Prove that the following utility function represents monotone and convex preferences. u(x,y)=xy,x,y≥0

Answer:

sinJ = \(\frac{12}{13}\)

Step-by-step explanation:

sinJ = \(\frac{opposite}{hypotenuse}\) = \(\frac{IK}{JK}\) = \(\frac{12}{13}\)

Answer:

\( \sf \large \: x = -1\)

Step-by-step explanation:

4x + 7 = 3

Substract 7 from both sides

4x + 7 - 7 = 3 - 7

4x = -4

Divide both sides by the coefficient of x

4x/4 = -4/4

calculate

x = -1

The completed statement based on two-dimensional motion in the x-y plane can be presented as follows;

The two-dimensional motion in the x-y plane, the x part of the motion and the y part of the motion are independent, whether or not there is an acceleration in any direction. The correct option is therefore;

D) Whether or not there is an acceleration in any direction

Two-dimensional motion in the x-y plane can be analyzed by separating them into its horizontal (x) and vertical (y) components, and analyze each component using the one dimensional equations of motion.

The meaning of the motion on the x-y plane is that the x-direction motion of an object exclusive or excludes the effect of the motion of the object in the y-direction, vis a vis, the y-direction motion.

The horizontal and vertical components of the motion can be analyzes individually or by themselves, by making use of the equations of motion for a one-dimensional motion, whether or not there is an acceleration in any direction as the acceleration are also evaluated using one dimensional equations.

The possible options in the question from a similar question on the internet are;

A) When there is no acceleration in any direction

B) When there is no acceleration in one direction

C) Only when an acceleration is present in both directions

D) Whether or not there is an acceleration in either direction

E) Only when the acceleration is in the y-direction

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The shapes C and F represent an enlargement of shape X by a scale factor of -1.

A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

For a scale factor of -1, we have that the size remains constant, as |-1| = 1, hence the figure is just reflected.

Thus the shapes are given as follows:

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Answer:

2 3/4

Step-by-step explanation:

this is the answer

Answer:

10

Step-by-step explanation:

2 butter = 160

160×4=910

According to Shelley Taylor, the female response to stress is to "tend and befriend," whereas the male response more often is "fight or flight."

Let's discuss it further below.

Here is an example of a possible answer to the given student question:

According to Shelley Taylor, the female response to stress is to "tend and befriend," whereas the male response more often is "fight or flight."

This theory suggests that in response to stress, females are more likely to take care of others and seek social support, while males are more likely to engage in aggressive or avoidant behaviors.

This theory has been supported by a variety of studies and has helped shed light on some of the gender differences in stress responses.

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To construct a confidence interval for the proportion of defectives, we should use the plus four method.

Since the sample size is 20, which is not very large, the large-sample interval is not appropriate. Instep, we ought to utilize a strategy that's suitable for little test sizes. 

The plus four method is one such method that is commonly used when the sample size is small. Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

The plus four strategies may be a strategy for building a certainty interim for an extent when the test estimate is little.

To utilize this strategy, we to begin with include four fanciful perceptions to our test, two of which are flawed and two of which are not imperfect.

This increments the test estimate to 24, which permits us to utilize the typical guess to the binomial dispersion to build the certainty interim.

The equation for the certainty interim utilizing the also four strategies is:

p ± zα/2 √((p + 2) (1 - p + 2) / n + 4)

where:

p is the test extent (number of defectives/test estimate)

zα/2 is the basic esteem from the standard typical dissemination at the level of importance α/2

n is the test estimate (counting the included four nonexistent perceptions)

Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

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Answer:

22 hens and 78 sheep

Step-by-step explanation:

Let the number of hens = x

Number of sheep = y

Total heads = 100

x +  y = 100      --------------------(I)

 x = 100 - y

Number of legs of 'x' hen = 2*x = 2x

Number of legs of 'y' sheep = 4*y = 4y

total legs = 356

2x + 4y =  356 -----------------------(II)

Substitute x = 100 -y in equation (II)

2(100 - y) + 4y = 356

2*100 - 2*y + 4y = 356

200 - 2y + 4y    = 356 {Combine like terms}

        200  + 2y = 356          {Subtract 200 from both sides}

                   2y = 356 - 200

                  2y = 156       {Divide both sides by 2}

                    y = 156/2

                  y = 78

Plugin  y = 78 in equation (I)

x + 78 = 100

       x = 100 - 78

       x = 22

22 hens and 78 sheep

Bring like terms together

on number line, we will have

Answer:

$2.20

Step-by-step explanation:

11/5=2.2

Answer:

0.45

Step-by-step explanation:

$5 for 11 lb

$5/(11 lb) = $0.45/lb

The amount of flour in the bag (x) plus the amount of flour in the jar (4.5 cups) must be greater than or equal to 12 cups.

x + 4.5 ≥ 12

Solve for x:

x ≥ 7.5

The problem states that Eduardo had 4.5 cups of flour in a jar, and then opened a bag of flour and poured it in until the jar was full. The question is how much flour was in the bag to start? To solve this problem, we can use an inequality. Let x represent the amount of flour in the bag to start. The equation we can use is x + 4.5 ≥ 12, which states that the amount of flour in the bag (x) plus the amount of flour in the jar (4.5 cups) must be greater than or equal to 12 cups. To solve for x, we can subtract 4.5 from both sides of the equation, which yields x ≥ 7.5. This means that the bag of flour must have contained at least 7.5 cups of flour for Eduardo to have enough to fill the jar.

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Answer:  7.5 4.5>12

Step-by-step explanation:

I already had this one and got it right

Answer: 16

Step-by-step explanation:

The sales tax rate for a specific type of wood-frame door priced at $1480 is 25%, or $370.

Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 questions correctly out of 100 on a test (75/100), you would have received a 75%. A percentage is a relative value that represents one hundredth of a quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given quantity. A percentage is a fraction of a whole expressed as a number between 0 and 100.

Here,

Sale tax=$370

Price of door=$1480

Sales tax percent=370/1480*100

=25%

The rate of sales tax for a particular type of wood-frame door is priced at $1480 is 25% that is $370.

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Answer:

i dont understand i dont understand

The inverse Laplace transform of f(s) = -e^(-4s) (4s+6)/(s^2+6^2) is f(t) = -2e^(-2t) sin(6t) u(t).

To find the inverse Laplace transform of f(s), we first factor the denominator of f(s) to obtain f(s) = -e^(-4s) (4s+6)/[(s+3i)(s-3i)]. Then we use partial fraction decomposition to write f(s) as f(s) = A/(s+3i) + B/(s-3i), where A and B are constants. Solving for A and B, we get A = -2/(3i+2) and B = 2/(3i-2).

Next, we use the table of Laplace transforms to find the inverse Laplace transforms of A/(s+3i) and B/(s-3i). We have L^-1[A/(s+3i)] = -2e^(-3t) sin(6t) u(t) and L^-1[B/(s-3i)] = 2e^(3t) sin(6t) u(t). Thus, the inverse Laplace transform of f(s) is f(t) = L^-1[f(s)] = L^-1[A/(s+3i)] + L^-1[B/(s-3i)] = -2e^(-3t) sin(6t) u(t) + 2e^(3t) sin(6t) u(t) = -2e^(-2t) sin(6t) u(t).

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Answer:

A C E

Both exact values are less than the approximate value.

The top model has a greater percent error.

The absolute error is the same for both.

Step-by-step explanation:

Answer:

Both exact values are less than the approximate value.

The top model has a greater percent error.

The absolute error is the same for both.

Step-by-step explanation:

Answer:

y = x + 5

Step-by-step explanation:

Slope: m = (y2-y1)/(x2-x1)

m = (16 - 5)/(9 - 0) = 9/9 = 1

Using m = 1, y = 5, x = 0

then y = mx + b

5 = 1(0) + b

b = 5

so y = x + 5

Answer:

im not gonna lie i dont know a lot about this but i would put no for all because no matter which way you count its more than 5 units away if thats what is asking

Step-by-step explanation:

Answer:

n = 1/3

Step-by-step explanation:

Given equation,

→ (2/3) + n = 1

Now the value of n will be,

→ (2/3) + n = 1

→ n = 1 - (2/3)

→ n = (3/3) - (2/3)

→ n = (3 - 2)/3

→ [ n = 1/3 ]

Hence, the value of n is 1/3.

The equation of the tangent line to the curve `y = 2ex cos(x)` at the point (0,2) is given by `y = 2ex + 2`.

To find an equation of the tangent line to the curve at the given point (0,2) whose equation is given by `y = 2ex cos(x)`, we need to determine the derivative `y'` of `y = 2ex cos(x)` first. Using the product rule, we have;

`y = 2ex cos(x)`...let `u = 2ex` and `v = cos(x)`, then `u' = 2ex` and `v' = -sin(x)`.`y' = u'v + uv'` `= 2ex cos(x) - 2ex sin(x)` `= 2ex(cos(x) - sin(x))`

Therefore, the derivative of `y = 2ex cos(x)` is `y' = 2ex(cos(x) - sin(x))`.

