missing number in this sequence 512;128;?;8;2

The solution to the initial value problem is [tex]y = (3 - e^x)/(e^x - 1)[/tex]. The domain of this solution is all values of x except x = ln(3).

A method for resolving specific kinds of first-order ordinary differential equations is called variable separation. It entails moving the equation's terms so that those involving the independent variable x are on the other side and those involving the dependent variable y are on the one side. In order to arrive at a general solution, we can then integrate both sides with respect to their respective variables. The name of the method comes from the fact that the variables on either side of the equation are separated.

The given differentiation is given as:

[tex]dy/dx = 9e^{x - y}[/tex]

Separating the variables we have:

[tex]dy/(9e^{x - y}) = dx[/tex]

Now, integrating on both sides we have:

[tex]\int dy/(9e^{x - y}) = \int dx[/tex]

Using partial fraction decomposition we have:

[tex]\int [1/(3-y) - 1/(3e^{x-y})] dy = x + C[/tex]

Integrating each term we have:

[tex]ln|3-y| - ln|3e^{x-y}| = x + C\\ln|3-y| - ln (\|y-3e^x\| = x + C\\ln|(3-y)/(y-3e^x)| = x + C\\(3-y)/(y-3e^x) = ke^x[/tex]

, where k is a constant of integration

We can solve for y:

[tex]y = (3ke^x + 3)/(ke^x + 1)[/tex]

Now, for the initial condition y = 4 and x = 0 we have:

[tex]4 = (3k + 3)/(k + 1)\\4k + 4 = 3k + 3\\k = -1[/tex]

Hence, the solution to the initial value problem is [tex]y = (3 - e^x)/(e^x - 1)[/tex].

Now, the domain of this solution is all values of x except x = ln(3)

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Answer:in your mouth

Step-by-step explanation:

The sum of the first 6 terms of the given sequence is -1350.

What is sum?

In mathematics, the term "sum" refers to the result of adding two or more numbers or quantities together. The sum of two numbers a and b is denoted by a + b. Similarly, the sum of three numbers a, b, and c is denoted by a + b + c.

The given sequence is a finite geometric sequence with a common ratio of -3. To find the sum of the first 6 terms of this sequence, we can use the formula for the sum of a finite geometric series:

[tex]S_n = a(1 - r^n) / (1 - r)[/tex]

where S_n is the sum of the first n terms of the sequence, a is the first term of the sequence, r is the common ratio, and n is the number of terms in the sequence.

Substituting the given values, we get:

[tex]S_6 = 18(1 - (-3)^6) / (1 - (-3))\\\\S_6 = 18(1 - 729) / 4\\\\S_6 = -1350[/tex]

Therefore, the sum of the first 6 terms of the given sequence is -1350.

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Answer:

Step-by-step explanation:

-1,092

The approximate value of P(adult ∣ rode a ferris wheel) is 0.6364, which is approximately 63.64%.

To find the approximate value of P(adult|rode a ferris wheel), we can use the conditional probability formula:

[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) = \frac{P(adult \ and \ rode \ a \ ferris \ wheel)}{P(rode \ a \ ferris \ wheel)} }[/tex]

From the data given in the table, you can see that:

Total number of people who rode the ferris wheel: 198 (children + adults)

Number of adults who rode the ferris wheel: 126.

So, P(rode a ferris wheel) = 198/264

And, P(adult and rode a ferris wheel) = 126/264

Now plug these values into the conditional probability formula:

​[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) = \frac{P(adult \ and \ rode \ a \ ferris \ wheel)}{P(rode \ a \ ferris \ wheel)} } \\\\= \frac{126/264}{198/264}[/tex]

[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) } = \frac{126}{198} \\\\ \approx 0.6364[/tex]

Rounded to four decimal places, the approximate value of P(adult ∣ rode a ferris wheel) is 0.6364, which is approximately 63.64%.

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Answer:

Step-by-step explanation:

6213.712

Answer:

10,000 Kilometers = 6,213.7119 Miles

Step-by-step explanation:

Going from top left to right then bottom left to right

Answers:

1st. answer: 94

2nd. answer: 82

3rd. answer: 142

4th answer: 88.2

5th. answer: 130

6th. answer: 178

(also I relearned how to do triangles)

(I'm going to follow you so if you have any more questions I can help)

Answer:

Rebecca and Brian each have 40 batteries, making a total of 80 batteries.

