If f(x)=3x-1 and g(x)=x+2, find (f-g)(x)

Answer:

3 feet

Step-by-step explanation:

To begin, find the width of the first painting by dividing 32 by 4. You get 8 feet as the width. Since the second painting has a width of 8, divide 24 by 8 to get the length (area of a rectangle is length times width). You get that the length of the second painting is 3 feet.

Hopefully this helps- let me know if you have any questions!

Answer:

1) 150°

2) 30°

3) 50°

4) 70°

5) 100°

Answer:

Step-by-step explanation:

In the diagram shown, the measure of angle 1 is oppositely directed to angle 2 and oppositely directed angles are equal.

Hence <1 = <3

Given < 1 = 3x-1 and <3 = 2x+9

Hence 3x-1 =  2x+9

collect like terms

3x-2x = 9+1

x = 10°

Since <1 = 3x-1

on substituting x = 10

<1 = 3(10)-1

<1 = 30-1

<1 = 29°

<1+<2 = 180 (angle on a straight line)

29+<2 = 180

<2 = 180-29

<2 = 151°

Similarly, on substituting x = 10 into <3

<3 = 2x+9

<3 = 2(10)+9

<3 = 20+9

<3 = 29°

<3+<4 = 180 (angle on a straight line)

29+<4 = 180

<4 = 180-29

<4 = 151°

Answer:

keeping it simple answers are 29 and 151 now thats simple

Step-by-step explanation:

Part A: For the method of buying new bulbs each year: new_bulbs(year): return 50*year + 6

Part B: we expect to have 506 plants if we buy new bulbs each year and 6144 plants if we divide existing bulbs after 10 years.

Part C: For the method of buying new bulbs each year: new_bulbs(5) = 256 new_bulbs(15) = 756

Part A:

Let's define two functions to model the expected number of plants for each year:

For the method of buying new bulbs each year:

new_bulbs(year):

   return 50*year + 6

For the method of dividing existing bulbs:

divide_bulbs(year):

   return 6*(2**year)

Part B:

To find the expected number of plants in 10 years for each method, we simply need to evaluate the functions at year = 10:

For the method of buying new bulbs each year:

new_bulbs(10) = 506

For the method of dividing existing bulbs:

divide_bulbs(10) = 6144

Therefore, we expect to have 506 plants if we buy new bulbs each year and 6144 plants if we divide existing bulbs after 10 years.

Part C:

To compare the expected number of plants in five years to the expected number of plants in 15 years, we can evaluate the functions at year = 5 and year = 15:

For the method of buying new bulbs each year:

new_bulbs(5) = 256

new_bulbs(15) = 756

For the method of dividing existing bulbs:

divide_bulbs(5) = 96

divide_bulbs(15) = 32768

We can see that the expected number of plants for both methods increases significantly between 5 and 15 years, but the method of dividing existing bulbs shows a much greater increase. This is because each year, the gardener can double the number of plants by dividing the existing bulbs. In contrast, the number of plants obtained by buying new bulbs increases linearly.

These patterns could affect the method the gardener decides to use depending on their goals and resources. If the gardener wants to have a larger number of plants in the short term (i.e., within five years), buying new bulbs each year may be a better option. However, if the gardener wants to have a larger number of plants in the long term (i.e., beyond five years), dividing existing bulbs may be more efficient and cost-effective. If the gardener has limited resources, dividing existing bulbs may be a more sustainable option as it allows them to multiply their existing plants without having to buy new bulbs every year.

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Complete question is in the image attached below

Hi there!

a. A stratified sample can be used by dividing the tenants into two groups: those who have children and those who do not have children. Then, a Sample Random Sample FROM EACH stratum can be conducted for a total of 16 tenants surveyed.

b. Using a cluster sample in this situation could introduce undercoverage or selection bias if there is a distinction between those on some floors and those on others. For example, tenants on lower floors might be more opposed to a playground  (ex: noise, crowd, etc.) in comparison to those on higher floors.

Here , we are going to use Trigonometric ratios.

In given right angled ∆ ;

\({:\implies \quad \sf \dfrac{x}{18}=\sin (60^{\circ}) \quad \bigg\{ \because \sin (\theta)=\dfrac{P}{H}\bigg\}}\)

\({:\implies \quad \sf x=\dfrac{18\sqrt{3}}{2} \quad \bigg\{\because \sin (60^{\circ})=\dfrac{\sqrt{3}}{2}\bigg\}}\)

\({:\implies \quad \bf \therefore \quad x=9\sqrt{3} \: units}\)

Also;

\({:\implies \quad \sf \dfrac{y}{18}=\cos (60^{\circ}) \quad \bigg\{ \because \cos (\theta)=\dfrac{B}{H}\bigg\}}\)

\({:\implies \quad \sf x=\dfrac{18}{2} \quad \bigg\{\because \cos (60^{\circ})=\dfrac{1}{2}\bigg\}}\)

\({:\implies \quad \bf \therefore \quad y=9 \: units}\)

Hence , The required values for x and y are 9√3 and 9 units

Answer:

Point D is the solution to the system of equations.

