2(x + y) – (3y – 2x) + 4(2 – y)

Answer:

2(5−12)

Hope this helps!

Let the initial intensity be I, then,

Here, x is the proportionality constant and d is the distance.

When the seat is changed o one that is thrice as far from the

speakers, we have the new intensity as,

Therefore, the new intensity in terms of the original intensity can be written as,

Thus, the required fraction is 1/9.

Hello!

Solve for x.

2x+3y=z

Step 1: Add -3y to both sides.

2x+3y+−3y=z+−3y

2x=−3y+z

Step 2: Divide both sides by 2.

2x/2=−3y+z/2

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The square root function is translated so that the endpoint is located at (-7,7), \(g(x)= \sqrt{x+7} +7\)  and this can be determined by using the transformation.

The square root parent function is translated so that the endpoint is located at (-7,1).

The following steps can be used to determine the equation that represents this new function:

                       \(f(x) =\sqrt{x}\)

\(g(x)= \sqrt{x+7} +7\)

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It should be noted that to move Trapezoid ABCD to its new location or shadow, we need to perform a series of rigid transformations, which include translation, rotation, and reflection.

Move Trapezoid ABCD to a new location in the same plane by shifting it horizontally and vertically. We can do this by adding or subtracting a certain number of units from the x and y-coordinates of each vertex.

After translation, Trapezoid ABCD will be at a new location, let's call it Trapezoid A'B'C'D'. This was illustrated on the diagram. Then, it was rotated around a certain point in the plane. We can rotate it clockwise or counterclockwise by a certain angle

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The statement that describes the solution of the equation is:

Option A: The equation has two valid solutions and no extraneous solution

The equation we want to solve is given as:

\(\frac{2}{x + 2} + \frac{1}{10} = \frac{3}{x + 3}\)

Multiply through by 10(x + 2)(x + 3) to get:

20(x + 3) + (x + 2)(x + 3) = 30(x + 2)

Expanding gives:

20x + 60 + x² + 5x + 6 = 30x + 60

x² - 5x + 6 = 0

Using quadratic equation calculator gives:

x = 2 or x = 3

Thus, the equation has two valid solutions and no extraneous solution

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Answer:(x-5)/8

Step-by-step explanation:

f(x)=8x+5

   let f(x)-1=y

y=8x+5

interchanging x and y

x=8y+5

y=(x-5)/8

Therfore f(x)-1=(x-5)/8

Answer:

x-5/8

Step-by-step explanation:

$0.64 is the monetary value.

We are given that a 4500 square foot roll of plastic wrap costs $23.95 and we are to determine the monetary value of a 120 square foot piece of plastic wrap.

Let us find the cost per square foot by dividing the total cost of the roll by the number of square feet in the roll:

$23.95/4500 = $0.005322 per square foot

Now, we can multiply the cost per square foot by the number of square feet needed for the party game (120) to find the monetary value of the piece of plastic wrap.

Therefore, the monetary value of that 120-square-foot piece of plastic wrap is:

$0.005322 x 120 = $0.64 (rounded to the nearest cent)

Hence, the monetary value of that 120-square-foot piece of plastic wrap is $0.64.

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The correct answer are as follows

a) True, b) False, c) False, d) False, e) False

(a) True. The standard deviation is always a non-negative value since it is a measure of the spread or variability of the data set.
(b) False. Since A and B are disjoint, they have no overlapping outcomes, which means P(A AND B) = 0.
(c) False. Although the mean and median are often close in a normal distribution, they are not always equal. The median is the middle value of the distribution, while the mean is the average of all values.
(d) False. A 95% confidence interval is narrower than a 98% confidence interval of the same parameter since it requires a higher level of confidence to have a wider interval.
(e) False. If the value of the test statistic is 1.5 and P(T<1.5)=0.98, then the p-value is 0.02. Since the p-value is less than the level of significance of 0.05, we reject the null hypothesis.
(a) True. The standard deviation of a data set cannot be negative because it is a measure of dispersion and is calculated as the square root of the variance, which is always non-negative.

(b) False. If A and B are disjoint, then P(A AND B) = 0, since disjoint events cannot occur simultaneously.

(c) True. For a normal distribution, the mean is always equal to the median, indicating a symmetrical distribution.

(d) False. A 95% confidence interval is narrower than a 98% confidence interval of the same parameter because a higher confidence level requires a wider interval to capture the true value with greater certainty.

