Find the general solution of the following differential equation. Primes denote derivatives with respect to x. 3x2y' + 6xy = 15y3

Out of the following, the statement Excel can add only linear trendlines to data in a scatter chart is  true  regarding   trendlines in scatter chart in excel.This means that the trendline in Excel will be a straight line that will best fit the data points in the scatter chart.

It will not be able to fit any other type of trendline, such as a polynomial or exponential trendline. Additionally, Excel cannot output the R Square value for a trendline in Excel for scatter charts of 3 or more variables. This is because the R Square value is a statistical measure that can only be calculated for linear regression models.

Finally, for simple linear regression models, the trendline in Excel will give the same equation as the data analysis toolpak regression tool. This means that the equation of the trendline in Excel will be the same as the equation of the regression line calculated by the data analysis.

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This indicates that the cutoff value for the amount of minutes before contacting the consumer is 674 minutes, rounded to the closest minute.

Quartiles are three numbers that divide sorted data into four equal portions with an equal amount of observations each. A quantile is a sort of quantile. The first quartile is sometimes known as the lower quartile or Q1. Second quartile: Also known as the median or Q2. Third quartile: Also known as the higher quartile or Q3.

Here,

To find the upper fence, we need to calculate the following statistics:

Q1 (first quartile), Q2 (median), and Q3 (third quartile) of the data

Interquartile range (IQR), which is the difference between Q3 and Q1

Upper fence, which is Q3 + 1.5 * IQR

First, we need to order the data in ascending order:

339, 350, 358, 388, 430, 458, 458, 463, 480, 489, 501, 536

Next, we can find the quartiles:

Q1 = 388

Q2 = 458

Q3 = 501

IQR = Q3 - Q1 = 501 - 388 = 113

Finally, we can calculate the upper fence:

Upper fence = Q3 + 1.5 * IQR = 501 + 1.5 * 113 = 674

This means that the cutoff point for the number of minutes at which the customer should be contacted is 674 minutes, rounded to the nearest minute.

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The equation y = e^-4 can be evaluated using a graphing calculator by plugging in -4 for x and finding the corresponding y-value.

On a graphing calculator, this is usually done by setting the calculator to the "y=" mode and entering the equation y = e^x. Then, by entering -4 as the value of x, the corresponding y-value can be found.

The result would be y = e^-4 = 0.0183. To four decimal places, this value is 0.0183.

Answer:

Figure 1 is vertical, through the cone's topmost point

Figure 2 is horizontal

Figure 3 is diagonal

Explanation:

The easiest way to think about this is that you have a cone-shaped cake and you are cutting it.

The frequency table using the six classes have been done below

Class interval Frequency

20 - 35 2

36 - 50 0

51 - 65 2

66 - 80 5

81 - 95 5

96 - 110 5

Note: The class intervals were created as follows: 20-35, 36-50, 51-65, 66-80, 81-95, and 96-110. The frequency is the number of data values that fall into each class interval.

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The scalar projection of vector b onto vector a is 57/289 and the vector projection of vector b onto vector a is (0.38, 0.92).

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

The scalar projection of vector b onto vector a is given by:

(b . a) / ||a||^2

= (3 * -8 + 5 * 15) / ( -8^2 + 15^2)

= 165 / 289

= (57/289)

The vector projection of vector b onto vector a is given by:

proj(b onto a) = (b . a) / ||a||^2 * (a / ||a||)

= (57/289) * (-8/√(-8^2 + 15^2), 15/√(-8^2 + 15^2))

= (0.38, 0.92)

Note: sqrt(-8^2 + 15^2) = sqrt(289) = 17

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Answer:

What is the question?

Step-by-step explanation:

If we select three balls, the probability of selecting exactly one white one is 16.

There are 6 balls in a box.

2 white and 4 black.

If we select three balls, then we have to determine the probability of selecting exactly one white.

First we determine the number of ways of selecting three balls in total of 6 balls. So

[tex]^{6}C_{3} = \frac{6!}{3!(6-3)!}[/tex]

[tex]^{6}C_{3} = \frac{6!}{3!3!}[/tex]

[tex]^{6}C_{3} = \frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]

Simplify

[tex]^{6}C_{3}[/tex] = 5 × 4

[tex]^{6}C_{3}[/tex] = 20

Now determining the probability of selecting the 3 balls out of non white balls.