Step-by-step explanation:

When asked for a solution involving 2 equations, the goal is to find a point (x,y) that would be a solution to both equations.  Any point on a line that is defined by an equation is a solution to that equation.  For an equation of y = 2x + 2, possible solutions are (1,4), (2,6), (5,12) etc.  These points all lie on the line formed by that equation.  There are an infinite number of possible solutions.  If a second eqaution is added, there is now a constraint on the possible answers.  The goal is to find a point that satisfies both equations.

If a seond equation of y = 1x + 3 were matced with y=2x+2, both are straight lines, but with different slopes.  So they will intersect at some point.  One may either solve mathematically using substitution, or by graphing, as was done here.  

Matematically:

y = 2x + 2

y = 1x + 3

Rearrange either equation to isolate a variable, x or y.  These are already isolated (since I made them up) so go to the next step of substituting one expression of y into the other:

y = 1x + 3

2x + 2 = 1x + 3

x = 1

Now use this value of x to find y:

y = 2x + 2

y = 2*(1) + 2

y = 4

The point these two lines intersect is (1,4) and is the "solution" to this series of equations.

See the attached graph.

Given:

The given vector is w.

Required:

We need to draw 3w.

Explanation:

Use the Pythagorean theorem to find the magnitude AB.

Let the origin be (0,0).

Point A is (0,4) and point B is (3,0).

The magnitude of AB is (3-0,0-4)

Multiply the equation by 3 to find 3w.

Consider any point on the graph and take it as the origin (0,0) and mark (9,-12) and joint them as follows.

Final answer:

Answer:

175 cm³

Step-by-step explanation:

Volume = área * thick

Volume = 35cm² * 5cn

Volume = 175 cm³

Answer:

7cm

Step-by-step explanation:

Area = 35cm²

Length= 5cm

Width=?

A=L×B

B=A/L

B=35/5

B=7cm

Answer:

The random process described is a symmetrical random walk.

A symmetrical random walk is a mathematical model that represents a series of steps taken in either a forward (+1) or backward (-1) direction, each with equal probability. Starting from point zero, the process involves taking a certain number of steps. The outcome at each step is independent of previous steps, making it a stochastic process. The key characteristic of a symmetrical random walk is that, on average, the process remains centered around its starting point. This means that over a large number of steps, the expected displacement from the starting point approaches zero.

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a. The radius of the circle O is 8 cm. 

c. The circle has an area of 213.66 square centimeters. 

e. AB's arc length equals 60 degrees 

f. ACE has arc measure of 240 degree. 

g. the arc length is 8.38 cm

h. area of the sector AOB is 33.51 cm²

a. The radius of the circle is solved using the properties of a regular hexagon

The radius is 8 cm since the base of one of the equilateral triangles is the radius.

b. Area of circle O

= 3.142 * 8^2

= 213.66 squared cm

e. measure of arc AB

The center angle that creates the intercepted arc is what is known as the arc measure, which is measured in degrees.

= 60 degrees

f. measure of arc ACE

= arc AB + arc BC + arc CD + arc DE

= 60 + 60 + 60 + 60

= 240 degrees

g. length of arc AB

= 60/360 * 2 * 3.142 * 8

= 8.38 cm

h. area of the sector AOB

= 60/360 * 3.142 * 8²

= 33.51 cm²

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Answer:

Y < 3x+2

Step-by-step explanation:

Alright so if you ever get stuck on something like this, Go on demos and put in (0,2) and then add in (-3,-7) and then add in the other answers to see if they match.

So your answer is:

y>3x+2

In order for a sample of the entire population to be considered representative in public opinion polls, it must correctly and fairly reflect the views of the entire population.

Public opinion surveys are used to collect data and information on the opinions and views of people in a given population. For the results of a survey to be valid and reliable, the sample of people chosen for the survey must be representative of the entire population. This means that the views of those in the sample must accurately and proportionately reflect the views of the whole population.

Public opinion surveys are designed to measure the opinions and views of people in a given population. To ensure the results of the survey are accurate and reliable, the sample of people chosen for the survey must be representative of the entire population. This means that the views of those in the sample must accurately and proportionately reflect the views of the whole population. It is not necessary for the sample to exceed 50% of the targeted population, nor does it need to be based on all registered voters in the population. Therefore, option d. is the correct answer, which states that the sample must be representative in that the views of those in the sample must accurately and proportionately reflect the views of the whole population.

