + c = 0.

Now, let's consider the inflection point at (1,4). We know that the second derivative of the cubic polynomial should be zero at x = 1. Taking the second derivative, we have:

f''(x) = 6ax + 2b.

Setting this equal to zero and substituting x = 1, we get:

6a(1) + 2b = 0.

6a + 2b = 0.

Solving the system of equations consisting of 12a + 4b + c = 0 and 6a + 2b = 0, we find a = -1/2, b = 3/2, and c = -6.

Therefore, the formula for the cubic polynomial is:

f(x) = -1/2x³ + 3/2x² - 6x + d.

The leading coefficient is 1, so we have:

f(x) = x³ - 3x² + 12x + d.

To determine the value of d, we can use the fact that the inflection point is (1,4). Substituting x = 1 and y = 4 into the equation, we get:

4 = 1 - 3 + 12 + d.

4 = 10 + d.

d = -6.

Therefore, the final formula for the cubic polynomial is:

f(x) = x³ - 3x² + 12x - 6.

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Complete question is:

Find the formula for a cubic polynomial, ax³+bx²+cx+d,  with a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1.

The given arguments are proved using logical inference rules.

To show that each of the following arguments is valid, we need to construct a proof using logical inference rules. Here is a proof for the given arguments:

Argument 1:

1. C ⊃ D (Premise)

2. ~(A ∨ B) ∨ C (Premise)

3. ~B ∨ D (Premise)

4. ~(A ∨ B) (Assumption)

5. ~A ∧ ~B (De Morgan's Law, 4)

6. ~B (Simplification, 5)

7. D (Disjunctive Syllogism, 3, 6)

8. ~(A ∨ B) ∨ D (Disjunction Introduction, 7)

9. C (Disjunction Elimination, 2, 8)

10. ~(A ∨ B) ∨ C (Disjunction Introduction, 9)

Therefore, the argument is valid.

Argument 2:

1. C ⊃ D (Premise)

2. ~(A ∨ B) ∨ C (Premise)

3. ~B ∨ D (Premise)

4. ~A ∨ ~B (Assumption)

5. ~(A ∨ B) (De Morgan's Law, 4)

6. C (Disjunction Elimination, 2, 5)

7. C ⊃ D (Premise)

8. D (Modus Ponens, 6, 7)

9. ~B ∨ D (Disjunction Introduction, 8)

10. ~(A ∨ B) ∨ D (Disjunction Introduction, 9)

Therefore, the argument is valid.

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Answer:

Number 1 is correct

4.5 x 12 = 54

Number 3 is wrong,

Formula of a triangle:

BH x 1/2(basically dividing by 2)

8 x 15 = 120,

120 DIVIDED BY 2 = 60 is your area, not 120.

Your plug in would be for the triangle:

8 x 15 x 1/2

Number 5 is wrong.

11 + 4 = 15

15 x 6 (you forgot to multiply by the height!) = 90

90 divided by 2 ( x 1/2) = 45 is your area, NOT 90.

Your formula for a trapezoid is:

(b1 + b2) x h x 1/2 Don't forget your height next time!

Plug in: (4 + 11) x 6 x 1/2

The total number of elements in an array is indeed equal to the product of its number of rows and columns. In this case, since the array has 4 rows and 7 columns, the total number of elements is 4 x 7 = 28.

The total number of elements in an array is equal to the product of its number of rows and columns. In this case, the array has 4 rows and 7 columns, so the total number of elements is:

4 x 7 = 28

Therefore, the answer is (c) 28.

The total number of elements in an array is indeed equal to the product of its number of rows and columns. In this case, since the array has 4 rows and 7 columns, the total number of elements is 4 x 7 = 28.

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Answer:

[tex]g \: y = 2x - 3 \\ [/tex]

if you insert x and y values in equation you can find the exact equation

Answer:

Step-by-step explanation:

(48x^2)(y) + (16x)(y^2).

This is addition, so the distributive property applies. [(48x^2)(y) + (16x)(y^2)]/8xy = (48x^2)(y)/8xy+(16x)(y^2)/8xy = 6x+2y.

Division rules are explained below.

I included the parentheses to emphasize the difference between x^2y, which means x to the 2y, and (x^2)(y), which is x^2 times y.

TELL ME IF THIS IS CONFUSING<,BECAUSE I DON'T THINK I EXPLAINED VERY WELL.

Answer:

I think! 3.5 feet wide

Step-by-step explanation:

the area of the pool is 240 square feet. divide by 68 square feet gives you 3.539= 3.5 feet wide. dont shoot me if I'm wrong lol

The width of the deck is approximately 2.65 feet.

