Complete the statement comparing Manuel’s and Gretchen’s data.

Select the correct answer from each drop-down menu.

Gretchen’s data values Manuel’s data values because the are for Manuel’s data.

The value of the constant in the function is c  = -√3π²/6(3-π).

A differential equation is an equation that relates an unknown function and one or more of its derivatives. The equation dy/dx = f(x) is a simple example of a differential equation. Solving this equation means finding a function y with a derivative f. Therefore, the solutions of dy/dx are the antiderivatives of f. If F is one antiderivative of f, every function of the form y = f(x) + c is a solution of that differential equation.

Initial-value problems arise in many applications. Next we consider a problem in which a driver applies the brakes in a car. We are interested in how long it takes for the car to stop. Recall that the velocity function v(t) is the derivative of a position function s(t), and the acceleration a(t) is the derivative of the velocity function. In earlier examples in the text, we could calculate the velocity from the position and then compute the acceleration from the velocity. In the next example, we work the other way around. Given an acceleration function, we calculate the velocity function. We then use the velocity function to determine the position function.

The given equation is xy = y + x² sinx

⇒ xy - y =  x² sinx

⇒ y(x-1) =  x² sinx

⇒ y =  x² sinx/(x-1) +c

Also, y(π/3) = 0

Put x = π/3 in above equation:

y(π/3) =  (π/3) ² sin(π/3) /((π/3)-1)  + c = 0

After solving the above equation, we get c  = -√3π²/6(3-π)

Thus, the value of the constant in the function is c  = -√3π²/6(3-π).

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The actual distance (in miles) between her town and the state capital is 90 miles.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, a map of the state where your friend lives has the scale 1/2 in : 2 mi.

Now, 10 ÷ 1/2

= 10×2

= 20

Her measurement was 4 1/2 =9/2 inches.

Now, 20×9/2

= 90 miles

Therefore, the actual distance (in miles) between her town and the state capital is 90 miles.

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"Your question is incomplete, probably the complete question/missing part is:"

A map of the state where your friend lives has the scale 1/2 in : 2 mi.

Your friend measured the distance between her town and the state capital on the map. Her measurement was 4 1/2 inches. Based on your friend's measurement ,what is the actual distance (in miles) between her town and the state capital?

Answer:

25 minutes

Step-by-step explanation:

5/12×60 minutes

5×60=300

300/12

Answer =25

The of sin^2-cos^2 = [tex]Sin 2x Cos 2x = 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]

The sine of the angle is the ratio of the hypotenuse, or the angle's opposite, to the perpendicular in a right-angled triangle. Sinus is defined as Sinus = Perpendicular / Hypotenuse.

Sin 180 has a value of 0 precisely. One of the fundamental trigonometric functions is sine, which may be used to calculate the angle or sides of a right-angled triangle. Another name for it is trigonometric ratio.

If theta is an angle, then sine theta is the ratio of a right triangle's hypotenuse to its perpendicular.

trigonometric double angle formulas,

[tex]Sin 2x = 2 sin x cos x[/tex] ————(i)

And,

[tex]Cos 2x = Cos2x - Sin2x[/tex]

[tex]= 2 cos2x - 1 [Since Sin2 x + Cos2 x = 1][/tex]             ————(ii)

[tex]= 1 - 2Sin2x[/tex] ————(iii)

Now, multiply equation I by (ii) or (ii) by equation I to obtain the value of Sin 2x Cos 2x (i)

Think about equation I and (ii),

[tex]Sin 2x = 2 sin x cos x[/tex]

And,

[tex]Cos 2x = 2 cos2x - 1[/tex]

Simplifying the above equation, then we get

[tex]Sin 2x Cos 2x = 2 Sin x Cos x (2 cos2x - 1)= 4 Sin x Cos3 x - 2 Sin x Cos x= 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]

Think about equation I and (iii),

[tex]Sin 2x = 2 sin x cos xCos 2x = 1 - 2 Sin2x[/tex]

