Can I get help with number 16

i) The cost function is x = 100,000 + 7n while the revenue function is y = 15n.

ii) The minimum number of customers for the business to break even is 12,500.

iii) The amount that Bob owes the bank after 3 years at 3% p.a. interest payable monthly, but without any repayment, is $109,272.70.

A function is a mathematical equation showing the equality of two or more algebraic expressions.

a) Renovation and appliances costs = $100,000

Average running cost per customer = $7

Selling price per customer = $15

i) Let the number of customers = n

Cost function, x = 100,000 + 7n

Revenue function, y = 15n

ii) For the business to break even, y must be equal to x:

15n = 100,000 + 7n

8n = 100,000

n = 12,500

iii) Bank loan = $100,000

Interest rate = 3% p.a.

Interest payment = monthly

Amount after 3 years without any repayment = $100,000 x 1.03^3

= $109,272.70 ($100,000 x 1.092727)

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The expected amount that you would win is approximately $0.334891, and the probability of losing $300,000 or more is approximately 0.00030986749 (or 0.030986749%).

To calculate the expected amount that you would win in this scenario, we need to consider the probabilities of various outcomes and their corresponding winnings.

(a) Expected Amount of Winnings:

Let's calculate the expected amount by considering the probabilities and winnings for different outcomes:

- Probability of matching exactly 5 out of 6 numbers:

The probability of matching 5 numbers correctly is given by the combination formula:

P(5) = C(6, 5) * C(40, 1) / C(46, 6) = 0.00000096739

The corresponding winnings are $100,000.

- Probability of matching exactly 4 out of 6 numbers:

The probability of matching 4 numbers correctly is given by the combination formula:

P(4) = C(6, 4) * C(40, 2) / C(46, 6) = 0.0000186101

The corresponding winnings are $5,000.

- Probability of matching exactly 3 out of 6 numbers:

The probability of matching 3 numbers correctly is given by the combination formula:

P(3) = C(6, 3) * C(40, 3) / C(46, 6) = 0.000290201

The corresponding winnings are $500.

Now, let's calculate the expected amount:

Expected Amount = (P(5) * $100,000) + (P(4) * $5,000) + (P(3) * $500)

Expected Amount = (0.00000096739 * $100,000) + (0.0000186101 * $5,000) + (0.000290201 * $500)

Expected Amount = $0.096739 + $0.093051 + $0.145101

Expected Amount = $0.334891

Therefore, the expected amount that you would win is approximately $0.334891.

(b) Probability of Losing $300,000 or More:

To derive a bound on the probability of losing $300,000 or more, we need to calculate the cumulative probability of having 3 or fewer of the 5 winning tickets.

Cumulative Probability = P(3) + P(4) + P(5)

Cumulative Probability = 0.000290201 + 0.0000186101 + 0.00000096739

Cumulative Probability = 0.00030986749

Therefore, the bound on the probability of losing $300,000 or more is approximately 0.00030986749, which is equivalent to 0.030986749%.

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Answer:

The population of Bear in 2050 is 4750000

Step-by-step explanation:

A) The exponential growth equation for bear is as follows -

dN/dT = rmax * N

Where dN/dT = change in population

rmax is the maximum rate of change

N = Base population

B) Here the per capita rate of increase (r) will always be a positive value irrespective of the and hence we will assume this population to be growing exponentially.

C) dN/dT = rmax * N

D) dN / 5 = 2.5 * 380,000

dN = 5*2.5 * 380000

= 4750000

Let's start solving the given problem. Suppose that an urn contains 3 different types of balls: red, green, and blue. Let pi denote the proportion of red balls, p2 denote the proportion of green balls, and p3 denote the proportion of blue balls.

Here Pi = 1.

Suppose also that 100 balls are selected with replacement, and there are exactly 38 red, 29 green and 33 blue.

We need to find the M.L.E. p; of p1, i = 1, 2, 3.

The probability of obtaining red ball from the urn = pi. The probability of obtaining green ball from the urn = p2. The probability of obtaining blue ball from the urn = p3

Given that, 100 balls are selected with replacement.

