The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9 each and will sell 500 tickets. There is one $2,000 grand prize, four $400 second prizes, and sixteen $10 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

Answer:

270

Step-by-step explanation:

For any arithmetic sequence

nth term is given by

nth term = a + (n-1)d

where a is first term,

d is common difference

d is given by nth term - (n-1)th term

sum of n terms given by

sum = n/2(2a + (n-1)d)

________________________________________________

Given arithmetic sequence

-2,0,2,4,6,8...

first term a = -2

lets take third term as nth term and second term as (n-1)th term to find common difference d.

d = 2 - 0 = 2

using a = -2 , d = 2, n = 18

thus, sum of first 18 terms = n/2(2a + (n-1)d)

                                           =18/2( 2*(-2) + (18-1) 2)

                                           =9 ( -4 + 34)

                                           =9 ( 30) = 270

Thus, sum of first 18 terms is 270.

Answer:

The quantity of salt at time t is [tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex], where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

[tex]\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}[/tex]

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

[tex](0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}[/tex]

Where:

[tex]c[/tex] - The salt concentration in the tank, as well at the exit of the tank, measured in [tex]\frac{pd}{gal}[/tex].

[tex]\frac{dc}{dt}[/tex] - Concentration rate of change in the tank, measured in [tex]\frac{pd}{min}[/tex].

[tex]V[/tex] - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

[tex]V \cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]

[tex]60\cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]

[tex]\frac{dc}{dt} + \frac{1}{10}\cdot c = 3[/tex]

This equation is solved as follows:

[tex]e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }[/tex]

[tex]\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }[/tex]

[tex]e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt[/tex]

[tex]e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C[/tex]

[tex]c = 30 + C\cdot e^{-\frac{t}{10} }[/tex]

The initial concentration in the tank is:

[tex]c_{o} = \frac{10\,pd}{60\,gal}[/tex]

[tex]c_{o} = 0.167\,\frac{pd}{gal}[/tex]

Now, the integration constant is:

[tex]0.167 = 30 + C[/tex]

[tex]C = -29.833[/tex]

The solution of the differential equation is:

[tex]c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }[/tex]

Now, the quantity of salt at time t is:

[tex]m_{salt} = V_{tank}\cdot c(t)[/tex]

[tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex]

Where t is measured in minutes.

Answer:

Rs 75,000

Step-by-step explanation:

Let the total value of property be x

If one-fifth of that is given to son

property with son = 1/5 of total value of property = 1/5 of x = x/5

If one-third of that is given to daughter

property with daughter = 1/3 of total value of property = 1/3 of x = x/3

remaining property after giving the portions to son and daughter

= total value of property - property with son -property with daughter

= x - x/5 - x/3

taking LCM of 5 and 3 (15)

= (15x - 3x - 5x)/15

= 7x/15

Given that remaining property was given to wife

property with wife = 7x/15

it is given that wife got 35000 Rs

thus,

7x/15 = 35,000

7x = 35,000*15 = 525,000

x =  525,000/7 = 75,000

Thus, total worth of property =Rs 75,000 Answer

Answer:

Rs 75,000

Step-by-step explanation:

Let the total value of property be x

If one-fifth of that is given to son

property with son = 1/5 of total value of property = 1/5 of x = x/5

If one-third of that is given to daughter

property with daughter = 1/3 of total value of property = 1/3 of x = x/3

remaining property after giving the portions to son and daughter

= total value of property - property with son -property with daughter

= x - x/5 - x/3

taking LCM of 5 and 3 (15)

= (15x - 3x - 5x)/15

= 7x/15

Given that remaining property was given to wife

property with wife = 7x/15

it is given that wife got 35000 Rs

thus,

7x/15 = 35,000

7x = 35,000*15 = 525,000

x =  525,000/7 = 75,000

Thus, total worth of property =Rs 75,000 Answer

[tex]\text{Solve:}\\\\3x^2+7=28\\\\\text{Subtract 7 from both sides}\\\\3x^2=21\\\\\text{Divide both sides by 3}\\\\x^2=7\\\\\text{Square root both sides}\\\\\sqrt{x^2}=\sqrt7\\\\x=\pm\sqrt7\\\\\boxed{x=\sqrt7\,\,or\,\,x=-\sqrt7}[/tex]

Answer:

volume of rectangular prism = 30 ft³

Step-by-step explanation:

The fishing trap he wants to build to house sea houses are mostly rectangular prism. The traps are mostly glass like. The volume of the fishing trap will be the volume of the rectangular prism.

