A manufacture has been selling 1750 television sets a week at $450 each. A market survey indicates that for each $26 rebate offered to a buyer, the number of sets sold will increase by 260 per week. a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price. p(x) 1 = b) How large rebate should the company offer to a buyer, in order to maximize its revenue? dollars c) If the weekly cost function is 131250 + 150x, how should it set the size of the rebate to maximize its profit? dollars

We need to find the simplified expression for

= cos(sin⁻¹(a/9)).

To solve this, let us use the trigonometric identity:

cos²θ + sin²θ = 1

where θ = sin⁻¹(a/9)

We have

sinθ = a/9

Hence

,cosθ = ± √(1 - sin²θ)

= ± √(1 - a²/81)

We take the positive sign because.

sinθ

is positive.

(a/9 is positive).

Now,

cos(sin⁻¹(a/9)) = cosθ= √ (1 - a²/81)

Therefore, the simplified expression for

= cos(sin⁻¹(a/9))

is [tax]

=[text]√ (1 - a²/81). [/text] [/text]

The answer should be more than 100 words to ensure that you fully understand the solution.

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Answer:

$8

Step-by-step explanation:

25% is .25, also known as 1/4. So if you think of it that way, $2 is 1/4 of the entire payment that was added to it. 2*4 is 8, so the price of the tacos was $8 before any tip was added. Andrea paid $10 in total if you include the tip.

Answer:16d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Correct option is c)

\( \huge \bf{explanation}\)

\( {i}^{54} \)

=>( i^2)^24

=> (-1)^27

=> -1

Answer:

x+y ≤20

3.50 x +8 y ≤150

Step-by-step explanation:

Hi, the rest of the question is:

How do you write a system of linear inequalities to model the situation?

So, for the first inequality:

The sum of the number of soil bags (x) and plants(y) bought must be less or equal to 20.

x+y ≤20

For the second inequality:

The product of the number of soil bags (x) and the price of each bag (3.50) ; plus the number of plants bought(y) and the price of each plant (8) must be less or equal to 150.

3.50 x +8 y ≤150

In conclusion, the system is:

x+y ≤20

3.50 x +8 y ≤150

The expression we need to solve is:

To solve this problem, we need to not that we can simplify the fraction 2/10 by dividing both number by 2:

Answer:

No solution

Step-by-step explanation:

We can solve for x using algebraic manipulation, exponent rules, and logarithmic functions.

\(4^{5x}-4 = 64^{2x}+12\)

↓ rewrite 64 as 4³

\(4^{5x}-4 = 4^{3(2x)}+12\)

↓ simplify

\(4^{5x}-4 = 4^{6x}+12\)

↓ subtract 12 from both sides

\(4^{5x}-16 = 4^{6x}\)

↓ substitute a variable (a) for \(4^x\).

\(a^{5}-16 = a^{6}\)

↓ move all the a's to one side

\(0 = a^{6} - a^{5} + 16\)

Now we can see that there is no solution for a, and by extension, for x.

Answer: x =-40

Step-by-step explanation: simplify 64 to have the same bottom number as the other side : 4

this way you can set the exponents equal to each other

4x4x4 =64

so 64 = 4^3

4^5x-4 = 4^3(2x+12)

set exponents = to each other

5x-4=3(2x+12)

5x-4=6x+36

-5x both sides

-4=x+36

-36 both sides

-40=x

x=-40

check by plugging in x

hope that helps

The mean of the distribution is 21 suits, the variance is 0.8 suits squared, and the standard deviation is approximately 0.894 suits.

To find the mean of the distribution, we multiply each value of X (number of suits sold) by its corresponding probability and sum up the products.

Mean (µ):

(19 * 0.2) + (20 * 0.2) + (21 * 0.3) + (22 * 0.2) + (23 * 0.1) = 21

To find the variance, we calculate the average of the squared differences between each value of X and the mean, weighted by their corresponding probabilities.

Variance (σ²):

[(19 - 21)² * 0.2] + [(20 - 21)² * 0.2] + [(21 - 21)² * 0.3] + [(22 - 21)² * 0.2] + [(23 - 21)² * 0.1] = 0.8

The standard deviation is the square root of the variance.

Standard deviation (σ):

√(0.8) ≈ 0.894

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Complete question:

The number of suits sold per day at a retail store is shown inthe table, with the corresponding probabilities. Find themean, variance, and standard deviation of the distribution.

Numer of suits

soldX 19 20 21 22 23

Probability 0.2 0.2 0.3 0.2 0.1

If the manager of the retail store wants to be sure that hehas enough suits for the next 5 days, how many should the managerpurchase?

The conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).

To show that the argument is invalid using the model universe method, we need to find a counterexample where the premises are true, but the conclusion is false.