Let's calculate the probability of getting 38 red, 29 green, and 33 blue balls from the urn,

P(38 Red and 29 Green and 33 Blue) = P(Red)38 x P(Green)29 x P(Blue)33 = p₁³⁸ x p₂²⁹ x p₃³³

Therefore, the likelihood of obtaining the 38 red, 29 green, and 33 blue balls is L(p1,p2,p3) = p₁³⁸ x p₂²⁹ x p₃³³

Since, L(p1,p2,p3) is a continuous function, so we have to find the critical points of the function to obtain the minimum value of p₁. Let's take natural logarithm on both sides of the function, we get ln

L(p1,p2,p3) = 38 ln p₁ + 29 ln p₂ + 33 ln p₃.

So, taking partial differentiation with respect to p1, p2 and p3 and equating them to 0. We get the following equations,∂ ln L / ∂p1 = 38/p1 = 0∂ ln L / ∂p2 = 29/p2 = 0∂ ln L / ∂p3 = 33/p3 = 0On

solving the above three equations, we get p1 = 38/100 = 0.38p2 = 29/100 = 0.29p3 = 33/100 = 0.33

Therefore, P₁= 0.38, S= 0.29, P3 = 0.33. Hence, the required solution is P₁= 0.38, S= 0.29, P3 = 0.33.

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Answer:

dogs - 13

cats - 39

Step-by-step explanation:

Let the number of dogs Ma Bernier have be represented with d

She has 3 times as many cats as dogs, the number of cats she has :

cats = 3d

The sum of the cats and dogs is 52

d + 3d = 52

4d = 52

divide both sides of the equation by 4

d = 13

She has 13 dogs

Cats = 3d

= 3 x 13 = 39

Answer:

200

Step-by-step explanation:

103+94

=100+100

=200

Answer:

197 the nearest ten is 200

Step-by-step explanation:

he need to put the nearest ten

Answer:

y intercept is (0, 2/3)

Step-by-step explanation:

the y-inetercept is 0

i don’t know the exponential

growth or exponential decay but you can use math.way to help you answer the question

circumference is around the circle the border of the circle the area of the circle is the space in the circle

Answer:

standard

Step-by-step explanation:

(a) Using these variables, the dimensionless variables that can be used for this problem are as follows:2d/gdgb/EiE/b

(b) If the density is the same, the model ice can have the same strength properties as that of the prototype ice.

(a) The suitable set of dimensionless variables for this problem includes: g, the acceleration of gravityd, depth of the iceb, pier width Ei, the strength of the ice ρ, density of the ice

Using these variables, the dimensionless variables that can be used for this problem are as follows:2d/gdgb/EiE/b

(b) Given that the length scale is 1/21, and prototype ice thickness and velocity are 12 in. and 11 ft/s, respectively.

We can determine the model ice thickness and velocity using the length scale as follows:

For ice thickness, Model ice thickness = Prototype ice thickness × Length scale= 12 in. × (1/21)= 0.571 in.

For ice velocity, Model ice velocity = Prototype ice velocity × (Length scale)-0.5= 11 ft/s × (1/21)-0.5= 0.765 ft/s≈ 0.77 ft/s(c)

The model ice can have the same strength properties as the prototype ice if their strengths are identical, although the densities are the same.

Therefore, if the density is the same, the model ice can have the same strength properties as that of the prototype ice.

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Answer:

A pyramid

Step-by-step explanation:

Answer: Its A

Step-by-step explanation: Just count the lines and since there is 8 lines it would be ?/8 so we going to count up until the dot which stops at 3 soo it would be 3/8

Answer: True

Explanation:

1 centimeter = 10 millimeters

Buster = 75 millimeters long

Bubbles = 60 millimeters long

Answer:

A is true and f is true

Step-by-step explanation:

Answer:

a, d, e, and g

Step-by-step explanation:

if you multiply two negatives, you get a positive

Answer:

30 times

Step-by-step explanation:

1. find the possibility of the spinner landing on each section

1 / 5 = 0.2

2. multiply # of spins by the possibility

150 * 0.2 = 30 times

Answer:

0.2857 is not a rational number.

Step-by-step explanation:

Because rational numbers have to be greater than 1. Decimals are not over 1 so it is not a rational number. Your welcome!