Simplifying the above equation, then we get

[tex]Sin 2x Cos 2x = 2 Sin x Cos x (1 - 2 Sin2x)= 2 Sin x Cos x - 4 Sin3 x Cos x= 2 Cos x (Sin x - 2 Sin3 x)So,Sin 2x Cos 2x = 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]

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The rate of change for a graph passing through (0, 0) and (2, -180) is -90 pieces of candy per day

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The slope intercept form of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Let y represent the total pieces of candy remaining after x days. Let us assume that the graph passes through (0, 0) and (2, -180). Hence:

[tex]Slope(rate\ of\ change) = \frac{y_2-y_1}{x_2-x_1}\\ \\substituting:\\\\slope=\frac{-180-0}{2-0} =-90[/tex]

The rate of change is -90 pieces of candy per day

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Given:-

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:)

After cost, the more money did Kevin make on Saturday than on Monday is $376.89.

The amount of Spends on monday is,

Sales = $397.35

Supply cost = $108.72

So the profit he is earning is

$397.35 - $108.72 = $288.63

The amount of Spends on Saturday is,

Sales = $914.06

Supply cost = $248.54

So the profit he is earning is

$914.06- $248.54= $665.52

Money did Kevin make on Saturday than on Monday is,

Money from saturday - money from monday

= $665.52 - $288.63

= $376.89

Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.

Any profits generated are returned to the company's owners, who can decide whether to keep the money for themselves, pay dividends to shareholders, or reinvest it in the company.

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The measure of angles becomes:

∠a = 30°

∠b = 60°

∠c = 105°

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

∠a and 30° are vertical angles and vertical angles are equal

∠a = 30°

We have a triangle with a, b and a right angle. Triangles have angles that add to 180°.

∠a + ∠b + 90° = 180°

30° + ∠b + 90° =180°

120° + ∠b = 180

∠b = 180° - 120°

∠b = 60°

Angle c and 70 form a straight line and straight lines are 180 degrees

∠c + 75° = 180°

∠c = 180° - 75°

∠c = 105°

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Answer:

46

Step-by-step explanation:

draw a line at 96° & make it parallel to bottom line

which will slice 96° into 2 angles

lower half is 180-130=50

top half is 96-50=46

angle 4r equals to top half

The exact length of line segment PQ is 22.4.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

Given;

p(x,y)=(17,4)

m(x,y)=(-2,16)

Now,

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

D^2= (-2-17)^2+(16-4)^2

D^2=361+144

D^2= 505

D=22.4

Therefore, the distance will be 22.4

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Answer:

Howdy so if you buy an item to which 6% tax is added, you pay 106% of the price. The price of the item is $50, you pay 50(1.06) = $53.

Answer: the answer is 180 km.

Step-by-step explanation:

Answer:

180 km

Step-by-step explanation:

1 cm to 20 km

9cm=20 times 9

180 kilometers

The standard parameterization for the tangent line  is x = 12t + 18 , y = 3t + 13 , z = 54t + 54

Equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables.

Given that,

Given that, t = t0 = 3, I + (3t + 4) j + (2t 3) k

In order to get the tangent line to the curve at t=3, (x, y, z) = 18, 13, and 54,

r'(t) = 4t, 3, > and r'(t=3) = 12, 3, 54>. (18, 13, 54)

finally,

x = 12t + 18

y = 3t + 13

z = 54t + 54

The tangent line's usual parameterization is as follows:

x=12t+18, y=3t+13, and z=54t+54

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You can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.

Determine the range of the data: 0.6 to 4.7.

Divide the range by the number of classes (5) to find the class width: (4.7 - 0.6) / 5 = 0.76.

Determine the lower limits of each class by starting at the minimum value (0.6) and adding the class width repeatedly: 0.6, 1.36, 2.12, 2.88, 3.64, 4.4.

Count the number of data values that fall into each class and record it in a table.

