PLEASE HELP!
To raise money for malaria research the New York City Rotary Club is going to sell 200,000
raffle tickets. One ticket will have a 8000 dollar prize attached to it. Ten tickets will have a
300 dollar prize attached to it. Seventy-five tickets will have a 50 dollar prize. (As a wam up,
answer for yourselves: what is the total amount of all the prize money?) In addition to the
prize money, to make sure that the tickets are secure, by hiring a company which specializes in
producing anti-counterfeit raffle tickets, the cost of raffle tickets is given by C(20) = 4500+6x.
To cover both the prize money and the cost of producing the raffle tickets, as a warm-up,
what should be the price of each of the 200,000 raffle tickets in order to break even?

From the constraint, we have

\(x+y+z=9 \implies z = 9-x-y\)

so that \(s\) depends only on \(x,y\).

\(s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy\)

Find the critical points of \(g\).

\(\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9\)

\(\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0\)

Using the given constraint again, we have the condition

\(x+y+z = 2x+y \implies x=z\)

so that

\(x = 9 - x - y \implies y = 9 - 2x\)

and \(s\) depends only on \(x\).

\(s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2\)

Find the critical points of \(h\).

\(\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3\)

It follows that \(y = 9-2\cdot3 = 3\) and \(z=3\), so the only critical point of \(s\) is at (3, 3, 3).

Differentiate \(h\) again and check the sign of the second derivative at the critical point.

\(\dfrac{d^2h}{dx^2} = -6 < 0\)

for all \(x\), which indicates a maximum.

We find that

\(\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)\)

The second derivative at the critical point exists

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\) for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

\($&\frac{\partial g}{\partial x}\) = 9 - 2x - y = 0

\($&\frac{\partial g}{\partial y}\) = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

\($\frac{d h}{d x}=18-6 x=0\)

⇒ x = 3

It pursues that y = 9 - 2 \(*\) 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\)

for all x, which suggests a maximum.

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Answer:

Rs 2150.81.

Step-by-step explanation:

The interest rate for the first two years is 6% per annum, which is halved for each six-month period. Therefore, the interest for the first two years would be (6950*(1+(0.03))^8) - 6950 = Rs 1373.53.

For the third year, the interest rate is 9% per annum, which is also halved for each six-month period. Therefore, the interest for the third year would be (6950*(1+0.045))^2 - 6950 = Rs 777.28.

Hence, the total compound interest for three years would be Rs 2150.81.

\(\textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y-2)^2}{16}-\cfrac{(x+1)^2}{144}=1\implies \cfrac{(y-2)^2}{4^2}-\cfrac{( ~~ x-(-1) ~~ )^2}{12^2}=1\)

now, since the positive fraction is the one with the "y" in it, that means the traverse axis is running over the y-axis in short the hyperbola is opening up and down.

From the same equation above, we can see the center is at (-1 , 2) and the conjugate axis has a half which is "b" or namely b = 12, since that's half of the conjugate axis, then the conjugate axis must be 2b or 24.

A + M = 18

M = 2A + 3

This is the SoE used, hope I helped

The system of the equations are M= 2 (A + 3) and M+A = 18

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given that Michael's age is 3 more than twice Ashley's age.

M= 2 (A + 3)

If M represents Michael's age and A represents Ashley's age.

The sum of their ages is 18.

M+A = 18

Simplifying the expression,

M= 2 (A + 3) and M+A = 18

Therefore, the system of the equations are M= 2 (A + 3) and M+A = 18

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Answer:

82.89

Step-by-step explanation:

Answer:

22.5oz and 0.22$

Step-by-step explanation:

Answer:

72ft²

Step-by-step explanation:

a square has 4 equal sides, when each one is 18ft, the total perimeter will be 18×4=72ft²

Hii!

_____________________________________________________

\(\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}\)

Perimeter of the rug = 72 ft

\(\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}}\)

\(\bullet\) Let's work out the perimeter

\(\twoheadrightarrow\sf P=4a\) a=length of one side

\(\bullet\) Stick in the values

\(\twoheadrightarrow\sf P=4\cdot18\)

\(\bullet\) Multiply

\(\twoheadrightarrow\sf P=72ft\)

--

Hope that this helped! Best wishes.