Answer:

75.39 in^2 (round to the nearest hundreds)

Step-by-step explanation:

I think that we have to find the lateral area

circumference = 2 x radius x pi = 2 x 4 x pi = 25,13 in^2 (round to the nearest hundreds)

lateral surface = (circumference x slant height)/2 = (25,13 x 6)/2 = 75,39 in^2 (round to the nearest hundreds)

A. The volume of the solid formed by rotating the region bounded above by the parabola y = 3x-x² and y = 0 around the vertical line x = -1 is approximately 9.74 cubic units and B. The inverse function is found to be ln(x/(1 - x)).

To find the volume of the solid, we can use the method of cylindrical shells. The integral for the volume is given by V = ∫[a,b] 2πxf(x) dx, where f(x) represents the height of the shell at each x-coordinate.

First, we need to find the bounds of integration. The parabola y = 3x - x² intersects the x-axis at x = 0 and x = 3. Therefore, the bounds of integration are [0, 3].

Next, we need to express the height of the shell, f(x), in terms of x.

Evaluating the integral, we get V = ∫[0,3] 2π(x + 1)(3x - x²) dx. After integrating and simplifying, the volume is approximately 9.74 cubic units.

(B) To find the inverse of the function f(x), we swap the roles of x and y and solve for y. So, we start with y = eˣ/(1 - eˣ).

Step 1: Swap x and y: x = eʸ/(1 - eʸ).

Step 2: Solve for y: x(1 - eʸ) = eʸ.

Step 3: Expand and isolate eʸ: x - xeʸ = eʸ.

Step 4: Factor out eʸ: eʸ(x - 1) = x.

Step 5: Divide both sides by (x - 1): eʸ = x/(x - 1).

Step 6: Take the natural logarithm of both sides: y = ln(x/(x - 1)). Thus, the inverse function is g(x) = ln(x/(x - 1)), where x ∈ (0, 1).

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Complete question - A. The region bounded above by the parabola y = 3x-x2² and y = 0 is rotated around a vertical line x=-1 forming a solid, find its volume.

B. Given the following function which is one to one f(x) = eˣ/1-eˣ Find its inverse.

Answer:

-2x+2

Step-by-step explanation:

it is directly underneath the original equation and they never intersect

The total money made by each court would be as follows:

Centre Court: £838,824, No 1 Court: £514,305

No 2 Court: £164,000, No 3 Court: £82,000

To calculate the amount of money made by each court if all seats were sold, we need to multiply the number of seats by the corresponding ticket price for each court. Here are the calculations for each court:

Centre Court:

Number of seats: 14,979

Ticket price: £56

Total money made: 14,979 seats ×£56/seat = £838,824

No 1 Court:

Number of seats: 11,429

Ticket price: £45

Total money made: 11,429 seats ×£45/seat = £514,305

No 2 Court:

Number of seats: 4,000

Ticket price: £41

Total money made: 4,000 seats ×£41/seat = £164,000

No 3 Court:

Number of seats: 2,000

Ticket price: £41

Total money made: 2,000 seats × £41/seat = £82,000

Therefore, if all seats were sold, the total money made by each court would be as follows:

Centre Court: £838,824

No 1 Court: £514,305

No 2 Court: £164,000

No 3 Court: £82,000

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The sum of the Arithmetic Progression 5 + 8 + 11 + ... + 122 is 2540.

Here we are given to find the sum of 5 + 8 + 11 + ... + 122

Here we can see that this is an Arithmetic Progression with the first term as 5 and the common difference as

second term - first term

= 8 - 5

= 3

Here we need to find the sum from 5 to 122

now, we know that for any term

aₙ = a + (n - 1)d

where,

a = first term

d = common difference

hence putting aₙ as 122 we get

5 + (n - 1)3 = 122

or, 5 + 3n - 3 = 122

or, 3n + 2 = 122

or, 3n = 120

or, n = 40

Hence, we need to find the sum of the first n terms

we know that the sum S is

S = 0.5n(a + aₙ)

here we know that n = 122, a = 5 and aₙ = 122

hence we get

S = 0.5 X 40(5 + 122)

= 20(127)

= 2540

Hence the sum is 2540.

