Students will present a play in an
auditorium that has 550 seats. Each
student performing in the play must
sell 12 tickets to the performance.
The remaining 370 tickets will be
sold by other students in the school.
Which equation could be used
to
find x, the number of students
performing in the play?

Rigid motions and dilations are transformations in Euclidean space. They are both types of transformations that preserve distances and angles.

Similarities between Rigid motions and Dilations:

Both preserve the length of lines and distances between points.

Both preserve angles between lines.

Differences between Rigid motions and Dilations:

Rigid motions are a combination of rotations, translations, and reflections, while dilations are just scaling transformations.

Rigid motions preserve orientation, while dilations change it.

Rigid motions preserve the shape of figures, while dilations change the size of figures but preserve the ratio of lengths of corresponding sides.

Properties and the transformations that preserve them:

Length of lines: Rigid motions and dilations preserve the length of lines.

Distances between points: Rigid motions and dilations preserve distances between points.

Angles between lines: Rigid motions and dilations preserve angles between lines.

Orientation: Rigid motions preserve orientation, while dilations change it.

Shape of figures: Rigid motions preserve the shape of figures, while dilations change the size of figures but preserve the ratio of lengths of corresponding sides.

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Part E: The area that Jordan can walk around is equal to the area of a circle with a radius of 6 feet is 113 square feet.

Part A: Wendell cannot make a triangular garden using pieces A, B, and F because the sum of the lengths of the two shorter sides of a triangle (in this case, pieces A, B, and F) must be greater than the length of the longest side (in this case, piece F, which is 2 feet long) in order for the triangle to be a valid one. Since the sum of the lengths of pieces A and B is 12 feet, which is greater than the length of piece F, it is not possible to make a triangular garden using these pieces.

Part B: Wendell cannot make a triangular garden using pieces D, E, and F because the sum of the lengths of the two shorter sides of a triangle (in this case, pieces D, E, and F) must be greater than the length of the longest side (in this case, piece D, which is 8 feet long) in order for the triangle to be a valid one. Since the sum of the lengths of pieces E and F is 5 feet, which is less than the length of piece D, it is not possible to make a triangular garden using these pieces.

Part C: Wendell can make a rectangular garden with the pieces of wood he has by using pieces A and C or pieces B and D. He cannot use pieces E and F because they are not long enough to make up one of the sides of a rectangle.

Part  D: Wendell can not create two triangular gardens using all six pieces of wood as the sum of the lengths of the two shorter sides of a triangle must be greater than the length of the longest side, and he only have 3 pieces with length greater than 3 feet which is required to create one triangle.

Wendell can create two rectangular gardens using all six pieces of wood by using pieces A and C, and pieces B and D.

Part E: The area that Jordan can walk around is equal to the area of a circle with a radius of 6 feet (since the chain is 12 feet long).

The formula to calculate the area of a circle is πr^2

where π is approximately 3.14 and

r is the radius of the circle,

so the area that Jordan has to walk around is approximately

3.14 x 6² =113 square feet.

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The solution for the system of inequalities is (-0.83,-1.34).

What is an inequality?

In algebra, the inequality symbol is used to show how two expressions are related in an inequality assertion. Uneven expressions can be seen on both sides of a sign of inequality.

We are given a graph on which two inequalities are plotted

So, first, we will have to frame the equations from the points.

For the blue line, we have points (0,-3) and (-1.5,0)

So, using slope-intercept form, we get the equation as

y + 2x ≥ -3

For the red line, we have points (-1,-2) and (0,2)

So, using slope-intercept form, we get the equation as

y - 4x ≥ 2

For finding the solution, we will subtract both the equations

On subtracting, we get

⇒(y+2x) - (y-4x) = -3 - 2

⇒y+2x - y + 4x = -5

⇒6x = -5

⇒x = -0.83

Substituting this value in the equation, we get

⇒y+2(-0.83) = -3

⇒y-1.66 = -3

⇒y = -1.34

Hence, the solution for the system of inequalities is (-0.83,-1.34).

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You can use this trigonometry calculator in two common situations when trigonometry is required. Use the calculator's first section to get the values of sine, cosine, tangent, and their reciprocal functions.

A subfield of mathematics is trigonometry. In particular, it describes and applies the connections and ratios between angles and sides in triangles. Trigonometry largely works with angles and triangles. Thus, solving triangles exactly correct triangles as well as any other kind of triangle you choose is the main application.

