How do you find the domain and range of a sequence?

Answer:

x < -7

Step-by-step explanation:

3(x-4)-2>5x

3x - 12 - 2 > 5x

3x - 14 > 5x

-2x > 14

x < -7

Answer: x<-7

Step-by-step explanation: 3(x-4)= 3x-12

3x-14>5x

5x-3x=2x

-14>2x

-14/2=-7

-7>x

The given expression 34(4h - 6) is equivalent to 4h + 6. To simplify  we distribute the 34 to each term inside the parentheses

To simplify the expression 34(4h - 6), we distribute the 34 to each term inside the parentheses. This means multiplying each term inside the parentheses by 4 and then multiplying by 3.

Distributing 4 to each term inside the parentheses gives us: 4 * 4h - 4 * 6 = 16h - 24.

Next, we multiply the result by 3: 3 * (16h - 24) = 48h - 72.

Therefore, expression 34(4h - 6) simplifies to 48h - 72.

Comparing this result to the answer choices:

a. 3h - (9/2) is not equivalent to 34(4h - 6).

b. 4h + (9/2) is not equivalent to 34(4h - 6).

c. 3h - 6 is not equivalent to 34(4h - 6).

d. 4h + 6 is equivalent to 34(4h - 6).

Therefore, the expression 34(4h - 6) is equivalent to 4h + 6, which is option d.

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Answer:

Step-by-step explanation:

Total weight of the barricade is 310 kg using 8 boxes of books

Each box of books weighs 30 kg

We need to determinethe weight of the table in order write the proper equation

Total wieght of the barricade = Table Weight + Book Weight

            solving for Table Weight       substract Book Weight from both sides

Total wieght of the barricade - Book Weight  = Table Weight

                   310 - 8(30)  =  Table Weight

                   310  - 240   = Table Weight

                                70  = Table Weight

Total wieght of the barricade = Table Weight + Book Weight

                        W = 70 + 30x               where x is the number of boxes

Answer:

2y=3x=-4

Step-by-step explanation:

grouping like terms

y+ly =4x-x=-4

2y=3x=-4

Answer:

v = 6

Step-by-step explanation:

Equation: 11.5v+70=139

The width of the rectangle in terms of A is A + 5

The area of a trapezoid can be calculated using the formula:

Area = (1/2) × height  × (sum of bases)

As the trapezoid and the rectangle have the same area and the same height, we can equate their areas:

Area of trapezoid = Area of rectangle

(1/2) ×  H ×  (A + A + 10) = H  ×  width of rectangle

(H/2)  ×  (2A + 10) = H  ×  width of rectangle

Dividing both sides by H:

(A + 5) = width of rectangle

Therefore, the width of the rectangle in terms of A is A + 5

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Answer:

The truck could drive 347.76 miles with 16.8 gal. of gas

1. I divided 229.77 by 11.1, then I multiplied that answer by 16.8.

HOPE THIS HELPS!

The cost of one rose bush is $10 and the cost of one pot of ivy is $10.

Let's assume the cost of one rose bush is represented by "R" and the cost of one pot of ivy is represented by "I".

According to the given information:

Jaidee spent $140 on 2 rose bushes and 12 pots of ivy:

2R + 12I = 140 ...(1)

Beth spent $120 on 6 rose bushes and 6 pots of ivy:

6R + 6I = 120 ...(2)

We now have a system of two equations with two variables. To solve this system, we can use either substitution or elimination method. Let's use the elimination method.

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of "R" in both equations equal:

6R + 36I = 420 ...(3)

12R + 12I = 240 ...(4)

Now, subtract equation (4) from equation (3):

(6R + 36I) - (12R + 12I) = 420 - 240

-6R + 24I = 180 ...(5)

Now we have a new equation (5) that relates "R" and "I".

