f (x) = 3x^2 - 7x - 32
What is the value of f(-4)?

Answer

what is?

STEP-BY-STEP-EXPLANATION

The correct option is the fourth one, the slope and y-intercept are different.

Here we have the linear equation:

3x - 5y = 4

We know that it is dilated by a scale factor of 5/3, so let's find the dilation.

We can rewrite the linear equation as:

-5y = 4 - 3x

y =  (3/5)x - 4/5

Now let's apply the dilation:

y = (5/3)*[ (3/5)x - 4/5]

y = x - 4/3

Then we can see that the slope and the y-intercept are different, the correct option is 4.

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The length of the actual car is 185 inches given that the scale of the model to the actual car is 1:10, and the model is 18 1/2 inches long.

Given that the scale of the model to the actual car is 1:10, and the model is 18 1/2 inches long, we can find the length of the actual car by multiplying the length of the model by the scale factor:

Length of actual car = Length of model x Scale factor

We can convert the length of the model from inches to the equivalent length in the scale using the following formula:

Length in scale = Length in real life ÷ Scale factor

Substituting the values:

Length in scale = 18.5 ÷ 1/10

= 185/10

= 18.5 x 10

= 185 inches

Therefore, the length of the actual car is 185 inches.

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Answer:

b. 1/6

c. 6^-1

d. 1/6^1

Step-by-step explanation:

Calculation:

Correct options:

Answer:

y=3(2)+5

Step-by-step explanation:

Formula: y = mx + b

m is your slope

x is your x

b is your y added onto

Answer:

Step-by-step explanation:

Total Hours = 30 h

Total Pay = $240

Work at movie theater = $9/h

Work at babysitting = $6/h

Tm = hrs work at movie theater

Tb = hrs work as babysitting

Total hours = Tm + Tb = 30

So,

Tm = 30 - Tb

Total pay = Tm * 9 + Tb * 6 = 240, substitute Tm

(30 -Tb) * 9 + Tb * 6 = 240, solve for Tb

270 - 9Tb + 6Tb = 240

270 - 3Tb = 240

3Tb = 270 - 240 = 30

Tb = 10

Tm = 30 - Tb = 30 - 10 = 20

Hours work at movie = 20 hrs

Hours work as babysitter = 10 hrs

The approximation for f(1.4) using Euler's method with two steps of equal size is -0.632.

Euler's method is a numerical method for approximating the solutions to differential equations. It works by approximating the derivative at each step and using it to estimate the next value of the function.

In this case, we are given the differential equation dy/dx = x-y-1 and the initial condition f(1)=-2. We want to find an approximation for f(1.4) using Euler's method with two steps of equal size, starting at x=1.

To use Euler's method, we first need to determine the step size, which is the distance between x-values at each step. Since we have two steps of equal size, the step size is (1.4-1)/2 = 0.2.

Next, we use the initial condition to find the first approximation:

f(1.2) ≈ f(1) + f'(1)*0.2

= -2 + (1 - (-2) - 1)*0.2

= -1.2

Now, we can use this approximation to find the second approximation:

f(1.4) ≈ f(1.2) + f'(1.2)*0.2

= -1.2 + (1.2 - (-1.2) - 1)*0.2

= -0.632

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Answer:

i think the endocytosis

Step-by-step explanation:

Given data:

The first equation is 2x+3y=-12.

The second equation is x+y=9.

The second equation can be written as,

y=9-x

Substitute the above value in second equation.

2x+3(9-x)=-12

2x+27-3x=-12

-x=-39

x=39

The value of y is,

39+y=9

y=-30.

Thus, the value of x is 39, and the value of y is -30.

The description that most accurate for a Zero-Based Budget is:

b. You put every dollar of your take-home pay into a budget category each month.

A zero-based budget is a budgeting method in which your total income minus your total expenses equals zero. This means that every dollar of your income is assigned a specific purpose, either to be saved or spent on specific expenses. The goal of this method is to ensure that you have accounted for all of your income and that you do not have any leftover funds that are not allocated to a specific purpose. In this sense, option b, "You put every dollar of your take-home pay into a budget category each month" is the most accurate description of a zero-based budget.

A zero-based budget can be applied to any source of income, whether it be a salary, freelance work, rental income, or any other type of income. The key is to allocate every dollar of that income to a specific purpose, such as savings, expenses, or investments, to ensure that all of the income is accounted for. This budgeting method can help individuals and households to better manage their finances by ensuring that they are not overspending and that they have a plan for all of their income.

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Answer:

(6,12)

Step-by-step explanation:

(Hopefully you can see the work if not then sorry)

Maintaining a balanced budget while influencing the output level of the economy is not necessarily macroeconomically neutral and requires careful consideration of the policy trade-offs involved.

The problem presents a scenario where governments aim to maintain a balanced budget while trying to influence the output level of the economy through changes in government spending (g) and taxes (t). To assess the macroeconomic neutrality of such policy changes, we use equation (3.8) to find the impact of a unit increase in g and t on the output level y.

