Find a power series representation for the function

Answer:

2^n

Step-by-step explanation:

So whenever you flip a coin, you can see it as 2 nodes branching off of each existing node. so for example when you flip a coin once you're going to have 2 sequences initially H and T, now when you flip a coin again for each of those 2 sequences 2 are going to branch off of that, making the total sequences 4, and the next flip 2 sequences are going to branch off each of the 4 sequences and so on. this can generally be described as: 2^n

I attached an image describing this a bit better but the bottom line is that for each 'end node'/sequence you're going to have 2 branch off of it, thus for each coin flip the number of sequences multiplies by 2

Answer:

2^n

Step-by-step explanation:

dont worry bout it ur welcome

The order that will result in a final output of -31 when the first input is 0 is as follows; Third → Second → Fourth → First

First gives;

y = -2·x + 34 = 18

Second gives;

y = -x/3 - 10 = -38/3

Third gives;

= -24

Fourth gives;

y = (x - 2)² = 36

We have after several iterations;

Third gives,

= -24

Next we input into the second to get,

y = -(-24)/3 - 10 = 24/3 - 10 = 8 - 10 = -2

Next we input into the fourth to get,

y = ((-2) - 2)² =  (-4)² = 16

Next we input into the first to get,

y = -2×16 + 34 = -32 + 34 = 2

Which gives the order as follows;

Third → Second → Fourth → First

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The maximum value of c=4x+2y subject to the constraints is 14

The objective function is given as:

c = 4x+2y

The constraints are given as:

x≥0 y≥0

2x+2y≤10

3x+y≤9

Rewrite 2x+2y≤10 and 3x+y≤9 as equations

2x+2y = 10

3x+y = 9

Divide 2x+2y = 10  through by 2

x+y = 5

Subtract x+y = 5 from 3x+y = 9

3x - x + y - y = 9 - 5

Evaluate the difference

2x = 4

Divide by 2

x = 2

Substitute x = 2 in x+y = 5

2+y = 5

Solve for y

y = 3

So, we have

(x, y) = (2, 3)

Substitute (x, y) = (2, 3) in c = 4x+2y

c = 4 * 2 + 2 * 3

Evaluate

c = 14

Hence, the maximum value of c=4x+2y subject to the constraints is 14

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Answer:

See the attached picture.

Step-by-step explanation:

The simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)

The expression is given as:

(2x+1)/(x²-3)

The above expression is a fraction and the numerator has 2 terms

For a fraction

A + B)/x

The fraction can be split as

A/x + B/x

Using the above as a guide, we have:

(2x+1)/(x²-3) = 2x/(x²-3) + 1/(x²-3)

Hence, the simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)

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Answer:

When the eqn cuts the x-axis , y=0

3x=12

x=12/3

x=4

So,at x=4 is the point at which the linear equation cuts the x-axis

Answer:

collect like terms

12xy=12

xy=1

From my analysis, the answer is likely to be D. I don't have a formula to prove it though.

Answer: 78 degrees.

Step-by-step explanation:

The other guy is wrong don't listen to him.

Answer:

4) 7a+20

5) 14+2b

6) 25c² - 15

Step-by-step explanation:

4) 9a+7-2a+13= 9a-2a+7+13 = 7a+20

5) 21-3b+5b-7= 21-7+5b-3b = 14+2b

6) (3c)² + (8c)² - 15 = 9c² + 16c² - 15 = 25c² - 15

Answer:

a = 3

Step-by-step explanation:

4(2a - 3) = -2(a - 9)

8a - 12 = -2a + 18

10a = 30

a = 3

Let's check if we got it correct by substituting 3 for a in the original equation.

4(2*3 - 3) = -2(3 - 9)

4(6 - 3) = -2(-6)

4(3) = 12

12 = 12

Answer:

x = 6

Step-by-step explanation:

First we divide both sides by 3 :

x² = 108 ÷ 3

x² = 36

Now we square root both sides :

x = √36

x = 6

Hope this helped and have a good day

Answer:

     x = ± 6

Step-by-step explanation:

Quick steps

[tex]3x^{2} =108[/tex]

[tex]x=\sqrt{\frac{108}{3} } =\sqrt{36}[/tex]

[tex]x=[/tex] ±6

A (positive) number has two square roots; one positive and one negative

Hope this helps

The equation that represents the  Myra's age given Talat age is as follows:

t = m + 5

Myra is 5 years younger than her sister Talat

Myra age is represented by m while Talat age is represented by t.