Let's solve equations (5) and (2) together:

-6R + 24I = 180 ...(5)

6R + 6I = 120 ...(2)

Add equation (5) and equation (2):

(6R - 6R) + (24I + 6I) = 180 + 120

30I = 300

Divide both sides of the equation by 30:

I = 10

Now substitute the value of "I" into equation (2) to find the value of "R":

6R + 6(10) = 120

6R + 60 = 120

6R = 120 - 60

6R = 60

Divide both sides of the equation by 6:

R = 10

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Answer:

The answer is 19.8m

Step-by-step explanation:

- The height of the tree is BC.
- The man's eye level is at point A,

- The angle of elevation at A is 61 degrees.

- The distance of the man at A to the tree BC is 11 meters.

Using Trigonometry:
tan0=BC/AC
tan61 degrees= h/11
h=t 11 x tan61 degrees
h=19.8m

The height of the tree is 19.8 meters to the nearest tenth of a meter.

The steady-state solution of the heat conduction equation refers to the temperature distribution that remains constant over time. This occurs when the heat flow into a system is balanced by the heat flow out of the system.

To find the steady-state solution of the heat conduction equation, follow these steps:

1. Set up the heat conduction equation: The heat conduction equation describes how heat flows through a medium and is typically given by the formula:

  q = -k * A * dT/dx,

  where q represents the heat flow, k is the thermal conductivity of the material, A is the cross-sectional area through which heat flows, and dT/dx is the temperature gradient in the direction of heat flow.

2. Assume steady-state conditions: In the steady-state, the temperature does not change with time, which means dT/dt = 0.

3. Simplify the heat conduction equation: Since dT/dt = 0, the equation becomes:

  q = -k * A * dT/dx = 0.

4. Apply boundary conditions: Boundary conditions specify the temperature at certain points or surfaces. These conditions are essential to solve the equation. For example, you might be given the temperature at two ends of a rod or the temperature at the surface of an object.

5. Solve for the steady-state temperature distribution: Depending on the specific problem, you may need to solve the heat conduction equation analytically or numerically. Analytical solutions involve techniques like separation of variables or Fourier series expansion. Numerical methods, such as finite difference or finite element methods, can be used to approximate the solution.

It's important to note that the exact method for solving the heat conduction equation depends on the specific problem and the boundary conditions given. However, the general approach is to set up the heat conduction equation, assume steady-state conditions, simplify the equation, apply the boundary conditions, and solve for the steady-state temperature distribution.

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Daniel ran an average of 0.14 miles per minute, which means he ran 1 2/3 miles in 12 1/2 minutes.

Daniel completed 1 2/3 miles in 12 1/2 minutes, which means that he ran an average of 0.14 miles per minute. This rate of speed can be quickly calculated by taking the total distance he ran divided by the amount of time it took him to run it. In this case, 1 2/3 miles divided by 12 1/2 minutes equals 0.14 miles per minute. This means that in one minute, Daniel ran approximately 0.14 miles. This rate of speed is an average rate and may vary depending on the terrain, how much rest he took in between running, and how hard he pushed himself.

1 2/3 miles / 12 1/2 minutes = 0.14 miles per minute

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The covariance of X and Y is 13/10, correlation coefficient of X and Y is 1,

the Covariance at (3X, 5Y) is also 3/200 of the given continuous random varaible.

a) To find E(XY), we need to calculate the double integral of xy times the joint pdf over the region where the pdf is nonzero:

E(XY) = ∫∫ xy * f(x,y) dx dy

      = ∫0¹ ∫0^(1-x) 24xy * dx dy     (since x + y < 1, the limits of y are from 0 to 1-x)

      = ∫0¹ 12x(1-x)^2 dy

      = ∫0¹ (12x - 24x^2 + 12x^3) dy

      = 4/3 - 6/5 + 3/4

      = 1/5

Therefore, E(XY) = 1/5.

(b) The covariance of X and Y is given by:

Cov(X, Y) = E(XY) - E(X)E(Y)

We have already calculated E(XY) in part (a), so we just need to calculate E(X) and E(Y):

E(X) = ∫∫ x * f(x,y) dx dy

= ∫0¹ ∫0^(1-x) 24xy * x dx dy

= ∫0¹ 6x(1-x)^3 dx

= 1/2 - 1/5

= 3/10

Similarly, we can find that E(Y) = 3/10.

Therefore, Cov(X, Y) = E(XY) - E(X)E(Y) = 1/5 - (3/10)*(3/10) = 1/100.