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Answer:

Quadrant II

Step-by-step explanation:

Answer:

46?

Step-by-step explanation:

23*2=46

Answer:

37.31 cm

Step-by-step explanation:

∡ AB = 180 - 148 = 32° = ∡ DE

∡ CD = 360 - ∡ AE - ∡ AB - ∡ BC - ∡ DE = 360 - 148 - 32 - 87 - 32 =61°

∡ CE = 61 + 32 = 93°

arc length = 2\(\pi\)r \(\frac{angle}{360}\) = 2×3.14×23×\(\frac{93}{360}\\\) = 37.31 cm

Answer: -13

Step-by-step explanation:

\(\frac{M(3)+M(2)}{2} =\frac{[-2(3)^{2}] +[-2(2)^{2}]}{2}=\frac{(-2)(9)+(-2)(4)}{2}=\frac{-18-8}{2}=\frac{-26}{2}=-13\)

The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

What is a normal distribution?

A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.

It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.

It is also known as probability distribution curve.

The normal distribution has two parameters:

What is the shape of the normal distribution?

The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.

Hence, the shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

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Answer:

2:5  

12:30

Step-by-step explanation:

If the algorithm has a constant number of steps independent of the input size, s(n) remains the same when n is doubled.

Then the effect on the number of steps required, denoted as s(n), when the number of items being processed (n) is doubled will depend on the specific algorithm and its complexity.

Here are a few possibilities:

1. Constant Time Complexity (O(1)): If the algorithm has a constant time complexity, it means that the number of steps required remains the same, regardless of the input size. In this case, doubling n would not have any impact on s(n).

2. Linear Time Complexity (O(n)): If the algorithm has a linear time complexity, it means that the number of steps required is directly proportional to the input size. Doubling n would approximately double the number of steps as well. Thus, s(n) would increase in a linear manner.

3. Quadratic Time Complexity (O(n^2)): If the algorithm has a quadratic time complexity, it means that the number of steps required grows quadratically with the input size. When n is doubled, the number of steps would be approximately four times the original amount. Thus, s(n) would increase significantly.

4. Logarithmic Time Complexity (O(log n)): If the algorithm has logarithmic time complexity, doubling n would not have a substantial impact on the number of steps required. The increase in s(n) would be relatively small compared to the increase in n.

These are just a few examples, and there are various other complexities that algorithms can exhibit.

Each algorithm has its own time complexity, which determines how the number of steps required changes as the input size is doubled.

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The line tangent to the curve defined by x = 4cos(t), y = 4sin(t) at t = -π/4 is y = -x - 2√2, and the value of d²y/dx² at that point is -1.

To find the equation of the tangent line, we need to determine the slope of the curve at the given point.

We can calculate the derivative of y with respect to x using the chain rule: dy/dx = (dy/dt) / (dx/dt). For x = 4cos(t) and y = 4sin(t), we have dx/dt = -4sin(t) and dy/dt = 4cos(t). At t = -π/4, dx/dt = -4/√2 and dy/dt = 4/√2. Therefore, the slope of the tangent line is dy/dx = (4/√2) / (-4/√2) = -1.

Using the point-slope form of a line, we obtain y - 4sin(-π/4) = -1(x - 4cos(-π/4)), which simplifies to y = -x - 2√2. The second derivative d²y/dx² represents the curvature of the curve. At the given point, d²y/dx² = -1, indicating a concave shape.


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Answer:

y=5/3x

Step-by-step explanation:

since the line crosses the y intercept at 0, nothing needs to be there. The 5/3 is from rise/run, so 5 up and 3 right

Answer:

a. y = 5/3x

Step-by-step explanation:

Since the line passes through the origin, there is no y-intercept so we can eliminate B and D. Now let's find two points on the graph;

(-3, -5) and (0, 0)

Find the slope using the formula [ y2-y1/x2-x1 ]

0-(-5)/0-(-3)

5/3

Input this into the slope-intercept form expression and we have our answer.

y = 5/3x

Best of Luck!

Explanation

Step 1

let x represents the year

let y represents the hours of electricity generated ( in millons)

then, we have two coordinates of the function

Using PEMDAS

We must first clear P which stands for Parentheses

The values in the parentheses are (12.9 -3.1)

so the first and right option is option c subtract 3.1 from 12.9

Since  

3

x

2

a

,

3

x

a

2

contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.

Steps to find the GCF for  

3

x

2

a

,

3

x

a

2

:

1. Find the GCF for the numerical part  

3

,

3

2. Find the GCF for the variable part  

x

2

,

a

1

,

x

1

,

a

2

3. Multiply the values together

Find the common factors for the numerical part:

3

,

3

The factors for  

3

are  

1

,

3

.