Numerous difficulties in daily life, such figuring out the height or separation between two objects, can be solved using trigonometry. Other uses include the satellite navigation system, astronomy, and geography.

Additionally, sine and cosine functions are essential for explaining periodic events; with their help, we can explain oscillatory movements (like those in our straightforward pendulum calculator) and waves like sound, vibration, and light.

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Answer:

To solve this problem we can use the formula for future value of an investment, which is:

FV = PV(1+r)^t

Where PV is the present value, r is the interest rate, t is the number of years, and FV is the future value.

In this case, we know that PV = $4,900, r = 3% = 0.03, and FV = $5,920.

So we can rearrange the formula to solve for t:

t = log(FV/PV) / log(1+r)

t = log($5,920 / $4,900) / log(1+ 0.03)

t ≈ 10.3 years

Therefore, it would take approximately 10.3 years for the account to reach $5,920.

(b) The probability of a positive test result is 0.0159.

(c) The probability that a person has the HIV antibody, given a positive test result, is 0.735. In this case, that would be 0.8 x 0.9 = 0.72.

This means that, if someone tests positive for the HIV antibody, there is a 73.5% chance that they actually have the HIV antibody. This number is determined by taking into account the false positive rate and true positive rate of the test.

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Answer:  C. proportion

Reason:

A fraction or ratio is something like [tex]\frac{2}{3}[/tex]

Something like [tex]\frac{2}{3} = \frac{4}{6}[/tex] is a proportion that ties together two fractions.

Answer:

C. proportion

Step-by-step explanation:

It is statement of equality of two ratios

A. fraction

B. ratio

C. proportion

D. rate

(I think the word should be "equality", not "quality".)

The ratio of a to b can be written as:

a to b, a:b, a/b

When you set a ratio equal to another ratio, then you have a proportion.

If ratio a/b is equal to ratio c/d, then you can write

a/b = c/d,

and now you have a proportion.

For the table of values gives, the equation of line is obtained as y = 1/3x.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The coordinate points for cups of flour, x and loaves of bread y is given in the table.

The slope-intercept form of an equation is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

(3 - 2)/(9 - 6)

1/3

So, the slope point is obtained as m = 1/3.

The equation becomes - y =1/3 x + b

To find the value of b substitute the values of x and y in the equation -

2 = 1/3(6) + b

2 = 2 + b

b = 2 - 2

b = 0

So, the value for b is 0.

Now, the equation becomes -

y = 1/3x + 0

y = 1/3x

The graph is plotted for the equation.

Therefore, the equation is y = 1/3x.

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The equation of the line passing through M and perpendicular to PR would be y = -x + 6.

What is the equation of the line?

An equation of a line is a mathematical expression that describes the relationship between the variables x and y that defines the position of a point on the line. There are several ways to write the equation of a line, including slope-intercept form (y = mx + b), point-slope form (y - y1 = m(x - x1)), and standard form (ax + by = c).

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line. To find the midpoint of a line segment, you need to take the average of the x-coordinates and the y-coordinates of the two endpoints.

Given the line segment Q(-6, 2) and R(10, 6), the midpoint is:

((-6+10)/2 , (2+6)/2) = (2,4)

So the midpoint of the line segment Q(-6, 2) and R(10, 6) is (2,4).

Now find the slope of PR = 6-(-4)/10 = 10/10=1

Hence, the slope of the line passing through M and perpendicular to PR would be = -1.

Now we can form the equation of the line:

y - 4 = -1(x - 2)

y - 4 = -x + 2

y = -x + 6

Hence, the equation of the line passing through M and perpendicular to PR would be y = -x + 6.

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Answer:

12 strawberries

28 honeydew

Step-by-step explanation:

[tex]\frac{strawberries}{grapes}[/tex] = [tex]\frac{3}{9}[/tex] = [tex]\frac{x}{36}[/tex]

9 x 4 = 36

so, 3 x 4 = 12

There are 12 strawberries

[tex]\frac{strawberries}{honeydew}[/tex] = [tex]\frac{6}{14}[/tex] = [tex]\frac{12}{x}[/tex]

6 x 2 = 12

so, 14 x 2 = 28

There are 28 honeydew

10.8 m = 10*(8/10)=54/5 m

1.5 h = 3/2 h

distance = 54/5

time = 3/2 h

Speed = distance /time

= 54/5 ÷ 3/2 = 7.2 m/h

how far will the snail travel in 5 minute ?