volume of rectangular prism = LWH

where

L = length

W = width

H = height

volume of rectangular prism = LWH

Length = 5 ft

width = 2 ft

Height = 3 ft

volume of rectangular prism = 5 × 2 × 3

volume of rectangular prism = 10 × 3

volume of rectangular prism = 30 ft³

Answer:

4.3 units

Step-by-step explanation:

In this question we use the Pythagorean Theorem which is shown below:

Data are given in the question

Right angle

a = 3.4

b = 2.6

These two are legs of the right triangle

Based on the above information

As we know that

Pythagorean Theorem is

[tex]a^2 + b^2 = c^2[/tex]

So,

[tex]= (3.4)^2 + (2.6)^2[/tex]

= 11.56 + 6.76

= 18.32

That means

[tex]c^2 = 18.56[/tex]

So, the c = 4.3 units

Answer:

The equation of the plane is

8(x - 5) - 7(y - 4) - 5(z - 5) = 0

8x - 7y - 5z + 13 = 0

Step-by-step explanation:

Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).

We can calculate the equation of the plane through those points as

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.

The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.

For this question,

P = (5, 4, 5)

Q = (-5, -1, -4)

R = (-2, 1, -2)

PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)

= (-10î - 5ĵ - 9ķ)

PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)

= (-7î - 3ĵ - 7ķ)

PQ × PR is then

| î ĵ ķ |

|-10 -5 -9|

|-7 -3 -7|

= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]

= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)

= 8î - 7ĵ - 5ķ

Hence, (a, b, c) = (8, -7, -5)

And using point P as (x₀, y₀, z₀) = (5, 4, 5)

The equation of the plane is

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0

8(x - 5) - 7(y - 4) - 5(z - 5) = 0

8x - 40 - 7y + 28 - 5z + 25 = 0

8x - 7y - 5z = 40 - 28 - 25 = -13

8x - 7y - 5z + 13 = 0

Hope this Helps!!!

Answer:

D) 0.7559

Step-by-step explanation:

Independent events:

If two events, A and B are independent:

[tex]P(A \cap B) = P(A)*P(B)[/tex]

In this question:

Four independent events, A, B, C and D.

So

[tex]P(A \cap B \cap C \cap D) = P(A)*P(B)*P(C)*P(D)[/tex]

Find the probability that the machine works properly.

This is the probability that all components work properly.

[tex]P(A \cap B \cap C \cap D) = P(A)*P(B)*P(C)*P(D) = 0.93*0.93*0.95*0.92 = 0.7559[/tex]

So the correct answer is:

D) 0.7559

Answer:

y = 12 + 6x

y = 12x

Step-by-step explanation:

From the information provided, the following equations are derived:

y = 12 + 6x    ------- Eqn 1

y = 12x          ------- Eqn 2

Since Eqns 1 and 2 have the same subject, we equate them to solve for x. We have:

12x = 12 + 6x

Putting like terms together, we have:

12x - 6x = 12 ⇒ (12 - 6)x = 12

6x = 12 ⇒ x = 2

x = 2

Substitute x into Eqn 1 or 2

Eqn 1

y = 12 + 6x

y = 12 + 6(2) = 12 + 12

y = 24

Eqn 2

y = 12x

y = 12(2)

y = 24

It means that it will take Ms. Ironperson and Mr. Thoro 2 days apiece to produce the same number of posters at the current rate (which is 24 posters). Both Ms. Ironperson and Mr. Thoro will individually take 2 days to produce 24 Avenger posters apiece.

Answer:

C

Step-by-step explanation:

Answer:

The solution is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex].

Step-by-step explanation:

An inequality is a mathematical relationship between two expressions and is represented using one of the following:

To find the solution of the inequality [tex]0>\:20x+2>\:-32[/tex] you must:

[tex]\mathrm{If}\:a>u>b\:\mathrm{then}\:a>u\quad \mathrm{and}\quad \:u>b\\\\0>20x+2\quad \mathrm{and}\quad \:20x+2>-32[/tex]

First, solve [tex]0>20x+2[/tex]

[tex]\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\\frac{20x}{20}<\frac{-2}{20}\\\\\mathrm{Simplify}\\\\x<-\frac{1}{10}[/tex]

Next, solve [tex]20x+2>-32[/tex]

[tex]20x+2-2>-32-2\\\\20x>-34\\\\\frac{20x}{20}>\frac{-34}{20}\\\\x>-\frac{17}{10}[/tex]

Finally, combine the intervals

[tex]x<-\frac{1}{10}\quad \mathrm{and}\quad \:x>-\frac{17}{10}\\\\-\frac{17}{10}<x<-\frac{1}{10}[/tex]

The interval notation is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex] and the graph is:

Answer:  24 square units

Explanation: The diagonals are 4+4 = 8 and 3+3 = 6 units long. Multiply the diagonals to get 8*6 = 48. Then divide this in half to get 48/2 = 24.

