The total revenue R (in dollars) earned from manufacturing and selling hand-held video games is given by R(p) = -25p² + 1200p, where p is the price per unit (in dollars). (a) Find the unit price that will yield the maximum revenue. (b) What is the maximum revenue? (c) Use the results from part (a) and part (b) to sketch the graph of R(p) indicating the coordinates of the vertex and all intercepts.

the (x,y) will be (-.381, 0) and (18.381, 0).

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

y=x^2-18x+7

take x^2-18x+7 = 0

\(x=(18-sqrt(352))/2=9-2sqrt(22)=-0.381\)

\(x=(18+sqrt(352))/2=9+2sqrt(22)=18.381\)

(x,y) = (-.381, 0) and (18.381, 0)

Hence the (x,y) will be (-.381, 0) and (18.381, 0).

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\(\bf Blue \ Color \ Line : y = x^2\)

When added all together:

\(\bf Black \ color \ Line: y=-\left(x+2\right)^{2}-10\)    =  Final answer.

Where the above are given,

(a) MLE of β: (nα + y₁ + y₂ + ... + yn)/n

(b) MLE of E(Y): (nα + y₁ + y₂ + ... + yn)/n

Maximum Likelihood Estimation (MLE) is   a statistical method used to estimate the parameters of a probability distribution by maximizing the likelihood function based on observed data.

(a) The MLE of β can be found by   maximizing the likelihood function. The likelihood function for  a gamma distribution is given by  -

L(β;  y₁, y₂, ..., yn) = (1/β^nαΓ(α))ⁿ * exp(-( y₁ + y₂ + ... + yn)/β)

Taking the logarithm of the likelihood function (log-likelihood) to simplify the calculations  -

log L(β;  y₁, y₂, ..., yn) =   n*log(1/β) + nα*log(β) - n*logΓ(α) - ( y₁ + y₂ + ... + yn)/β

To find the MLE of β, we differentiate the log-likelihood with respect to β, set it equal to zero, and solve for β  -

d/dβ(log L(β;  y₁, y₂, ..., yn)) = -n/β + nα/β² + ( y₁ + y₂ + ... + yn)/β² = 0

Simplifying the equation -

-n/β + nα/β^2 + ( y₁ + y₂ + ... + yn)/β² = 0

Multiplying through by β²

-nβ + nα + ( y₁ + y₂ + ... + yn) = 0

Rearranging  whave

nβ = nα + ( y₁ + y₂ + ... + yn)

Finally, solving for β -

β = (nα +  y₁ + y₂ + ... + yn)/n

Therefore, the MLE of β is (nα +  y₁ + y₂ + ... + yn)/n.

(b) The MLE of E(Y), the expected value of Y, is simply the MLE of β.

So, the MLE of E(Y) is (nα +  y₁ + y₂ + ... + yₙ)/n.

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The actual factor of safety is 0.0874. a) One roof support load data: P = (600 × 100) / 4 = 150000 N

b) The value of z that corresponds to a reliability of 0.995 against compressive failure is 2.81.

c) The design factor associated with a reliability of 0.995 against compressive failure is 3.15.

d) The required diameter dowel for a reliability of 0.995 is calculated by:

\[d = \sqrt{\frac{4P}{\pi Su N_{d}}}\]

Where, \[Su\]-N[10.18, 0.4) ksi\[N_{d}\]= 0.2\[d

= \sqrt{\frac{4(150000)}{\pi (10.18) (0.2)}}

= 1.63 \,inches\]

The diameter of the dowel needed for a reliability of 0.995 is 1.63 inches.

e) A standard dowel with a diameter of at least 1.63 inches is required for a minimum reliability of 0.995 against failure. From the standard diameters given in the question, a 6-inch diameter dowel is the most suitable.

f) The actual factor of safety is the load that will cause the dowel to fail divided by the actual load. The load that will cause the dowel to fail is

\[P_{f} = \pi d^{2} Su N_{d}/4\].