5 min = 5/60 = 1/12 h

In 1/12 h the snail will travel

7.2 * 1/12 m = 0.6 m = 60 cms

Based on the constant rate of painting, Owen will paint 1600 square feet in 80 minutes.

The expression for calculation to find the area painted in 80 minutes is -

Area to be painted in 80 minutes = area painted in one minute × time spent

Keep the values in formula to find the area painted

Area to be painted in 80 minutes = 20 × 80

Performing multiplication on Right Hand Side of the equation

Area to be painted in 80 minutes = 1600 square feet

Thus, the painted area by Owen will be 1600 square feet.

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30.6% of survey respondents do not like both hamburgers and burritos, with the strongest association being that customers who like hamburgers are more likely to not like burritos.

Part A: The number of survey respondents that do not like hamburgers is 205 - 81 = 124.

Of these 124 respondents, 38 do not like burritos as well, so the percentage of respondents that do not like both hamburgers and burritos is 38 / 124 * 100% = 30.6%.

Part B: The marginal relative frequency of all customers who like hamburgers is 81 / (81 + 205) = 28.2%.

Part C: The conditional relative frequency of customers that like burritos given they like hamburgers is 49 / 81 = 60.5%.

The conditional relative frequency of customers that do not like burritos given they like hamburgers is 32 / 81 = 39.5%.

The conditional relative frequency of customers that like hamburgers given they like burritos is 49 / 141 = 34.8%.

The conditional relative frequency of customers that do not like hamburgers given they like burritos are 92 / 141 = 65.2%.

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Answer:

No.

Step-by-step explanation:

A linear function can be identified if the function is a line when graphed or if the x is to the first power. X is to the third power, so it's not linear.

Hope it helped!

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Looking for improper or mixed fraction:}[/tex]

[tex]\mathsf{310\% \rightarrow \dfrac{310}{100} \rightarrow 3.1}[/tex]

[tex]\mathsf{\rightarrow 3.1 \times \dfrac{10}{10}}[/tex]

[tex]\mathsf{\rightarrow \dfrac{3.1}{1}\times\dfrac{10}{10}}[/tex]

[tex]\mathsf{\rightarrow \dfrac{3.1\times10}{1\times10}}[/tex]

[tex]\mathsf{\rightarrow \dfrac{31}{10}}[/tex]

[tex]\mathsf{\rightarrow 3 \dfrac{1}{10}}[/tex]

[tex]\huge\text{Therefore, your answers should be:}[/tex]

[tex]\huge\boxed{\mathsf{Fraction \rightarrow \dfrac{310}{100}\ \& \ Mixed\ Number \ \rightarrow 3\dfrac{1}{10}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Mary's speed, given the kilometers she rode in 7 hours, can be found to be 12. 8 km / hr

To find the speed that Mary was going in order to have been able to travel 89.6 kilometers in 7 hours, you can use the speed formula which is:

= Distance / Time

Distance =  89. 6 kilometers

Time = 7 hours

The speed that Mary was going at is therefore :

= 89. 6 km / 7 hours

= 12. 8 km / hr

In conclusion, the speed that Mary was going at was 12. 8 km / h.

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Answer:

sin-1(-1/2), 180 + sin-1(-1/2), 360 + sin-1(-1/2)

The equations c = 18z, 3s = P, and L = 60w represent a proportional relationship, but A = s² does not represent a proportional relationship.

The equation that represents a proportional relationship, or a line, is y = kx, where k is the constant of proportionality.

If we take the first equation, Volume measured in cups (c) vs The same volume measured in ounces (z): c = 18z

Here, 18 is a constant

∴It is a proportional relationship.

If we take the second equation, the Area of a square (A) vs The side length of the square (s): A = s²

This is a quadratic equation.

∴It is not a proportional relationship.

If we take the third equation, Perimeter of an equilateral triangle (P) vs The side length of the triangle (s): 3s = P

Here, 3 is a constant

∴It is a proportional relationship.

Finally, If we take the fourth equation, Length (L) vs Width (w) for a rectangle whose area is 60 square units: L = 60 w

Here, 60 is a constant

∴It is a proportional relationship.