[tex]^{4}C_{3}=\frac{4!}{3!(4-3)!}[/tex]

[tex]^{4}C_{3}=\frac{4!}{3!1!}[/tex]

Simplify

[tex]^{4}C_{3}=\frac{4\times3!}{3!\times1}[/tex]

[tex]^{4}C_{3}[/tex] = 4

Now, the probability of selecting exactly one white one = The number of ways of selecting three balls in total of 6 balls - The probability of selecting the 3 balls out of non white balls

The probability of selecting exactly one white one = 20 - 4

The probability of selecting exactly one white one = 16

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Time it will take to reach the same location driving at an average speed of 50 miles per hour,  4.4 hour

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

Given that,

The time it takes to travel to a location varies inversely to the speed traveled,

Time = 4 hours

Average speed = 55 miles per hour

If average speed  = 50 miles per hour

then time = ?

First, it is required to calculate distance covered,

Distance = Time × Speed

               =  4 x 55

               = 220 miles

Now, when average speed is 50 miles per hour,

Distance = Time × Speed

Speed   = Distance/Time

             = 220/50

             = 4.4 hour

Thus, the required time is 4.4 hour

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There is 700 number of $5 bills and 200 number of $10 bills

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

Let x represent the number of $5 bills and y represent the number of $10 bills.

There is a total of 900 $5, $10 dollar bills, hence:

x + y = 900        (1)

The value of all the bills is $5500, hence:

5x + 10y = 5500     (2)

From both equation, solving simultaneously:

x = 700, y = 200

There are 700 $5 bills and 200 $10 bills

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The solution is Option B.

The angle ∠AEC is a right angle by definition of perpendicular bisector

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as AB

Let the second line be represented as CD

Now , AB is perpendicular to the line CD

where , the measure of ∠CEB = 90°

And , angles on a straight line has a sum of 180°

So , the measure of ∠AEC is a right angle by perpendicular bisector theorem

Hence , the measure of the perpendicular angle ∠AEC is 90°

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Answer: Definition of Perpendicular Bisector

Step-by-step explanation:

Took the test!

The equation represents the relationship between the independent variable, x, and the dependent variable is y= 2x

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

The table of values

On the yable of values, we can see that

y is twice of x

When represented as an equation, we have

y = 2x

Hence, the equation is y = 2x

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The range of the function shown in the graph below is [-6, ∞].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph,

The y-coordinate value is the range of the function.

We see that,

The y-coordinate value is from -6 to ∞.

So,

Range = [-6, ∞].

Thus,

The range of the function is [-6, ∞].

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The longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.

The longest a blender can last and still be in the lowest 6% of life spans is calculated by using the inverse normal distribution formula. This formula is P(X ≤ x) = 1 - P(X > x). The X is the longest a blender can last and P(X ≤ x) is 6%. First, we need to calculate the z-score for 6%. This can be done by P(X ≤ x) = 0.06 and using the z-score formula z = (x - μ) / σ , where μ is the mean and σ is the standard deviation. Substituting the values into the equation, we get z = 0.06 = (x - 8.2) / 0.8. Solving for x gives us x = 7.96. Therefore, the longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.

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Peter is right and Nadia is wrong.

Equivalent fractions are fractions that represent the same value, even though they look different.

Given is that Peter says 3/4 of a pizza is always the same as 6/8 of a pizza. Nadia says while 3/4 and 6/8 are equivalent fractions, 3/4 and 6/8 of a pizza could represent different amounts.

{ 1 } -

3/4 = (3 x 2)/(4 x 2) = 6/8

Peter is right.

Now -

3/4 = 6/8

So it could not represent two different quantities. So, Nadia is wrong.

{ 2 } -

3/4 = 6/8 = 9/12 = 12/15

These all represent the same quantity. Division of all the expressions will result in same value.

Therefore, Peter is right and Nadia is wrong.

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The number of times both services left the interchange together from 9am to 12 noon is 0.

Let's call the number of 15-minute intervals that have passed since 9 am "t".

So, the time that bus number 801 leaves the interchange after t intervals is 9am + 15t minutes.

Similarly, the time that bus number 802 leaves the interchange after t intervals is 9 am + 20t minutes.

For both services to leave the interchange at the same time, the number of 15-minute intervals that have passed since 9 am must be the same for both buses.

In other words, 15t must equal 20t.

Dividing both sides of this equation by 5, we get 3t = 4t.