Step-by-step explanation:

Rebecca:

Rebecca has 4 packs of batteries, and if each one contains 10 batteries, then she has 40 batteries.

Brian:

Brian also has 4 packs of batteries, each one contains 10 batteries, so he also has 40 batteries.

In total, they have a combined 80 batteries.  hope this helps ;)

Based on the information we can infer that the area of the figure is 464 ² units.

To calculate the area of this figure we must assume that it is a complete square and find its area as shown below:

Now we must find the area of the non-grid regions and subtract them from the area we found previously:

576 - 112 = 464 units ²

According to the above, the area of the figure is 464 units ²

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No, 3 is not greater than 5. This is because 5 is larger than 3.

From the question, we have the following parameters that can be used in our computation:

3 and 5

No, 3 is not greater than 5. This is because 5 is larger than 3.

In other words, 5 is further to the right on the number line than 3.

We can also say that 5 is the greater number and 3 is the lesser number.

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From the given table, Player A is the most consistent, with an IQR of 1.5. So, correct option is A.

To find the best measure of variability for this data, we need to consider a measure that is robust and resistant to outliers. The interquartile range (IQR) is a good choice as it is calculated based on the range of values that fall within the middle 50% of the data and is therefore less affected by extreme values.

To calculate the IQR, we first need to find the median, which is the middle value in the dataset. For Player A, the median is 3 and for Player B, the median is 2.5.

Next, we calculate the first quartile (Q₁) and the third quartile (Q₃) which represent the 25th and 75th percentiles of the data, respectively. For Player A, Q₁ is 2 and Q₃ is 3.5, while for Player B, Q₁ is 2 and Q₃ is 4.5.

The IQR is the difference between Q₃ and Q₁. For Player A, the IQR is 1.5 (3.5 - 2) and for Player B, the IQR is 2.5 (4.5 - 2). Therefore, Player A is more consistent as their IQR is smaller, indicating that their runs earned are more tightly clustered around the median.

The range, which is the difference between the largest and smallest values in the dataset, is also a measure of variability, but it is sensitive to extreme values. In this case, the range for Player A is 7 (8 - 1) and for Player B is 5 (6 - 1), but these values do not provide as accurate an indication of consistency as the IQR.

So, correct option is A.

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Complete question is:

The table shows the number of runs earned by two baseball players.

Player A

2, 1, 3, 8, 2, 3, 4, 3, 2

Player B

2, 3, 1, 4, 2, 2, 1, 4, 6

Find the best measure of variability for the data and determine which player was more consistent.

Player A is the most consistent, with an IQR of 1.5.

Player B is the most consistent, with an IQR of 2.5.

Player A is the most consistent, with a range of 7.

Player B is the most consistent, with a range of 5.

As per the given Equation Each sister received 1 piece of jewelry.

Let's the number of pieces of jewelry that each sister received "x". Since there are 5 sisters, the total number of pieces of jewelry that the sisters received is 5x.

We can then set up an equation to represent the total number of pieces of jewelry that the sisters received from both grandmothers:

13 + y = 5x

This equation says that the total number of pieces of jewelry the sisters received is equal to the sum of 13 pieces from Grandma Gertrude and y pieces from Grandma Fien, and this total is also equal to the number of sisters (5) times the number of pieces each sister received (x).

To solve for x, we can first simplify the equation:

y = 5x - 13

Now we can substitute this expression for "y" into the original equation:

13 + (5x - 13) = 5x

5x = 5x

This equation is true for any value of x, which means that x can be any number. However, we are looking for the number of pieces of jewelry that each sister received, so we need to find a specific value of x.

Dividing both sides of the equation by 5, we get:

x = 1

This means that each sister received 1 piece of jewelry.

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If Robert ate lunch at 11:am and he ate a snack 4and a half hours later, Robert ate his snack at 3:30 pm

To find out what time Robert ate his snack, we need to add 4 and a half hours to the time he ate lunch.

Since he ate lunch at 11:00 am, we can convert this time to 24-hour format by adding 12 hours to get 11:00 + 12:00 = 23:00.