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The average rate of change of f(x) from x = 1 to x = 3 is 0.5

The average rate of change of a function over an interval is the change in the function value (y) divided by the change in the input value (x) over that interval.

To find the average rate of change of f(x) = [tex]x^{3}[/tex] - [tex]4x^{2}[/tex] + 5 from x = 1 to x = 3, we can use the following formula:

(f(3) - f(1)) / (3 - 1)

substituting the function value, we get

([tex]3^{3}[/tex] - 4[tex](3)^{2}[/tex] + 5 - ([tex]1^{3}[/tex] - 4[tex](1)^{2}[/tex] + 5)) / (3 - 1)

= (27 - 36 + 5 - (1 - 4 + 5)) / 2

= (1) / 2

So the average rate of change of f(x) from x = 1 to x = 3 is 0.5

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Answer:

87.5/100

Step-by-step explanation:

Percents are parts of a whole. So if we imagine that the whole is 100, then 87 1/2% would be 87.5/100

A square rotated about its center by 360º maps onto itself at 4  different angles of rotation. You can reflect a square onto itself across 4  different lines of reflection.

It is important to note that a square has 4 angles of rotation and 4 lines of symmetry.

The 4 angles of rotation implies that you can tend to  rotate it  4 times so as to have it line up with its main  image before hitting 360°.

The 4 lines of symmetry which are:

Therefore the first and second blank is both 4.

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Answer:

Joe graphed the wrong y-axis. The y-axis is (0,2) Also the x-axis is wrong, its supposed to be (4,0).

Step-by-step explanation:

(a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, (d) boxplot is attached, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

(a) The mean = sum of all values divided by the number of values

μ = (x1 + x2 + ..... + xn)/n

n = 20

μ = (0.0395 + 0.0443+ 0.0450 + ... + 0.0550 + 0.0571)/20

μ = 0.9878/20

μ = 0.0494

(b) Variance = sum of squared deviations from the mean divided by n-1

s² = {(x1-μ)² + (x2-μ)² + .... (xn - μ)²)/(n-1)

s² = {(0.0395-0.0494)² + (0.0443-0.0494)² + .... +(0.0571-0.0494)²}/19

s² = 0.000016

(b) The minimum is 0.0395 and the maximum is 0.0571.

since the number of data is even, the median will be the average of two middle values.

M = Q2 = (0.0496+0.0499)/2 = 0.04975

Now, the first quartile is the median of the data values below the median

so Q1 = (0.0470+0.0485)/2 = 0.04775

And third quartile will be the median of the data values above the median

Q3 = (0.0504+0.0516)/2 = 0.0510

(c) Since we know that the number of data values is even, the median will be the average of the two middle values of the data set

so M = (0.0496+0.0499)/2

or M = 0.04975

(d) The boxplot is at maximum and minimum values. It will start in Q1 and end in Q3 and has a vertical line at the median or Q2.

The boxplot is attached.

(e) The 5th percentile means 0.05(n+1)th data value

or = 0.05(20+1) = 1.05th data value

5th percentile = 0.0550 + 0.05(0.0443-0.0395) = 0.03974

similarly,

95th percentile = 0.0550 + 0.95(0.0571-0.0550) = 0.056995

Therefore, (a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

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If three inches are cut off each piece, the expression represents the new total length of all five pieces of wood will be 5 x (initial length) - 15 .

To derive the expression:

Multiply 5 (the number of pieces) times the initial length of each piece
5 x (initial length)

Subtract 3 (the amount cut off each piece) times 5 (the number of pieces)

5 x (initial length) - (3 x 5)

Simplify

5 x (initial length) - 15

New total length of all five pieces of wood:

5 x (initial length) - 15

Hence the required expression is 5 x (initial length) - 15.

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We can start solving this problem by using a system of equations. Let x be the selling price of a card and y be the selling price of a photo frame.

From the information given, we know that on the first day:

3x + 9y = 75 (1)

And on the second day:

8x + 5y = 67 (2)

Now we have two equations with two variables. To find the value of x and y, we can use either substitution or elimination method.