This equation has no solution, which means that bus number 801 and bus number 802 never leave the interchange at the same time from 9am to 12 noon.

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The midpoint of the  1/3 and 6/11 as a fraction is, 29/33

The midpoint of two numbers can be found by taking the average of the two numbers. To find the average of two fractions, you need to find a common denominator, add the numerators, and divide the sum by the denominator.

Given that,

Two fractions,

1/3 and 6/11

To find the common denominator for 1/3 and 6/11, you can find the least common multiple (LCM) of the denominators:

LCM(3, 11) = 33

Next, convert each fraction to an equivalent fraction with a denominator of 33:

1/3 = 11/33

6/11 = 18/33

Finally, add the numerators and divide the sum by the denominator to find the average:

(11 + 18) / 33 = 29/33

The midpoint of 1/3 and 6/11 as a fraction is 29/33.

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The required percentage of regular grade gasoline are;

a) 34%

b) 95.5%

c)4.5%

(a) To determine the percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon, we need to find the proportion of the data that falls within this range. Assuming a bell-shaped distribution, we can use the standard deviation and mean to find the z-scores for these two prices, and then look up the cumulative probability in a standard normal table.

$3.25$ is $1$ standard deviation below the mean and $3.65$ is $0.5$ standard deviation above the mean.

Using a standard normal table, we find that approximately 68% of the data falls within one standard deviation of the mean, and approximately 34% falls between $-0.5$ and $0.5$ standard deviations.

Therefore, approximately 34% of regular grade gasoline is sold between $3.25 and 3.65 per gallon.

(b) To find the percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon, we need to find the cumulative probability for the range $3.25$ to $3.85$.

$3.85$ is $1.5$ standard deviations above the mean.

Using a standard normal table, we find that approximately 95.5% of the data falls within $1.5$ standard deviations of the mean.

Therefore, approximately 95.5% of regular grade gasoline is sold between $3.25 and $3.85 per gallon.

(c) To find the percentage of regular grade gasoline sold for more than $3.85 per gallon, we need to find the cumulative probability for values greater than $3.85$.

Using a standard normal table, we find that approximately 100% - 95.5% = 4.5% of the data falls above $1.5$ standard deviations from the mean.

Therefore, approximately 4.5% of regular grade gasoline is sold for more than $3.85 per gallon.

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The X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.

The lowest 2.5% boundary for a normal distribution with a mean of 50 and standard deviation of 4 can be calculated using the Z-score formula.

Z = (X - mean) / standard deviation

We want to find the X value for which Z = -1.96 since -1.96 represents the boundary for the lowest 2.5% of a standard normal distribution.

Plugging in the mean and standard deviation:

-1.96 = (X - 50) / 4

Solving for X:

X = 50 - 1.96 × 4

X = 43.04

So, the X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.

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Answer:

To determine whether the ball will eventually reach a pocket, we need to determine if the ball will collide with any other balls or obstacles on the way to its target. If there are no obstacles, and the ball has enough force and the correct trajectory, it will reach the target pocket.

To show the path of the ball, we can draw a straight line connecting the starting position and the target pocket. This line represents the trajectory of the ball if it is not obstructed by any other balls or obstacles.

In conclusion, without any obstacles in the way, if Montana hits the ball with enough force and the correct trajectory, the ball will reach the target pocket. It is important to consider any potential obstacles or interference when planning a shot in billiards.

Two puppy's Max and Ruby will have equal weight after 6 weeks

In the arithmetic sequence  the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

Given that,

Two puppy's

Max, currently weighs 5 pounds and is expected to gain 1 pound per week,

Ruby, currently weighs 8 pounds and is expected to gain 0.5 pounds per week

The number of weeks when both will have equal weight = ?

Suppose, it number of weeks = n

It can be solved by using concept of arithmetic sequence,

a₁ = 5 pounds

d₁ = 1 pound per week

Tₙ = 5 + 1xn = 5 + n

a₂ = 8 pounds

d₂ = 0.5 pounds per week

Tₙ = 8 + 0.5xn = 8 + 0.5n

Both should be equal,

5 + n = 8 + 0.5n

0.5n  = 8 - 5

n  = 6

Hence, after 6 weeks they will have same weight

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Answer:

A) 2/5

B) 4/15

Step-by-step explanation:

A)

adults : students

1          :  10

year 10 : year 11

1            : 4

fraction of all the people on the trip are year 11 students =

4   : 10

4 / 10

2 / 5

B)

adults : children

2         : 3 _____________(1)

boys    : girls

5         : 2 _____________(2)

multiplying ratio (1) with 5

adults : children

10 : 15

multiplying ratio (2) with 2

boys : girls

10     :  4

fraction of all the people in the cinema are girls

4  : 15

4 / 15

Scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.

