What is the equation of the line that passes through the point (8,1) and has a slope
Answer:

The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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To convert the polar equation r = 4sin(θ) + 4cos(θ) into a Cartesian equation, we can use the identities:

x = r cos(θ)

y = r sin(θ)

Substituting r = 4sin(θ) + 4cos(θ) into these identities, we get:

x = (4sin(θ) + 4cos(θ))cos(θ) = 4sin(θ)cos(θ) + 4cos²(θ)

y = (4sin(θ) + 4cos(θ))sin(θ) = 4sin²(θ) + 4sin(θ)cos(θ)

Simplifying these expressions using the trigonometric identity sin²(θ) + cos²(θ) = 1, we obtain:

x = 4cos(θ) + 4cos²(θ)

y = 4sin(θ) + 4sin(θ)cos(θ) = 4sin(θ) + 4cos(θ)sin(θ)

Therefore, the Cartesian equation for the curve is:

(x - 4)² + y² = 16

This equation represents a circle with center (4, 0) and radius 4. The original polar equation r = 4sin(θ) + 4cos(θ) can be interpreted as the distance from the origin to a point on the circle, measured along a line that makes an angle of θ with the positive x-axis.

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Answer:

8n+7

Step-by-step explanation:

The value of x in the given similar triangles ADB and BCE is 4.5.

To solve for x in the given similar triangles ADB and BCE, we can set up the proportion of corresponding sides:

In triangle ADB, we have:

AB/BD = x/DE

Substitute the given values:

3/4 = x/6

Now, cross-multiply and solve for x:

3 * 6 = 4x

18 = 4x

x = 18/4

x = 4.5

So, the value of x is 4.5.

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The outstanding principal after the 93rd repayment is approximately $532.81.  The correct answer is 1) $532.81.

To calculate the outstanding principal after the 93rd repayment, we need to determine the loan's initial principal and the monthly interest rate.

- Monthly repayment: $180.00

- Number of repayments: 96

- Interest rate: 12 = 8.0730% per annum

First, let's calculate the monthly interest rate by dividing the annual interest rate by 12:

Monthly interest rate = j12 / 12

Monthly interest rate = 8.0730% / 12

Monthly interest rate = 0.67275% or 0.0067275 (as a decimal)

Next, we can use the loan amortization formula to calculate the initial principal (P) of the loan:

Initial principal (P) = Monthly repayment / ((1 + Monthly interest rate)^(Number of repayments) - 1)

P = $180.00 / ((1 + \(0.0067275)^(96) - 1)\)

P ≈ $14,557.91

Now, we can determine the outstanding principal after the 93rd repayment. We need to calculate the remaining principal after 93 repayments using the following formula:

Outstanding principal = Initial principal * ((1 + Monthly interest rate)^(Number of repayments) - (1 + Monthly interest rate)^(Number of repayments made))

Outstanding principal = $14,557.91 * ((1 + 0.0067275)^(96) - (1 + \(0.0067275)^(93))\)

Outstanding principal ≈ $532.81

Therefore, the outstanding principal after the 93rd repayment is approximately $532.81.

The correct answer is 1) $532.81.

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Answer:

They are disjoint.

Answer: The answer is C.

Step-by-step explanation: The hypotenuse in special case isosceles right triangles is always x√2, x being one of the leg lengths since they are the same.

Answer:

Well, Your answer is 12 units.

Because, It was on edgunity

Good Luck with your homework!!~

Answer:

Hello There. The answer to this is The length of W'X' will be exactly given by, 12 unit. Explanation: The Rectangle WXYZ is dialated by a factor of 12/5 to form the rectangle W'X'Y'Z'. So, if the length of WX is 5 unit, the length of W'X' will be exactly given by, the lenght WX x Dialation factor. = (5 x 12/5) unit. = 12 unit

Hope It Helps! :) ♡

ItsNobody~

The coefficients and constant in the quadratic function f(x) = x² - 5x + 6 are coefficients: 1, -5 and constant: 6.

A quadratic function is an algebraic function with one or more variables where the largest exponent of the variable is two. The equation for a quadratic function is of the form f(x) = ax² + bx + c, where 'a' is a non-zero integer and a, b, and c are real numbers. A quadratic function is a polynomial of degree 2, and its definition is as follows.

The "a", "b", and "c" from "ax2 + bx + c" are used in the quadratic formula; they are known as the "numerical coefficients" of the quadratic equation. Therefore,

f(x) = x²– 5x + 6

a = 1

b = -5

c = 6

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Question:

Identifying the Coefficients and Constanta

Consider the quadratic function f(x) = x2 – 5x + 6.

What are the values of the coefficients and constant in the function?

Answer:

3/11 for two red balls

2/11 for two green balls

Step-by-step explanation:

6 red and 5 green balls

Answer:

3/11

2/11

Step-by-step explanation:

The original recipe had 0.9 cups of bananas.