Using the value of d = 1.63 inches,

\[P_{f} = \frac{\pi (1.63)^{2} (10.18) (0.2)}{4}

= 13110.35 \, N\]

The actual factor of safety is: \[\frac{P_{f}}{P} = \frac{13110.35}{150000} = 0.0874\]

Therefore, the actual factor of safety is 0.0874.

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The height h will be equal to 13 cm for the parallelogram.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called the area of the parallelogram.

Given that a right-angled triangle and a parallelogram are shown b

13 cm and 6 cm. The area of the parallelogram is 4 times the area of the right angle.

The height h will be calculated as,

A= 1/2 x6 x 13 = 3 x 13 =39 square

Area of the parallelogram is,

39=156cm square

156 divided by 12

h=13 cm

Therefore, the height h will be equal to 13 cm for the parallelogram.

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When solving the equation 5y - 3 = 7 - 2y, the operation that would not be performed is division.

The equation 5y - 3 = 7 - 2y is a basic linear equation.

In order to solve this equation, we need to rearrange it into a form that expresses y in terms of other numbers. To do this, we use operations like addition, subtraction, multiplication, and division.

However, there is one operation that we would not perform when solving this equation: division.

5y - 3 = 7 - 2y (original equation)

To begin, we want to isolate y on one side of the equation. To do this, we will add 2y to both sides of the equation:

5y - 3 + 2y = 7 - 2y + 2y (add 2y to both sides)

Simplifying:

7y - 3 = 7 (combine like terms on the right side)

Next, we want to isolate y further by adding 3 to both sides:

7y - 3 + 3 = 7 + 3 (add 3 to both sides)

Simplifying:

7y = 10

Finally, we need to solve for y by dividing both sides by 7:

y = 10/7

Therefore, the operation that we would not perform when solving the equation 5y - 3 = 7 - 2y is division.

We would use addition, subtraction, and multiplication to rearrange the equation into a form that expresses y in terms of other numbers.

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Our answer will be Silty Loam.

Silt loam is a type of soil that needs at least 70% silt and clay mixed, and at least 20% sand. This kind of soil, which belongs to the loam soil kinds, is actually ideal for virtually every plant's growth. The silt loam's exceptional productivity and suitability for virtually all plants are due to the precise proportions of silt, clay, and sand particles that make up its composition. Although it is not a particularly common soil in nature, it is nonetheless present on enough land all over the world.

So, therefore based on the given data it is clear that the soil sample contains the necessary percentages to be categorized as Silty Loam.

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Thus, the fully simplified answer in the form a + b i is:128(cos 315° + i sin 315°) = 90.5 - 90.5 i

In order to find the indicated power using De Moivre's Theorem, first we should understand

what is De Moivre's Theorem?

De Moivre's Theorem states that for any complex number

z = r (cos θ + i sin θ),

we have:

(cos θ + i sin θ)n = cos nθ + i sin nθ

For finding the indicated power using De Moivre's Theorem, we have:

Given, (1 + i)7

We can write it as

(1 + i) = √2 (cos 45° + i sin 45°)

Thus, we get

(1 + i)7= (√2 (cos 45° + i sin 45°))^7

(1 + i)7 = 128(cos 315° + i sin 315°)

(1 + i)7 = 128(cos (360° - 45°) + i sin (360° - 45°))

(1 + i)7 = 128(cos 315° + i sin 315°)

The indicated power using De Moivre's Theorem is 128(cos 315° + i sin 315°).

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Their ages will become in the ratio 8 : 7 after 350 years.

Let's break down the information given step by step:

The ratio of the ages of the two friends initially is 6 : S.

This means that one friend's age is 6 years and the other friend's age is S years.

The sum of their ages is 55, which can be represented as 6 + S = 55.

Solving the equation, we find S = 49.

This means one friend is 6 years old and the other friend is 49 years old.

We want to determine after how many years their ages will become 8 : 7. Let's denote the number of years as Y.

After Y years, the first friend's age will be 6 + Y and the second friend's age will be 49 + Y.

According to the given condition, (6 + Y) : (49 + Y) = 8 : 7.

Cross-multiplying, we have 7(6 + Y) = 8(49 + Y).

Expanding the equation, we get 42 + 7Y = 392 + 8Y.