Let's consider the following interpretation:

Domain of discourse: {1, 2}

A(x): x is even

B(x): x is odd

Under this interpretation, the premises "(x)(A(x) ∧ B(x))" and "(∃x)A(x)" are true because all elements in the domain satisfy A(x) ∧ B(x), and there exists at least one element (e.g., 2) that satisfies A(x).

However, the conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).

In this counterexample, the premises are true, but the conclusion is false, demonstrating that the argument is invalid using the model universe method.

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Answer:

Solution:
4 (x/8-2)
= 4 times 1/16 (16 x x/8 - 2x 16)
= 1/4 (2x-32)
Hence 4, (x/8-2) = 1/4 (2x-32) and it has infinitely many solutions

Step-by-step explanation:

The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours."  

What does the frequency distribution in the table reveal about the homework habits of the two samples of high school students?

The frequency distribution in the table provides insights into the distribution of homework habits among the two samples of high school students. By examining the frequency counts in each time category, we can determine the proportion of students spending different amounts of time on homework each night. This information helps identify patterns and differences in homework habits between the two samples, allowing for a comparison of their study behaviors.

Here is an example of a 4-column table with 2 rows representing the results of a random survey asking two samples of 100 high school students about the amount of time they spend on homework each night:

Sample 1:

  Sample 1                                                     Number of Students

    Time                                                                   Frequency

   <1 hour                                                                     20

  1-2 hours                                                                    40

 2-3 hours                                                                     30

    >3 hours                                                                   10

Sample 2:

 Sample 2                                                        Number of Students

Time                                                                      Frequency

<1 hour                                                                        30

1-2 hours                                                                    35

2-3 hours                                                                   20

>3 hours                                                                      15

In this table, each sample represents a different group of 100 high school students, and the frequency of students spending a particular amount of time on homework each night is recorded. The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours." The table provides an overview of the distribution of homework time among the two samples of high school students.

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Answer: 7200

Step-by-step explanation: the formulae is w times l times h. So you just multiply them all together. 24x15x20= 7200

Answer:

SSS

Step-by-step explanation:

if two of the sets of angles show they are congruent then the third set of angles must be congruent too. There are no sides showing they are congruent either.

Step-by-step explanation:

2x = x + 11

x = 11

The Cause and Effect diagram, also known as the Fishbone diagram or Ishikawa diagram, can be used to identify the causes of a problem and understand the relationship between these causes and their effects. It is a tool commonly employed to improve productivity, reduce costs, define Six Sigma, and enhance the quality and performance of products or processes.

The Cause and Effect diagram is a visual tool that helps analyze the potential causes contributing to a specific problem or effect. It allows for the identification and categorization of various factors that could be influencing the desired outcome. By using this diagram, organizations can systematically investigate the root causes of issues and develop strategies to address them.

The diagram is typically structured with the effect or problem of interest at the right side, represented by a horizontal line. Then, several "bones" or lines stem from the main line, resembling a fish skeleton. These bones represent different categories of potential causes, such as people, methods, materials, machines, measurements, or the environment, depending on the nature of the problem being analyzed.

The Cause and Effect diagram helps teams brainstorm and map out potential causes within each category, allowing for a comprehensive understanding of the factors influencing the problem. This visual representation aids in identifying patterns, relationships, and interdependencies among causes, enabling organizations to develop targeted solutions to address the identified issues.

The tool is versatile and can be applied to various contexts, including improving productivity, reducing costs, defining Six Sigma goals and metrics, and enhancing the fit and finish of a product or process.

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A triangle with an area of 108 square feet has a base length and height equal to 24 feet and 9 feet, respectively.

Given that the cross-section of the lean-to shelter is in the shape of a triangle, its area is the area of a triangle.

A = 1/2bh

where b is the length of the base

h is the height

If the base of the triangle is 6​ feet more than twice its height, then we have b = 6 + 2h.

A = 1/2bh

A = 1/2(6 + 2h)(h)

A = h^2 + 3h

If the area of the triangle is 108 square feet, then

A = h^2 + 3h

108 = h^2 + 3h

h^2 + 3h - 108 = 0

Getting the roots of the polynomial.

h^2 + 3h - 108 = 0

(h - 9)(h + 12) = 0

h = 9     ;     h = -12

Since h must be a positive number, h = 9 feet.

Substitute the value of h in the equation for b.

b = 6 + 2h

b = 6 + 2(9)

b = 6 + 18

b = 24 feet

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Answer:

42 students

Step-by-step explanation:

5 out of 7 students are car riders. This means 2 out of 7 students are bus riders. 12 students are bus riders.

12 = 2x/7, where x is the total number of students.

So, 84 = 2x

This means that x = 42. 2/7 of 42 is 12 so this is correct.

The drive-thru that  is able to estimate their wait time more consistently and why is: A. Burger Quick, because it has a smaller IQR.