The equation of the tangent line to the curve at the point (0,2) is obtained by using the point-slope formula, which is given by: `y - y1 = m(x - x1)`where `(x1,y1)` is the point of tangency, `m` is the slope of the tangent line.

Substituting the values of `m`, `x1` and `y1`, we obtain: `m = y' |(0,2)` `= 2e(1 - 0)` `= 2e`Using the point-slope formula with `(x1,y1) = (0,2)` and `m = 2e`, we have: `y - 2 = 2e(x - 0)` `y - 2 = 2ex` `y = 2ex + 2`

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It can be concluded that there is a significant positive correlation between the time it takes to complete a puzzle and the IQ scores of these participants.

To determine the correct decision about the null hypothesis test, we need to compare the calculated Pearson's correlation coefficient (r) of 0.31 to a critical value based on the sample size and level of significance.

Assuming a significance level of 0.05 (or alpha = 0.05) and a two-tailed test, we can use a t-distribution with degrees of freedom (df) equal to n-2, where n is the sample size. For a sample size of 97, df = 95.

Using a table or calculator, we can find the critical t-value that corresponds to a significance level of 0.05 and 95 degrees of freedom. The critical t-value is approximately 1.984.

Next, we can calculate the t-value for the observed correlation coefficient using the formula:

\(t = r * sqrt(n-2) / sqrt(1-r^2)\)

where r is the observed correlation coefficient and n is the sample size.

Plugging in the values, we get:

t = 0.31 * sqrt(97-2) / sqrt(1-0.31^2) = 3.23

The absolute value of the calculated t-value (3.23) is greater than the critical t-value (1.984), indicating that the correlation coefficient is statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no correlation between the time it takes to complete a puzzle and the IQ scores of the adult participants.

Therefore, we can conclude that there is a significant positive correlation between the time it takes to complete a puzzle and the IQ scores of these participants. However, we cannot make any causal claims based on this correlation alone, as there may be other variables that could explain the relationship.

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To find where the function f(x) = 3x^4 - 12x^3 - 108x^2 + 9 is increasing and decreasing, we need to determine the intervals for which the first derivative, f'(x), is positive or negative.

First, find the first derivative of f(x):
f'(x) = 12x^3 - 36x^2 - 216x

Now, to find the critical points, set f'(x) = 0 and solve for x:
12x^3 - 36x^2 - 216x = 0

Factor out the common factor, 12x:
12x(x^2 - 3x - 18) = 0

Solve the quadratic equation for x:
x^2 - 3x - 18 = 0
(x - 6)(x + 3) = 0

The critical points are x = 0, x = 6, and x = -3.

Now, test intervals around these critical points to determine where f'(x) is positive (increasing) or negative (decreasing).

Choose test points: x = -4, x = -2, x = 3, and x = 7.

f'(-4) = 12(-4)^3 - 36(-4)^2 - 216(-4) > 0 (positive, so increasing)

f'(-2) = 12(-2)^3 - 36(-2)^2 - 216(-2) < 0 (negative, so decreasing)

f'(3) = 12(3)^3 - 36(3)^2 - 216(3) > 0 (positive, so increasing)

f'(7) = 12(7)^3 - 36(7)^2 - 216(7) < 0 (negative, so decreasing)

So, the function is increasing on the intervals (-∞, -3) and (0, 6), and decreasing on the intervals (-3, 0) and (6, ∞).

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Answer:

f(x) = 0.5x + 15

Step-by-step explanation:

Here, we want to get the total charge

From the question;

we have a flat rate of $15

now, $0.5 per mile for x miles will be a charge of 0.5 * x = $0.5x

We now add this to the flat fee to get the total score

That will be;

f(x) = 15 + 0.5x

a. 2n² - 3n = θ(n²) (Both upper and lower bounds are n²).

b. n³ ≠ O(n²) (There is no upper bound).

To find the upper bound, lower bound, and tight bound ranges for the functions F(n) = 10n² + 4n + 2 and G(n) = n²/11, we need to determine their asymptotic behavior.

1. Upper Bound (Big O):

For F(n) = 10n² + 4n + 2, the highest-order term is 10n². Ignoring the lower-order terms and constants, we can say that F(n) is bounded above by O(n²). This means that there exists a constant c and a value n₀ such that F(n) ≤ cn² for all n ≥ n₀.

For G(n) = n²/11, the highest-order term is n². Ignoring the constant factor and lower-order terms, we can say that G(n) is also bounded above by O(n²).

2. Lower Bound (Big Omega):

For F(n) = 10n² + 4n + 2, the lowest-order term is 10n². Ignoring the higher-order terms and constants, we can say that F(n) is bounded below by Ω(n²). This means that there exists a constant c and a value n₀ such that F(n) ≥ cn² for all n ≥ n₀.

