as part of an animation the length and width of the image are decreased by 8 pixels every second. The total number of pixels in the image after t seconds is given by the function A(t)=(256-8t)(192-8t). After how many seconds will the number of pixels be reduced to 0. Answer

The results obtained from part (b) can be used to make the following conclusions: Warshall's Algorithm takes less time than Algorithm 0.1 for all values of n between 10 and 100.

The pseudocode for both Algorithm 0.1 and War shall's Algorithm is as follows: Algorithm 0.1:Warshall's Algorithm:

Here is the sequence of steps to calculate and record completion time as well as the 10-run average: Define the range of values n from 10 to 100, and then for each value of n, randomly generate a zero-one matrix M of size nxn (this is an adjacency matrix for a directed graph)

Run Algorithm 0.1 on M and record the time it takes to complete. Repeat this process for ten random matrices of size nxn, then calculate the average of the completion times of the ten runs. Run War shall's Algorithm on M and record the time it takes to complete. Repeat this process for ten random matrices of size nxn, then calculate the average of the completion times of the ten runs. Repeat this for all values of n from 10 to 100. Plot the results on an appropriate graph.

Warshall's Algorithm is more efficient than Algorithm 0.1 in computing the transitive closure of a given relation.

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380 liters of natural oil is needed

The ratio of natural oil to synthetic oil is 4:5

Total number of petrolyn oil is 855

4x + 5x= 855

9x= 855

x= 855/9

x= 95

The number of natural oil is 4x

= 4(95)
= 380

Hence the number of liters of natural oil that is needed is 380

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Let \(n=0\). Then \(0^3 = 0\) but 0 > 0 is a false statement.

A discrete function is a function with distinct and separate values. This means that the values of the functions are not connected with each other. For example, a discrete function can equal 1 or 2 but not 1.5.

Let's analize the options:

• Option A: This is continuos, the faucet can fills with 1 gallon, 1.1 gallon, and so. Also any previous value is connected with the next.

• Option B: As in option B, the car drives for a continuos time.

• Option C: This is a discrete relation, because Jacqueline could not sells a half of a chocolate bar, she sells discrete values of chocolate bars 1, 2, 3, ....

• Option D: This is the same as option A.

Answer:

1 pound is 453.6 grams appox

Step-by-step explanation:

to calculate how many grams is 2 pounds, u can do 2x453.6 which would be 907.2

for all others i have an attached file :)

Answer:

2,A because it's a line with a specified direction

Answer:

A is the correct answer

Step-by-step explanation:

Thats your answer

The revenue function when the assumed values and parameters are used is F(x) = (60 + 8x)(250 - 30x)

Let the number of people be x, and the revenue function be F(x).

Using the assumed values, the revenue function is:

F(x) = (60 + 8x)(250 - 30x)

We have:

F(x) = (60 + 8x)(250 - 30x)

Expand

F(x) = 15000 - 1800x + 2000x - 240x²

Differentiate the function

F'(x) = -1800 + 2000 - 480x

Evaluate

F'(x) = 200 - 480x

Set to 0

200 - 480x = 0

This gives

480x = 200

Divide both sides by 480

x = 0.42

Substitute x = 0.42 in F(x)

F(x) = (60 + 8 * 0.42)(300 - 30* 0.42)

Evaluate

F(x) = 18210

Hence, the maximum revenue is $18210, at a rate of $0.42 per person.

We start by setting F(x) to 5000.

So, we have:

15000 - 1800x + 2000x - 240x² = 5000

Evaluate the like terms

10000 + 200x - 240x² = 0

Using a graphing tool, we have:

x = 6.89

Hence, they would reach their goal at a rate of $6.89 per ticket.

We have:

People = x

Cost per person = 20

So, the cost function is:

C(x) = 20x

Profit is calculated using:

P(x) = F(x) - C(x)

So, we have:

P(x) = 15000 - 1800x + 2000x - 240x² - 20x

Evaluate

P(x) = 15000 + 180x - 240x²

This is the point where P(x) = 0.

So, we have:

15000 + 180x - 240x²  = 0

Using a graphing tool, we have:

x = 8.29

Hence, the break even price is $8.29

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To solve the quadratic equation \(x^{2}\) + bx + c = 0, one can use the quadratic formula, which states that the solutions are given by x = (-b ± √(\(b^2\) - 4ac))/(2a).

The quadratic equation \(x^{2}\) + bx + c = 0 represents a parabola in the Cartesian coordinate system. To find the solutions, one can use the quadratic formula, which is derived from completing the square. The formula states that the solutions, denoted by x, can be found by substituting the coefficients a, b, and c into the formula x = (-b ± √(\(b^2\) - 4ac))/(2a).