The IQR is a measure of the spread of the middle 50% of the data, and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). A smaller IQR indicates that the data is less spread out around the median, and therefore more consistent.

In this case, the IQR for Super Fast Food is 15.5 - 12 = 3.5, while the IQR for Burger Quick is 24 - 15.5 = 8.5. Therefore, Burger Quick has a larger range (24 - 2 = 22) than Super Fast Food (27 - 3 = 24), but a smaller IQR, indicating that their wait time estimates are more consistent.

Therefore Quick is able to estimate their wait time more consistently because it has a smaller interquartile range (IQR).

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The general solution of the given recurrence equation is Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n.

The given recurrence equation is

Qn-1 + 5Qn-2 + 3Qn-3 = 3

Let's find the characteristic equation of the given recurrence equation:

By assuming Qn = rn,

the characteristic equation can be derived as:

r3 - r2 - 5r - 3 = 0

So, the characteristic polynomial is

(r + 1)(r - 3)2

Let α = -1 and β = 3 (repeated roots)

Now, the solution of the given recurrence equation is:

Qn = Arn + Bnαn + Cnβn

As α = -1 and β = 3 are the roots of the characteristic equation, substitute these values in the above equation.

We have

A(-1)n + Bn(-1)n + Cn(3)n ... (1)

As we are going to find the general solution of Qn, the constants A, B, and C need to be determined.

Let's solve for A, B, and C by considering the first few terms of the given recurrence equation.

Suppose n = 3 in the recurrence equation Qn-1 + 5Qn-2 + 3Qn-3 = 3, we have

Q2 + 5Q1 + 3Q0 = 3 ... (2)

Now, substitute n = 2 in the general solution (1), we have

Q2 = A(-1)2 + B2(-1)2 + C23 ... (3)

Now, substitute n = 1 in the general solution (1), we have

Q1 = A(-1)1 + B1(-1)1 + C31 ... (4)

Now, substitute n = 0 in the general solution (1), we have

Q0 = A(-1)0 + B0(-1)0 + C30 ... (5)

Now, let's solve for A, B, and C using equations (2), (3), (4), and (5).

Q2 + 5Q1 + 3Q0 = 3:

2A + 5B + 3C = 3A(-1)2 + B2(-1)2 + C23:

A - B + 9C = 3A(-1)1 + B1(-1)1 + C31:

-A - B + 3C = 1A(-1)0 + B0(-1)0 + C30:

A + B + C = 1

On solving the above equations,

we get A = -1/4, B = 1/4, and C = 1/2

So, the general solution of the given recurrence equation is  

Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n

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(a) The probability that a wave will crash onto the beach exactly 0.6 seconds after the person arrives is: P(X = 0.6) = 0. b) P(1.5 < X < 2.3) = 0.511 c)  P(X > 1) = 0.7778.

A probability density function (PDF) expresses the likelihood at which a continuous random variable will take on a particular value. The integral of f(x) across a range is used to determine the likelihood that a continuous random variable X will fall within that range when the PDF f(x) is specified for that variable. Namely, the likelihood that X falls inside of the range [a,b].

The probability density function of random variable X in the interval [a, b] is given as:

f(x) = 1/(b-a), for a ≤ x ≤ b

and its cumulative distribution function is given by:

F(x) = (x-a)/(b-a), for a ≤ x ≤ b

(a) The probability that a wave will crash onto the beach exactly 0.6 seconds after the person arrives is:

P(X = 0.6) = 0, since the Uniform distribution is a continuous distribution and the probability of a specific value is always zero.

(b) For 1.5 and 2.3 seconds after the person arrives is:

P(1.5 < X < 2.3) = F(2.3) - F(1.5)

= (2.3 - 0)/(4.5 - 0) - (1.5 - 0)/(4.5 - 0)

= 0.5111

c) It will take longer than 1 second:

P(X > 1) = 1 - F(1)

= 1 - (1 - 0)/(4.5 - 0)

= 0.7778

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The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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Answer:

Please refer to the attached figure.

Step-by-step explanation:

Given the function:

\(f(x) =cosx \ where\ \{0^\circ\leq x\leq 360^\circ\}\)

OR, the given function can also be written as:

\(y = f(x) = cosx\)

We know that graph of cosine is a wave.

and the range of cosine function is [-1, 1]

First of all, let us have a table of values at major values of x.

\(x = 0, f(x) = 1\\x = 90, f(x) = 0\\x = 180, f(x) = -1\\x = 270, f(x) = 0\\x = 360, f(x) = 1\)

So, the table of values for f(x) is:

\(\begin{center}\begin{tabular}{ c c }x & cosx \\0 & 1 \\90 & 0\\180 & -1\\270 & 0\\360 & 1\\\end{tabular}\end{center}\)

Let us mark these points on the xy coordinate axis where x axis represents value of x and y axis represents value of \(f(x) = cosx\) and then join the points using a wave.