To solve the problem, we need to first find the total area of the pool and deck combined, and then subtract the area of the pool to find the area of the deck.

The total area of the pool and deck can be represented as follows:

(12 + 2x) x (20 + 2x)

where x is the width of the deck.

The area of the pool is:

12 x 20 = 240

So, the area of the deck can be found by subtracting the area of the pool from the total area:

(12 + 2x) x  (20 + 2x) - 240 = 68

Expanding the left side and simplifying, we get:

4x²+ 64x - 208 = 0

Dividing both sides by 4, we get:

x²+ 16x - 52 = 0

Using the quadratic formula, we get:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = 16, and c = -52.

Plugging in these values, we get:

x = (-16 ± √(16² - 4(1)(-52))) / 2(1)

x = (-16 ± √(960)) / 2

x = (-16 ± 4√(15)) / 2

x = -8 ± 2√(15)

Since the width of the deck cannot be negative, we can discard the negative solution, and we are left with:

x = -8 + 2√(15)

So, the width of the deck is approximately 2.65 feet.

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Step-by-step explanation:

True

false

false

true

i think its that I'm sorry if its wrong

Answer:

-4 + -6 = -10

Step-by-step explanation:

From the line at negative 4 it goes to negative 10 you need to add six to four to make ten. Though since it is negative numbers we add a negative 6

The value of ∠FGJ = x⁰ is 45⁰.

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Here, we know that sum of angles on linear pair is 180⁰.

        ∠FGJ = x⁰ and ∠JGH = 135⁰

∠FGJ + ∠JGH = 180⁰

    x⁰ + 135⁰ = 180⁰

    x⁰ = 180⁰ - 135⁰

    x⁰ = 45⁰

Thus, the value of ∠FGJ = x⁰ is 45⁰.

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Given that X₁, X₂, ..., Xₙ are iid according to a uniform continuous distribution over the open interval (0,0+1).

Now, we have to find a sufficient statistics for 8.Let T = ∑Xᵢ, then T ~ U(n*0,n).Thus, T is a sufficient statistic for θ.Hence, T is a sufficient statistics for 8.

Given that X₁, X₂, ..., Xₙ are iid according to a uniform continuous distribution over the open interval (0,0+1).

We have to find a minimally sufficient statistics for

Let T = (X(n), X(1)), where X(n) = max{X₁,X₂, .... Xₙ} and X(1) = min{X₁,X₂, .... Xₙ}.As Xᵢ follows uniform distribution, so T can take any value in [0, 1].

Let Y = nX(n)/(1-X(n)), thenY = (nX(n))/(1-X(n)) = (nX(n))/(X(n)-X(1)) = 1/[(X(n)-X(1))/n].Now, 0 < X(1) ≤ X(n) < 1. Therefore, 0 < (X(n)-X(1))/n ≤ 1/n. Then, Y takes values in [0,∞).Thus, Y is a one-to-one function of T.

Hence, T is a minimally sufficient statistics for 8.

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Answer:

Step-by-step explanation:

a. annual premium: 79.35

b. monthly premium: 7.14

Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten-year term. Annual premium = $1,500 per year and monthly premium = $125 per month.

One type of operation is division in mathematics. In this procedure, the phrases or numbers are divided into the same number of components.

Given: Marcie Ann Weber,

insured amount of term insurance plan = $15,000.

Number of year = 10 year

To find the amount of annual premium:

Divide the total insured amount by number of years.

Annual premium = Insured amount of term insurance plan / Number of year

Annual premium = $15,000 / 10

Annual premium = $1,500 per year

To find the amount of monthly premium:

Monthly premium = Insured amount of term insurance plan / Number of month in 10 year

Monthly premium = 15,000 / (10 x 12)

Monthly premium = 15,000 / 120

Monthly premium = $125 per month.

Therefore, annual premium = $1,500 per year and monthly premium = $125 per month.

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Answer:

The factors of x²-64 is equal to (x-8)(x+8).

Step-by-step explanation:

The given expression is:

x²-64

we know that, 8² = 64

So,

(x²-8²) = (x-8)(x+8) [As (a-b)(a+b) = a²-b²]

So, the factors of x²-64 i equal to (x-8)(x+8).

Answer:

1±√2=q

or

q=2.41, -0.41

Step-by-step explanation:

we are given the equation q²-2q-1=0, and we want to use the quadratic equation, which is (-b±√(b²-4ac))/2a

a is 1 (there is a 1 in front of q²)

b is -2

c is -1

substitute into the equation:

q=(2±√(4-4*1*-1))/2

solve for the discriminant:

√(4-4(1*-1))

√8

now the equation:

(2±√8)/2=q

simplify:

1±√2=q

or if your application asks for a decimal:

√2≈1.41

so:

1+1.41=2.41=q

or

1-1.41=-0.41=q

Hope this helps!