The evidence that allowed scientists to conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus comes from the application of the quantum mechanical model. The quantum mechanical model states that the energy of an electron is quantized, meaning it can only occupy discrete energy levels rather than any random energy level in between. This is expressed mathematically through the equation E n = nhf, which states that the energy of an electron is equal to the product of Plank's constant (h) and the frequency (f) of the electron's orbit multiplied by the quantum number (n). This equation demonstrates that electrons can only occupy certain energy levels and not any random energy level. Therefore, scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.

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The expanded form of 8! is 8×7×6×5×4×3×2×1.

A whole number's factorial is the result of multiplying the integer by each natural number below it.

The sign '!' can be used to indicate a factorial symbolically.

Therefore, 'n factorial' is denoted by the number n and is the product of n up to whole numbers below n except zero.

Given, A factorial number 8!.

Therefore, 8! = 8×7×6×5×4×3×2×1.

The product of all whole numbers below 8 and except zero.

We use factorials in permutation and combination also.

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The quadratic regression equation for the data-set in this problem is given as follows:

y = 0.96x² - 5.77x + 1.38.

Regression equations are obtained inserting the points of a data-set into a calculator.

In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.

The points are given as follows:

(-1,8), (5,-4), (7,8), (2,-6).

Inserting these points into a calculator, the regression equation is given as follows:

y = 0.96x² - 5.77x + 1.38.

Meaning that the second option is the correct option.

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The segment drawn from the apex to the edge of the circular base is 24.19 units.​

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

Volume = 72π

Diameter = 6

The volume of a cone is

V = 1/3πr^2h

Where

r = 6/2 = 3

So, we have

1/3π * 3^2h = 72π

This gives

3h = 72

Divide by 3

h = 24

The slant height is then calculated as

l = √(h² + r²)

So, we have

l = √(24² + 3²)

Evaluate

l = 24.19

Hence, the slant height is 24.19 units

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In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.

There are 3 centers to choose from, and for each center there are 4 choices for each of the two guard positions and 4 choices for each of the two forward positions. So, there are:

3 * 4 * 4 * 4 = 192

different starting lineups without x.

Lineups with x as guard: There are 3 centers, 3 choices for the first guard (since x can play either guard or forward), 4 choices for the second guard, and 4 choices for each forward. So, there are

3 * 3 * 4 * 4 = 144

different lineups with x as guard.

Lineups with x as forward: There are 3 centers, 4 choices for each guard, 3 choices for the first forward (since x can play either guard or forward), and 4 choices for the second forward. So, there are 3 * 4 * 3 * 4 = 144 different lineups with x as forward.

In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.

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The larger the p-value, the more likely it is that the null hypothesis that the population coefficient is equal to 0 is true regarding p-value.

In a linear regression model, p-values are associated with the estimated coefficients and provide information about the statistical significance of each predictor variable. The null hypothesis for each predictor is that the population coefficient for that predictor is equal to 0, meaning that it has no effect on the response variable.

The p-value is the probability of observing the estimated coefficient given the null hypothesis is true. If the p-value is small, it means that the observed coefficient is unlikely to be due to chance, If the p-value is large, it means that the observed coefficient could easily be due to chance and we cannot reject the null hypothesis.

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Equation used to represent the amount of interest that was paid​ is S.I = 900 × 0.11 × 0.5 and the amount is $49.5.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Simple interest amount can be calculated using the formula,

S.I = Prt

Here P is the principal amount, r is the rate of interest and t is the time in years.

Given a loan of $900 at a rate of 11% with paid off in 6 months.

P = $900,

r = 11% = 0.11 and

t = 6 months = 0.5 year

S.I = 900 × 0.11 × 0.5

    = 49.5

Hence the amount of simple interest is $49.5.

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Answer:

Use SAS postulate

Step-by-step explanation:

In triangles LAT and SAT,
AT = AT (common side)
ang. LAT = ang. SAT (given, as angle is bisected)
SA = LA (from figure)
Hence, the triangles are congruent