how could lola solve this colored pencil problem quickly?

dz/dt for the given function z = sin(x)cos(y), where x = t and y = 2/t, is equal to cos(t)cos(2/t) + 2sin(t)sin(2/t)/\(t^{2}\)

To find dz/dt using the chain rule, we need to differentiate z with respect to x and y separately, and then multiply the derivatives by the corresponding derivatives of x and y with respect to t. Given z = sin(x)cos(y), where x = t and y = 2/t, let's calculate dz/dt.

First, differentiate function z with respect to x:

∂z/∂x = cos(x)cos(y)

Next, differentiate z with respect to y:

∂z/∂y = -sin(x)sin(y)

Now, differentiate x = t with respect to t:

dx/dt = 1

Differentiate y = 2/t with respect to t:

dy/dt = -2/\(t^{2}\)

Now, applying the chain rule, we have:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

= cos(x)cos(y)(1) + (-sin(x)sin(y))(-2/\(t^{2}\))

= cos(t)cos(2/t) + 2sin(t)sin(2/t)/\(t^{2}\)

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Answer:

7

Step-by-step explanation:

Hello~ Fluffy Strawberry here

Answer: 185

I hope this helps

From: Fluffy Strawberry~

the distributive property to factor out the greatest common factor is 6⋅1+6⋅5.

What is greatest common factor?

The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. To find the GCF of two or more numbers, you can use various methods such as prime factorization, listing factors, and using the Euclidean algorithm.

The GCF is a useful concept in many areas of mathematics, such as simplifying fractions, finding equivalent fractions, and solving equations involving fractions.

6 is the greatest common factor of 6 and 30.

=6+30:

=6⋅1+6⋅5

Hence the distributive property to factor out the greatest common factor is 6⋅1+6⋅5.

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x = 2

Answer:

x = 2

Step-by-step explanation:

Each triangle is made up of 2 radii (each of 5 units in length) and an included 30° angle.  

Therefore, the triangles are congruent.

So, DC = AB ⇒ x = 2

the analyst anger is answer B

Answer:

reflection

Step-by-step explanation:

if you look at it, its like its mirrored itself, so its reflection

Answer:

x+14.  

Sum of a number and 14 is x+14.

For various levels of output, businesses in a competitive market have the following production costs. Right now, the price on the market is $4. Total Cost Quantity 0 1 10 2 13 3 18 4 25 34. Therefore,

1. Each firm maximizes profit by supplying 2 units where MR = MC.

2. At $4 market price, market not in long-run equilibrium as ATC ($6.5) > price.

3. Market reaches long-run equilibrium at $6, the minimum point of ATC curve.

To determine the units each firm will supply to maximize profit and calculate the profit, we need to examine the cost and revenue associated with each quantity of output.

Quantity                    Total Cost

0                                       1

1                                       10

2                                      13

3                                      18

4                                     25

1. To find the quantity that maximizes profit for each firm, we need to compare the marginal cost (MC) and marginal revenue (MR) at each quantity level.

Quantity   Total Cost   MC       MR

0                  1                   -       -

1                  10                 9       4

2                  13                 3       4

3                  18                 5       4

4                  25                 7       4

To maximize profit, a firm will produce where MR equals MC. Looking at the table, we can see that at a quantity of 2, the MR and MC are equal. Therefore, each firm will supply 2 units to maximize profit.

2. To determine if the market is in long-run equilibrium at a market price of $4, we need to compare the market price with the average total cost (ATC) for each firm. If the market price is equal to or greater than the ATC, the market is in long-run equilibrium.

Let's calculate the ATC for each firm at a quantity of 2:

\(ATC = \frac{Total Cost}{Quantity}\)

\(ATC = \frac{13}{2}\)

ATC = 6.5

The ATC for each firm is $6.5, which is greater than the market price of $4. Therefore, the market is not in long-run equilibrium because firms are not covering their costs and would not continue to operate in the long run.

3. To determine the price at which the market will be in long-run equilibrium, we need to find the minimum point of the average total cost (ATC) curve. This point represents the price at which firms can cover their costs and earn a normal profit in the long run.

Looking at the table, we can observe that the minimum ATC occurs at a quantity of 3. Let's calculate the ATC at this quantity:

\(ATC = \frac{Total Cost}{Quantity}\)

\(ATC = \frac{18}{3} = 6\)

Therefore, the market will be in long-run equilibrium at a price of $6, which corresponds to the minimum point of the ATC curve.