Answer:

Georgio has to earn $1,800 and borrow $2,700.

Answer:

each glass will have 0.75 of a cup or 3/4 of a cup * 0.75 and 3/4 is the same*

The statement is true that:

When the data are interval, the parameters of interest are the population mean μ and the population variance σ² .

Given,

Mean and standard variance .

Here,

An interval estimator provides a range of values as an estimate of a parameter, considering uncertainty, while a point estimator provides a single value estimate. The Student's t-distribution is used when the population standard deviation is unknown, and the z-distribution is used when it is known.

Support for the statement:

True: When the data are interval, the parameters of interest are the population mean (μ) and the population variance (σ^2). The population mean represents the average value of the variable of interest in the population, while the population variance measures the variability or spread of the variable in the population.

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Answer:

B) y=3.5x^2 +0.5

Step-by-step explanation:

the (0,0.5) tells you what the y-intercept is :)

hope this helps :)

The equation that states (x, y) is equidistant from (4, 1) and the x-axis is -8x - 2y + 17 = 0.

To express that the point (x, y) is equidistant from both the point (4, 1) and the x-axis, we can set up an equation using the distance formula.

The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, we want the distance from (x, y) to (4, 1) to be equal to the distance from (x, y) to the x-axis. The x-axis can be represented by the equation y = 0.

Let's set up the equation:

√((x - 4)² + (y - 1)²) = √((x - x)² + (y - 0)²)

Simplifying, we get:

√((x - 4)² + (y - 1)²) = √(x² + y²)

To remove the square roots, we can square both sides of the equation:

((x - 4)² + (y - 1)²) = (x² + y²)

Expanding and simplifying further, we have:

x² - 8x + 16 + y² - 2y + 1 = x² + y²

Combining like terms, we obtain:

-8x - 2y + 17 = 0

Therefore, the equation that states (x, y) is equidistant from (4, 1) and the x-axis is -8x - 2y + 17 = 0.

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Alex and Jack work for a computer software company. Alex can write a computer program in 24 hours, while

Jack can write it in 16 hours. How long will it take them to write the program together?

Answer: 9.6 hours

Answer:

The answer would be Y= 1/4X -3

Step-by-step explanation:

Hope it was helpful .

Good luck ^.^

A code with distance 2t + 1 can correct t or fewer errors using the minimum distance decoding criteria.

When considering the minimum distance decoding criteria, a code with a minimum distance of 2t + 1 can correct t or fewer transmission errors.

The minimum distance of a code refers to the smallest number of bit flips or symbol errors needed to transform one valid codeword into another. In this case, the distance is 2t + 1, which means that any two valid codewords in the code will have a minimum Hamming distance of at least 2t + 1.

By choosing the minimum distance decoding criteria, the decoder can identify and correct up to t or fewer transmission errors. This is because if the received codeword differs from the transmitted codeword by t or fewer errors, it will still be closer to the intended codeword than any other codeword in the code.

Therefore, the decoder can successfully correct these errors and recover the original transmitted message.

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Answer:

Step-by-step explanation:

x+3 - x = 3 = width

2(x+3) = 2x + 6 = length

2x + 6 +2x +6 +3 +3 = 4x + 18 = Perimeter of T

Answer: 40% i think

Step-by-step explanation:

Answer:

13.9%

Step-by-step explanation    :

Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.

 0.138613961 ------ when multiplying by 100 you move two spots the decimal point:     13.8613961 %

The tenth digit is 8 the number after that is 6  

If the digit after tenth is greater than or equal to 5, add 1 to tenth. Else remove the digit.

6 is greater than 5 so we add 1 to 8 and becomes 9

If the digit  after the tenth was 4 instead 6, for example,then it would be 13.8%

Answer:

it's just a angle that is 3D

Step-by-step explanation:

Answer:

The experimental probability should get closer to the theoretical probability of 1/6 with more trials.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Experimental probability:

The number of desired outcomes is taken from the results of an experiment.

Theoretical probability:

Found before the experiment happens.

For a large number of trials, the experimental probability will be closer to the theoretical probability.

In this question:

A standard die has 6 sides, one which is 3. So the theoretical probability of rolling a 3 is 1/6.

After six rolls of a standard die, the experimental probability of rolling a 3 is 2/6.

The experimental probability, after six rolls, is 2/6 = 1/3.

What do you expect will happen to the experimental probability if the die is rolled 90 more times?

As the number of trials increase, the experimental probability is expected to get closer to the theoretical probability, which in this case is 1/6.