\(\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}\)

--

The missing sides of the figure are

3. x = 6

5. x = 40

3. Given that the area is 42

Area of trapezoid is = 1/2 (sum of parallel lines) * height

42 = 1/2(x + 10) * 6

8 = 1/2 (x + 10)

16 = (x + 10)

16 - 10 = x

x = 6

5. Area = 140

Area = area of triangle + area of square

140 = 1/2 * x * 4 + x * 5

140 = 2x + 5x

280 = 7x

x = 280/7

x = 40

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Answer:

21+4

Step-by-step explanation:

3 times 7=21

3 times4=12

21d+4e

Answer:

21d+12e

Step-by-step explanation:

I'm pretty sure thats it if its expanding.

Answer:

\(\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|\)

Step-by-step explanation:

Cost of a bowl of salad = $5.00

Cost of a slice of pizza = $2.00

If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation:

Next, we make P the subject of the equation above.

2P=E-5S

\(P=\dfrac{E-5S}{2} \\P=0.5(E-5S)\)

Therefore, The quantity of pizza he buys can be represented by the equation:

When E=$40, we are required to complete the table below.

\(\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&\\40.00&4&\\40.00&&0\end{array}\right|\)

When S=0, E=$40

From P=0.5(E-5S)

P=0.5(40-5(0))=20

When S=4, E=$40

P=0.5(40-5(4))

=0.5(40-20)

=0.5*20

=10

When P=0, E=$40

P=0.5(E-5S)

0=0.5(40-5S)

40-5S=0

5S=40

S=8

Therefore, the completed table is:

\(\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|\)

Answer:

19

Step-by-step explanation:

57 divided by 3 is 13

Answer:

one side is 19 inches

Step-by-step explanation:

57 / 3 = 19

since it is an equilateral triangle the sides are equal so you can just divide by 3

Answer:

9.5

Step-by-step explanation:

You're welcome have a nice

Answer:

19.98

Step-by-step explanation:

A batting average is simply the ratio of hits/at-bats.  So, if Irene were up to bat 1,000 times and she got a hit 444 times, that makes her batting average 444/1,000 = .444.

The good news is you can multiply this ratio by number of at bats to get the number of hits.

So, 45 hits x .444 = 19.98

Hope this helps!

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.

Answer: B

Step-by-step explanation: Hope this helps:)

The total surface area of the clubhouse including the floor is approximately 95.98 square feet.

We have,

The surface area of a square pyramid can be found by adding the area of the base to the sum of the areas of the four triangular faces.

Since the base is a square, its area is 6^2 = 36 square feet.

Each triangular face is an equilateral triangle with a side length of 6 feet, so its area can be found using the formula.

A = (√(3)/4) x s²,

where s is the length of a side.

The area of each triangular face.

A = (√(3)/4) x 6² = 9 √(3) square feet.

The total surface area is then:

A = 4 x 9 √(3) + 36

A = 36 √(3) + 36  ≈ 95.98 square feet

(rounded to the nearest hundredth)

Therefore,

The total surface area of the clubhouse including the floor is approximately 95.98 square feet.

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sorry but I don't know, I'm in the 3rd grade and I don't know much about this, I hope this will be useful to you, I just could do it! I'm sorry❤️

Answer:

\(\frac{20}{13}\)

Step-by-step explanation:

74/48.1 = 1.53 repeating

1.53 repeating = \(\frac{20}{13}\)

Answer:

Step-by-step explanation:

Add two cube numbers and

one square

number.​

Answer

Joseph's level after all of this is 121 feet below the sea level.

Explanation

Joseph dove 47 feet below the sea level.

Current level that Joseph is at = -47

Then, they dove 137 feet further below sea level

Their current level is now = -47 - 137 = -184 (That is, 184 feet below the sea level)

Then, he and his dive partner swam up 63 feet in order to swim with the turtles.

Their current level is now = -184 + 63 = -121 feet (That is, 121 feet below sea level).

Hope this Helps!!!

Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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Answer?: I believe its C

No Explanation Because No

Answer: C is the answer

Step-by-step explanation:

the answer is D

The figure can be divided into a rectangle and 2 triangles

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

The number of gorillas at the safari park is 4.

Let the number of gorillas at the safari park be x.

It is given that there are 24 more buffalo than there are gorillas.

Number of buffalo at the safari park = 24 + x

There are 7 times as many wallabies as there are gorillas.

Number of wallabies at the safari park = 7x

Now, the number of buffalo is the same as the number of wallabies.

So, we equate their numbers to find the value of x i.e. number of gorillas.

24 + x = 7x

7x - x = 24

6x = 24

x = 4

Therefore, the number of gorillas at the safari park is 4.

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