Simplifying, we find Y = 350.

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False. Scaling, in the context of graphics, refers to the process of resizing an image or graphic while maintaining its aspect ratio. It involves changing both the vertical and horizontal size of the graphic by the same percentage.

When scaling a graphic, the goal is to resize it proportionally, preserving the original aspect ratio. This means that both the vertical and horizontal dimensions are changed by the same factor or percentage. For example, if an image is scaled by 50%, both its height and width will be reduced by 50% of their original values. This ensures that the graphic maintains its original proportions and does not appear distorted.

Scaling graphics is commonly used in various applications, such as graphic design, image editing, and web development, to resize images without distorting their appearance. It allows for consistent resizing across different devices or platforms while maintaining the integrity of the original graphic.

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The substitution effect, denoted by ε*, measures the change in quantity demanded of q1 due to the relative price change, while the income effect, denoted by θξ, measures the change in quantity demanded of q1 due to the change in purchasing power. The total effect, denoted by ε, combines both the substitution and income effects.

To calculate the substitution effect, we need to evaluate the price elasticity of demand for q1, which measures the responsiveness of quantity demanded to a change in price. The income effect depends on the income elasticity of demand, which measures the responsiveness of quantity demanded to a change in income. These elasticities can be calculated using the given utility function, but specific price and income data are required.

Without the actual price and income data, it is not possible to provide the exact numerical values for the substitution, income, and total effects. The effects can only be determined with the necessary information and by performing the appropriate calculations using the utility function. The values of ε*, θξ, and ε will depend on the specific price and income changes that are considered.

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A person's cardiovascular fitness, age, weight, gender, and the severity of the activity performed may all play a role in how fast a person attains steady-state and fully recovers. When an individual is fit, they tend to have a lower resting heart rate than an unfit person. Furthermore, a fit person's heart rate is less likely to climb to high levels during activity, and their muscles are more efficient, requiring less oxygen to function. Finally, fit people tend to have better cardiovascular health and are more capable of removing waste products from their muscles, allowing for a quicker recovery time.

RQ stands for respiratory quotient and represents the ratio of carbon dioxide produced to oxygen consumed. During exercise, RQ rises because the body is using more carbohydrates than fats to generate energy, which increases carbon dioxide production. During the recovery period, RQ decreases as the body switches back to using fat as its primary energy source and oxygen consumption increases.The graph/plot of RQ as a function of time during rest, physical activity, and recovery phases should show a steady increase during physical activity and a decline during recovery. This variation makes sense because during exercise, the body's demand for energy increases, and RQ increases as a result. Conversely, during recovery, the body switches back to using fat as its primary energy source, resulting in a decrease in RQ.

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Answer:

no

Step-by-step explanation:

Add the digits of the number 40,156,235:

4 + 1 + 5 + 6 + 2 + 3 + 5 = 26

Since 26 is not divisible by 9, then 40,156,235 is also not divisible by 9.

The annual effective rate of interest is approximately 3.218%.

To find the annual effective rate of interest, we can use the formula for the present value of a perpetuity:

PV = C / i

where PV is the present value, C is the cash flow, and i is the interest rate.

In this case, the present value (PV) is given as 0.5 and the cash flow (C) is 1, as the perpetuity pays 1 at the end of every 6 years. Plugging these values into the formula, we have:

0.5 = 1 / i

Rearranging the equation to solve for i, we get:

i = 1 / 0.5

i = 2

So the annual effective rate of interest (i) is 2.

However, since the interest is paid at the end of every 6 years, we need to convert the rate to an annual rate. We can do this by finding the equivalent annual interest rate, considering that 6 years is the period over which the cash flow is received.

To find the equivalent annual interest rate, we use the formula:

i_annual = \((1 + i)^(^1^ /^ n^)\) - 1

where i is the interest rate and n is the number of periods in one year. In this case, n is 6.

Plugging in the values, we have:

i_annual =\((1 + 2)^(^1 ^/^ 6^) - 1\)

i_annual = \((3)^(^1 ^/^ 6^) - 1\)

i_annual ≈ 0.03218

So the annual effective rate of interest (i_annual) is approximately 3.218%.