An alternative is to find the area of one smallest triangle, and then multiply that by 4 to get the total area of the rhombus. You should find the area of one smallest triangle to be 0.5*base*height = 0.5*4*3 = 6, which quadruples to 24.

Answer:

32

Step-by-step explanation:

if u do pythagoras, sq root of 20^2-12^2=16

16x2=32

Answer:

The 95% confidence interval for the true mean is between $0 and $342,729

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448

The margin of error is:

M = T*s = 2.1448*81000 = 173,729.

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 169,000 - 173,729 = -4,... = $0(cannot be negative)

The upper end of the interval is the sample mean added to M. So it is 169,000 + 173,729 = $342,729

The 95% confidence interval for the true mean is between $0 and $342,729

Answer:

Step-by-step explanation:

155

The number of boxes required by the school to order is 155.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.  If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have been given that the school needs 1,860 pencils for its students. Also, the pencils are sold in boxes of 12.

We need to find the school needs to requires boxes to order.

Total number of pencil = 1,860

Number of boxes = 12

Therefore, boxes needed = 1,860 / 12

= 155

Hence, the number of boxes required by the school to order is 155.

To learn more about the unitary method, please visit the link given below;

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Answer:

x = 5

Step-by-step explanation:

3x - 7 + 4x = 28

Combine like terms

7x -7 = 28

Add 7 to each side

7x - 7 +7  = 28+7

7x = 35

Divide each side by 7

7x/7 = 35/7

x = 5

Answer:

(x, y) → (4/5 x, 4/5 y)

Question:

The answer choices to determine the rule that represent the dilation were not given. Let's consider the following question:

A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?

A) (x, y) → (0.5 − x, 0.5 − y)

B) (x, y) → (x − 7, y − 7)

C) (x, y) → ( 5/4 x, 5/4 y)

D) (x, y) → (4/5 x, 4/5 y)

Step-by-step explanation:

To determine the rule that could represent the dilation, we would multiply each coordinate by a dilation factor (a constant) to create a dilation. Since the dilation would be used to create a smaller polygon, the constant multiplied with the coordinates of x and y would be less than 1.

Let's check the options out.

In option (A), the coordinates is subtracted from the constant (0.5).

In option (B), the constant (7) is subtracted from the coordinates.

In option (C), the coordinates are multiplied by constant (5/4).

But 5/4 = 1.25. This is greater than 1.

In option (D), the coordinates are multiplied by constant (4/5).

4/5 = 0.8

The constant multiplied with the coordinates of x and y is less than 1 in option (D) = (x, y) → (4/5 x, 4/5 y)

4/5 = 0.8

0.8 is less than 1

Answer:

6.8

Step-by-step explanation:

27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.

Answer:

Option (3)

Step-by-step explanation:

Given functions are f(x) = 4 - x² and g(x) = 6x

We gave to find the expression for (g - f)(3).

(g - f)(x) = g(x) - f(x)

            = 6x - (4 - x²)

            = 6x - 4 + x²

By substituting x = 3 in this expression,

(g - f)(x) = 6(3) - 4 + (3)²

Therefore, option (3) will be the answer.

Answer:

Step-by-step explanation:

At 300 miles per week, Chris drives 300×52 = 15,600 miles per year. His gas cost can be figured as ...

  (5 years)×(miles per year)÷(miles/gallon)×($ per gallon) = $273,000/(miles per gallon)

__

a) old car cost = repair cost + gas cost + insurance cost

  = 5($1200) + $273,000/22 + 5($500) ≈ $20,909 . . . over 5 years

__

b) new car cost = purchase cost + gas cost + insurance cost

  = $20,000 + $273,000/50 +5($900) = $29,960 . . . over 5 years

Answer:

6

Step-by-step explanation:

When the cube is folded, 6 is the opposite of 1.

2 is the opposite of 4 and 5 is the opposite of 3.

When the given net is folded into a cube, the number that we will find opposite 1 is 6.

