Given the differential equation dy/dx= -x/2y, find the particular solution, y = f(x), with the initial condition f(4) = 3.

The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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Answer:

1. 69/14 or 4 13/14

2. 13/15

Step-by-step explanation:

Answer:

Percent increase : 20%

Step-by-step explanation:

First month: 4,264 phone calls.

Second month: 25% more phone calls than in the first month.

To know the total phone calls received during this month you must take 25% of 4,264 and then add it to the 4,264 call of the first month:

64,264*25%=1,066

Total phone calls of the second month: 1,066+ 4,264= 5,330

You can also calculate the total phone calls of the second month by multiplying 4264 times 1,25 because times 1 is the same number and times 0,25 is the percent increase in the number of calls:

4,264*1,25= 5,330

Third month: 6,396 phone calls

To know the percent increase in the number of phone calls from the second month to the third month you must use the percent change formula:

Percent change: ((value2-value1)/ value 1 )*100%

Value 2: phone calls received during the third month

Value 1: phone calls received during the second month

Percent change: ((6,396-5,330)/ 5,330 )*100%

Percent increase: 20%

Brainliest?!

The value of ∫C F. dr is 2π. Option (B) is the correct answer.

Stoke’s Theorem states that the integral of the curl over a surface is equal to the line integral of the curve bounding the surface.

In other words, the Stoke’s theorem is a mathematical statement that connects line integral of a vector field to the double integral of the curl of the vector field over the surface.

The given vector field is:

F(x,y,z) = (ycos(x), x+sin(x), cos(z))

Let’s calculate the curl of F using cross products as shown below:

Curl of F(x,y,z) = (∂P/∂y - ∂N/∂z)i + (∂M/∂z - ∂P/∂x)j + (∂N/∂x - ∂M/∂y)k= (-sin(x))i + (0)j + (0)k= -sin(x)i

The line integral of F along the curve C is given by:

∫C F. dr = ∫C F(x,y,z) . (dx/dt)i + (dy/dt)j + (dz/dt)k dt

where r(t) = (1 + cos(t))i + (1 + sin(t))j + (1 - sin(t) - cos(t))k

dr/dt = -sin(t)i + cos(t)j - sin(t) + sin(t)k= -sin(t)i + cos(t)j dt

\(\int C F. dr = \int0^(2\pi) [(-sin(t))((-sin(t))i + cos(t)j) . (-sin(t)i + cos(t)j + sin(t)k)] dt\\=\int0^(2\pi) sin^2(t) + cos^2(t) dt\\= \int0^(2\pi) dt\\= 2\pi\)

Hence, the value of ∫C F. dr is 2π.

Option (B) is the correct answer.

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Answer: Day 4 and 15

Step-by-step explanation:

Set up system of equations:

\(25x+136=-x^2+44x+76\)

Simplify:

\(x^2-19x+60=0\)

Factor: Both factors must be positive as the days can only be natural numbers.

\((x-15)(x-4)=0\)

x=4,15

Answer:

20

12

16

Step-by-step explanation:

if the y colume is equal to whatever is in the x column if you multiply the x column by 4, so 5 times 4 is 20 ec.

In order for the ratio of AP to PB to be 3/2, the coordinates of point P along the directed line segment AB are (14/5, -1).

The section formula returns the coordinates of a point that divides the line connecting two points in a ratio, either internally or externally.

Section formula is given as follows:

\((\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})\)

It is given that the coordinates of the points A and B are A(-2, -4), B(6, 1) and   AP/PB = 3/2

Let the coordinates of the point P be (a, b).

By using section formula,

(a, b) = \((\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})\)

(a, b) =  \((\frac{3(6)+2(-2)}{3+2} , \frac{3(1) +2(-4)}{3+2} )\)

(a, b) = \((\frac{18 - 4}{5} , \frac{3-8}{5})\)

(a, b) = \((14/5, -5/5)\)

(a, b) = \((14/5, -1)\)

Therefore, the coordinates of the point P along the directed line segment AB so that the ratio of AP to PB is 3/2 are (14/5, -1).

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Answer:

\(\frac{49}{60}\)

We can conclude that, both of them have eaten almost the complete bag of Tootsie rolls

Step-by-step explanation:

Given that:

Fraction of Tootsie rolls eaten by Jaxton = \(\frac{3}{5}\)

Fraction of Tootsie rolls eaten by Drake = \(\frac{5}{12}\)

Here, we have to use the Benchmark fractions to estimate what fraction of tootsie roll bags was eaten by Jaxton and Drake.

