if f(x)= -3-5 and g(x)= 4x-2, find (f-g)(x)

For a poll of randomly selected voters in a local election, the sample proportion of sample is equals to the 0.258. The margin of error for the 95% confidence level is equals to 0.0271.

We have a randomly selected sample of voters. Number of selected voters in a local election = 1000 so, Sample size, n

= 1000

Number of voters who in favor of fire department bond measures = 248 ( no. of success)

Sample proportion is calculated by following formula, \(\hat p = \frac{x}{n} \)

where, X -->the number of successes

\( \hat p = \frac{258}{1000}= 0.258\)

Now, confidence interval, CI = 95%

Level of significance = 1 - 0.95 = 0.05

Margin of error helps the which percentage points results will differ from the real population value. Formula for margin of error is written as \(E = z_{\frac{\alpha}{2}} \sqrt{ \frac{\hat p ( 1 - \hat p)}{n}}\), where

Using the normal distribution table, the value of z-score for 95% of confidence interval is 1.96. Substitute all known values in above formula, \(E = 1.96 \sqrt{ \frac{0.258 ( 1 - 0.258)}{1000}}\)

\(= 1.96 \sqrt{ 0.00019144}\)

= 0.0271

Hence, required value is 0.0271.

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Complete question:

in a poll of 1000, randomly selected voters in a local election, 248 voters were in favor of fire department bond measures.what is the sample proportion ?what is the margin of error for the 95% confidence level?ex: 0.123

Answer:

$11.25

Step-by-step explanation:

1.25 × 9 = 11.25

Answer:

$11.25

Step-by-step explanation:

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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6.29117647059

This is the answer

Answer: 6.29117647059

Step-by-step explanation:

divide the problem :)

Answer:

Slope: 2/3

Step-by-step explanation:

You have to first write the equation into slope-intercept form...

y = mx + b

So...

-2x + 3y = -6

becomes...

3y = 2x - 6

y = 2/3x - 2

Which means...

2/3 is the slope

Hope this help :)

Let me know if there are any mistakes!!

To prove angle abd and angle cbd are congruent using a proof by contradiction, the assumption statement that starts the proof is Angle abd and angle cbd are not congruent.

Proof by contradiction is a technique used in logic and mathematics to verify the truth or validity of a claim by demonstrating how presuming the proposition to be incorrect results in a contradiction.

A proof by contradiction first starts with the negation, or opposite of the hypothesis.

In context of the problem, the proof by contradiction will start by the opposite . Since we are to prove that angle abd and angle cbd are congruent, the opposite is Angle abd and angle cbd are not congruent.

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Looking at the function, there are two sections of the graph, one on the interval [-1, 1) and the other on the interval [1, ∞). On the first interval, the function corresponds to a quadratic function. The endpoints are (-1, 1) and (1, 1), so the function should be:

On the other hand, the second section of the graph is a horizontal parabola, so the function corresponds to a square root function. It passes through the points (1, 1), (4, 2), and (9, 3), so the function should be:

Then, the piecewise function is:

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Answer: look at the picture

Step-by-step explanation: Hope this help :D

The polynomial (8x³ + 12x) / 2x is equivalent to expression 4x² + 6. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (8x³ + 12x) / 2x

Simplify the expression, then we have

⇒ (8x³ + 12x) / 2x

⇒ 4x(2x² + 3) / 2x

⇒ 2 (2x² + 3)

⇒ 4x² + 6

The polynomial (8x³ + 12x) / 2x is equivalent to expression 4x² + 6. Then the correct option is A.

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The complete question is attached below.

Answer:

x ≥ 9

Step-by-step explanation:

Answer:

Search it up then you will get the answer

Step-by-step explanation:

Answer:

D.9

Step-by-step explanation:

Plug in 3 for x.

2^3=8

8+1=9

Answer:

1 feet

Step-by-step explanation:

15-14

Answer:

6

Step-by-step explanation:

We are given:

f(x)=4x-2

and are asked to find the answer when f(2)

We can see that the 2 replaces x in the original equation, so we are asked to find what the answer is when x=2

To start, replace x with 2:

f(2)=4(2)-2

multiply

f(2)=8-2

simplify by subtracting

f(2)=6

So, when f(2), the answer is 6.

