Which values of a, b, and c correctly represent the answer in simplest form?
3
- 2
b
32
O a=38, b= 14, C = 1
O a=1,5=14, C= 38
O a=1,b=7.C= 19
O a= 19, b=7,C= 1

The utility functions in options a, b, c, and f are not risk-averse on the interval [a,b], while the utility functions in options d and e are risk-averse on the interval [a,b].

In economics and finance, risk aversion refers to a preference for less risky options over riskier ones. Utility functions are mathematical representations of an individual's preferences, and they help determine whether someone is risk-averse, risk-neutral, or risk-seeking. A risk-averse individual would have a concave utility function, indicating a decreasing marginal utility of wealth.

For options a, b, c, and f, the utility functions are and f(x) = -ln(x), g(x) = \(-e^(^-^x^)\), h(x) = \(-4x^2\) - 10x, respectively. These utility functions do not exhibit concavity, which means they are not risk-averse. Instead, they either show risk-seeking behavior (options a and b) or risk-neutrality (options c and f).

On the other hand, options d and e have utility functions f(x) = ln(x), g(x) = 1/(e^(2x)), h(x) = \(-x^2\) + 10,000x and f(x) = ln(-2x), g(x) = -1/(\(e^(^2^x^)\)), h(x) = \(x^2\) - 100,000x, respectively. These utility functions display concavity, indicating a decreasing marginal utility of wealth. Thus, options d and e can be considered risk-averse on the interval [a,b].

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If you want to make 1/2 the recipe, then \(1\frac{11}{16}\) tablespoon of sugar you need.

In the given question, a recipe calls for \(3\frac{3}{8}\) tablespoons of sugar.

If you want to make 1/2 the recipe, then we have to find how much sugar you need.

As given that;

1 recipe = \(3\frac{3}{8}\) tablespoons of sugar

Before solving the question, we convert the mixed fraction into simple fraction.

To convert in simple fraction we multiply 3 by 8 then we add 3 on the result of multiplication of 3 and 8.

1 recipe = 27/8 tablespoons of sugar

We have to find sugar need for making 1/2 recipe.

1/2 recipe = \(\frac{27}{8}\times\frac{1}{2}\) tablespoons of sugar

1/2 recipe = 27/16 tablespoons of sugar

1/2 recipe = \(1\frac{11}{16}\) tablespoons of sugar

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Answer:

please be more specific

Answer:

Step-by-step explanation:

complete the circle and place the segment where point Q on R, and P on the arc of circle

When you copy a line from one position to another, it means you want to recreate the original line in the new position.

The endpoints of a compass are:

The following steps would allow you to copy line segment PQ to endpoint R.

Using the above explanation to analyze the attached figure;

You still need to label the line as PQ, for the figure to be completely correct.

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Answer:

Step-by-step explanation:

h(1) = 0 ⇒

h'(1) = 4 ⇒ h(4) = 1 ⇒

Considering the equation (1) in the equation (2)

and

True, a data warehouse allows users to specify certain dimensions or characteristics.

In a data warehouse, dimensions represent the different aspects or characteristics by which data can be categorized or analyzed. These dimensions can include various attributes or variables that provide context and organize the data.

Users of a data warehouse can specify these dimensions based on their analytical needs and the nature of the data being stored.

For example, in a sales data warehouse, common dimensions may include product, customer, time, and location.

By specifying these dimensions, users can slice and dice the data based on different criteria and gain insights from various perspectives.

By defining dimensions, users can navigate through the data warehouse and perform multidimensional analysis using tools such as OLAP (Online Analytical Processing).

Dimensions provide a structure for organizing and querying data in a way that facilitates analysis and reporting.

In summary, a data warehouse allows users to specify dimensions or characteristics that help organize and analyze the data stored in the warehouse. These dimensions provide a framework for users to navigate and explore the data from different perspectives.

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Answer:

The answer is:f(x,y)=(2x,2y)

The slope of the graph of the function f(x) = 2x^4 - 4x^3 + 5x^2 - 14x at the point (1, -11) is 40.

To find the slope of the graph at a given point, we need to calculate the derivative of the function and substitute the x-coordinate of the point into the derivative. The derivative of \(f(x) = 2x^4 - 4x^3 + 5x^2 - 14x\) can be found by applying the power rule. Taking the derivative term by term, we get \(f'(x) = 8x^3 - 12x^2 + 10x - 14\).