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Answer:

77 degrees

Step-by-step explanation:

All triangle add up to 180 degrees and right triangle all have one angle that is 90 degrees so 90 + 14 is 104 and 180 - 104 is 77.

Answer:

76 degrees

Step-by-step explanation:

What we know:

1. the triangle is a right triangle, meaning on angle has to be 90 degrees

2. One angle is 14 degrees

3. A triangle's angles add up to 180 degrees.

----------------------------------------------------------------------------------------------------

90+14+x=180

104+x=180

x=76

Answer:

y = -1/3x + 4

Step-by-step explanation:

(-9, 7) and (3, 3)

Slope:

m=(y2-y1)/(x2-x1)

m=(3-7)/(3+9)

m=(-4)/12

m= -1/3

Slope-intercept:

y - y1 = m(x - x1)

y - 7 = -1/3(x + 9)

y - 7 = -1/3x - 3

y = -1/3x + 4

Step-by-step explanation:

[tex]soln \\ \frac{3 - 7 }{3 - - 9} \\ = \frac{ - 4}{ - 12} \\ = \frac{1}{3 } \\ \frac{y - 7}{x - 3} = \frac{1}{3} \\ then \: you \: cross \: multiplication. \\ 3(y - 7) = 1(x - 3) \\ 3y - 7 = x - 3 \\ 3y = x - 3 + 7 \\ 3y = x + 4 \\ \frac{3y}{3} = \frac{x}{3} + \frac{4}{3} \\ y = \frac{x}{3} + \frac{4}{3} [/tex]

a) The probability of drawing 17 red balls and 8 blue balls from boxes with even-numbered labels is 0.0051.

b) The probability of drawing 17 red balls and 8 blue balls from boxes with even-numbered labels, given that the fifth ball drawn was red, is 0.1926.

a) The probability of drawing 17 red balls and 8 blue balls from boxes with even-numbered labels can be calculated as follows:

P(drawing 17 red balls and 8 blue balls from boxes with even-numbered labels) = (C(25, 17) × C(25, 8)) / C(50, 25)

= (12620256 / 2462624626080)

= 0.0051 (approx)

Therefore, the probability of drawing 17 red balls and 8 blue balls from boxes with even-numbered labels is 0.0051 (approx).

b) If accidentally, you see the fifth ball after being drawn is red, then the corresponding box will be removed, and there are now 49 boxes remaining on the table.

The number of even-numbered boxes among these 49 boxes is 24.

Therefore, the probability of drawing 17 red balls and 8 blue balls from boxes with even-numbered labels, given that the fifth ball drawn was red, can be calculated as follows:

P(drawing 17 red balls and 8 blue balls from boxes with even-numbered labels, given that the fifth ball drawn was red)

= (C(24, 16) × C(25, 7)) / C(49, 23)

= (8751600 / 45379690908)

= 0.1926 (approx)

Therefore, the probability of drawing 17 red balls and 8 blue balls from boxes with even-numbered labels, given that the fifth ball drawn was red, is 0.1926 (approx).

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Answer:

It converges

Step-by-step explanation:

dx/dy = x∧4 + 9x∧21

f(x) = ∫(x∧4 + 9x∧21)dy        0  > f(x) > ∞

= x∧5/5 + 9x∧22/22 + c  

    x = ∞ and x = 0

∴ c = 1 /5 +  9/22 = 27/22

Y Let f:R → R be defined by f(3) = Then x2 +1' a is (b) f is not a measurable function.

To determine if f is a measurable function, we need to check if the preimage of any measurable set in the codomain (R) is a measurable set in the domain (R).

In this case, the function f(3) = x^2 + 1 is defined only at x = 3. Since the domain R is continuous and f is only defined at a single point, the preimage of any set in the codomain will either be an empty set or a singleton set containing only the point x = 3.

For example, consider the set [f > 3] in the codomain R. The preimage of [f > 3] under f would be the set of all x in the domain R such that f(x) > 3. However, since f is only defined at x = 3, the preimage would be the singleton set {3}.  Since {3} is not a measurable set in the domain R, f is not a measurable function.

Therefore , the correct option is (B) f is not a measurable function.

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