The discriminant, \(b^2\) - 4ac, plays a crucial role in determining the nature of the solutions. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution, which is called a double root. If the discriminant is negative, the equation has two complex solutions, which are conjugates of each other.

By plugging in the values of a, b, and c into the quadratic formula and simplifying, one can obtain the solutions for the given quadratic equation. The ± symbol in the formula indicates that there will be two solutions, one with a positive sign and the other with a negative sign, corresponding to the two possible roots of the equation.

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Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent.

So if one of your answers have equivalent ratios, that is your answer

Andrew can paint the neighbors house 3 times as fast as Bailey.

The year Andrew and Bailey worked together, it took them 7 days.

How long would it take each to paint the house?

:

Let t = time required by A to do it alone

then

3t = time required by B to do it alone

:

Let the completed job = 1

:

7%2Ft + 7%2F%283t%29 = 1

Multiply equation by 3t to get rid of the denominators, results:

21 + 7 = 3t

28 = 3t

t = 28%2F3

t = 91%2F3 days, Andrew alone

then

3*91%2F3 = 28 days, Bailey alone

:

:

Check solution on calc using decimals

(7/9.33) + (7/28) = 1.00

The single natural logarithm expression is ln(2). Therefore, correct answer is (a)

The expression in the form \(e^a=b\) can also be written as In b = a  which is called as logarithmic expression.

Properties of Logarithms:

1. In (mn) = In m + In n

2. In \(a^m =\) m In a

3. In \(e^a\) = a.

The natural logarithm expression is:

4 + ln 2 - ln 4

Apply the product and quotient rule of natural logarithm:

4 + ln 2 - ln 4  = In (4 × 2/4)

Evaluate the quotient:

4 + ln 2 - ln 4  = In (2)

Hence, the single natural logarithm expression is ln(2).

The correct option is (a)

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Answer:

B: ln 4.

Step-by-step explanation:

Answer: the slope intercept form of 2x+y=6 is y=-2+6

Step-by-step explanation:

2x+y=6  (subtract 2x from both sides)

-2x    -2x  (the -2x and the 2x cancel leaving...)

y=-2x+6  →( y equals negative two x plus six)

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

Answer:

72.27

Step-by-step explanation:

Answer:

72.27

Step-by-step explanation:

that's what I got on the calculator.

The value of x from the given expression is -10

Given the following expression

AC = x + 24,

AB = 2x + 28,

and BC = 6.

Using the addition property, we will have:

AC = AB + BC

Substitute the expression to have:

x+24 = 2x + 28 + 6

x-2x = 34 - 24

-x = 10

x = -10

Hence the value of x from the given expression is -10

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Answer:

X=-10

Step-by-step explanation:

In this case, "X+24" is the sum of "2x+28" and "6"

The correct equation would be:

2x+34=x+24

Now, subtract X from both sides and add 34 to both sides

Now:

x=-10

Hence, -10 is the answer

Solution:

Starting point = (4, -12)

Length = units

Along the y axis, the endpoints could be

(4, -7) and (4, -17)

Along the x- axis, the endpoints could be

(9, -12) and (-1, -12).

The answer is (4, -7), (4, -17), (9, -12), (-1, -12).

Answer:

B=30,000

Y=The Plane's altitude

M= -2,000

X= Minutes

Equation: y=-2,000x+30,000

Slope= ?

Y-intercept= the point where you start at

what is the altitude after 10 minutes?=10,000

How Long does it take to get to 0 altitudes?=15 (Minutes)

Step-by-step explanation:

What are the choices for slope

Based on the current real and the full employment real GDP, Rayton's economy is at a Recession stage.

The current budget balance in Rayton is -$1,000. The budget can be balanced by reducing government spending or increasing taxes. Both of these would decrease real GDP.

The fact that the current real GDP is less than the full employment GDP shows that the nation is at a recession stage where it is underperforming.

This can be found as:

= Government revenue(taxes) - government spending

= 3,000 - 1,000 - 3,000

= -$4,000

In order to make a balanced budget where government revenue will equal government spending, the government either needs to reduce spending or increase revenue ( taxes ).

Increasing taxes or reducing spending, will lead to less money available for spending in the economy which will lead to a decrease in real GDP.

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The value of g(-5) is 7.5, g(-2) is 4, and g(5) is 7.5 if the value of function g(x) = 1/2x²-5 if x≠-2 and g(x) = 4 if x = -2.

A function is a rule that associates each element in a set (called the domain) with a unique element in another set (called the range). A function takes an input from the domain and produces an output in the range.

To find the value of g(-5), substitute the value in given function

g(-5) = 1/2×(-5)² - 5

= 1/2×25 - 5

= 12.5 - 5 = 7.5

The value of g(-2) is 4 as it is defined in the question only.