Substituting x = 1 into the derivative, we find \(f'(1) = 8(1)^3 - 12(1)^2 + 10(1) - 14 = 8 - 12 + 10 - 14 = -8\). Therefore, the slope of the graph at the point (1, -11) is -8.

Note: It seems that there was a slight error in the question, as the slope mentioned in the question does not match the given function and point. The slope calculated using the provided function and point is -8, not 40.

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Answer:

\(10 \sqrt{3} \)

Step-by-step explanation:

\( \sqrt{48} + \sqrt{108} \: \: in \: \: \: form \: \: of \: \: k \sqrt{6} \\ \sqrt{48} + \sqrt{108} = \sqrt{(4 \times 4 \times 3)} + \sqrt{(9 \times 3 \times 4)} = \\ 4 \sqrt{3} + 6 \sqrt{3} = 10 \sqrt{3} \)

Answer:

1/3=2/6

Step-by-step explanation:

1*2=2

3*2=6

Answer: 1/3=2/6

Step-by-step explanation: the numerator (1) in the first fraction is half it is in the second (2). This means the denominator in the first question (unknown) will be half the second (6). Half of (6) is (3). Your answer is 3.

(i) The marginal propensity to consume (MPC) is 0.8.

(ii) The marginal propensity to save (MPS) is 0.2.

(iii) The level of consumption is $360.

(iv) The average propensity to consume (APC) is 0.9 or 90%.

(v) The level of savings is $40.

The given linear equation for consumption, C = $40 + 0.8Y, and the income (Y) is $400, let's calculate the following:

(i) The marginal propensity to consume (MPC):

The marginal propensity to consume represents the change in consumption resulting from a change in income. It is the coefficient of the income term in the consumption function.

MPC = ∆C / ∆Y = 0.8

(ii) The marginal propensity to save (MPS):

The marginal propensity to save represents the change in savings resulting from a change in income. It is equal to 1 minus the marginal propensity to consume.

MPS = 1 - MPC = 1 - 0.8 = 0.2

(iii) The level of consumption when income (Y) is $400:

Plug the given income value into the consumption function.

C = $40 + 0.8Y = $40 + 0.8 * $400 = $40 + $320 = $360

Therefore, the level of consumption when income is $400 is $360.

(iv) The average propensity to consume (APC):

The average propensity to consume represents the proportion of income that is spent on consumption. It is calculated by dividing consumption by income.

APC = C / Y = $360 / $400 = 0.9

Therefore, the average propensity to consume is 0.9 or 90%.

(v) The level of savings:

Savings (S) is the difference between income (Y) and consumption (C).

S = Y - C = $400 - $360 = $40

Therefore, the level of savings is $40.

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Answer: \(16x^2-102x+77\)

Step-by-step explanation:

1) distribute

\((-8x+7)(4x+2)\\-32x^2-16x+28x+14\\-32x^2+12x+14\)

2) distribute

\((-8x+7)(6x-9)\\-48x^2+72x+42x-63\\-48x^2+114x-63\)

3) solve

\((-32x^2+12x+14)-(-48x^2+114x-63)\\(-32x^2+12x+14)+(48x^2-114x+63)\\16x^2-102x+77\)

Answer:

C

Step-by-step explanation:

$101 times 6 is $606...

Answer:

90/5 = 18 mph

Step-by-step explanation:

(x - 3 ) (2x + 4) = 0

Either

x - 3 = 0

Therefore x = 3

Or.,

2x + 4 = 0

2x = - 4

x = - 4 /2

Therefore x = -2

Now the value of x is 3 or - 2.

Hope it will help :)♥

Answer:

x = 3   &  x = -2

Step-by-step explanation:

(x-3) = 0    so x = 3    

(2x+4) = 0          so 2x = -4     x = -2

The scalar projection of x onto y is 10, and the dot product of x and y is 240.

The scalar projection of x onto y is given by the formula:

proj_y x = |x| cos(θ),

where |x| is the length of x, cos(θ) is the cosine of the angle between x and y, and proj_y x is the scalar projection of x onto y.

So we have:

proj_y x = |x| cos(θ) = 18 (5/9) = 10.