First of all, let us add the given two fractions to find the total amount of Tootsie rolls eaten by both of them together.

Total Tootsie rolls eaten by both of them =

\(\dfrac{3}{5} + \dfrac{5}{12}\\\\\text{Taking LCM of denominator i.e. 5 and 12 = 60}\\\Rightarrow \dfrac{3\times 12 + 5\times 5}{60}\\\Rightarrow \dfrac{49}{60}\)

The most commonly used benchmark fractions are 0, \(\frac{1}{2}\) and 1.

Here, with the fraction we can write our benchmark fractions as:

\(\dfrac{0}{60}, \dfrac{30}{60}, \dfrac{60}{60}\)

We can see that, \(\frac{49}{60}\) is near to \(\frac{60}{60}\).

Therefore, we can conclude that, both of them have eaten almost the complete bag of Tootsie rolls.

Answer:

y = 8x - 5

Step-by-step explanation:

Given:

To find:

How to find:

The slope is always known as "constant of variation" or "rate of change", but it's basically the increase of both y and x axes in simple terms. The decrease or increase in two points together and then found with the formula of rise/run (increase and decrease) (horizontal line/vertical line).

The y-intercept is always on the y-axis and is the beginning of what is learned in pre-algebra as a "story" which helps students practice finding the slope which again, is the change with "per" or "each".

Make sure to use the formula:

y = mx + b

Now we insert.

y = 8x <---------- slope

y = 8x - 5 <------ y-intercept and completed slope-intercept equation.

The reason it has a negative is because it started out as a negative y-intercept and is increasing by 8 through ordered pairs.

Answer:

y = 8x - 5

Step-by-step explanation:

because if its has a slope of 8 then m is 8

if the y intercept is -5 the b is -5

y = mx + b

y = 8x -5

Answer:

9(4x+3y)

Step-by-step explanation:

Answer:

9 (4x+3y)

Step-by-step explanation:

9(4x)+27y

9(4x)+9(3y)

9(4x+3y)

Through a review of census records, Rebecca was able to determine that the mean age of the population she was studying was 23.4 years old. This is known as a(n) "average."

Through her analysis of census records, Rebecca was able to calculate the average age of the population she was studying. This value, which is the sum of all ages divided by the total number of individuals, is known as the mean. In this case, the mean age of the population was 23.4 years old. This statistic provides a useful summary of the age distribution of the population, but it should be noted that there may be variability or outliers that could impact the interpretation of the mean. Therefore, it is important to also consider other measures of central tendency and dispersion when analyzing data.

The average is calculated by adding up all the ages in the population and dividing the sum by the total number of individuals. This statistical measure helps provide a general understanding of the age distribution in the population, allowing for further analysis and comparisons to be made.

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Therefore , the solution of the given problem of expressions comes out to be  students can develop their factoring abilities and avoid mistakes with practise and instruction.

Estimates that combine joining, disabling, and rather than randomly divide should be produced when variables are shifting. If they got together, they could solve a mental puzzle, provide some data, and instead software. A declaration of truth contains formulas, components, and mathematical processes like combination, subtraction, omission, and grouping. Both phrases and words can be assessed and analysed.

Here,

are some pointers to assist students B and C prevent incorrect factoring in the future:

Regularly practise factoring: Since factoring is a talent that must be honed, students should make sure to factor problems frequently. They will be better able to understand the procedure and spot trends in the expressions they are factoring as a result of this.

Verify the indications again because they are prone to error when factoring. Students should double-check their distribution of the signs and make sure no negative indicators are being left out.

Students should double-check their work by multiplying the factors back together after factoring an equation. They'll be able to correct any errors they may have made thanks to this.

If students need assistance with factoring, they should ask an instructor or tutor for assistance. Although factoring can be a challenging ability to master, students can develop their factoring abilities and avoid mistakes with practise and instruction.

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The statement B. "The diagonals are perpendicular and one pair of adjacent sides are congruent." is not sufficient to prove that a parallelogram is a square.

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. It has opposite angles equal in measure. The diagonals of a parallelogram bisect each other.

A square is a type of rectangle and a type of parallelogram. It is a four-sided polygon with all sides of equal length and all angles right angles. The opposite sides of a square are parallel and congruent, and opposite angles are congruent as well. The diagonals of a square are congruent and bisect each other. Additionally, the diagonals of a square are also perpendicular to each other.

Note that a rhombus also has congruent adjacent sides and perpendicular diagonals, but it's not a square.