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Answer:

16

Step-by-step explanation:

-2 × 2 = -4 but any number squared is positive

so -4^2 is still (+)16

1. R = {(a, b, c): a, b, c are positive integers and a < b < c} ; 2. S = {(x, y): x is a multiple of y}

For the first relation R, we can see that it is an n-ary relation with n = 3. The condition a < b < c ensures that the triplets (a, b, c) are in increasing order. For example, (1, 2, 3) is a valid element of R, but (3, 2, 1) is not.

For the second relation S, we can see that it is a binary relation with n = 2. The condition x is a multiple of y means that for every pair (x, y) in S, x must be divisible by y. For example, (12, 2) is a valid element of S, but (5, 3) is not.

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Step-by-step explanation:

x varies directly as y

x=ky

12=4k

k=12/4

k=3

Answer:

The answer is c.

Consider using 3D printing technology to create the spherical fountain. This would allow for precise and customizable designs, and could potentially be more cost-effective than traditional manufacturing methods for complex shapes.

Use a mathematical formula to design the fountain. Here are the steps to design a spherical fountain:

Determine the desired size of the fountain. This will be the diameter of the sphere. Let's say your client wants a fountain with a diameter of 6 feet.

Calculate the radius of the sphere by dividing the diameter by 2. In this case, the radius is 3 feet.

Use the formula for the surface area of a sphere to determine the surface area of the fountain. The formula is: SA = 4π\(r^2\), where r is the radius of the sphere and π is a mathematical constant (approximately 3.14). In this case, the surface area is:

SA = 4π\((3)^2\)

SA = 4π(9)

SA = 36π

SA ≈ 113.1 square feet

Use the desired water flow rate to determine the volume of water that will flow through the fountain per minute. Let's say your client wants a flow rate of 50 gallons per minute.

Use the formula for the volume of a sphere to determine the volume of the fountain. The formula is: V = (4/3)π\(r^3\). In this case, the volume is:

Calculate the amount of time it will take for the fountain to cycle through all of its water. This is known as the turnover time, and it is important to maintain water quality. The turnover time is calculated by dividing the volume of water in the fountain by the flow rate. In this case, the turnover time is:

Use these calculations to design the fountain, taking into account any necessary adjustments for the manufacturer's limitations.

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Full Question: Your client wants you to design a spherical fountain for a new garden bed. It is hard to find a manufacturer that can create perfect curved surfaces. You will need to modify the sphere to a series of cylindrical slabs with gradually decreasing radii.

Statement 1: Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey, statement 2: There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window and statement 3: Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

The given categorical propositions and their forms are as follows:

(1) Some cats like turkey - Form: I:

Subject class: Cats,

Predicate class: Turkey

(2) There are burglars coming in the window - Form: E:

Subject class: Burglars,

Predicate class: Not coming in the window

(3) Everyone will be robbed - Form: A:

Subject class: Everyone,

Predicate class: Being robbed

In the first statement:

Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey.

In the second statement:

There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window.

In the third statement:

Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.

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H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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Answer:

First, we write the augmented matrix.

⎡

⎢

⎣

1

−

1

1

2

3

−

1

3

−

2

−

9

|

8

−

2

9

⎤

⎥

⎦

[1−1123−13−2−9 | 8−29]

Next, we perform row operations to obtain row-echelon form.

−

2

R

1

+

R

2

=

R

2

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

3

−

2

−

9

|

8

−

18

9

⎤

⎥

⎦

−

3

R

1

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

0

1

−

12

|

8

−

18

−

15

⎤

⎥

⎦

−2R1+R2=R2→[1−1105−33−2−9|8−189]−3R1+R3=R3→[1−1105−301−12|8−18−15]

The easiest way to obtain a 1 in row 2 of column 1 is to interchange

\displaystyle {R}_{2}

R 2

and

\displaystyle {R}_{3}

R 3

.