Draw a bar for each class using the lower limit of the class as the x-axis value and the height of the bar equal to the number of data values in the class.

After creating the histogram, you can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.

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n−4  out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex],  [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.

Now, According to the question:

It is easy to show that a tree with  n ≥ 9 can have at most one vertex of degree n - 3. It is [tex]v_0[/tex].

Now, there are n - 1 - (n - 3) = 2 vertices that are not adjacent to [tex]v_0[/tex], it is also

[tex]v_n_-_1[/tex] and [tex]v_n[/tex]

Then a desired tree can be of 3 possible forms:

1. n - 4 out of n - 3  neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 2 and is adjacent to both [tex]v_0[/tex] and [tex]v_n_-_1[/tex]. [tex]v_n_-_1[/tex] has degree 2 and is adjacent to [tex]v_k[/tex] and [tex]v_n.v_n[/tex] is a leaf.

2. n − 5  out of the n − 3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_j[/tex] and [tex]v_k[/tex]. [tex]v_j[/tex]has degree 2 and is adjacent to [tex]v_0[/tex] and  [tex]v_n_-_1[/tex]. [tex]v_k[/tex] also has degree 2 and is adjacent to[tex]v_0[/tex] and [tex]v_n[/tex]. [tex]v_n[/tex] and  [tex]v_n_-_1[/tex] are both leaves.

3. n−4  out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex],  [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.

It is then easy to computer the number of trees in each form and sum them up.

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The mean in the above distribution is 1.84

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

The figure

The mean value is then calculated as

Mean = SUm of the product of children and familes/Sum of families

So, we have

Mean = (0 * 23 + 1 * 19 + 2 * 29 + 3 * 9 + 4 * 20)/(23 + 19 + 29 + 9 + 20)

Evaluate

Mean = 1.84

Hence, the mean is 1.84

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The probability of p(copper)=0.28

Probability is a measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. Probability is a fundamental concept in mathematics, statistics, and science that is used to quantify uncertainty and forecast the likelihood of future events based on available data. Probability is a measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

Given

Total Beads =112+96+192=400

Placing the bead back to the crate

so the total beads are always 400

copper:112

p(copper)=112/400=0.28

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Janet hiked a distance of 2.5 miles which is equivalent to 4 km

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

Speed is the ratio of total distance to total time travelled. It is given by the equation:

Speed = distance / time

Janet hiked 2.5 miles in one hour. Hence:

Speed = distance / time = 2.5 miles / one hour = 2.5 miles per hour

1 mile = 1.609 km

2.5 miles = 2.5 miles * 1.609 km per mile = 4 km

Janet hiked 4 km

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Answer:

39°

Step-by-step explanation:

Information we need to know

As we know, one of the angles in this triangle is 39° this means that the angle opposite it would also be 39°! This is because as the triangle is SAS v and the given 39 has to be equal

Have a lovely day :)

Answer:

39°

Step-by-step explanation:

Triangle HJI is an isosceles triangle.

In isosceles triangles the base angles are congruent which means their measures are equal.

So the measure of m∠HIJ = 39°

Option (B) and (E) functions are solutions of the differential equation y′′+2y′+1y=0.

An equation known as a differential equation describes the derivative or derivatives of an unknown function. Because they are equations involving a function and its derivatives (where the variable is a function rather than a number) (the functions obtained by differentiating it). Save this response. Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.

Given that,

y′′+2y′+1y = 0

A.E = m² + 2m + 1 = 0

or, (m + 1)² = 0

or, m = ± 1

y = (c₁ + c₂x)e⁻ˣ

y = c₁e⁻ˣ + c₂xe⁻ˣ

Thus, option (B) and (E) are solutions  of the differential equation:

y′′+2y +1y = 0.