Using only fresh ingredients, strawberry banana smoothie is a simple, nutritious dish. It is creamy, sweet, nutritious, and dairy- or dairy-free can be used to make it. The ideal summertime smoothie. Putting the strawberries, frozen banana, milk, and yoghurt in a blender and mixing until smooth and creamy is all that is required to make it.

Cups of strawberries = 1.75

No. of cups added of banana = 1/2

                                            = 0.5

No. of cups of banana smoothie have = 14.

The original recipe had = 1.4 - 0.5

                                   = 0.9

Hence, the original recipe had 0.9 cups of bananas.

Correct Question :

to make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. to make the recipe taste more like banana, 1/2 cup more banana was added to the blender. the smoothie now has 1.4 cups of bananas. how many cups of bananas were in the original recipe?

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Answer:

15

Step-by-step explanation:

Answer:

w=-6

Step-by-step explanation:

2(w-9)=5w+6+w

multiply 2 to the (w-9), also add the 5w to the other w

2w-18=6w+6

subtract 2w to 6w

-18=4w+6

subtract 6 to -18

-24=4w

divide 4 to -24

THE ANSWER IS -6

Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators.


Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators. These variables help measure and track progress towards a goal by providing a quantitative or qualitative measure of how far the target is from the desired level of achievement.

Performance metrics can be represented in various forms, such as distance covered, percentage completed, points earned, or even subjective evaluations. For example, in a fitness program, a performance metric could be the number of miles run or the number of push-ups completed.

These metrics enable individuals or organizations to assess their progress and make necessary adjustments to reach their desired outcomes.

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Answer:

C underfined

Step-by-step explanation:

I just took the test

Answer:

x = 6

Step-by-step explanation:

10x = 5 x 12 = 60

x = 6

Answer:

heyy Vrooo....

alr ans is 49

Step-by-step explanation:

see let number be x

so as per ques.. product of x and 9/7 = 9x/7

which is 63

so \(\frac{9x}{7}\) = 63

9x = 63*7

x = \(\frac{63*7}{9}\)

x = 7*7 = 49

Possible to brainliest <3 ?

Answer:

  (b)  (x^2 + 8x + 16) + (y^2 − 6y + 9) = 11 + 16 + 9

Step-by-step explanation:

To complete the square of a binomial, the constant term of the perfect square trinomial is the square of half the coefficient of the linear term. It will always be positive.

__

a) 9 is subtracted, incorrectly

b) 16 and 9 are correctly added . . . this is the correct Step 3

c) half the linear term is added, incorrectly

d) the magnitude of half the linear term is added, incorrectly

Answer: 82 is the answer

Step-by-step explanation: I just did this question and worked it out and it said it was right

100.48 square inches make up half of the cookie cake. The solution has been obtained by using area of circle.

What is area of circle?

The territory that a circle's circumference encloses or includes is referred to as its area. The square is its unit of measurement.

We are given that the diameter of a circular cookie cake is 16 inches.

Area of circle = π \(r^{2}\)

The radius (r) = 8 inches

So, from this we get

⇒ Area of circle = π \(8^{2}\)

⇒ Area of circle = 64 * 3.14

⇒ Area of circle = 200.96 square inches

So, half cookie cake = 100.48 square inches

Hence, 100.48 square inches make up half of the cookie cake.

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Answer:

if the first equation 3x - 3y = -2 is multiplication by 3

therefore, 3x - 3y = -2

multiplied by 3

:9x - 9y = -6

then the equations are added,

9x - 9y = -2 + 10x + 710x + 118x + 7

9x + 10x + 710x + 118x + 9y + 7

947x + 9y = 7

Step-by-step explanation:

15+10z=105

10z=105-15

10z=90

z=9

Answer For two events A and B,P(A)−0.36,P(B)−0.37, and P(A∩B)−0.11 a. Find P(A∣B). b. Find P(B∣A). c. Determine whether or not A and Bare independent. I think

Step-by-step explanation:

The correlation coefficient of .78 indicates a strong positive correlation between math achievement and math attitude.

This means that as math attitude increases, so does math achievement. It also suggests that math attitude can be a good predictor of math achievement. However, it is important to note that correlation does not imply causation, and other factors may also influence math achievement.

The correlation of .78 between math achievement and math attitude indicates a strong positive relationship between the two variables. This means that as one's math attitude improves, their math achievement is likely to improve as well, and vice versa.

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The percentage of tourists who do not know Huancayo or Cuzco is 6%.

In this scenario, we are given information about a group of tourists. Among them, 12% do not know Huancayo, 14% do not know Cuzco, and 80% know both cities. To determine the percentage of tourists who do not know Huancayo or Cuzco, we need to subtract the percentage of those who know both cities from 100%.

Let's calculate it step by step. First, we find the percentage of tourists who know at least one of the cities. Since 80% know both, the remaining percentage of tourists who know only one city is 100% - 80% = 20%.