The dot product of x and y is given by the formula:

x · y = |x| |y| cos(θ),

where |x| and |y| are the lengths of x and y, and cos(θ) is the cosine of the angle between x and y.

So we have:

x · y = |x| |y| cos(θ) = 18 × 24 × (5/9) = 240.

Therefore, the scalar projection of x onto y is 10, and the dot product of x and y is 240.

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Answer:

i dont ill tell u when im ready

Step-by-step explanation:

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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Fixed-Width is data format does each column start and end at the same place in every row.

What do statisticians mean by nominal data?

Nominal data have a quality?

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Answer:

C) 13

Step-by-step explanation:

f(x) = 5x -2

f(3) = 5(3) -2

f(3) = 15 - 2

f(3l) = 13

A recipe for flapjacks uses only syrup sugar butter and oats in the ratio 1:2:2:4. Using this recipe 250g of syrup are needed to make 12 flapjacks. The quantity of oats needed to make 18 of these flapjacks is 375g.

The recipe for flapjacks has a ratio of syrup to sugar to butter to oats of 1:2:2:4. This means that for every 1 unit of syrup, there are 2 units of sugar, 2 units of butter, and 4 units of oats.

We know that 250g of syrup are needed to make 12 flapjacks. To find out how much oats are needed to make 18 flapjacks, we can set up a proportion:

syrup: sugar: butter: oats = 1:2:2:4

250g:x = 12:18

To solve for x, we can cross-multiply and simplify:

250g * 18 = 12x

4500g = 12x

x = 375g

Therefore, we need 375g of oats to make 18 flapjacks using this recipe.

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Answer:

The third option (9+\(3\sqrt{7}\)-\(3\sqrt{7}\)-\(\sqrt{49}\))

Step-by-step explanation:

With FOIL, this can be expanded. (a+b)(a-b) is equal to a²+ab-ab-b² or a²-b².

In this case, all the answers have 4 terms, so we want the first option. This makes the equation 3²+(3×\(\sqrt{7}\))-(3×\(\sqrt{7}\))-(\(\sqrt{7}\))².

Solving these gives 9+\(3\sqrt{7}\)-\(3\sqrt{7}\)-7. This is the same as  9+\(3\sqrt{7}\)-\(3\sqrt{7}\)-\(\sqrt{49}\).

**This content involves multiplying with surds and expanding perfect squares, which you may wish to revise. I'm always happy to help!

The equivalent expression is (c) \(9 - 3\sqrt 7 + 3\sqrt 7 - \sqrt {49}\)

The difference of squares equation is given as:

\((a + b)(a - b) = a^2 -b^2\)

And the radical expression is given as:

\( (3+ \sqrt 7)(3- \sqrt7)\)

By comparing the above expression to \((a + b)(a - b) = a^2 -b^2\), we have:

\(a =3\)

\(b = \sqrt 7\)

Substitute these values in \((a + b)(a - b) = a^2 -b^2\)

\( (3+ \sqrt 7)(3- \sqrt7) = 3^2 - (\sqrt 7)^2\)

This gives

\( (3+ \sqrt 7)(3- \sqrt7) = 9 - \sqrt {49}\)

By complete expansion, we have:

\( (3+ \sqrt 7)(3- \sqrt7) = 9 - 3\sqrt 7 + 3\sqrt 7 - \sqrt {49}\)

Hence, the equivalent expression is (c)

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Use the limit definition to find the slope of the tangent line to the graph of f at the given point. f(x) = 14 − x2, (3, 5)

The slope of the tangent line to the graph of f at (3, 5) is -6.

The slope of the tangent line to the graph of f at (3, 5) can be found using the limit definition of the slope. The slope of the tangent line can be calculated as the limit of the average rate of change of the function f(x) between two points as the distance between the points approaches zero. The formula is given by: lim _(h → 0) [f(x + h) - f(x)] / h

where h is the change in x, which is the difference between the x-value of the point in question and the x-value of another point on the tangent line. The given function is f(x) = 14 - x². To find the slope of the tangent line at x = 3, we need to calculate the limit of the average rate of change of f(x) as x approaches 3.

Using the formula,

lim_(h → 0) [f(x + h) - f(x)] / h

= lim_(h → 0) [(14 - (x + h)²) - (14 - x²)] / h

= lim_(h → 0) [14 - x² - 2xh - h² - 14 + x²] / h

= lim_(h → 0) [-2xh - h²] / h

= lim_(h → 0) [-h(2x + h)] / h

= lim_(h → 0) [-2x - h] = -2x

When x = 3, the slope of the tangent line is -2(3) = -6.