When the net is folded, two will be folded left and up with 3 being the base. 4 will be folded right with 5 being the top of the cube.

We will then observe the following pairs opposite each other:

This means that the number that we will see opposite 1 will be the number 6.

Find out more on folding nets at https://brainly.com/question/16670460.

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Answer:

the elevation of base camp is 35 ft

Step-by-step explanation:

Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation

Answer:

35 feet

Step-by-step explanation:

65 feet- 30 feet= 35 feet is the elevation of the base

9514 1404 393

Answer:

  32°

Step-by-step explanation:

The law of cosines can be used for this:

  h^2 = f^2 +g^2 -2fg·cos(H)

  cos(H) = (f^2 +g^2 -h^2)/(2fg)

  cos(H) = (650,500/763,600)

  H = arccos(6505/7636) ≈ 31.5826°

Angle H is about 32°.

Answer:

(See explanation below for further details)

Step-by-step explanation:

The domain of the function is:

[tex]x \in \mathbb{R} - \{ \pm \pi \cdot i \}[/tex] for [tex]i \in \mathbb{N}_{O}[/tex]

The range of the function is:

[tex]f(x) \in \{-\infty, +\infty \}[/tex]

There are no absolute extrema and such function is not bounded.

Function is symmetric, whose period is π.

Lastly, the set of asymptotes is:

[tex]x = \pm \pi \cdot i[/tex], for [tex]i \in \mathbb{N}_{O}[/tex]

Answer:

Step-by-step explanation:

edge

Answer:

b

Step-by-step explanation:

Answer:

he

Step-by-step explanation:

hi

Answer:

y = 1/4x + (any number)

Step-by-step explanation:

m = -8/2 = -4, the equation shown is y = -4x + 8

perpendicular is  y = 1/4x + (any number), you didn't say where the line was perpendicular.

Answer:

514 square meters

Step-by-step explanation:

Consider the length of p;

[tex]11 * p * 3 = 528,\\33 * p = 528,\\p = 528 / 33 = 16 meters[/tex]

11, 3, and p act as the length, width, and height of this rectangular prism. We can apply the volume formula length * width * height, and thus made 11 * p * 3 equivalent to the volume 528. Now let us determine the surface area;

[tex]Area of Side 1 = 16 * 11 = 176 square meters,\\Area of Side 2 = 3 * 16 = 48 square meters,\\Area of Side 3 = 11 * 3 = 33 square meters,\\\\Surface Area = 2 * ( 176 ) + 2 * ( 48 ) + 2 * ( 33 ) = 352 + 96 + 66 = 514 square meters[/tex]

Hope that helps!

Answer:

514 square meters

Step-by-step explanation:

Since the volume of a rectangular prism is the product of the width, length, and height, 11*3*p=528. Therefore, p=528/(11*3)=16. Now, you can find the surface area. The surface of a rectangular prism is made up of 3 pairs of rectangles. One pair has dimensions of 11 by 3, one pair has dimensions of 16 by 3, and the last pair has dimensions of 16 by 11. The surface area of this figure is therefore:

[tex]2(11\cdot 3)+2(16\cdot 3) + 2(16\cdot 11)=66+96+352=514 m^2[/tex]

Hope this helps!

Answer:

Brainelist~~~!!!

Step-by-step explanation:

4c=3

c=3/4

c=0.75

The solution of the linear equation 4·c = 3, obtained by solving for the variable c is; c = 3/4

A linear equation is an equation that can be expressed in the form; y = m·x + c

The equation 4·c = 3 is a linear equation

In order to solve the equation 4·c = 3 for the variable c, the variable c needs to be isolated to one side of the equation, by dividing both sides of the equation by 4 as follows;

4·c = 3

(4·c)/4 = 3/4

c = 3/4

Therefore, the solution of the equation, 4·c = 3 is; c = 3/4

Learn more on linear equations here: https://brainly.com/question/30338252

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Answer:

Dear User,

Answer to your query is provided below

(i) Total Loss = Rs.15

(ii) Loss percent = 5%

Step-by-step explanation:

Eggs purchased = 5x12 = 60

Total Cost = 60x5 = Rs 300

Eggs Broken = 10

Eggs Broken cost = 10x5= Rs. 50

Eggs sold = 60-10 = 50

Egg Sale cost = 50x5.70 = Rs 285

(i) Total Loss = C.p. - S.p. = 300 - 285 = 15

(ii) Loss Percent = (Loss/CP)x100 = (15/300)x100 = 5%