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When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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Answer:

C (-4, 2)

Step-by-step explanation:

When rotating a point 90 degrees counterclockwise about the origin our point P(x,y) becomes P'(-y,x).

(-4, 2) is  the coordinates of M’, the image of M(2,4), after a counterclockwise rotation of 90° about the origin.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, The coordinates of M(2,4)

Coordinates of the image after counterclockwise rotation.

Since,

When a point with coordinate ( x , y ) is rotated 90° counterclockwise then the new coordinates of the point are given by ( -y , x ).

thus,

Coordinates of image(M') = (-4, 2)

Therefore, the coordinates of M’, the image of M(2,4), after a counterclockwise rotation of 90° about the origin is (-4, 2).

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Answer:

I think the answer is 20

Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For this problem, the parameters are given as follows:

\(\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2\)

The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:

X = 42:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

Z = (42 - 40)/2

Z = 1

Z = 1 has a p-value of 0.8413.

X = 38:

\(Z = \frac{X - \mu}{s}\)

Z = (38 - 40)/2

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

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It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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Answer:

13

Step-by-step explanation:

Just In case you want explanation-

1. 4 squared Meaning 4 x 4 = 16

2. 16 x 6 = 96

3x 6 = 18

96- 18 = 78

in the denominator, 25/ 5 = 5

11 minus 5 = 6

78 divided by 6

it gives you 13

Answer:

13

Step-by-step explanation:

Order of operations:

Parenthesis, exponents, multiplication and division, addition and subtraction

Answer:

The Larger bag contains more trail mix. Why because the larger bag has 10 more ounces than the smaller bag.

Algebra test because the correlation is higher.

What does a statistical correlation mean?

A statistical metric known as correlation, which is given as a number, describes the strength and direction of a relationship between two or more variables.

                         Although there may be a correlation between two variables, this does not necessarily imply that the change in one variable is what led to the change in the values of the other variable.

Why correlation, you ask?

In common conversation, we use the word correlation to describe situations where two or more items seem to be connected.

                       In the field of analytics, correlations are certain numbers that are computed to express how closely related variables are to one another.

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Answer:x=4+

16+m

​

x=4−

16+m

Step-by-step explanation:

Question

−x

2

+8x+m=0

Solve the equation

​

x=4+

16+m

​

x=4−

16+m

​

​

Evaluate

−x

2

+8x+m=0

Multiply both sides

x

2

−8x−m=0

Substitute a=1,b=−8 and c=−m into the quadratic formula x=

2a

−b±

b

2

−4ac

​

​

x=

2

8±

(−8)

2

−4(−m)

​

​

Simplify the expression

x=

2

8±

64+4m

​

​

Simplify the radical expression

x=

2

8±2

16+m

​

​

Separate the equation into 2 possible cases

​

x=

2

8+2

16+m

​

​

x=

2

8−2

16+m

​

​

​

Solve the equation

​

x=4+

16+m

​

x=

2

8−2

16+m

​

​

​

Solution

​

x=4+

16+m

​

x=4−

16+m

​

​

Question

−x

2

+8x+m=0

Solve the equation

​

x=4+

16+m

​

x=4−

16+m

​

​

Evaluate

−x

2

+8x+m=0

Multiply both sides

x

2

−8x−m=0

Substitute a=1,b=−8 and c=−m into the quadratic formula x=

2a

−b±

b

2

−4ac

​

​

x=

2

8±

(−8)

2

−4(−m)

​

​

Simplify the expression

x=

2

8±

64+4m

​

​

Simplify the radical expression

x=

2

8±2

16+m

​

​

Separate the equation into 2 possible cases

​

x=

2

8+2

16+m

​

​

x=

2

8−2

16+m

​

​

​

Solve the equation

​

x=4+

16+m

​

x=

2

8−2

16+m

​

​

​

Solution

​

x=4+

16+m

​

x=4−

16+m

​

​

After solving the equation, the number obtained is 4/3 and its reciprocal will be 3/4.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

Let the number be x.

Then the sum and reciprocal of the number is 25/12.