Next, we add 4 and a half hours to 23:00 by converting the half hour to minutes and adding it to the minutes portion of the time:

23:00 + 4 hours + 30 minutes = 27:30

However, since there are only 24 hours in a day, we need to convert this time back to 12-hour format. To do this, we subtract 12 hours from 27:30 to get 15:30.

Therefore, Robert ate his snack at 3:30 pm (or 15:30 in 24-hour format).

In summary, we added 4 and a half hours to the time Robert ate lunch, converted the resulting time to 24-hour format, subtracted 12 hours to account for the excess of 24 hours, and then converted the time back to 12-hour format to obtain the time Robert ate his snack.

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Cash paid for interest during 2014 was $12,750. Based on the provided Phoenix Corp. information, the question requires you to calculate the cash paid for interest throughout the 2014 calendar year.

Also provided are the amounts for the year's interest expenditure and the balance of interest payable as of December 31, 2013 and 2014.

These are the formulas that can be used to determine the cash paid in interest in 2014:

Interest paid in 2014 minus any increases in interest due equals the cash paid in interest.

The difference between the balance of interest payable as of December 31, 2014, and as of December 31, 2013, can be used to compute the increase in interest payable:

Interest payable at December 31, 2014 minus interest payable at December 31, 2013 equals $6,200 minus $5,700, which equals $500 in

additional interest.

This signifies that the corporation incurred more interest expense than it paid during the year Since the balance of interest payable increased from 2013 to 2014, the corporation incurred more interest expense than it paid in that period. As a result, the money used to pay interest in 2014 is:

Interest paid in 2014 plus the increase in interest due is $12,250 plus $500.= $12,750

Thus, $12,750 is the correct response (D).

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Answer:

Step-by-step explanation:

Thus, with 99% confidence, we can say that the proportion of smeared ink in the 200 sheets of paper inspected falls between 1.3% and 15.7%.

To calculate the confidence interval of the proportion smeared in 200 sheets of paper inspected for smeared ink, we can use the formula:

Confidence Interval = sample proportion ± (critical value) x (standard error)

The sample proportion is the number of sheets containing smeared ink divided by the total number of sheets inspected, which is 17/200 = 0.085.

The critical value for a 99% two-sided confidence interval with 200 observations can be found using a t-distribution table or calculator, and is approximately 2.576.

The standard error can be calculated as the square root of [(sample proportion) x (1 - sample proportion) / sample size], which is the square root of [(0.085) x (1 - 0.085) / 200] = 0.028.

Plugging in these values, we get:

Confidence Interval = 0.085 ± (2.576) x (0.028)
Confidence Interval = 0.085 ± 0.072
Confidence Interval = (0.013, 0.157)

Therefore, with 99% confidence, we can say that the proportion of smeared ink in the 200 sheets of paper inspected falls between 1.3% and 15.7%. This means that we are 99% confident that the true proportion of smeared ink in the population of printed sheets falls within this range.

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Answer: The probability that a millet seed will fall next can be found by dividing the number of millet seeds by the total number of remaining seeds.

Total number of remaining seeds = 40 + 65 + 60 + 35 = 200

Probability that a millet seed will fall next = Number of millet seeds / Total number of remaining seeds

= 65 / 200

= 0.325 or 32.5% (rounded to one decimal place)

Therefore, the probability that a millet seed will fall next is 0.325 or 32.5%.

Step-by-step explanation:

Answer: [tex]\frac{16}{15}[/tex]

Step-by-step explanation:

    First, we will turn 6 and 2/5 into a single improper fraction.

6 * 5 = 30

30 + 2 = 32

6 and 2/5 = 32/5

    Next, we will multiply across:

[tex]\displaystyle \frac{32}{5} *\frac{1}{6} =\frac{32}{30}[/tex]

    Lastly, we will simplify by dividing both the numerator and the denominator by 2:

[tex]\displaystyle \frac{16}{15}[/tex]

The height of the cone is approximately 1.5 cm.

Both a cone and a cylinder have circular bottoms and are three-dimensional shapes. The lateral surfaces of the two shapes differ most noticeably from one another. A cone has a lateral surface that tapers from a point at the apex to a circular base, whereas a cylinder has a curved lateral surface that is parallel to its base. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height, whereas the volume of a cone is calculated using V = (1/3)πr²h.