(e) True. In a two-tailed test, if the test statistic follows a Student's t-distribution with P(T<1.5)=0.98, this means that P(T>1.5)=0.02. For a two-tailed test at a 0.05 level of significance, the rejection regions are in both tails, with 0.025 in each tail. Since P(T>1.5)=0.02 < 0.025, we fail to reject the null hypothesis.

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Answer:

Step-by-step explanation:

To calculate the probability that the student will answer at least half of the questions correctly, we need to consider the different possible outcomes.

Since the student has not studied and guesses at the answers, each question has a 1/4 chance of being answered correctly by random chance. Let's calculate the probabilities for different scenarios:

Answering exactly half of the questions correctly:

This means the student answers 10 out of 20 questions correctly. We can calculate this probability using the binomial probability formula:

P(X = k) = (nCk) * (p^k) * ((1-p)^(n-k))

P(X = 10) = (20C10) * (0.25^10) * (0.75^10) ≈ 0.185

Answering more than half of the questions correctly:

This means the student answers 11, 12, 13, ..., or 20 questions correctly. We need to calculate the probabilities for each of these individual cases and sum them up:

P(X > 10) = P(X = 11) + P(X = 12) + ... + P(X = 20)

P(X > 10) = Σ[(20Ck) * (0.25^k) * (0.75^(20-k))] for k = 11 to 20

Calculating this sum will give us the probability of answering more than half of the questions correctly.

To find the probability that the student will answer at least half of the questions correctly, we need to sum the probability of answering exactly half (10) correctly with the probabilities of answering more than half (11 to 20) correctly. These probabilities can be calculated using the binomial probability formula.

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A. N, B ≥ 0 (non-negativity constraint)

B. The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.

C.  You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

D. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

(a)

The linear programming model to find the best investment strategy for this client can be formulated as follows:

Maximize: 0.09N + 0.08B

Subject to:

N + B ≤ 85 (maximum investment of $85,000)

N ≤ 55 (maximum investment of $55,000 in the internet fund)

6N + 4B ≤ 410 (maximum risk rating of 410 for a moderate investor)

N, B ≥ 0 (non-negativity constraint)

(b)

To solve the problem using Excel Solver, you can set up the following spreadsheet model:

Cell A1: N (amount invested in the internet fund)

Cell B1: B (amount invested in the Blue Chip fund)

Cell C1: =0.09A1 + 0.08B1 (annual return for the portfolio)

Constraints:

Cell A2: ≤ 85

Cell B2: ≤ 85

Cell C2: ≤ 55

Cell D2: ≤ 410

The objective is to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints.

Using Excel Solver, set the objective to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints in cells A2, B2, C2, and D2.

The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.

(b)

For the aggressive investor with a maximum portfolio risk rating of 450, the linear programming model remains the same, except for the constraint on the maximum risk rating.

The new constraint would be: 6N + 4B ≤ 450

Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

(d)

For the conservative investor with a maximum portfolio risk rating of 320, the linear programming model remains the same, except for the constraint on the maximum risk rating.

The new constraint would be: 6N + 4B ≤ 320

Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

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Answer:

Step-by-step explanation:

area of garden = 38 m²

width = 4 m

find Length

area = L x W

38 = L (4)

L = 38 / 4

L = 9.5 m

The length of the other parallel side is 3x

The given parameters are:

Midsegment= 2x

One parallel side = x

The midsegment is calculated as:

Midsegment = 0.5 * (sum of parallel sides)

So, we have

2x = 0.5 *(x + Other side)

Divide by 0.5

4x = x + Other side

Evaluate the like terms

Other side = 3x

Hence, the length of the other parallel side is 3x

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Answer:

see below

Step-by-step explanation:

1. (x² - 4x - 10) + (x² - 9x + 3)

=  x² - 4x - 10 + x² - 9x + 3

=  x² + x² - 4x - 9x + 3 - 10

4. (3x² - x + 1) + (15 - 9x - 2x²)

=  3x² - x + 1 + 15 - 9x - 2x²

= 3x² - 2x² - x - 9x + 1 + 15

7.  (6 - 2x + 7x²) - (10x - 3 + 3x²)

=   6 - 2x + 7x² - 10x + 3 - 3x²

=  7x² - 3x² - 2x - 10x + 6 + 3

Step-by-step explanation:

I hope it helps...I just put it in point slope form

The probability of selecting 4 red marbles out of the bag is approximately 0.0303, or 3.03%.