Next, we find the percentage of tourists who do not know either city by subtracting the percentages of those who know each city individually from the percentage who know at least one city. From the given information, 12% do not know Huancayo and 14% do not know Cuzco. Therefore, the percentage of tourists who do not know either city is 20% - 12% - 14% = 6%.

In conclusion, 6% of the tourists do not know Huancayo or Cuzco.

By using the principle of set theory and subtraction, we can determine the percentage of tourists who are unfamiliar with specific cities based on the information given about overlapping knowledge. This approach allows us to analyze and understand the distribution of knowledge among the group of tourists. It is a valuable technique in various fields, such as market research, demographics, and social studies.

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The percent of increase between the average low and high temperatures in July is 26°F

Given

The average daily high temperature for July in Richmond, Virginia = 90°F

The average daily low temperature for the same month = 69°F

We have to find the percent of increase between the average low and high temperatures in July.

Here,

The temperature difference between morning and afternoon = 90 - 69 = 21°F

Compare the temperatures, we get;-

90+69/2

= 159/2

= 79.5°F

Then,

The percentage increase in daily low temperature;-

= 21/79.5 × 100/1

= 2100/79.5

= 26.4

= 26°F

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(a) The Null-Hypotheses is H₀ : μ = 12, Alternate-Hypotheses is Hₐ : μ ≠ 12.

(b) The "test-statistic" is 10.36,

(c) The "p-value" is 0.0001,

(d) We make a decision to reject the "Null-Hypothesis",

(e) We conclude that the cans of "regular-Coke" have volumes with mean different from 12 ounces.

Part (a) : The "Null-Hypothesis" is that the mean volume of cans of regular Coke is 12 ounces, as stated on the label. The alternative-hypothesis is that the mean volume is different from 12 ounces.

So, H₀ : μ = 12

Hₐ : μ ≠ 12.

Part (b) : The "test-statistic" for a one-sample t-test is calculated as:

t = (x' - μ)/(s / √n),

where "s" = sample standard-deviation, μ = population mean, x' = sample mean, and n = sample size,

In this case, x' = 12.19, μ = 12, s = 0.11, and n = 36.

So, t = (12.19 - 12)/(0.11/√36) = 10.36,

Part (c) : We know that for "significance-level" of 0.01. The p-value is 0.0001.

Part (d) : Since the p-value is less than the significance-level of 0.01, we reject the null hypothesis.

Part (e) : Based on the results of the hypothesis test, we can conclude that there is sufficient evidence to suggest that cans of regular-Coke have volumes with a mean different from 12 ounces.

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The portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

To calculate the portfolio weights for stock A and stock B, we need to determine the total value of the portfolio and the proportion of each stock's value within that total.

The total value of the portfolio can be calculated as follows:

Total value = (Number of shares of stock A × Price per share of stock A) + (Number of shares of stock B × Price per share of stock B)

Total value = (135 × $84) + (110 × $82)

Total value = $11,340 + $9,020

Total value = $20,360

Now, we can calculate the portfolio weights for each stock:

Weight of stock A = (Value of stock A ÷ Total value) × 100%

Weight of stock A = (($84 × 135) ÷ $20,360) × 100%

Weight of stock A = $11,340 ÷ $20,360

Weight of stock A ≈ 0.5569 or 55.69%

Weight of stock B = (Value of stock B ÷ Total value) × 100%

Weight of stock B = (($82 × 110) ÷ $20,360) × 100%

Weight of stock B = $9,020 ÷ $20,360

Weight of stock B ≈ 0.4431 or 44.31%

Therefore, the portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

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Answer:

8.80

Step-by-step explanation:

(S. D.)^2=summation(x-mean)^2/(n-1)

S. D.=sqrt(388/5)

S. D.=8.80

D) A^2 = A + 1 this equation represents diagonal matrices with the same eigenvalues on the diagonal.

Let λ be an eigenvalue of the matrix A, and let v be the corresponding eigenvector. Since A is diagonalizable, we can write A = PDP^(-1), where D is the diagonal matrix containing the eigenvalues on the diagonal, and P is the matrix whose columns are the eigenvectors.

We know that A^2 = A + 1, so we can substitute A with its diagonalizable form:

(PDP^(-1))^2 = PDP^(-1) + 1.

Expanding the square and applying the matrix multiplication rules, we get:

PD^2P^(-1) = PDP^(-1) + 1.

Since D is a diagonal matrix, D^2 will have the eigenvalues squared on the diagonal. Therefore, we have:

P(D^2)P^(-1) = PDP^(-1) + 1.

Multiplying both sides by P^(-1) on the right, and by P on the left, we obtain:

D^2 = D + 1.

This equation holds because P^(-1)P = I (the identity matrix), and D and D^2 are diagonal matrices with the same eigenvalues on the diagonal.

Therefore, the correct answer is D) A^2 = A + 1.

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