(a) The impact of a unit increase in g on the output level y is given by the multiplier (1/1-c1), where c1 is the marginal propensity to consume. Therefore, an increase in g by one unit will increase output by the multiplier times the change in g.

(b) The impact of a unit increase in t on the output level y is given by the negative multiplier (-c1/1-c1). Therefore, an increase in t by one unit will decrease output by the negative multiplier times the change in t.

(c) The answers to (a) and (b) are different because an increase in g will increase aggregate demand, leading to a higher equilibrium level of output, while an increase in t will decrease disposable income and hence decrease consumption and aggregate demand, leading to a lower equilibrium level of output.

In the scenario where the government starts with a balanced budget, any increase in government spending will have to be financed through an increase in taxes or a reduction in government transfers. The impact of such policy changes on the output level will depend on the size of the multiplier and the extent to which the increase in taxes or reduction in transfers affects consumption and aggregate demand.

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For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.

Non occurrence patterns identifies the absence of events when detecting a pattern.

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The most appropriate level of measurement for the income range of attendees at a research conference, classified as upper, middle, and low levels, is ordinal.

Levels of measurement classify the nature and properties of data. In this case, the income range is categorized into upper, middle, and low levels.

Nominal measurement is the simplest level, where data is categorized into distinct categories without any specific order. However, the income range categories in this scenario have an inherent order or ranking. For example, "upper" is higher than "middle," and "middle" is higher than "low." Thus, nominal measurement is not suitable.

Ordinal measurement is appropriate when data can be ranked or ordered but lacks equal intervals or meaningful differences between categories. In this case, the income range categories can be ranked based on their position on the income spectrum. However, the difference between "upper" and "middle" may not be the same as the difference between "middle" and "low."

Ratio and interval measurements involve numerical values with equal intervals and a meaningful zero point, respectively. These measurements do not apply to the income range categories since they do not represent numerical values or possess equal intervals.

Therefore, the income range of attendees at the research conference is best classified as an ordinal level of measurement.

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Answer:

log[x⁵/(x-8)⁶]

Step-by-step explanation:

5log(x) - 6log(x-8)

log(x⁵) - log((x-8)⁶)

log[x⁵/(x-8)⁶]

Answer:

It costed $1200

Step-by-step explanation:

First Month Saved 1/3 of total cost

Second Month (1/3 of total cost) - 125

Third Month 525

525-125= 1/3 of total (If she saved the same amount the second month as the first month, then she's already saved 2/3 of the money)

400 = 1/3 of total cost

3X400=1200

Answer:

10 mi³

Step-by-step explanation:

The are of the base will be (4*3)/2, so 6.

Plug that in to the formula for B.

V = 1/3(6)5 and you should get 10 mi³

Hope this helps.

Answer:

Hello, have a great day.

Told to walk in first week = 5km

Told to walk in second week = 8km

Told to walk in third week = 11km

It is forming a pattern,

5km      8km      11km       ..........

     +3       +3        +3

5km      8km     11km     14km     17km     20km    23km     26km   29km     32km

    +3       +3        +3       +3        +3        +3        +3         +3      +3  

The patient has to walk 32km in the 10th week.

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Answer:

7 food orders in 21 minutes

Step-by-step explanation:

Well lets see. 15 food orders in 45 minutes. So, she can make 1 food order in 3 minutes. So times 7, she can make 7 food orders in 21 minutes.

(a) A monotonic transformation of a utility function refers to a transformation that preserves the relative ranking of utility levels but does not change the underlying preferences. It involves applying a strictly increasing function to the original utility function.

(b) The indifference curves for utility levels u(x1, x2) = 10, u(x1, x2) = 20, and u(x1, x2) = 30 can be drawn based on the utility function u1(x1, x2) = 6x1 + 9x2. These curves represent combinations of goods (x1, x2) that provide the same level of utility.

(c) Similarly, the indifference curves for utility levels u(x1, x2) = 10, u(x1, x2) = 20, and u(x1, x2) = 30 can be drawn based on the utility function u2(x1, x2) = 2x1 + 3x2.

(d) u1(x1, x2) is a monotonic transformation of u2(x1, x2) because it involves multiplying the utility function u2 by a positive constant. Both utility functions describe the same preferences as they represent different linear transformations of the same underlying preferences, resulting in parallel but equally informative indifference curves.

(a) A monotonic transformation of a utility function is a transformation that does not alter the preferences of an individual. It involves applying a strictly increasing function to the original utility function. This transformation preserves the ranking of utility levels, meaning that if one combination of goods gives higher utility than another in the original function, it will still give higher utility in the transformed function.

b) For the utility function u1(x1, x2) = 6x1 + 9x2, we can draw indifference curves for utility levels u(x1, x2) = 10, u(x1, x2) = 20, and u(x1, x2) = 30. These curves represent all the combinations of goods x1 and x2 that provide the same level of utility according to the utility function u1.

(c) Similarly, for the utility function u2(x1, x2) = 2x1 + 3x2, we can draw indifference curves for utility levels u(x1, x2) = 10, u(x1, x2) = 20, and u(x1, x2) = 30. These curves represent the combinations of goods x1 and x2 that provide the same level of utility according to the utility function u2.