To find the probability of selecting 4 red marbles out of a bag containing 6 red, 4 blue, and 2 white marbles, we first need to determine the total number of possible combinations of 4 marbles that can be selected from the bag. This can be calculated using the formula for combinations, which is:
\(nC_{r}=    \frac{n!}{r!(n-r)}\)

where n is the total number of items in the set, and r is the number of items being chosen. In this case, we have:

n = 12 (6 red + 4 blue + 2 white)
r = 4 (the number of marbles being chosen)

So the total number of possible combinations is:

\(12C_{4}=    \frac{12!}{(4!8!)} = 495\)

Next, we need to determine the number of combinations that contain 4 red marbles. Since there are 6 red marbles in the bag, the number of ways to choose 4 of them is:

\(6C_{4}=    \frac{6!}{(4!2!)} = 15\)

Therefore, the probability of selecting 4 red marbles out of the bag is:

\(p( 4 red) = \frac{15}{495}=\frac{1}{33}\)

So the probability of selecting 4 red marbles out of the bag is approximately 0.0303, or 3.03%.

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Answer:

6) a) y = −7/2 x , b) y = −1/2 x , c) y = −5/4 x , d) y = −17/10 x

Step-by-step explanation:

For question 5 it needs to have the input and output values or having a domain and range value. So it can't be solved.

(there's an error in this question)

As for question 6,

a) with coordinate (x,y) = (-2,7)

1. To find the equation of a line or gradient,

first find the slope via the formula: -> m = (y2-y1/x2-x1)

If we let (0,0) ➡️ (x1,y1) and

(-2,7) ➡️ (x2,y2) then,

m = (7-0/-2-0) = -7/2 ⬅️ This is the slope of the line/gradient

Now that we have found the slope we can find the equation via the point-slope formula:

(y−y1) = m(x−x1) ;

2. Substituting the slope = -7/2 for

m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)

Thus,

y−0 = −7/2 (x-0)

If we simplify this, we simply get

y = −7/2 x ← This is our equation for coordinate (-2,7)

b) with coordinate (x,y) = (2,-1)

1. To find the equation of a line or gradient,

first find the slope via the formula: -> m = (y2-y1/x2-x1)

If we let (0,0) ➡️ (x1,y1) and

(2,-1) ➡️ (x2,y2) then,

m = (-1-0/2-0) = -1/2 ⬅️ This is the slope of the line/gradient

Now that we have found the slope we can find the equation via the point-slope formula:

(y−y1) = m(x−x1) ;

2. Substituting the slope = -1/2 for

m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)

Thus,

y−0 = −1/2 (x-0)

If we simplify this, we simply get

y = −1/2 x ← This is our equation for coordinate (2,-1)

c) with coordinate (x,y) = (4,-5)

1. To find the equation of a line or gradient,

first find the slope via the formula: -> m = (y2-y1/x2-x1)

If we let (0,0) ➡️ (x1,y1) and

(2,-1) ➡️ (x2,y2) then,

m = (-5-0/4-0) = -5/4 ⬅️ This is the slope of the line/gradient

Now that we have found the slope we can find the equation via the point-slope formula:

(y−y1) = m(x−x1) ;

2. Substituting the slope = -5/4 for

m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)

Thus,

y−0 = −5/4 (x-0)

If we simplify this, we simply get

y = −5/4 x ← This is our equation for coordinate (4,-5)

d) with coordinate (x,y) = (10,-17)

1. To find the equation of a line or gradient,

first find the slope via the formula: -> m = (y2-y1/x2-x1)

If we let (0,0) ➡️ (x1,y1) and

(2,-1) ➡️ (x2,y2) then,

m = (-17-0/10-0) = -17/10 ⬅️ This is the slope of the line/gradient

Now that we have found the slope we can find the equation via the point-slope formula:

(y−y1) = m(x−x1) ;

2. Substituting the slope = -17/10 for

m and any of the two coordinates given. I will use (0,0) be make things easier. We let (0,0) → (x1,y1)

Thus,

y−0 = −17/10 (x-0)

If we simplify this, we simply get

y = −17/10 x ← This is our equation for coordinate (10,-17)

Answer:

6.75 x 10^2 g

Step-by-step explanation:

Mass of Red Blood Cells

The mass of a red blood cell is about 2.7 X 10−112.7 X 10 −11 grams. There are about 2.5 X 10132.5 X 10 13 red blood cell in a human body. What is the total mass, in grams, of the red blood cells in a human body? Express your answer in standard form

To find the total mass of red blood cells in a human body, we need to multiply the mass of one red blood cell by the total number of red blood cells in the body:

Total mass = (mass of one red blood cell) x (total number of red blood cells)

Total mass = (2.7 x 10^-11 grams) x (2.5 x 10^13 red blood cells)

Multiplying these two numbers gives:

Total mass = 6.75 x 10^2 grams

In standard form, this is:

Total mass = 6.75 x 10^2 g

The equation you mentioned, "15px," does not specify a conic section or provide enough information to determine the standard equation or describe the graph.

To determine the standard equation of a conic section with its center or vertex at the origin, you need more specific details about the conic section, such as its shape (circle, ellipse, parabola, or hyperbola) and additional parameters like the radius, semi-major axis, semi-minor axis, eccentricity, or focal length.
Once you have the necessary information, you can use the properties and characteristics of the specific conic section to derive its standard equation. The standard equations for different conic sections will have different forms and coefficients.
Please provide more information or clarify the conic section you are referring to so that I can assist you further in determining its standard equation and describing its graph.


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Answer: x=49

Step-by-step explanation:

Triangle's internal angles produce a sum of 180, and this is a right triangle. This means we can write an equation for x:

180-(3x-8)+90+x=180

And then just solve for x:

-3x+8+90+x=0

-2x+98=0

2x=98

x=49

Answer:

Its -5

Step-by-step explanation:

-100 divided by 10= -10 divided by -5= 2

The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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For given equation x_(n+1) = ((x_n)^3 - 5)/10,

a) (i) x2 = -0.6

(ii) x3 = -0.5216

b)  the solution to 6 decimal places, x5 = -0.513594

Given equation, x_(n+1) = ((x_n)^3 - 5)/10

also, x1 = -1

a)

(i) we need to find the value of x2

Substitute n = 1 in given equation,

x_(1+1) = ((x1)^3 - 5)/10

x_2 = [(-1)^3 - 5]/10

x_2 = (-1 - 5)/10

x2 = -6/10

x2 = -0.6

(ii) we need to find the value of x3

Substitute n = 2 in given equation,

x_(2+1) = ((x2)^3 - 5)/10

x3 = [(-0.6)^3 - 5]/10

x3 = (-0.216 - 5)/10

x3 = -5.216/10

x3 = -0.5216

b)

We need to find the solution to 6 decimal places.

First we find the value of x4.

Substitute n = 3 in given equation,

x_(3+1) = ((x3)^3 - 5)/10

x4 = [(-0.5216)^3 - 5]/10

x4 = (-0.1419 - 5)/10

x4 = -5.1419/10

x4 = -0.51419

Substitute n = 4 in given equation,

x_(4+1) = ((x4)^3 - 5)/10

x5 = [(-0.51419)^3 - 5]/10

x5 = (-5.13595)/10

x5 = -0.513594

Therefore, for given equation x_(n+1) = ((x_n)^3 - 5)/10,

a) (i) x2 = -0.6

(ii) x3 = -0.5216

b)  the solution to 6 decimal places, x5 = -0.513594

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In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.

Given the demand equations and the total cost function:

Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1

Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2

Total Cost: TC = 120 + 4Q

To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:

MR1 = MC:

16 - 0.2Q1 = 4

0.2Q1 = 12

Q1 = 60

MR2 = MC:

10 - 0.1Q2 = 4

0.1Q2 = 6

Q2 = 60

Substituting the quantities back into the demand equations, we find:

P1 = 16 - 0.1(60) = 10

P2 = 10 - 0.05(60) = 7

The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:

TR = P1 * Q1 + P2 * Q2

TR = (10 * 60) + (7 * 60)

TR = 600 + 420

TR = 1020

The total cost (TC) is given by the total cost function:

TC = 120 + 4Q

TC = 120 + 4(60 + 60)

TC = 120 + 480

TC = 600

Finally, the profit (π) can be calculated by subtracting total cost from total revenue:

π = TR - TC

π = 1020 - 600

π = 420

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

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The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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Answer:

k < 9/8

Step-by-step explanation:

let me know if you want an explanation :))