(c) The correlation coefficient of X and Y is given by:

ρ(X, Y) = Cov(X, Y) / (σ(X)σ(Y))

where σ(X) and σ(Y) are the standard deviations of X and Y, respectively. To find σ(X) and σ(Y), we need to first find the variances of X and Y:

Var(X) = E(X^2) - [E(X)]^2

      = ∫∫ x^2 * f(x,y) dx dy - (3/10)^2

      = ∫0¹ ∫0^(1-x) 24xy * x^2 dx dy - 9/100

      = ∫0¹ 2x(1-x)^3 dx - 9/100

      = 1/18 - 1/40

      = 11/360

Similarly, we can find that Var(Y) = 11/360.

Therefore, σ(X) = sqrt(Var(X)) = sqrt(11/360), and σ(Y) = sqrt(Var(Y)) = sqrt(11/360).

Now, we can find ρ(X, Y) as follows:

ρ(X, Y) = Cov(X, Y) / (σ(X)σ(Y))

= (1/100) / (sqrt(11/360) * sqrt(11/360))

= 1

Therefore, the correlation coefficient of X and Y is 1.

(d) To find Cov(3X, 5Y), we can use the property that Cov(aX, bY) = ab Cov(X, Y) for any constants a and b:

Cov(3X, 5Y) = 3 * 5 * Cov(X, Y)

            = 15 * 1/100

            = 3/200

Therefore, Cov(3X, 5Y) = 3/200

e)we can find the covariance of X + 1 and Y - 2:

Cov(X+1, Y-2) = E[(X+1)(Y-2)] - E[X+1]E[Y-2]

Using the definition of expected value and the joint pdf, we have:

E[(X+1)(Y-2)] = ∫∫(x+1)(y-2) f(x,y) dx dy

             = ∫[0,1] ∫[0,1-x] (x+1)(y-2) 24xy dy dx

             = ∫[0,1] 24x ∫[0,1-x] (xy-2x-2y+2) dy dx

             = ∫[0,1] 24x [x(1-x)^2 - 2x(1-x) - 2(1-x)^2 + 2(1-x)] dx

             = 2/3

Similarly, we can find:

E[X+1] = E[X] + 1/2 = 1

E[Y-2] = E[Y] - 2/3 = 1/3

Therefore,

Cov(X+1, Y-2) = E[(X+1)(Y-2)] - E[X+1]E[Y-2] = 2/3 - 1*(1/3) = 1/3

f)To find the covariance of X + 1 and 5Y - 2, we can use the same formula as above and compute the required expected values:

E[(X+1)(5Y-2)] = ∫∫(x+1)(5y-2) f(x,y) dx dy

              = ∫[0,1] ∫[0,1-x] (5xy-2x+5y-2) 24xy dy dx

              = ∫[0,1] 24x ∫[0,1-x] (5xy-2x+5y-2) dy dx

              = 4/3

E[X+1] = 1

E[5Y-2] = 5E[Y] - 2/3 = 13/3

g)Cov(3X + 5, X) = E[(3X + 5)X] - E[3X + 5]E[X]

To find E[(3X + 5)X], we'll use the definition of expected value for continuous random variables:

E[(3X + 5)X] = ∫∫ (3x+5)x f(x,y) dy dx

       = ∫∫ (3x^2 + 5x) (24xy) dy dx from y=0 to y=1-x and x=0 to x=1

       = ∫ 0^1 ∫ 0^(1-x) (72x^2y + 120xy) dy dx

       = ∫ 0^1 36x^2(1-x)^2 + 60x(1-x)^3 dx

       = 6/5

Next, we need to find E[3X + 5]:

E[3X + 5] = 3E[X] + 5

To find E[X], we'll integrate the marginal pdf of X:

f_X(x) = ∫ (24xy) dy from y=0 to y=1-x = 12x(1-x) for 0<x<1

E[X] = ∫ x f_X(x) dx from x=0 to x=1

 = ∫ 0^1 x (12x(1-x)) dx

 = 1/2

Putting it all together:

Cov(3X + 5, X) = E[(3X + 5)X] - E[3X + 5]E[X]

           = 6/5 - (3(1/2) + 5)(1/2)

           = -2/5

Therefore, Cov(3X + 5, X) = -2/5.