Therefore, if the diagonals are perpendicular and one pair of adjacent sides are congruent, the parallelogram is not necessarily a square.

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The graph that shows two lines, which appear as one line shows a system of equations with infinitely many solutions. This is because two lines that are exactly the same have infinitely many points in common, and therefore infinitely many solutions.

Coexistent Lines refer to those that are merged or placed on top of each other. This pair of two overlapping lines is labeled coincident lines, and when simplified, their equations become identical.

Precise graphing of the lines and using correct equations is a crucial step towards avoiding such instances.

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Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

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The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, 91.2 is the standard deviations is the point estimate from 7%.

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

The standard deviation can be abbreviated SD, and is most commonly used in mathematical texts and equations with the lowercase Greek letter σ (sigma) for the population standard deviation, or the Latin letter s for the standard deviation of the sample.

The standard deviation of a random variable, sample, population, data set, or probability distribution is the square root of its variance. It is algebraically simpler than the mean absolute deviation, although less robust in practice. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data.

According to the Question:

Given that:

Defective widgets produced by ACME corporation was 7%

Total sample was 856 widgets.

Therefore, the Standard Deviation estimates from 7% is:

856 of 7% = 91.2

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Explanation

By definition.

so

Let

hence

I hope this helps you

Answer:

an abolitionist

Step-by-step explanation:

a person who favors the abolition of a practice or institution, especially capital punishment or

Answer: D An Abolitionist

Step-by-step explanation:

a person who favors the abolition of a practice or institution, especially capital punishment or (formerly) slavery

pls give me brainlest <3

f (4) = 61

g (4) = 2

Step-by-step explanation:

f(4) = 2(4)² - 3

f(4) = 8² - 3

f(4) = 64 - 3

f(4) = 61

g (4) = -4 + 6

g (x) = 2

The probability is\($\boxed{\frac{1}{3}}$.\)

To find the probability that the product of two numbers chosen from {3, 4, 5, 6} is a multiple of 9, we first need to determine the total number of possible pairs of numbers that can be chosen without replacement from this set.

There are \($\binom{4}{2} = 6$\) ways to choose two numbers from the set. These pairs are:

(3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)

Next, we need to determine which of these pairs have a product that is a multiple of 9. A number is a multiple of 9 if and only if it is divisible by 9, so the product of two numbers is a multiple of 9 if and only if at least one of the numbers is a multiple of 3.

From the set {3, 4, 5, 6}, only the numbers 3 and 6 are multiples of 3. Therefore, the pairs with a product that is a multiple of 9 are:

(3, 6), (6, 3)

Note that we have listed both (3, 6) and (6, 3) because the order in which the numbers are chosen does not matter.

Therefore, the probability that the product of two numbers chosen from {3, 4, 5, 6} is a multiple of 9 is:

\(\frac{number of pairs with product divisible by 9 }{total number of pairs} = \frac{2}{6} =\frac{1}{3}\)

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9514 1404 393

Answer:

Step-by-step explanation:

Assuming the lines that look parallel are parallel, all of the acute angles are congruent, and all of the obtuse angles are congruent. Any obtuse angle is the supplement of any acute angle.

∠C = ∠F

3x -10 = x +70 . . . . substitute the given values

2x = 80 . . . . . . . . . add 10-x

x = 40

__

∠D +∠F = 180

(x +27) +(2x -39) = 180 . . . . substitute

3x -12 = 180 . . . . . . . . . . . . . simplify

x -4 = 60 . . . . . . . . . . . divide by 3

x = 64 . . . . . . . . . add 4

__

∠B = ∠G

2(x +40) = 5x +44 . . . . . substitute

2x +80 = 5x +44 . . . . . . simplify

36 = 3x . . . . . . . . subtract 2x+44

12 = x . . . . . . divide by 3

_____

Additional comment

If you use the given values of x to find the angle measures, you quickly see that the figure is not drawn to scale, and that angles shown as acute may actually be obtuse.

To determine which point could be on the line that is perpendicular to Line MN and passes through point K, we need to analyze the slopes of the two lines.

First, let's find the slope of Line MN using the given points (2, 3) and (-3, 2):

Slope of Line MN = (2 - 3) / (-3 - 2) = -1 / -5 = 1/5

Since the lines are perpendicular, the slope of the perpendicular line will be the negative reciprocal of the slope of Line MN. Therefore, the slope of the perpendicular line is -5/1 = -5.