Please refer to the attached graph for the answer image.

Answer:

3rd option

Step-by-step explanation:

probability (P) is calculated as

P = \(\frac{desired outcome}{total outcomes}\)

deired outcome is red marble = 4

total outcomes = 4 + 2 + 3 = 9

then

P(red) = \(\frac{4}{9}\)

since the marble is not replaced then total outcomes = 8

desired outcome is yellow marble = 2

P(blue) = \(\frac{2}{8}\) = \(\frac{1}{4}\)

then

P(red and yellow ) = \(\frac{4}{9}\) × \(\frac{1}{4}\) = \(\frac{1}{9}\)

Based on the given simple statements, "The scroll is open" and "The writings are visible," we can determine which compound statements would also be true.

The scroll is not open or the writings are visible.

This compound statement would be true. Since the first simple statement states that the scroll is open, the negation of this statement would be that the scroll is not open. The second simple statement states that the writings are visible, which aligns with this compound statement. Therefore, this compound statement is true.

The scroll is open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, the second part of this compound statement contradicts the given information.

The scroll is open or the writings are visible.

This compound statement would be true. It directly matches the given simple statements, where both the scroll being open and the writings being visible are mentioned. Therefore, this compound statement is true.

The scroll is not open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, neither part of this compound statement aligns with the given information.

The compound statements that would be true are:

The scroll is not open or the writings are visible.

The scroll is open or the writings are visible.

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Thus, the area of the region inside the polar curve r = 2cos(θ) is given by 2 [(b + (1/2)sin(2b)) - (a + (1/2)sin(2a))].

The area of the region inside the polar curve r = 2cos(θ) can be found using the formula for the area enclosed by a polar curve:

A = (1/2) ∫[a, b] (r(θ))^2 dθ

In this case, we have r(θ) = 2cos(θ). Therefore, substituting r(θ) into the formula, we get:

A = (1/2) ∫[a, b] (2cos(θ))^2 dθ

Simplifying further:

A = (1/2) ∫[a, b] 4cos^2(θ) dθ

Using the trigonometric identity cos^2(θ) = (1 + cos(2θ))/2, we can rewrite the integral:

A = (1/2) ∫[a, b] 4(1 + cos(2θ))/2 dθ

A = 2 ∫[a, b] (1 + cos(2θ)) dθ

Integrating term by term:

A = 2 [θ + (1/2)sin(2θ)] [a, b]

Evaluating the integral limits:

A = 2 [(b + (1/2)sin(2b)) - (a + (1/2)sin(2a))]

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Answer

Check Explanation

Explanation

The volume of cone is given as

Volume of a cone = ⅓ (πr²h)

where

r = radius of the cone

h = height of the cone

also note that radius of a cone = ½ (Diameter of the cone)

1) Dylan's cone

Radius = 4.5 inches

Height = 6 inches

Volume = ⅓ (πr²h)

= ⅓ (π × 4.5² × 6)

= ⅓ (381.7035)

= 127.23 in³

2) Shane's cone

Radius = ½ (Diameter of the cone)

Diameter of the cone = 4.5 inches

Radius = ½ (4.5) = 2.25 inches

Height = 6 inches

Volume = ⅓ (πr²h)

= ⅓ (π × 2.25² × 6)

= ⅓ (95.426)

= 31.81 in³

3) Jake's cone

Radius = ½ (Diameter of the cone)

Diameter of the cone = 6 inches

Radius = ½ (6) = 3 inches

Height = 4.5 inches

Volume = ⅓ (πr²h)

= ⅓ (π × 3² × 4.5)

= ⅓ (127.2345)

= 42.41 in³

4) Grace's cone

Radius = 6 inches

Height = 4.5 inches

Volume = ⅓ (πr²h)

= ⅓ (π × 6² × 4.5)

= ⅓ (508.938)

= 169.65 in³

Hope this Helps!!!

Answer:

16 + 9 = 25

Step-by-step explanation:

For each term in the sequence, we can see that the second number being added increases by 2 each time (3, 5, 7)

And that the first number of each term increases by the value of the second term

(1 increases by 3; 4 increases by 5)

we can follow out these two observations to find T4

the first term (9) will increase by the value of the second term (7)

{the sum of the previous term is the first number}

so the first number of T4 will be 16.

Because we left off on +7, we are now on +9

so, T4 is

16 + 9 {and then do the math accordingly}

16 + 9 = 25

So, T4 is

16 + 9 = 25

hope this helps!! have a lovely day!! :)

Answer:

210

Step-by-step explanation:

Lets use BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, Subtraction)

45 ÷ 2 = 22.5

22.5 × 8 = 180

180 - 12 = 168

168 + 42 = 210

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Have a great summer :)