Hope this helps! :)

Answer:

f(2)=6

Step-by-step explanation:

1) Since 2 is substituting the x, we are going to do the same for the expression 4x-2. 4(2)-2

2) We are going to simplify the equation using the distributive property and order of operations, you get 6. This means that f(2)=6.

Answer:

  173.82 cm²

Step-by-step explanation:

You want the area of a regular octagon, given its side length is 6 cm.

A regular n-gon can be divided into n congruent isosceles triangles, each with its a.pex at the center of the polygon. The a.pex angle will have a measure of 360°/n.

The central angle of one sector of a regular octagon is 360°/8 = 45°. That means the triangle interior angle at A or B will be ...

  ∠OAM = (180° -45°)/2

  ∠OAM = 67.5°

The apothem of a regular polygon is the distance from its center to the midpoint of one side. Here, it is the length of segment OM.

We know ∠OAM is 67.5°. The side OM of triangle OAM is related to the side AM by the tangent function:

  Tan = Opposite/Adjacent

  tan(67.5°) = OM/AM

Since M is the midpoint of the 6 cm length AB, the measure of AM = 3 cm. That lets us find OM:

  OM = AM·tan(67.5°) = (3 cm)tan(67.5°)

  OM ≈ 7.2426 cm

The area of the octagon will be 8 times the area of a sector triangle. This, ...

  A = 8(1/2sa) . . . . . . . . . . where s is the side length, and a is the apothem

  A = 4(6 cm)(7.2426 cm)

  A ≈ 173.82 cm²

__

Additional comment

Effectively, we have found a formula for the area of any regular n-gon using only the side length.

  a = s/2·tan(90° -180°/n)

  A = ns/2·a = (1/2)ns·(1/2)s·tan(90° -180°/n)

  A = ns²/(4·tan(180°/n))

For this octagon, the formula gives ...

  A = 8·(6 cm)²/(4·tan(22.5°)) ≈ 173.82 cm²

The formula A = (n/2)sa is often written A = 1/2Pa, where P is the perimeter (=ns).

You may notice that many regular polygon area problems give inconsistent values for the side length and apothem. Specifying one is sufficient for finding the area. Specifying numerical values for both is trouble.

Answer:

-4z

Step-by-step explanation:

Hi student! Let me help you out.

_____________________

Note that, -3z and -z are like terms. This means we can combine them right off the bat, which gives us \(\mathrm{-4z}\).

\(\mathrm{-3z-z=-4z}\). -4z is our final answer.

Hope that this helped you! have a good day ahead.

Best Wishes!

\(\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. AIm high. Dream big.}}}}}\bigstar\star\)

◈◈-Greetings!-◆◆

___________________

Answer:

-4z

Step-by-step explanation:

-3z-z

On combining like terms,

= -4z

Answer:

180% ; 5

Step-by-step explanation:

Purchase price per coat = 55

Sales price per coat = 99

% of purchase price is sales price :

X% * 55 = 99

(x / 100) * 55 = 99

0.01x * 55 = 99

0.55x = 99

x = 99 / 0.55

x = 180

180% of purchase price

B.)

180% * 45 = 81 per jacket

Number of jackets to sell to make atleast $390 in sales

$390 / $81 = 4.8

Hence, 5 jackets

There are many ways to find f and g, so the composition of those is  (f o g)(x) = 4/(x² + 9).

A function whose values are obtained from two given functions by first applying one to an independent variable and then using the result to apply the second, and whose domain is made up of those independent variable values for which the first function's result falls within the second function's domain.

Find f and g, so that                        

(f o g)(x)  =  4/x²+9                

Well, there is more than one possibility.                                                  

For instance, It can be:  f(x)  = 4/x  and  g(x) = x² + 9

and then you have                          

(f o g)(x)  =  f[ g(x) ]                    

(f o g)(x)  = 4/g(x)                      

(f o g)(x)  =  4/x²+9                                                      

Another possibility:   f(x)  =  4/x+9    and g(x) = x²

and for those, you get

(f o g)(x)  =  f[ g(x) ]              

(f o g)(x)  =   4/g(x)+9      

(f o g)(x)  =  4/x²+9                                                              

Since f and g can be found in a variety of ways, as you can see above, the composition of those is  (f o g)(x) = 4/(x² + 9).

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Answer:

hahah 0x

Step-by-step explanation:

Jordan is right. Walkden Reds scored 13 points in their 11th game.