Now let's check the given points to see which one satisfies the condition of having a slope of -5 when passing through point K (3, -3):

For point (0, -12):

Slope = (-12 - (-3)) / (0 - 3) = -9 / -3 = 3 ≠ -5

For point (2, 2):

Slope = (2 - (-3)) / (2 - 3) = 5 / -1 = -5 (Matches the slope of the perpendicular line)

For point (4, 8):

Slope = (8 - (-3)) / (4 - 3) = 11 / 1 = 11 ≠ -5

For point (5, 13):

Slope = (13 - (-3)) / (5 - 3) = 16 / 2 = 8 ≠ -5

Therefore, the point (2, 2) could be on the line that is perpendicular to Line MN and passes through point K.

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40 pieces of gum are in the jar.

Given:

Mrs cooper has a jar of candy on her desk with 150 pieces.

2/3 of the candy is chocolate 1/5.

1/5 is sour candy and the rest of the pieces is gum.

Total pieces = 150

= 2/3 * 150

= 300/3

= 100 candy is chocolate.

gum + sour candy = 150 - 100

= 50

From 50 pieces 1/5th are sour candy

= 50 * 1/5

= 50/5

= 10 are sour candy.

pieces of gum = 150 - 100 - sour candy

= 50 - 10

= 40 are gum pieces

Therefore 40 pieces of gum are in the jar.

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The ordered pair of the equation is (1, - 1) or (3, 3).

The ordered pair of the equation is calculated by choosing a value of x and substituting it into the original equation and solving for the value of y as shown below.

The given equation is;

2x - y = 3

let x = 1

Now substitute the value of x into the original equation and solve for y as follows;

2x - y = 3

2 (1) - y = 3

2 - y = 3

y = 2 - 3

y = -1

We can also choose another value of x, say 3;

2(3) - y = 3

6 - y = 3

y = 3

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The information for the man's path in pieces are added below

The missing figure is added as an attachment, where the equation of the function that passes through the three points is calculated as

f(x) = -x^2/3 - x + 10/3

Using the above as a guide, we have the following:

Track direction "cutting hole":

The track direction of the man's path is downward as the coefficient of x^2 is negative (-1/3).

Route starting point:

From the graph, we have the starting point to be (-5, 0)

Path end point:

From the graph, we have the path end point to be (2, 0)

The highest point

Recall that

f(x) = -x^2/3 - x + 10/3

Differentiate and set to 0

-2x/3 - 1 = 0

So, we have

-2x/3 = 1

This gives

x = -3/2

So, we have

Highest = -(-3/2)^2/3 + 3/2 + 10/3

Highest = 49/12

So, the highest point is 49/12 units high

Maximum value:

This is the same as the highest point

i.e. Max = 49/12

Axis of Symmetry

We have

x = -3/2

This means that axis of symmetry is x = -3/2

The field:

The area under the curve represents the area of the region covered by the man's path on the mountain.

Term:

These are the terms of the function

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The derivative of the function f(x) = 1 / √9 + x using the definition of derivative is f'(x) = -1 / 2√9 + x.

The definition of derivative states that the derivative of a function at a point is the limit of the difference quotient as the difference between the points approaches 0. In this case, the difference quotient is

f'(x) = lim_{h→0} \frac{1/√{9+x+h} - 1/√{9+x}}{h}

To evaluate the limit, we can simplify the difference quotient as follows:

f'(x) = lim_{h→0} \frac{(9+x+h) - (9+x)}{2√{9+x+h}√{9+x}h}

We can then cancel the terms 9+x from the numerator and denominator, and we get the following limit:

f'(x) = lim_{h→0} \frac{h}{2√{9+x+h}√{9+x}h}

The limit of this expression as h approaches 0 is -1 / 2√9 + x, so the derivative of the function is f'(x) = -1 / 2√9 + x.

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Without changing the value, Marcus can add 3 positive counters and 3 negative counters. Option d is correct.

To determine the difference -8 - 3 (+3), Marcus wants to use a model with counters. He starts with 8 negative counters, and in order to add 3 positive counters without changing the value, he can add 3 positive counters and 3 negative counters.

By adding 3 positive counters, he is increasing the value by 3. However, since he wants to maintain the same value, he also needs to add 3 negative counters. This ensures that the net change in value remains zero.

So, by adding 3 positive counters and 3 negative counters to the model, Marcus can represent the difference -8 - 3 (+3) without changing the overall value. Therefore, d is correct.

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Answer:

= 33.3333% decrease

Step-by-step explanation:

(200−300)|300|×100

=−100300×100

=−0.333333×100

=−33.3333%change

=33.3333%decrease