Therefore, the slope of the tangent line to the graph of f at (3, 5) is -6.

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Answer:

5 kilometers per hour

Step-by-step explanation:

look at where the line meets a point. the first line is 1 hr and 5 kilometers. the second one would be 2 hrs and 10 kilometers.

hope this helps!

a. The alternative hypothesis (H1) specifies that is greater than 26, indicating a directed alternative, this is a one-tailed test.

b. The alternative hypothesis is one-sided and argues that > 26, hence the critical value is 1.645.

c. The value of the test statistic (z-score) is z ≈ 3.82.

d. We reject the null hypothesis (H0) because the test statistic (z = 3.82) is higher than the crucial value (1.645).

In this case, the p-value is the probability of observing a sample mean of 28 or greater, assuming the population mean is 26.

a. This is a one-tailed test because the alternative hypothesis (H1) states that μ is greater than 26, indicating a directional alternative.

b. The decision rule for a one-tailed test at a significance level of 0.05 is to reject the null hypothesis (H0) if the test statistic is greater than the critical value. In this case, the critical value is 1.645 because the alternative hypothesis is one-sided and states that μ > 26.

c. The value of the test statistic (z-score) can be calculated using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case:

x = 28

μ = 26

σ = 4

n = 34

Substituting the values into the formula:

z = (28 - 26) / (4 / √34) ≈ 3.82

d. Since the test statistic (z = 3.82) is greater than the critical value (1.645), we reject the null hypothesis (H0).

e-1. To calculate the p-value, we need to find the area under the standard normal distribution curve to the right of the test statistic (z = 3.82). We can use a standard normal distribution table or a calculator to find this area.

The p-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis.

e-2. Interpreting the p-value: The p-value represents the probability of obtaining a sample mean as extreme as the one observed (or more extreme) if the null hypothesis is true.

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performance is depicted as a function of arousal level, forming an inverted-U shaped curve.

The two arousal theories among the options provided are A) Drive and Inverted U Hypothesis.

Drive theory suggests that arousal is directly related to the level of physiological need or drive, where an increase in physiological need or drive leads to an increase in arousal level.

On the other hand, the Inverted U Hypothesis proposes that moderate levels of arousal lead to optimal performance, while too little or too much arousal may result in poor performance. Therefore, performance is depicted as a function of arousal level, forming an inverted-U shaped curve.

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Answer:

Step-by-step explanation:

a)

median= 25

interquartile range= 19

b)

On average The Braineys was the slowest at completing the test because they have a median time of 32 minutes whereas The Cleverites have a median time of 25 minutes.

30 hours of use by the Washington family sprinkler and 35 hours of use by the Bennett family sprinkler.

We can find how long was each sprinkler used by substitution method.

Let W = hours of use by the Washington family

65 - W = hours of use by the Bennett family

According to the question we get

15W + 40(65 -W) = 1850

15W + 2600 - 40W = 1850

-25W = -750

W = 30

Now, put the value of W in 65 - W to calculate the hours used by the Bennett family

65 - W = 65 - 30 = 35

Thus, the amount of time used for sprinklers by the Washington family and the Bennett family is 30 hours and 35 hours, respectively.

--The given question is incomplete, the complete question is

"The Washington family and the Bennett family each used their sprinklers last summer. The water output rate for the Washington family's sprinkler was 15L per hour. The water output rate for the Bennett family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850L. How long was each sprinkler used?"--

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Answer:

Approximately 13.9 units.

Step-by-step explanation:

First, note that ΔTVW is a right triangle.

Since we are given that ∠UTV is 112°, this means that ∠WTV is 68° because 180-112 is 68°.

Now that we know ∠WTV is 68°, we can use the basic trigonometric ratios to solve for VW. VW is the side opposite ∠WTV. We also know the hypotenuse. So, we would use sine. Recall that:

\(\sin(\theta)=opp/hyp\)

Plug in 68° for theta, VW for the opposite, and 15 for the hypotenuse:

\(\sin(68)=VW/15\\VW=15\sin(68)\\VW\approx13.9078\approx13.9\)