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Answer:

9 : 7

Step-by-step explanation:

given the ratio

4.5 : 3 [tex]\frac{1}{2}[/tex] , that is in decimal form

4.5 : 3.5 ( multiply both parts by 10 to clear the decimal )

= 45 : 35 ( divide both parts by 5 )

= 9 : 7 ← in simplest form

Answer:

9:7

Step-by-step explanation:

Convert all the numbers to either decimal or fraction. The operation becomes simple.

Simplifying after converting to decimal

Convert 3 1/2 to decimal 3 1/2 = 3 + 1/2

1/2 = 0.5

3 + 1/2 = 3 + 0.5 = 3.4

Ratio 4.5:3.5 = 4.5/3.5

Divide by 5 to give
[tex]\dfrac{4.5 /5 }{3.5/5} = 0.9/0.7\\\\[/tex]

Multiply both numerator and denominator by 10
0.9 x 10 = 9

0.7 x 10 = 7

So the ratio becomes 9/7 = 9:7

Simplifying after converting to fraction

4.5 = 4 + 0.5

0.5 = 1/2

5.5 = 4 + 1/2 = 4 1/2

Convert to mixed fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2

Convert 3 1/2 to fraction

3 1/2 = (3 x 2 + 1)/2 = 7/2

So 4.5 : 3 1/2 = 9/2 : 7/2

Multiplying by 2 we get the same answer: 9:7

Choose whichever approach you feel comfortable with

70 degrees is the measure of MQN from the provided figure.

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

From the given figure, we are to determine the measure of angle <MQN. Applying the sum of angles on a straight line:

<MQN + 80 +30 = 180

<MQN + 110 = 180

<MQN = 180 - 110

<MQN = 70 degrees

Hence the measure of <MQN from the given figure is 70 degrees.

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Answer:

That's what I got, not sure but I tried so I hope it helps.

The solution to the system is x1 = -4, x2 = 10.

What is the solution to the system?

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitute solutions to the system. (5, 4) is a solution of the first equation, but not the second.

The given system can be converted to an augmented matrix as follows:

[ 2 1 | 2 ]

[-1 -1 -1 | 6 ]

To find all solutions, we will reduce the system to echelon form and back substitute.

Step 1: Echelon Form

We can perform row operations to reduce the matrix to echelon form:

[ 2 1 | 2 ] R1 = R1 * 1/2

[-1 -1 -1 | 6 ]

[ 1 1/2 | 1 ] R2 = R2 + R1

[ 0 -3/2 -1 | 5 ]

Step 2: Reduced Row Echelon Form

Next, we can perform additional row operations to reduce the matrix to a reduced row echelon form:

[ 1 1/2 | 1 ] R2 = R2 * 2

[ 0 1 | 10 ]

The reduced row echelon form of the matrix represents the system of equations in a simplified form and the solution to the system can be obtained by back substituting.

Step 3: Back Substituting

x2 = 10

x1 = 1 - 1/2 x2 = 1 - 1/2 * 10 = 1 - 5 = -4

Therefore, the solution to the system is x1 = -4, x2 = 10.

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Answer:

x = -39

-39 + 27 = -12

Step-by-step explanation:

Hope it helps! =D

Answer:

Here you have

Step-by-step explanation:

x + 27 = -12

x= -12 - 27

x= - 39

From 9:00 a.m. to 9:27 a.m., the temperature changed from 54°F to -4°F, a change of 58°F. This change took 27 minutes.

The temperature change per minute was 58°F / 27 minutes = 2.15°F per minute.

The depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units is 15000.

Cost of machine = Rs. 1,70,000; Scrap value = Rs. 20,000;

Depreciation in production during the first year =  6,000 units;

Production units during the life of the machine = 60,000 units

Depreciation rate per unit = (Rs. 1,70,000 -  Rs. 20,000)/ 60,000 units

=  Rs. 2.5

Depreciation of first year =  6,000 * Rs. 2.5 = Rs. 15,000

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Complete question

If the original cost of a machine is Rs. 170,000, estimated scrap value Rs. 20,000, what is the depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units.