To find the value of g(5), substitute the value in given function

g(5) = 1/2×(5)² - 5

= 1/2×25 - 5

= 12.5 - 5 = 7.5

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We have 3 non-removable restrictions at x = -4, x = 1, and x = -1.

Here we have the expression:

\(\frac{x - 3}{x + 4} /\frac{x^2 - 1}{x}\)

This can be rewritten as:

\(\frac{x-3}{x + 4} *\frac{x}{x^2 - 1}\)

We can rewrite the denominator of the second fraction as:

\(x^2 - 1 = (x - 1)*(x + 1)\)

Then we rewrite the expression as:

\(\frac{x-3}{x + 4} *\frac{x}{(x- 1)*(x + 1)} = \frac{x*(x - 3)}{(x + 4)*(x + 1)*(x - 1)}\)

So, none of the factors in the denominator is also in the numerator meaning that none of the restrictions is removable.

Then we have 3 non-removable restrictions at:

x = -4, x = -1, x = 1.

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Answer: He needs 80 cups.

Step-by-step explanation:$12/$.15=80 cups

The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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Answer:

Calculate 5% of what she sold. Then add it to her weekly salary

5% =0.05

Commission 4600×0.05=$230

Total pay is 380+230 = $610

A study with a larger sample is more likely than a smaller study to get the result that p < 0.05. If we assume the null hypothesis is true, the correct statement is: a.

When the null hypothesis is true, any observed effect is due to random chance.

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Answer:

the scaled sail has lengths 1.5 inches, 2 inches, and 2.5 inches. the diagram is attached.

Step-by-step explanation:

a scale factor of 1/4 means that the lengths of each side of the sail will be reduced by 0ne-forth (0.6) its original length. Therefore the lengths of the scale drawing before and after scaling are:

6 inches = 6 × 1/4 = 6 × 0.25 = 1.5 inches

8 inches = 7 × 0.25 = 2 inches

10 inches = 10 × 0.25 = 2.5 inches.

Therefore the scaled sail has lengths 1.5 inches, 2 inches, and 2.5 inches as shown in the diagram attached.

The rational root of the function is x = -1/2, and the complex roots are x = 21/4 and x = 1.

To find the rational root of the function f(x) = 4x³ - 17x² - 39x - 18, we can apply the Rational Root Theorem. According to the theorem, any rational root of the function must be of the form p/q, where p is a factor of the constant term (in this case, -18) and q is a factor of the leading coefficient (in this case, 4).

Let's list the factors of -18: ±1, ±2, ±3, ±6, ±9, ±18.

And now the factors of 4: ±1, ±2, ±4.

Possible rational roots are formed by dividing a factor of the constant term by a factor of the leading coefficient. So the possible rational roots are:

±1/1, ±1/2, ±1/4, ±2/1, ±2/2, ±2/4, ±3/1, ±3/2, ±3/4, ±6/1, ±6/2, ±6/4, ±9/1, ±9/2, ±9/4, ±18/1, ±18/2, ±18/4.

Now, test each of these possible roots by substituting them into the function f(x) and see if any of them result in f(x) = 0.

By evaluating the function for each of these possible roots, the rational root is x = -1/2.

Now let's proceed to find the complex roots of the function. To do this, use polynomial division or synthetic division to divide f(x) by (x - (-1/2)).

Performing the synthetic division, we have:

4 | 4 -17 -39 -18

| -8 60 -105

| ___________________

| 4 -25 21 -123

The result of the synthetic division is 4x² - 25x + 21 with a remainder of -123. Now we have a quadratic equation. To solve it, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our quadratic equation 4x² - 25x + 21, the coefficients are:

a = 4

b = -25

c = 21

Applying the quadratic formula, we get:

x = (-(-25) ± √((-25)² - 4 x 4 x 21)) / (2 x 4)

= (25 ± √(625 - 336)) / 8

= (25 ± √289) / 8

= (25 ± 17) / 8

So the two complex roots are:

x = (25 + 17) / 8 = 42 / 8 = 21 / 4

x = (25 - 17) / 8 = 8 / 8 = 1

Therefore, the rational root of the function is x = -1/2, and the complex roots are x = 21/4 and x = 1.

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Using the given information, the volume of the rectangular prism is 6,048 cubic units.

A rectangular prism is a three-dimensional geometric shape that has six rectangular faces, each with an identical size and form.

To compute the volume of a rectangular prism, multiply the length (L), width (W), and height (H).  

In this case, we are given:

L = 18

W = 21

H = 16

Volume = L × W × H

= 18 × 21 × 16

= 6,048 cubic units

Therefore, the volume of the rectangular prism is 6,048 cubic units.

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