One possible way to solve for x and y is to use substitution method:

Solve equation (1) for x in terms of y:

x = (75 - 9y) / 3

Substitute this expression into equation (2) to eliminate x:

8((75 - 9y) / 3) + 5y = 67

Solving this equation for y:

y = 3

Now we can substitute this value of y back into equation (1) or (2) to find the value of x:

3x + 9(3) = 75

3x = 48

x = 16

So the selling price of a card is $16 and the selling price of a photo frame is $3.

Answer:

Photo frame = $7

Card = $4

Step-by-step explanation:

Define the variables:

Given information:

Create a system of linear equations using the given information and defined variables:

[tex]\begin{cases}3c + 9p = 75\\ 8c + 5p = 67\end{cases}[/tex]

Rearrange the first equation to isolate c:

[tex]\implies 3c+9p=75[/tex]

[tex]\implies 3(c+3p)=75[/tex]

[tex]\implies \dfrac{3(c+3p)}{3}=\dfrac{75}{3}[/tex]

[tex]\implies c+3p=25[/tex]

[tex]\implies c+3p-3p=25-3p[/tex]

[tex]\implies c=25-3p[/tex]

Substitute the expression for c into the second equation and solve for p:

[tex]\implies 8c+5p=67[/tex]

[tex]\implies 8(25-3p)+5p=67[/tex]

[tex]\implies 200-24p+5p=67[/tex]

[tex]\implies 200-19p=67[/tex]

[tex]\implies 200-19p-200=67-200[/tex]

[tex]\implies -19p=-133[/tex]

[tex]\implies \dfrac{-19p}{-19}=\dfrac{-133}{-19}[/tex]

[tex]\implies p=7[/tex]

Therefore, the selling price of a handmade photo frame was $7.

Substitute the found value of p into the expression for c and solve for c:

[tex]\implies c=25-3p[/tex]

[tex]\implies c=25-3(7)[/tex]

[tex]\implies c=25-21[/tex]

[tex]\implies c=4[/tex]

Therefore, the selling price of a handmade card was $4.

Answer:

Step-by-step explanation:Math

An autonomous first order ordinary differential equation is any equation of the form: dy/dt = f(y).

1. Stable: The equilibrium solution y(t) = c is stable if all solutions with initial conditions y0 ‘near’

y = c approach c as t → ∞.

2. Unstable: The equilibrium solution y(t) = c is unstable if all solutions with initial conditions y0 ‘near’ y = c do NOT approach c as t → ∞.

3. Semi-stable: The equilibrium solution y(t) = c is semistable if initial conditions y0 on one side of c lead to solutions y(t) that approach c as t → ∞, while initial conditions y0 on the other side of c do NOT approach c.

Find the equilibrium points for the differential equation (1) and determine whether each is asymptotically stable, semistable, or unstable.

The graph of y0 as a function of y, and the phase line. (It’s important that α is positive – if it were negative, we’d have very different behavior).

We can see that there are two equilibrium solutions: y = 0, which is unstable, and y = 1, which is stable.

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The given are two scalene triangles are similar with a scale of 2:3. The correct option is 4th i.e, PQ/GH = 3/2.

The triangles GHI and PQR are similar with a scale of 2:3.

The corresponding sides of similar triangles are proportional and the corresponding angles are congruent.

GH/PQ = HI/QR = GI/PR = 2/3

∠G ≅ ∠P

g = p

g/p = 1

So, the third option is incorrect.

∠H ≅ ∠Q

h = q

∠I ≅ ∠R

i = r

i/r = 1

So, the second option is incorrect.

Now,

HI/QR = 2/3 ≠ 3/2

So, the first option is incorrect.

PQ/GH = 3/2

Thus, fourth option is correct.

The question is incomplete. The figures are attached in the below attachment. The options are missing. They are ' A. HI/QR = 3/2 B.i/r = 2/3

C.g/r = 1 D. PQ/GH = 3/2'

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The solution to the system of equations is (7.5, 1)

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

2x−3y=12

−12y+8x=48

divide the first equation by 2

So, we have

x - 1.5y = 6

This gives

x = 6y + 1.5

By substitution, the second equation becomes

-12y + 8 (6y + 1.5) = 48

So, we have

-12y + 48y + 12 = 48

Evaluate

36y = 36

Divide by 36

y = 1

So, we have

x = 6 + 1.5

x = 7.5

Hence, the solution is (7.5, 1)

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Complete question

What is the solution to this system?

2x−3y=12

−12y+8x=48

Enter the solution as an ordered pair, (x, y).