Mean is a measure of central tendency that is used to determine the average of a set of numbers.

Mean = sum of numbers / total numbers

Sum of numbers = mean x total numbers

Sum of scores at the end of 11 games = mean x total number of games

33 x 11 = 363

Sum of scores at the end of 10 games = mean x total number of games

10 x (33 + 2)

10 x 35 = 350

Score in the 11th game = 363 - 350 = 13

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Answer:

7,200

Step-by-step explanation:

Let's start by calculating how many students the university accepts. The problem says they accept 60% of the students. 60% as a decimal is 0.6. To calculate 60% of something, you multiply .60 by whatever quantity. In this case, it would be the students.

Number of accepted students = \(.6 * 30000\) = 18,000

The university accepts 18,000 students.

Now, the next problem is that of those accepted students, we need to find out how many actually enroll. The problem says they accept 40% of the accepted students. Applying the same principle,

Number of enrolled students = \(.4 * 18000\) = 7,200

The number of students that actually enroll is 7,200.

Alternatively, \(.6 * 30000 * .4\) would give you the same result.

Combining the pieces together, we are asking for 60% of 30,000. Then getting 40% of that 60%.

The first sentence is "True", the second sentence is "True", the third sentence is "True" and fourth sentence is "True".

a.) True. The leftmost different element in the lexicographic ordering establishes the hierarchy. The third digit, where 1 comes before 3, is where 641253 and 641352 diverge in the provided permutations. Consequently, 641253 comes before 641352.

b.) True. The fifth digit, where 2 comes before 5, is where 314256 and 314265 diverge in the permutations given. Consequently, 314256 comes before 314265.

c.) True. Both of the given permutations begin with "D," however the second element differs in that it starts with "A" in the first permutation and "E" in the second. The permutation D A H B G E C F precedes the permutation D E B C F H G A since "A" comes before "E" in the standard alphabetical order.

d.) True. Both of the given permutations have the same second digit and both begin with "B". "F" in the first permutation and "G" in the second permutation make up the third differentiating element. The permutation B E F G A C H D comes before the permutation B E F G C A H D because "F" comes before "G" in the standard alphabetical order.

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Answer:

does that say 7.19 or 7-19

Step-by-step explanation:

Rapunzel can load 5 trucks in 10 minutes, given her rate of loading 22 trucks every 44 minutes.

Assuming that Rapunzel maintains a consistent pace of loading 22 trucks every 44 minutes, we can use a proportion to determine how many trucks she can load in 10 minutes.

First, we need to determine the rate at which Rapunzel loads trucks.

We can do this by dividing the number of trucks she loads by the time it takes her to load them:

22 trucks / 44 minutes = 0.5 trucks per minute

This means that Rapunzel loads an average of 0.5 trucks every minute.

Now, we can set up our proportion using this rate:

0.5 trucks/minute = x trucks/10 minutes

To solve for x, we can cross-multiply:

0.5 trucks/minute × 10 minutes = x trucks

5 trucks = x

The ratio of trucks loaded to time taken is 22 trucks per 44 minutes.

Divide both the number of trucks and minutes by their greatest common divisor (22) to get a simplified ratio:

22 trucks ÷ 22 = 1 truck

44 minutes ÷ 22 = 2 minutes

The simplified ratio is 1 truck per 2 minutes.

The simplified ratio to find the number of trucks loaded in 10 minutes.

Since Rapunzel can load 1 truck in 2 minutes, we will multiply both sides of the ratio by 5 to find out how many trucks she can load in 10 minutes:

1 truck × 5 = 5 trucks

2 minutes × 5 = 10 minutes

Therefore, if Rapunzel maintains her current rate of loading 22 trucks every 44 minutes, she would be able to load approximately 5 trucks in 10 minutes.

Rapunzel can load 5 trucks in 10 minutes.

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Riya earns $45 in commission for selling 15 newspaper ads at $50 each.

A commission is a charge or payment given to a person or group in exchange for a good or service. When selling goods or services on behalf of a corporation, sales representatives or agents are frequently compensated with commissions in the business world. For instance, a stockbroker may receive a fee for carrying out a trade on behalf of a customer, while a real estate agent may receive a commission depending on the sale price of a property they assist in selling.