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Answer:

\(n=1\)

Step-by-step explanation:

\(8n - 5 = -2n + 5\)

First, add 5 to both sides.

\(8n-5+5=-2n+5+5\\\)

\(8n=-2n+10\)

Then, add 2n to both sides.

\(8n+2n=-2n+10+2n\)

\(10n=10\)

Finally, divide both sides by 10.

\(\frac{10n}{10}=\frac{10}{10}\)

\(n=1\).

Answer:

\(n=1\)

Step-by-step explanation:

So we have the equation:

\(8n-5=-2n+5\)

First, add 2n to both sides. The right side cancels:

\(10n-5=5\)

Add 5 to both sides:

\(10n=10\)

Now, divide both sides by 7:

\(n=1\)

And we're done!

Answer:

13

Step-by-step explanation:

a. Population proportion: 6,232/12,164

b. Sample proportion: 157/400

c. Representativeness cannot be determined without comparing proportions.

a. The population proportion of people who moved to the suburb in the last five years can be calculated by dividing the number of people who moved to the suburb in the last five years by the total population: 6,232 / 12,164.

b. The sample proportion of people who moved to the suburb in the last five years can be calculated by dividing the number of people in the sample who moved to the suburb in the last five years by the sample size: 157 / 400.

c. To determine if the sample is representative of the population, we compare the sample proportion to the population proportion. If they are similar, it suggests that the sample is representative.

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the absolute maximum shear stress developed in the beam is (3wL)/(4ht).

To determine the absolute maximum shear stress developed in the beam, we need to find the maximum shear force and the corresponding location of that force. Then we can use the given formula for shear stress to calculate the absolute maximum shear stress.

Assuming that we have a simply supported beam with a distributed load of w per unit length, the maximum shear force occurs at the supports and is equal to wL/2, where L is the span of the beam.

The maximum bending moment occurs at the center of the span and is equal to wL²/8. The corresponding maximum shear stress occurs at the top and bottom surfaces of the beam at this location.

The moment of inertia of the beam cross-section is given by I = (b*h³)/12, where b is the width of the beam and h is the height.

The first moment of area of the beam cross-section about the neutral axis is given by Q = (b*h²)/8.

Using the given formula for shear stress, we have:

Shear stress = (VQ)/(I*t)

where V is the shear force, t is the thickness of the beam, and I and Q are as defined above.

Substituting the maximum values, we have:

Shear stress = ((wL/2)((bh²)/8))/((bh³)/12t)

Simplifying this expression, we get:

Shear stress = (3wL)/(4ht)

Therefore, the absolute maximum shear stress developed in the beam is (3wL)/(4ht).

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The absolute maximum shear stress developed in the beam can be determined by calculating the shear force and the first moment of area of the cross-section of the beam, and then using the equation Shear stress = (V * Q) / (l * t).

To determine the absolute maximum shear stress developed in the beam, we need to calculate the shear force and the first moment of area of the cross-section of the beam.

Step 1: Calculate the shear force (V) acting on the beam. The shear force can be obtained from the given equation:

V = (Shear stress) * (lt) / Q

Step 2: Calculate the first moment of area (Q) of the cross-section of the beam. The first moment of area can be calculated using the formula:

Q = ∫y * dA

Step 3: Determine the location where the shear force is maximum. This can be done by analyzing the loading conditions and the geometry of the beam.

Step 4: Once the maximum shear force is determined, substitute the values of V, Q, l, and t into the equation for shear stress:

Shear stress = V * Q / (l * t)

By following these steps, you can determine the absolute maximum shear stress developed in the beam.

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Answer:

It falls in the integer category. The attached picture is a chart if you want to specify a number in a category.