The volume of the cone is given as:

V = (1/3)πr²h

Rearranging the equation to isolate h we get:

3V = πr²h

h = (3V)/(πr²)

Now, for  volume

of 48 cm³ and a base with a radius of 4 cm we have:

h = (3(48))/(π(4)²)

h ≈ 1.5 cm

Hence, the height of the cone is approximately 1.5 cm.

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Area of rectangle = 50 [tex]unit^2[/tex].

Perimeter of rectangle =30 unit.

Area of dilated rectangle = 1250  [tex]unit^2[/tex].

Perimeter of dilated rectangle = 150 unit.

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here the given rectangle length l = 10 unit and width = 5 unit.

Now using formulas,

Area of rectangle = lw square unit.

=> A = 10*5 = 50 [tex]unit^2[/tex].

Perimeter of rectangle = 2(l+w) unit

=> P =2(10+5) = 2(15) = 30 unit.

Here scale factor= 5

The dilated rectangle length [tex]l_1[/tex]= 10*5 = 50 unit and

width [tex]w_1 = 5\times5 = 25[/tex] unit

Now area of dilated rectangle [tex]A_1[/tex]= [tex]l_1w_1[/tex] square unit.

=>  [tex]A_1[/tex]= 50*25 = 1250  [tex]unit^2[/tex].

Perimeter of dilated rectangle [tex]P__1[/tex] = 2([tex]l_1+w_1)[/tex] unit.

=>  [tex]P__1[/tex] = = 2(50+25) = 2(75) = 150 unit.

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The probability of picking blue ball by Liz and Mike are equal =1/3

Probability is a branch of mathematics that deals with the study of random events or experiments. It is concerned with quantifying the likelihood or chance of a particular event occurring, given certain assumptions or conditions.

The probability of an event is typically represented as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain. For example, if you flip a fair coin, the probability of getting heads is 0.5, and the probability of getting tails is also 0.5.

There are different methods for calculating probabilities, depending on the nature of the event or experiment being considered. Some of the most commonly used methods include the classical probability method, the empirical probability method, and the subjective probability method.

Probability has many applications in various fields, including statistics, finance, engineering, and science. It is used to model and analyze complex systems and to make predictions and decisions based on uncertain information.

Given : X contains 9 blue balls and 18 red balls.

Y contains 7 blue balls and 14 red balls.

Probability of picking blue ball is 9/9+18

=9/27=1/3

Now Mike pick ball from bag Y one ball not affect these pick ball

so, 7/7+14=7/21=1/3

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Horatio has 6 trophies by equating the resultant linear equation in one variable.

Hence option b  is the correct option.

Patel has 19 trophies in total.

Its is said that Patel has five less than four times as many trophies as Horatio has.

Let the number of trophies Horatio has be x and that of Patel be y.

From the given relation of trophies of Patel and Horatio we get,

y = 4x - 5

This forms a linear equation.

We have y = 19.

Thus y = 4x - 5 can be written as,

19 = 4x - 5

Thus we have the equation in the form of a linear equation in one variable.

Simplifying the linear equation in one variable we get,

19 = 4x - 5

⇒ 19 + 5 = 4x

⇒ 24 = 4x

or, 4x = 24

⇒ x = 24/4

⇒ x = 6

Hence, Horatio has x = 6 trophies in total.

Hence option b is correct option.

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Answer:

x+2

hope this helps ;)

and cute pfp

Answer:

Step-by-step explanation:

x-1, because 3 fits the criteria, x>=1

You will have $5,333.85 in your CD at the end of the 5 years.

The formulation for the future value of an investment with monthly compounding is:

[tex]CD = P(1 + \frac{r}{n} )^{(nt)}[/tex]

Wherein:

Plugging in the given values:

[tex]CD= 5000(1 + \frac{0.0125}{12} )^{(12*5)}[/tex]

[tex]CD = 5000(1.00104)^{60}[/tex]

CD = 5000(1.06677)

CD = $5,333.85

Consequently, you will have $5,333.85 in your CD at the end of the 5 years.

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The angle of depression is always measured from the horizontal.