For G(n) = n²/11, the lowest-order term is n². Ignoring the constant factor and higher-order terms, we can say that G(n) is also bounded below by Ω(n²).

3. Tight Bound (Big Theta):

For F(n) = 10n² + 4n + 2, and G(n) = n^2/11, both functions have the same highest-order term of n². Therefore, we can say that F(n) and G(n) have the same tight bound range of Θ(n²). This means that there exist positive constants c₁, c₂, and a value n₀ such that c₁n² ≤ F(n) ≤ c₂n² for all n ≥ n₀.

In summary:

- F(n) = 10n² + 4n + 2 has an upper bound of O(n²), a lower bound of Ω(n²), and a tight bound of Θ(n²).

- G(n) = n²/11 has an upper bound of O(n²), a lower bound of Ω(n²), and a tight bound of Θ(n²).

Now let's move on to proving the given statements:

a. To prove that 2n² - 3n = θ(n²), we need to show both the upper bound and lower bound.

- Upper Bound (Big O):

For 2n² - 3n, the highest-order term is 2n². Ignoring the lower-order terms and constants, we can say that 2n² - 3n is bounded above by O(n²). This means there exists a constant c and a value n₀ such that 2n² - 3n ≤ cn² for all n ≥ n₀.

- Lower Bound (Big Omega):

For 2n² - 3n, the highest-order term is 2n². Ignoring the lower-order terms and constants, we can say that 2n² - 3n is bounded below by Ω(n²). This means there exists a constant c and a value n₀ such that 2n² - 3n ≥ cn² for all n ≥ n₀.

Since we have shown both the upper and lower bounds to be n², we can conclude that 2n² - 3n = θ(n²).

b. To prove that n³ ≠ O(n²), we need to show that there is no upper bound.

Assuming n³ = O(n²), this would mean that there exists a constant c and a value n₀ such that n³ ≤ cn² for all n ≥ n₀.

However, this statement is not true because as n approaches infinity, n³ grows faster than cn² for any constant c. Therefore, n³ is not bounded above by O(n²), and we can conclude that n³ ≠ O(n²).

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Complete Question:

To solve the problem we will calculate the amount of food consumed by Deon's dog in 2.5 weeks.

The new bag of food will last for 2.5 weeks.

Given to us

To know the amount of food consumed by Deon dog in 2.5 weeks, we will multiply the food consumed by Deon dog in 1-week by the Number of weeks for which food is been consumed.

Food consumed by Deon dog in 2.5 weeks

= Food consumed by Deon dog in 1-week x Number of weeks

= 62 cups of dog food x 2.5

= 155 cups of dog food

Thus, the food consumed by Deon's Dog is 155 cups.

As we can see the Dog will consume 155 cups of dog food in 2.5 weeks, therefore, the new bag of food will last for 2.5 weeks.

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The equation of the mirror line for the segment with endpoints (5, 4) and (-1, -1) is y= 5/6 x-1/6.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given coordinate points are (5, 4) and (-1, -1).

Put (5, 4) and (-1, -1) in slope m = (y₂-y₁)/(x₂-x₁), we get

m= (-1-4)/(-1-5)

m= -5/(-6)

m =5/6

Substitute m=5/6 and (x, y)=(5, 4) in y=mx+c, we get

4=5/6 (5)+c

c=4-25/6

c=-1/6

Substitute m=5/6 and c=-1/6 in y=mx+c, we get

y= 5/6 x-1/6

Therefore, the equation of the mirror line for the segment with endpoints (5, 4) and (-1, -1) is y= 5/6 x-1/6.

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Answer:

The answer is 2880 I might be wrong

Therefore, the dimensions of the largest area he can enclose are 749 yards by 1498 yards with an area of 1,121,502 square yards.

Let the length of the rectangular grazing land be x and the width be y. Then we know that the total amount of fencing used is given by:

2x + y = 2996

We want to maximize the area A of the grazing land, which is given by:

A = xy

We can solve the first equation for y:

y = 2996 - 2x

and substitute into the equation for A:

A = x(2996 - 2x)

Expanding the equation, we get:

A = 2996x - 2x^2

To find the maximum value of A, we take the derivative and set it equal to zero:

dA/dx = 2996 - 4x = 0

Solving for x, we get:

x = 749

Substituting this value back into the equation for y, we get:

y = 1498

Therefore, the dimensions of the largest area he can enclose are 749 yards by 1498 yards. The area is:

A = xy = 749 * 1498 = 1,121,502 square yards.

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