So, the equation will be,

x + 1/x = 25/12

(x² + 1)/x = 25/12

12x² + 12 = 25x or,

12x² - 25x + 12 = 0

Now, find the roots:

D = b² - 4ac

(-25)² - 4× 12× 12

D = 49

Then,

-(b ± √D)/2a

(25 ± 7)/24

So, the roots are,

(25 + 7)/24 = 4/3 and,

(25 - 7)/24 = 3/4

Then, the number is 4/3 and its reciprocal is 3/4.

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The measure of angle k will be 17 degree.

The length of KL will be 1.2 yards.

The length of JK will be 0.83 yards.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is the right triangle.

Now,

Since, The triangle is the right triangle.

Hence, The measure of the angle L = 90 degree

So, The measure of K = 180 - (73 + 90)

                                   = 17 degree

And, We know that;

sin θ = perpendicular / Base

⇒ sin 90° = JK / 0.83

⇒ 1 = JK / 0.83

⇒ JK = 0.83 yards

And, The triangle is the right triangle.

So, Apply the Pythagoras theorem, we get;

⇒ KL² = KJ² + JL²

⇒ KL² = 0.83² + 0.83²

⇒ KL² = 2 × 0.83²

⇒ KL = √2 × 0.83²

⇒ KL = 0.83 × 1.414

⇒ KL = 1.2

Thus, We get;

⇒ The length of KL will be 1.2 yards.

The length of JK will be 0.83 yards.

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Data that are accurate, consistent, and available in a timely fashion are considered C) high-quality.

High-quality data is characterized as being reliable, consistent, and timely. High-quality data offers a strong foundation for analysis and decision-making because it is accurate, error-free, and consistent.

It is a valuable asset for organizations because it promotes accurate reporting and analysis, increases operational efficiency, and allows for informed decision-making. Although database management systems like Oracle and Microsoft SQL Server can assist with managing and storing data, the quality of the data is unrelated to the particular technology or program employed.

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Let's see

\(\\ \rm\rightarrowtail x=0.444\dots\)

\(\\ \rm\rightarrowtail 10x=4.44\dots\)

From both

The linear function in slope-intercept form that represents the equation is given as follows:

y = 15 + 25x.

The variables are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which:

He began the year with 15 terms on the list, hence the parameter b is given as follows:

b = 15.

Of the 35 new terms in each chapter, Mr. Snow puts the definitions of 10 terms on the wall and adds the remaining terms to the vocabulary list to be memorized, hence the slope m is obtained as follows:

m = 35 - 10

m = 25.

Then the function is:

y = 25x + 15.

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Answer:

x - 2

Step-by-step explanation:

The reciprocal of each of the following fractions:

i) 7/3 - improper fraction

ii) 8/5 - improper fraction

iii) 7/9 - proper fraction

iv) 5/6 - proper fraction

v) 7/12 - proper fraction

vi) 8 - whole number

vii) 11 - whole number

To find the reciprocal of a fraction, we simply invert the fraction by swapping the numerator and the denominator.

i) Reciprocal of 3/7: 7/3

  - Classification: Improper fraction

ii) Reciprocal of 5/8: 8/5

   - Classification: Improper fraction

iii) Reciprocal of 9/7: 7/9

    - Classification: Proper fraction

iv) Reciprocal of 6/5: 5/6

   - Classification: Proper fraction

v) Reciprocal of 12/7: 7/12

  - Classification: Proper fraction

vi) Reciprocal of 1/8: 8/1 or simply 8

   - Classification: Whole number

vii) Reciprocal of 1/11: 11/1 or simply 11

    - Classification: Whole number

So, to summarize the classifications:

- Proper fractions: 7/9, 5/6, 7/12

- Improper fractions: 7/3, 8/5

- Whole numbers: 8, 11.

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The graph that represents the equation y - 4.5 = 2.5(x - 5) is the third graph

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, y - 4.5 = 2.5(x - 5).

y - 4.5 = 2.5x - 12.5.

y = 2.5x - 8.

Now, to determine the graph we'll choose some random values of x for which we'll have different values of y.

When x = - 1 , y = - 10.5 ⇒ (-1, -10.5 ).

When x = 0 , y = - 8 ⇒ (0, - 8).

When x = 1 , y = -5.5 ⇒ (1, -5.5).

When x = 2 , y = -3 ⇒ (2, -3).

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Answer:

6

Step-by-step explanation:

Answer:

$10.11

Step-by-step explanation:

Answer:

10.11

Step-by-step explanation:

7% of 9.45 is 0.66, and 9.45 + 0.66 = 10.11, so the answer is 10.11