Interchange

R

2

and

R

3

→

⎡

⎢

⎣

1

−

1

1

8

0

1

−

12

−

15

0

5

−

3

−

18

⎤

⎥

⎦

InterchangeR2andR3→[1−11801−12−1505−3−18]

Then

−

5

R

2

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

57

|

8

−

15

57

⎤

⎥

⎦

−

1

57

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

1

|

8

−

15

1

⎤

⎥

⎦

−5R2+R3=R3→[1−1101−120057|8−1557]−157R3=R3→[1−1101−12001|8−151]

The last matrix represents the equivalent system.

x

−

y

+

z

=

8

y

−

12

z

=

−

15

z

=

1

x−y+z=8 y−12z=−15 z=1

Using back-substitution, we obtain the solution as

\displaystyle \left(4,-3,1\right)

(4,−3,1)

Answer:

x = -10

Step-by-step explanation:

Step 1: Write equation

180 + 8x = 160 + 6x

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

180 + 8(-10) = 160 + 6(-10)

180 - 80 = 160 - 60

100 = 100

The protagonist, a detective, stumbles upon a series of crimes connected to the labeled tickets.

Box A: The plot that matches Box A is a thrilling mystery. The protagonist, a detective, stumbles upon a series of crimes connected to the labeled tickets.

As the detective investigates, they discover that the tickets with the number "1" are linked to a notorious gang involved in illegal activities. The tickets labeled "2" lead the detective to a secret society that uses the tickets for initiation rituals.

The plot unfolds as the detective races against time to unravel the connections between the tickets and bring the culprits to justice.

Box B: The plot that matches Box B is a heartwarming tale of friendship and adventure. The protagonist, a young child, finds one of the tickets labeled "3" and realizes it grants them access to a magical world. In this world, they meet a group of unique and colorful characters who also possess tickets labeled "5."

Together, they embark on a journey to restore harmony to their realm, battling against an evil force that seeks to exploit the power of the tickets. Through their shared experiences, the group learns valuable lessons about courage, loyalty, and the true meaning of friendship.

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The three consecutive odd numbers of the number 105 are:

107, 109 and 111

Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 10 will be 11 onwards.

To solve this problem we must have clear which is our base number, and this is 105, as we will determine the consecutive numbers we must add +1, +2.... as many times as we want, now as we only want the odd numbers and 105 is odd we will proceed to add multiplies of 2:

+2, +4 and +6, having as a result the following numbers:

The consecutive and odd numbers will be 107, 109, 111.

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Answer:

3x² + 9x + 1

Step-by-step explanation:

5x - 2 + 3x² + 4x + 3

= 9x - 2 + 3x² + 3

= 9x + 1 + 3x²

= 3x² + 9x + 1

In the 3rd quarter of year 5, the approximate total sales in the coastal region is; $7 million

The image of the graph showing the quarterly sales has been attached. From the graph, the red lines indicates the coastal region, the blue lines indicates the northern region, and the green lines indicates the southern region.

From the graph, in the third quarter, we can trace the total sales on the y-axis to be approximately $7 million dollars.

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Based on this evaluation, the correct answer is:

d. "false : 14 is 104"

The value of 's' after the given statement can be determined by evaluating each part of the expression step by step:

1. Evaluate (!true): Since 'true' is negated using the '!' operator, this expression becomes 'false'.

2. Concatenate " : " to "false": The resulting string also becomes "false : ".

3. Calculate (10 + 4): This arithmetic expression is equals to  14.

4. Concatenate "14" to "false : ": The resulting string becomes equal to "false : 14".

5. Finally, concatenate " is 104" to "false : 14": The final value of 's' becomes "false : 14 is 104".

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Explanation:

1) sin(37º)=x/10.3————>trigonometric ratio (sine)

2)7²+10²=c²—————-> pythagorean theorem

3) using sine—————> sin(51º)=9/x

using tangent —————> tan(51º)=9/x and x = 7.3 (rounded)

4)using pythagorean theorem————> 6²+7²=c²

angle b is tanx=6/7 where x = 40.6 degrees, angle a is tanx=7/6 where x = 49.4

Answers:

1)x= 6.2

2)x= 12.2

3)x= 11.6 (rounded)

4)x= 9.2

credit to genan for question 3 and 4

ur welcome :)

correct me if im wrong

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