Tap for more steps...

1

,

3

The factors for  

3

are  

1

,

3

.

Tap for more steps...

1

,

3

List all the factors for  

3

,

3

to find the common factors.

3

:  

1

,

3

3

:  

1

,

3

The common factors for  

3

,

3

are  

1

,

3

.

1

,

3

The GCF for the numerical part is  

3

.

GCF

Numerical

=

3

Next, find the common factors for the variable part:

x

2

,

a

,

x

,

a

2

The factors for  

x

2

are  

x

⋅

x

.

x

⋅

x

The factor for  

a

1

is  

a

itself.

a

The factor for  

x

1

is  

x

itself.

x

The factors for  

a

2

are  

a

⋅

a

.

a

⋅

a

List all the factors for  

x

2

,

a

1

,

x

1

,

a

2

to find the common factors.

x

2

=

x

⋅

x

a

1

=

a

x

1

=

x

a

2

=

a

⋅

a

The common factors for the variables  

x

2

,

a

1

,

x

1

,

a

2

are  

x

⋅

a

.

x

⋅

a

The GCF for the variable part is  

x

a

.

GCF

Variable

=

x

a

Multiply the GCF of the numerical part  

3

and the GCF of the variable part  

x

a

.

3

x

a

Answer: 3xa

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor

The margin of error associated with the 95% confidence interval for the population mean volume is: D. 5.62.

To calculate the 95% confidence interval for the population mean volume, we can use the formula:

CI = x ± (t * (s/√n))

Where CI represents the confidence interval, x is the sample mean, t is the t-score associated with the desired confidence level (95%), s is the sample standard deviation, and n is the sample size.

In this case, x = 64 cc, s = 12 cc, and n = 20 orangutans. We need to find the t-score for a 95% confidence interval with 19 degrees of freedom (n-1). Using a t-table, we find that the t-score is approximately 2.093.

Now we can calculate the margin of error:

Margin of Error = t * (s/√n) = 2.093 * (12/√20) ≈ 5.62

Therefore, the margin of error associated with the 95% confidence interval for the population mean volume is: D. 5.62.

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Answer:

1134.1 [cm²]

Step-by-step explanation:

A=πr2

Circle area = π * r² = π * 361 [cm²] ≈ 1134.1 [cm²]

π ≈ 3.14159265 ≈ 3.14

d = r * 2 = 19 [cm] * 2 = 38 [cm]

It is most important to have a random sample in inferential statistics, particularly in making statistical inferences about a population based on the sample data.

Random sampling is a critical component of inferential statistics because it helps to ensure that the sample is representative of the population. When a sample is randomly selected, each member of the population has an equal chance of being included in the sample, which reduces the risk of bias in the results. Without a random sample, the results of statistical analyses may not be accurate or generalizable to the population, and the conclusions drawn from the data may be flawed or misleading.

Therefore, random sampling is crucial in making valid statistical inferences about a population.

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The true statements about the function \(g(x) = x^2 - 6x + 9\) are that it is a quadratic function, it opens upwards, and it has a minimum point.

To determine the true statements about the function \(g(x) = x^2 - 6x + 9,\)we can analyze its properties and characteristics.

The function is a quadratic function: True.

The expression\(g(x) = x^2 - 6x + 9\) represents a quadratic function because it has a degree of 2.

The function opens upwards: True.

Since the coefficient of \(x^2\) is positive (1), the parabola opens upwards.

The vertex of the parabola is at the minimum point: True.

The vertex of a quadratic function in the form \(ax^2 + bx + c\)  is given by the formula x = -b/2a.

In this case, the vertex occurs at x = -(-6)/(2\(\times\)1) = 3.

Substituting x = 3 into the function, we find g(3) = 3^2 - 6(3) + 9 = 0. Therefore, the vertex is at (3, 0), which represents the minimum point of the parabola.

The parabola intersects the x-axis at two distinct points: True. Since the coefficient of \(x^2\) is positive, the parabola opens upwards and intersects the x-axis at two distinct points.

The function has a maximum value: False.

Since the parabola opens upwards, the vertex represents the minimum point, not the maximum.

The function is always increasing: False.

The function is not always increasing since it is a quadratic function. It increases to the left of the vertex and decreases to the right of the vertex.

In summary, the true statements about the function \(g(x) = x^2 - 6x + 9\) are:

The function is a quadratic function.

The function opens upwards.

The vertex of the parabola is at the minimum point.

The parabola intersects the x-axis at two distinct points.

The function is not always increasing.

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Answer:

the answer is 5 here you go

Answer:

56%, 4/5, 1.07, 5/4

Step-by-step explanation:

5/4=1.25

56%=0.56

1.07

4/5=0.8

so the order is

56%, 4/5, 1.07, 5/4