Hope this helps :)

The nth term of a sequence is given as

f(n) = 2 + (-3)(n-1)

To find the 10th term, Let n = 10

Substitute the value of n= 10 into the expression

f(10) = 2 + (-3) (10 - 1)

f(10) = 2 + (-3) (9)

f(10) = 2 + (-27)

F(10) = 2 - 27

f(10) = -25

The answer is -25

Answer:

D

Step-by-step explanation:

9514 1404 393

Answer:

  C.  Residuals aren't random; linear is not a good fit

Step-by-step explanation:

The attached graph shows the given points (black) and the best-fit line (red). The residuals are connected by the dashed red line. They are decidedly NOT random. It appears that an exponential fit would work better than this linear fit.

The residual values are not randomly dispersed around the horizontal axis, so a linear fit is not appropriate.

Answer: 1 tablespoon

Step-by-step explanation:

An adolescent is typically considered to be in the age range of 12 to 16 years. Hence, option B is correct.

This stage of development is characterized by physical, cognitive, and social changes as individuals transition from childhood to adulthood. It is important to note that the exact age range can vary depending on cultural and societal factors. However, in general, adolescence begins around the onset of puberty, which typically occurs between the ages of 10 and 14 for girls and between 12 and 16 for boys.

During this period, individuals experience significant physical growth, hormonal changes, and the development of secondary sexual characteristics.

Additionally, adolescents undergo cognitive changes, such as increased abstract thinking and reasoning abilities. Socially, they may seek more independence and explore their identity, forming new relationships and facing new challenges.

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Answer:

sdgsdgsdgsdgsdgsd

Step-by-step explanation:

gsdgsdgsdgsdgsd

The expression given is:

Two times a number, increased by 2

We can go step-by-step to write this expression as an algebraic expression.

[Let the unknown number be "x"]

First part is:

Two times a number

This means twice a number, or, twice the number "x", thus we can write:

Then we have:

Increase by 2

This means we add 2 to the expression we got earlier. We had "2x", now we add 2 to it, so it becomes:

Hence, the final algebraic expression will be:

Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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Answer:

23 =x

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

132 = x+109

132 -109 = x

23 =x

Answer:

x = 23°

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Let's solve for value of x,

→ x + 109° = 132°

→ x = 132° - 109°

→ [ x = 23° ]

Thus, the value of x is 23°.

Answer:

the combined percentage of key lime pies sold and pumpkin pies sold was less than 50%

The correct statement is:

E) The combined percentage of key lime pies sold and pumpkin pies sold was less than 50%

Data is referred to as a collection of information gathered by observations, measurements, research, or analysis. It may comprise facts, figures, numbers, names, or even general descriptions of things. Data can be organized in the form of graphs, charts, or tables for ease in our study. Data scientists help in analyzing the collected data through data mining.

For example, information gathered can be represented in the form of data as given below,

As, per the table

all the statements are not related to the table but except the statement

the combined percentage of key lime pies sold and pumpkin pies sold was less than 50%.

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Answer:

Based on the function, the growth rate is 4.5%

Step-by-step explanation:

In this question, we are given the exponential equation and we are told to deduce the growth rate.

Mathematically, we can rewrite the exponential equation as follows;

S(t) = 152(1.045)^t = 152(1 + 0.045)^t

What we see here is that we have successfully split the 1.045 to 1 + 0.045

Now, that value of 0.045 represents the growth rate.

This growth rate can be properly expressed if we make the fraction given as a percentage.

Thus the issue here is converting 0.045 to percentage

Mathematically, that would be;

0.045 = 4.5/100

This makes is 4.5%

So the growth rate we are looking for is 4.5%

Answer:

92%

Step-by-step explanation:

since i helped can i have brainlst please that would be greatly apericated

Answer:

85%

Percentage solution with steps:

Step 1: We make the assumption that 80 is 100% since it is our output value.

Step 2: We next represent the value we seek with x.

Step 3: From step 1, it follows that 100% = 80.

Step 4: In the same vein, x% = 68.

Step 5: This gives us a pair of simple equations:

100% = 80(1)

x% = 68(2)

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left-hand side) of both equations have the same unit (%); we have

100%/x% = 80/68

Step 7: Taking the inverse (or reciprocal) of both sides yields

x%/100% = 68/80

__>x = 85%

Therefore, 68 is 85% of 80.

200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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