A triangle is formed by the lighthouse, the ground and the boat. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the boat. (Alternate angles on parallel lines)

The angle at the top of the lighthouse, inside the triangle is:

[tex]90^\circ-27^\circ=63^\circ[/tex]

The distance to the boat is the side opposite the angle of 63° while the height of the lighthouse is the adjacent side.

[tex]\dfrac{\text{opposite}}{\text{adjacent}} =\text{tan 63}^\circ[/tex]

[tex]\dfrac{\text{distance}}{245} =\text{tan 63}^\circ[/tex]

[tex]\text{distance}=245\times \text{tan 63}^\circ[/tex]

[tex]=480.83=480.84\thickapprox\boxed{\bold{480.8}}[/tex]

A dot plot is a simple type of graph that represents data using dots. It is a one-dimensional display of data where each dot represents a single data point. Dot plots are useful for showing the distribution of a set of values, particularly when the data set is small.

To create a dot plot, you simply draw a horizontal or vertical line and plot a dot above or beside the line for each data point. The dots are usually stacked vertically or horizontally if there are multiple data points with the same value.

    |         x

 8  |     x  

 7  | x x x  

 6  | x x x x

 5  | x x x x

 4  | x x x x x

 3  | x x x x x

 2  | x x x x x x

 1  | x x x x x x x

     ---------------

        1 2 3 4 5 6 7

In this example, the dot plot shows the number of times a dice roll resulted in a particular value. The x's represent the data points, and the numbers on the left indicate the frequency of each value.

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the value of the expression sin A cos B - cos A sin B is √34/5. use the trigonometric identities

what is expression ?

Trigonometric identities are mathematical equations that relate the values of trigonometric functions to one another. They are true for all possible values of the variables involved, and can be used to simplify and solve trigonometric equations.

In the given question,

To solve this problem, we need to use the properties of trigonometric functions to find the values of other trigonometric functions for angles A and B.

We know that:

tan A = opposite/adjacent = 4/3

tan B = opposite/adjacent = 3/5

Using the Pythagorean theorem, we can find the hypotenuse of the right triangles for angles A and B:

For angle A: hypotenuse = √(opposite² + adjacent²) = √(4² + 3²) = 5

For angle B: hypotenuse = √(opposite² + adjacent²) = √(3² + 5²) = √34

Now, we can use the definitions of sine, cosine, and tangent to find their values for angles A and B:

sin A = opposite/hypotenuse = 4/5

cos A = adjacent/hypotenuse = 3/5

sin B = opposite/hypotenuse = 3/√34

cos B = adjacent/hypotenuse = 5/√34

We can simplify these values by rationalizing the denominators:

sin B = 3√34/34

cos B = 5√34/34

Finally, we can use the trigonometric identities to find the value of the expression:

sin A cos B - cos A sin B

Substituting the values we found:

sin A cos B - cos A sin B = (4/5)(5√34/34) - (3/5)(3√34/34)

Simplifying:

sin A cos B - cos A sin B = √34/5

Therefore, the value of the expression sin A cos B - cos A sin B is √34/5.

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if tan A=4/3 and tan B=3/5 calculate and simplify the following expression sin A cos B - cos A sin B ?

Answer:

Set your calculator to degree mode.

1) sin(X)/x = sin(Z)/z

sin(57.5°)/15 = sin(Z)/13

sin(Z) = 13sin(57.5°)/15

Z = 47.0°

2) sin(M)/m = sin(L)/l

sin(32°)/9 = sin(L)/12

sin(L) = 12sin(32°)/9

L = 45.0°, so N = 180° - (32° + 45°)

= 103.0°

3) sin(Q)/q = sin(P)/p

sin(48°)/19 = sin(P)/17

sin(P) = 17sin(48°)/19

P = 41.7°, so R = 180° - (48° + 41.7°)

= 90.3°

4) sin(A)/a = sin(B)/b

sin(85°)/8 = sin(B)/7

sin(B) = 7sin(85°)/8

B = 60.7°

5) sin(D)/d = sin(F)/f

sin(D)/24 = sin(56°)/23

sin(D) = 24sin(56°)/23

D = 59.9°

6) sin(U)/u = sin(V)/v

sin(U)/30 = sin(130°)/45

sin(U) = 30sin(130°)/45

U = 30.7°