(d) u1(x1, x2) is a monotonic transformation of u2(x1, x2) because it involves multiplying the utility function u2 by a positive constant. Both utility functions describe the same preferences as they represent different linear transformations of the same underlying preferences. The indifference curves for both utility functions are parallel but equally informative, meaning they represent the same ranking of utility levels. Therefore, u1(x1, x2) and u2(x1, x2) can describe the same preferences.

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Answer:

2/4

Step-by-step explanation:

The new method and the old method are illustrations of exponential functions.

(a) Old method week 0

The old method is given as:

\(\mathbf{g(x) = 65(1.1)^x}\)

At week 0, x = 0

So, we have:

\(\mathbf{g(0) = 65(1.1)^0= 65}\\\)

65 chocolates were produced using the old method in week 0

(b) New method week 0

At week 0, x = 0

From the graph

\(\mathbf{y = 60.282\ when\ x = 0}\)

60.281 chocolates were produced using the new method in week 0

(c) The positive difference between the methods

An exponential function is represented as:

\(\mathbf{y = ab^x}\)

Where: b represents rate

For the old method,

\(\mathbf{b =1.1}\)

For the new method, we have:

\(\mathbf{(x_1,y_1) = (0,60.282)}\)

\(\mathbf{(x_2,y_2) = (1,72.337)}\)

So, we have:

\(\mathbf{y = ab^x}\)

\(\mathbf{ab^0 = 60.282}\)

\(\mathbf{a = 60.282}\)

\(\mathbf{y = ab^x}\)

\(\mathbf{ab^1 = 72.337}\)

Substitute \(\mathbf{a = 60.282}\)

\(\mathbf{60.282 \times b=72.337}\)

Divide both sides by 60.282

\(\mathbf{ b=1.20}\)

So, the positive difference between both methods is their rate.

The difference in their rates is:

\(\mathbf{d = |b_2 - b_1|}\)

\(\mathbf{d = |1.20 - 1.1|}\)

\(\mathbf{d = 0.1}\)

Hence, the positive difference between both methods is 0.1

(d) Which made more initially

In (a), we have:

\(\mathbf{g(0) = 65}\)

In (b), we have:

\(\mathbf{y = 60.282}\)

These values represent the initial chocolate

Hence, the old method made more initially.

(e) New method week 3

At week 3, x = 3

From the graph

\(\mathbf{y = 104.167\ when\ x = 3}\)

104.167 chocolates were produced using the new method in week 3

(f) Old method week 3

The old method is given as:

\(\mathbf{g(x) = 65(1.1)^x}\)

At week 3, x = 3

So, we have:

\(\mathbf{g(3) = 65(1.1)^3= 86.515}\)

86.515 chocolates were produced using the old method in week 3

(f) Which made more initially

In (e), we have:

\(\mathbf{y = 104.167\ when\ x = 3}\)

In (f), we have:

\(\mathbf{g(3) = 86.515}\)

These values represent the amount of chocolate made in the week 3

Hence, the new method made more in week 3.

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Answer:

0.60.

Step-by-step explanation:

We divide the percent by 100.

60 / 100 = 0.60.

Answer:

4791.7

i believe its correct not 100%

Answer:

3^2 + 11^2 = 130

7^2 + 9^2 = 130

---

1^2 + 18^2 = 325

6^2 + 17^2 = 325

Step-by-step explanation:

We want to express 130 and 325 as the sum of two squares in two different ways.

Then, we want to find two integers a and b such that:

a^2 + b^2 = 130

There is not an analytical way to do this, we just need to try with different integers.

Let's start with 130.

So we start by defining a as a really small integer, for example 1, and try to find b.

1^2 + b^2 = 130

b^2 = 130 - 1

b^2 = √129 = 11.3

This is not an integer, so let's try with another value of a.

a = 2

2^2 + b^2 = 130

4 + b^2 = 130

b^2 = 130 - 4

b = √126 = 11.2

This can be discarded again.

Now let's try with a = 3

3^2 + b^2 = 130

9 + b^2 = 130

b^2 = 130 - 9

b = √121 = 11

Nice.

So we can express 130 as:

3^2 + 11^2 = 130

Now let's find another pair.

In the same way, we can see that for a = 7 we get:

7^2 + b^2 = 130

42 + b^2 = 130

b^2 = 130 - 49

b = √81 = 9

Then we can write:

7^2 + 9^2 = 130

Now for 325:

With the same reasoning than before, we want to find two integers such that:

a^2 + b^2 = 325

Then we start evaluating a by the smallest values:

a = 1

1^2 + b^2 = 325

b^2 = 325 - 1 = 324

b = √324 = 18

Then we can write 325 as:

1^2 + 18^2 = 325

Now to find the next pair we need to keep testing values for a, we will get for a = 6:

6^2 + b^2 = 325

36 + b^2 = 325

b^2 = 325 - 36 = 289

b = √289 = 17

Then we can write:

6^2 + 17^2 = 325.