Riya receives a 6% commission for selling newspaper ads, and if she sells 15 ads for $50 each, her total earnings can be calculated as follows:

Total earnings = Total sales x Commission rate

The total sales from selling 15 ads at $50 each are:

Total sales = 15 x $50 = $750

The commission rate is 6%, which can be written as 0.06 as a decimal.

Plugging these values into the formula, we get:

Total earnings = $750 x 0.06 = $45

Therefore, Riya earns $45 in commission for selling 15 newspaper ads at $50 each.

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The equation for the trigonometric graph given above is:

y = 4sin(2x + (π/2))

y = 4 cos 2x

It is to be noted that the domain value of θ  is displayed on the horizontal x-axis and the range value is depicted on the vertical y-axis in the graphs of trigonometric functions.

Note that

y = A Sin (Bx - C) + D

The vertical shift → D

Horizontal [Phase] shift → C/B

Wavelength [Period] →  (2/B) π

Amplitude → | A |

Vertical Shift → 0
Horizontal | Phase | Shift → C/B → [- (π/4)] → (-π/2/2)

Wavelength | Period | → (2/B)π → π → (2/2)π

Amplitude → 4

Hence, working the above further we get:

y = 4sin(2x + (π/2))

y = 4 cos 2x

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Answer(s):

\(\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = -4cos\:(2x \pm \pi) \\ y = 4cos\:2x\)

Step-by-step explanation:

\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

OR

\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = 4sin\:2x,\)in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{4}\:unit\)to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD \(\displaystyle \frac{\pi}{4}\:unit,\)which means the C-term will be negative, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.\)So, the sine graph of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).\)Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit \(\displaystyle [-1\frac{1}{4}\pi, 0],\)from there to \(\displaystyle [-\frac{\pi}{4}, 0],\)they are obviously \(\displaystyle \pi\:units\)apart, telling you that the period of the graph is \(\displaystyle \pi.\)Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\)in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

A ternary string is a string composed of characters 0, 1, and 2. The number of ternary strings that contain exactly n characters, each of which is one of three types, is 3^n.Exactly 5 0s, 5 1s, and 5 2s are required for the ternary string, which means that the total number of characters is 15.

Each of these characters can be one of three types (0, 1, or 2). As a result, the total number of possible strings is 3^15. This is equivalent to 14,348,907. We arrived at this conclusion by computing 3 to the fifteenth power.Explanation:When constructing a sequence of three symbols, the first symbol has three alternatives, the second symbol has three alternatives, and so on. There are n choices for each of the n characters, resulting in a total of 3^n possible sequences.Example 1:Let's assume we have to create 5-character sequences with three symbols: a, b, and c. There are 3*3*3*3*3 = 243 possible sequences since there are three choices for each symbol.Example 2:Let's assume we have to construct a 10-character sequence using three symbols: 0, 1, and 2. There are 3*3*3*3*3*3*3*3*3*3 = 59,049, a total of 59,049 possible 10-character sequences. We can perform the same calculation for 15-character strings using the same logic.

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Solving the equation r1(t) = r2(t) will give us the values of t at which the two vector-valued functions r1(t) and r2(t) have the same position. However, it does not guarantee that all the points where the graphs of these functions intersect will be captured.

There are a few reasons why solving the equation r1(t) = r2(t) may miss some intersection points:

Parametrization Differences: The two functions, r1(t) and r2(t), may have different parametrizations, meaning they cover their respective curves at different rates.

As a result, there might be some points on the curves where they intersect but have different parameter values.

Solving r1(t) = r2(t) would only give us the values of t that correspond to the overlapping points and may miss other points of intersection.

Multiple Intersection Points: The graphs of r1(t) and r2(t) can intersect at multiple points.

Solving the equation r1(t) = r2(t) would only provide us with the values of t corresponding to one particular intersection point. Other intersection points may occur at different values of t that are not captured by the equation.

Singular Points: There might be singular or discontinuous points on one or both of the curves that cannot be represented parametrically. These points could be missed when solving r1(t) = r2(t) because they do not have a well-defined t-value.

In summary, while solving the equation r1(t) = r2(t) can identify some intersection points, it may not account for all the points of intersection between the graphs of the vector-valued functions r1(t) and r2(t) due to differences in parametrization, multiple intersection points, or singular points.

Additional methods, such as graphical analysis or further calculations, may be necessary to identify all the points of intersection accurately.

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