Hence,

m = age of Myra

t = age of Talat

Myra is 5 years younger than Talat. This means Talat is 5 years older than Myra.

Therefore, the equation that represents the  Myra's age given Talat age is as follows:

t = m + 5

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Answer:

Step-by-step explanation:

Taking into account the definition of a system of linear equations, the value of x is -4.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, the system of equations to be solved is

[tex]\left \{ {{3x+4y=-16} \atop {x=4y}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

3×4y +4y= -16

Solving:

12y +4y= -16

16y= -16

y= (-16)÷ 16

y= -1

Remembering that x=4y, then x= 4×(-1)= -4.

Finally, the value of x is -4.

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Answer:

When dividing both sides by a negative.

Step-by-step explanation:

When dividing OR multiplying both sides by a negative, we need to flip the inequality signs.

Answer: third store

Step-by-step explanation:

1

First store: 95

Second store: 0.8*115=92

Third store: 0.9*105=94.5

Using it's concept, the experimental probability of getting an odd number and a number greater than 6 is given by:

1/5.

A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.

In this problem, there are 10 trials, and of those, 2 of them, trial 8 and trial 10, resulted in an odd number and a number greater than 6, hence the probability is:

p = 2/10 = 1/5.

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Answer: 21[tex]x^{2}[/tex] - 52x - 48

Step-by-step explanation:

Using the expanding rule we get

5x * 3x - 5x * 10 + (6[tex]x^{2}[/tex] - 18x + 16x -48)

15[tex]x^{2}[/tex] - 50x + 6[tex]x^{2}[/tex] - 2x - 48

21[tex]x^{2}[/tex] - 52x - 48

Answer:

21x^2-52x-48

Step-by-step explanation:

5x(3x-10) + (2x-6)(3x+8)

Distribute

5x^2 -50x+6x^2-2x-48

Combine like terms

21x^2-50x-2x-48

21x^2-52x-48

Answer:

y = 4x + 3

Step-by-step explanation:

as the line is parallel to the given equation, the gradient (4x) must stay the same, and as it must pass through the point (-2, -5), we can solve for the y intercept:

to calculate for the y intercept, it is best to express the equation in slope intercept form:

y = mx + b

in this equation, mx stands for the gradient, which ive already highlighted remains 4x, and b stands for the y intercept (which we don't know yet).

y = 4x + b

what we have been given instead is the coordinates for the point this line crosses through (-2,-5) meaning when x = -2, y = -5.

Using this information, we can replace x and y in the equation:

-5 = 4(-2) + b

with consideration to the order of operations, it is important to solve the brackets first

-5 = -8 + b

now to get b by itself add 8 to both sides of the equation:

-5 + 8 = -8 + 8 + b

3 = b

now we remember from the slope intercept equation, b = the y intercept, so we can now solve the equation.

y = 4x + b  

replace b with the number we solved for (3).

y = 4x + 3

this is the equation of the line that is parallel to y = 4x + 1, and passes through the point (-2, -5)

hope this helps :)

The angle that vector makes with the x-axis is closest to [tex]340^\circ[/tex].

What is a vector?

An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.

If the magnitude and direction of two vectors match, they are the same vector. This indicates that if we take a vector and move it to a different point (without rotating it), the vector we finish up with is the same vector we started with.

Given,

[tex]x[/tex]-component of vector = 5.3

[tex]y[/tex]-component of vector = -2.3

angle = [tex]tan^{-1}(\frac{y}{x})[/tex]

angle = [tex]tan^{-1}(\frac{-2.3}{5.3} )[/tex]

angle = [tex]340^\circ[/tex]

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Answer:

1/2

Step-by-step explanation:

50% = 50/100 = 1/2

1/2 of the students rode the first bus.

1 - 1/2 = 1/2

1/2 of the students rode the second bus.

Answer:

Step-by-step explanation:

Let's look at this in this perspective. There are 60 minutes in 1 hour. What I would do first is get rid of the 39 minutes at the end of 8:39. Now you have 8:00. Count until you get to 7 AM.  9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7. That's 11 hours from 8 PM to 7 AM.  60 x 11 = 660. Now, there are 11 minutes more on that 7-o clock and the 39 minutes we got rid of in the beginning. 11 + 39 = 40. 660 + 40 = 700.

Answer: Kenny's energy was off for 700 minutes, or 11 hours and 40 minutes.

Answer:9

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

The approximate difference between the theoretical and experimental probabilities for rolling an even number is 8%

Theoretical probability is what we expect to happen, whereas experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes. As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.

Theoretical probability of rolling a cube and getting a even number is 1/2 or 50% as number of odd numbers and number of even numbers are equal.

Experimental probability = Favorable outcomes/Total outcomes

Experimental probability = 10/24 = 5/12 ≅ 42%

Thus approximate difference between these two equals 50% - 42% = 8%

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Answer:

[tex]154 $\ m^2[/tex]

Step-by-step explanation:

If 88 m of long rope is wrapped twice around the base of the drum, the circumference of the drum is 44m. We can use this information to find the radius of the base.

The equation for circumference is [tex]C=2\pi r[/tex]. We can substitute the value we found for circumference into the equation:

[tex]44=2\pi r[/tex]

Divide both sides by 2

[tex]22=\pi r[/tex]

Divide both sides by π

[tex]r=\frac{22}{\pi}[/tex]

The area of a circle is [tex]A=\pi r^2[/tex]. We can substitute the value we found for the radius into the equation:

[tex]A=\pi (\frac{22}{\pi})^2\\[/tex]

[tex]A=\pi (\frac{22}{\pi})(\frac{22}{\pi})[/tex]

[tex]A=22*\frac{22}{\pi}[/tex]

[tex]A=\frac{484}{\pi}[/tex]

[tex]A\approx154[/tex]

[tex](x-5)(x+5)-(x+1)^2\\=x^2 -25-(x^2+2x +1)\\=x^2 -25-x^2-2x -1\\=-2x-26[/tex]

ANSWER: -2x -26

Ok done. Thank to me :3

Using the normal distribution, the probability that x is less than 110 is:

A. 0.975.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 98, \sigma = 6[/tex]

The probability is the p-value of Z when X = 110, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 98}{6}[/tex]

Z = 2

Z = 2 has a p-value of 0.975.

Hence option A is correct.

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The difference of the means of the two data sets is = 4.57

The mean absolute deviation of the roller coaster speeds in North America is 13.3

The mean absolute deviation of the roller coaster speeds in Asia is 16.8

First we have to start with the data for North America

128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77

To get the mean you have to sum up the values and divide through by the total number 10

937.8/10

Mean = 93.78

Mean Absolute Deviation  = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10

133.32/10 = 13.3

For Asia, we have the data as

149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4

Mean for Asia = 892.1/10

= 89.21

Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10

= 168.32/10

16.8

The difference in the means = 93.78 -89.21

=  4.57

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The statement that <A > <C and <B > <D has been proved

In geometry, the side length opposite the largest angle is the longest side.

Similarly, the side length opposite the smallest angle is the shortest side.

From the given figure of quadrilateral, we have the following sides in increasing order:

The angles opposite the side lengths are:

This means that:

<A > <C and <B > <D

Hence, the statement that <A > <C and <B > <D has been proved

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The given height of this trapezoid is given to be 4.5m

We have to solve for this by making use of the height of a trapezoid. The height is given as

A = (1/2) h (b1 + b2)

The variables here are

h = height

b1 = lenght at base 1

b2 = length at base 2

If the trapezoid that we have is a isosceles triangle, then base 1 is going to be the same length as that of the first base

b1 = 4 ft is the area. Given that the height has to be at least 4.5feet, then this would ensure that the trapezoid would be able to hold the shed.

Hence the height would begiven as 4.5 ft

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Answer: 4.5

Step-by-step explanation: