The length, d, of a violin string varies inversely as the frequency, f, of its vibrations (cycles per second). Suppose it is known that a 16-in.-long violin string vibrates 320 cycles per second.

A. Write an inverse variation equation modeling this information

B. Use your inverse variation equation from Part A to determine the frequency of an 8-inch-long violin string.

Answer:

98 ÷ 98 = 1 OR 98 ÷ 1 = 98

Step-by-step explanation:

Division is breaking something up into equal parts. The "dividend" is the whole you start with, the "divisor" is what you use to divide up the whole, and the "quotient" is the answer like this: Dividend ÷ Divisor = Quotient. So, the quotient of 98 and a number would be represented as such: 98 ÷ 1 = 98 or 98 ÷ 98 = 1

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The linear equation represented in the table is:

y = -3x + 20

A general linear equation of the form is:

y = a*x + b

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

slope = (y₂ - y₁)/(x₂ - x₁)

Here we can use the last two points on the table:

(-2, 26) and (-4, 32)

Then the slope is:

slope = (26 - 32)/(-2 + 4) = -6/2 = -3

So this is like:

y = -3*x + b

To find the value of b we can use one of the points, i will use (-2, 26), then:

26 = -3*-2 + b

26 = 6 + b

26 - 6 = b = 20

The linear equation is y = -3x + 20

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We are increasing every professor's salary by 4000, let this new salary be Yi for every professor then mean of new salary Y will be

Y = 1/n∑Yi

Y  = 1/n∑(Xi + 4000)

Y  = 1/n(∑Xi + ∑4000/n)

Y  = X + 4000

Median Xm is the middle most value of the Professor's old salary, since new salary is

            Yi = Xi + 4000

then new median salary Ym will be

            Ym = Xm + 4000

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Answer:

Step-by-step explanation:The mean and Median salary would increase by $4,000.

Let sum of the salaries be n1+n2+n3+.......... +n30

   Mean = sum of observation / no. of observation

Thus,

   Initial mean, M1 = n1+n2+n3+.......... +n30 / 30

When $4,000 is added to every salary 4000 is added 30 times to the sum.

Thus,

  New mean, M2 = n1+n2+n3+.......... +n30 +( 4000 * 30)

                                                30

                           = M1 + ( 4000 * 30)

                                              30

  Thus,         M2 = M1+ 4000

Therefore, The mean salary increase by $4,000.

We know Median of even number of observation =  [(n/2)th term + ((n/2) + 1)th term]/2

Here n/2th term is n15 and (n/2 +1)th term is n16

Thus,

    Initial Median, Median 1 = n15 + n16  

                                                     2

When $4,000 is increased in each salary

    New Median, Median 2 = n15 + 4000 + n16 + 4000

                                                                 2

                                         = Median 1 + 2 * 4000

                                                                    2

Thus,                  Median 2= Median 1 + 4000

Therefore, The median salary increases by $4,000

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m<A, which is 48 degree.

The values of mL and mJ are 55 and 61 degrees, respectively.

Since vertical angles are equal in magnitude and are created by intersecting two lines, they are known as the opposing angles.

what are the explanation of the problems?

1.Angles in the vertical plane coincide. They are equal in size, thus this indicates. Calculate x x = 4x - 24 by putting them on an equal footing. In the equation, deduct x from both sides.

o = 3x - 24 On both sides, add 24.

24 = 3x Divide both sides by 3

Multiply both sides by 3 

8 to get x 

m<A, which is 8.

4x-24

=3*8+24=24+24=48 degree

2.We can thus write,

The angles L and Z are vertical.

∠L = 2x + 9 and,

∠Z = 3x - 14.

Given that both angles are vertical,

∠L = ∠Z

2x + 9 = 3x - 14

Continuing to solve

3x - 2x = 9 + 14

x = 23

The value of L is therefore,

= 2(23)+9

= 46+9

= 55°

Angle L has a value of 55°.

2. Y and J are equal because they are both vertical angles.

∠Y = 7x + 12

∠J = 10x - 9

∠Y = ∠J

7x + 12 = 10x - 9

Continuing to solve

3x = 21

x = 7

So, the value of ∠J is, = 10(7) - 9 = 70 - 9 = 61°

The value of ∠J is 61°.

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Answer:

D. −8.2s − 6.8

Step-by-step explanation:

Hope this helps you! :))

We want to find a series of transformations that change the polygon ABCD into the polygon A'B'C'D'.

We see that a counter-clockwise rotation must be necessary, as:

By doing a traslation of 4 units to the right, and a dilation by a scale factor of 2, we obtain the desired figure. This is, the answer is B.

Answer:

[tex](g \circ f)(0)=216[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=2x+6\\g(x)=x^3\end{cases}[/tex]

(g o f)(x) is a composite function.  

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function (g o f)(0) means to substitute the function f(x) when x=0 in place of the x in function g(x).

[tex]\begin{aligned}\implies (g \circ f)(0)&=g[f(0)]\\& = g(2(0)+6)\\&=g(0+6)\\&=g(6)\\&=6^3\\&=216\end{aligned}[/tex]

Given:

A linear graph

To find:

the equation of the line

The formula for linear equation is given as:

y = mx + b

m = slope

b = y-intercept

We need to get the slope and y-intercept of the line. To get the slope, two points will be picked on the line

Using points: (-8, -1) and (0, 2)

The y-intercept is the value of y when x = 0. On the graph, it is the value of y when the line crosses or touches the y-axis.

The line crosses the y axis at y = 2

b = y-intercept = 2

The equation of the line in slope-intercept form becomes:

If Justin bought a calculator and a binder that were both 15% off the original price. The original price of the binder was $6.20. Justin spent a total of $107.27. Then $120 the original price of the calculator

A percentage is a number or ratio expressed as a fraction of 100.

Let,

x be the original price of the calculator

y be the original price of the binder

we know that

15%=15/100=0.15

(x+y)(1-0.15)=$107.27

(x+y)(0.85)=$107.27....(1)

y=6.20....(2)

substitute the value of y in the equation A and solve for x

(x+6.20)(0.85)=107.27

(x+6.20)=107.27/0.85

x=107.27/0.85-6.20

x=126.20-6.20

x=120

Hence the original price of calculator is $120.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{3}{4}x - 9[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 9x +12y = -108[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 12y = - 108- 9x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ -108}{12} - \frac{9x}{12} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{3}{4}x - 9[/tex]

And this the equation of same line in its slope intercept form, where slope (m) = -3/4 and y - intercept = -9

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

a) 14.81 J of work is needed to stretch the spring from 29 cm to 31 cm.

b) 2 cm far beyond its natural length will a force of 15 N keep the spring in stretched position.

It is mentioned that 3 J of work is needed to stretch a spring from its natural length of 24 cm to 33 cm.

We know the work done on the spring is expressed by the following given equation:

[tex]W=\frac{1}{2} ke^{2}[/tex]

Where, W = workdone that is done on the spring

k = elastic constant

e = extension of the given material

So, Work (W) = 3 J and e = 33 cm - 24cm = 9 cm = 0.09 m

So, putting the above values we calculate the value of 'k' as below:

[tex]W=\frac{1}{2} ke^{2}[/tex]

⇒ [tex]3=\frac{1}{2} k(0.09)^{2}[/tex]

⇒ 3 x 2 = 0.0081k

⇒ k =  [tex]\frac{6}{0.0081}[/tex] N/m

⇒ k = 740.74 N/m

a) Now using the same formula for work, we will determine the amount of work that is needed to stretch the spring from 29 cm to a length of       31 cm.

k =  740.74 N/m

e = 31 cm - 29 cm = 2 cm = 0.02 m

[tex]W=\frac{1}{2} ke^{2}[/tex]

⇒ W = [tex]\frac{1}{2} (740.74) (0.02)^{2}[/tex]

⇒ W = 14.81 J

The work that is done to stretch the spring from 29 cm length to 31 cm is   14.81 J.

b) From the Hooke's law we have, F = ke, where F is the force applied on the spring. Now here we have been given that a force of 15N is applied and we have to find the 'e' that is the extennsion in the natural length of the given spring.

k = 740.74 N/m

F = 15 N

F = ke

⇒ 15 N = 740.74 x e

⇒ e = [tex]\frac{15}{740.74}[/tex] m

⇒ e = 0.02 m = 2 cm

Therefore the natural length of the spring will be stretched by a length of 2 cm when a force of 15 N is applied.

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The 200 sound cards represent the sample if they are randomly selected from a large production line.

A sample in statistics can be defined as a small part or subset of a population or group that intends to represent what the whole population is like. A sample may be randomly selected or may be selected non-randomly.

In this case, the whole production line of the sound card can be considered as a population. Out of this population of sound cards, 200 are randomly selected to estimate the average lifetime thus determining the characteristic of the whole population, therefore it is said to be the sample of the sound cards and the 5 years is the value of the statistic.

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The trigonometric functions for the angle of 195º are given as follows:

1. cos(195º) = -0.9659.

2. sin(195º) = -0.2589.

3. tan(195º) = 0.2680

The identity is verified at the end of the answer.

One of the functions have to be given/found using a calculator, hence:

cos(195º) = -0.9659.

The sine and the cosine of the same angle are related according to the following identity:

sin²(x) + cos²(x) = 1.

Hence:

sin²(195º) + cos²(195º) = 1

sin²(195º) + (-0.9659)² = 1

sin²(195º) + 0.93296281 = 1

sin²(195º) = 1 - 0.93296281.

sin(195º) = ±sqrt(1 - 0.93296281)

sin(195º) = -0.2589. (the angle of 195º is on the third quadrant, where both the sine and the cosine are negative).

The tangent of an angle is given by the sine of the angle divided by the cosine of the angle, hence:

tan(195º) = sin(195º)/cos(195º) = -0.2589/(-0.9659) = 0.2680. (negative divided by negative is positive)

The identities for the sine of the sum and of the subtraction are given as follows:

Hence the subtraction is:

sin(x + y) - sin(x - y) = (sin(x)cos(y) + cos(x)sin(y)) - (sin(x)cos(y) - cos(x)sin(y))

sin(x + y) - sin(x - y) = sin(x)cos(y) + cos(x)sin(y) - sin(x)cos(y) + cos(x)sin(y)

sin(x + y) - sin(x - y) = 2cos(x)sin(y).

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After conversion, the percentages in fractions and decimals are:

Recall that a percentage is over 100 and the symbol is %

Therefore, for 89%, it would be 89/100.

This is the fraction, then the decimal would be 0.89

For 35%, the fraction would be 35/100

We break it down to the lowest value possible, it would be 7/20. This is the fraction, the decimal is 0.35

For 64%, it would be 64/100

It would be broken down to the lowest value possible which would be 14/25

The decimal would be 0.64

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To keep the total seats still at 20,000 but change the ratio to 4 : 1; the number of premium and bleachers seats the stadium would have are; 16,000 and 4,000 respectively.

It follows from the task content that the total number of seats which the stadium would have if the ratio is to be changed to 4:1 be determined.

Since the number of seats, 20,000 remains constant.

To divide the number 20,000 in the ratio; 4 : 1;

The number of premium seats would be; (4/5) × 20,000 = 16,000 seats.

And the number of bleacher seats would be; (1/5) × 20,000 = 4,000 seats.

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Travis should include A. Chicago, St Paul, Bismarck and Fargo on his lost because these cities had temperature of 6°F below zero for the month of January.

The only countries which Travis is including on his list are those which has a temperature of 6 degrees Fahrenheit   below zero in the month of January.

The correct choices are provided in the option A.

He should include Chicago, St. Paul, Fargo and Bismarck.

He should add these cities because they all had temperature of 6 degrees Fahrenheit below zero for the month of January.

These cities are very cold because of their geological location.

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Answer:

There are two different categories of transformations: The rigid transformation, which does not change the shape or size of the preimage. The non-rigid transformation, which will change the size but not the shape of the preimage.

Step-by-step explanation:

yep sorry if you get it wrong it is

B

The slope of the line that passes through the points (-7, -10) and (-19,-10) is 0.

Slope is simply expressed as change in y over the change in x.

It is expresses as;

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1 ( -7, -10 )

Point 2 (-19,-10)

Plug the given x and y values into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -10 - (-10) )/( -19 - (-7) )

Slope m = ( -10 + 10 )/( -19 + 7 )

Slope m = ( 0 )/( -12 )

Slope m = 0/-12

Slope m = 0

Therefore, the slope of the line is 0.

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Given

Values of winning and losing scores

Find

Make a stem and leaf ploy for the given values

Explanation

Final answer

Above is the

The statement that correctly compares two numbers is: A. 3.02 = 3.020

An inequality can be defined as a mathematical relation that compares two (2) or more numbers such as integers, and variables in an equation based on any of the following arguments (symbols):

Next, we would evaluate the given inequalities in order to determine the correct statement as follows:

3.02 = 3.020 (True).

4.05 < 4.05 (False) because 4.05 is equal to 4.05.

5.17 < 5.07 (False) because 5.17 is greater than 5.07.

6.08 > 6.08 (False) because 6.08 is equal to 6.08.

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Angle 6, Angle 16 and Angle 11 are not congruent.

We need to check ∠5 is not equal to which angle from the figure.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Here,

Angle 5 = Angle 2 (Vertically opposite angles)

Angle 5 = Angle 7 (corresponding angles are equal)

Angle 5 = Angle 13 (corresponding angles are equal)

Therefore, Angle 6, Angle 16 and Angle 11 are not congruent.

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Answer:

B)  Angle 6

C)  Angle 16

E)  Angle 11

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Corresponding Angles Theorem

When a straight line intersects two parallel straight lines, the angles in the same relative position are congruent.

According to the corresponding angles theorem:

According to the vertical angles theorem:

Therefore:

As angle 5 is not a right angle, the angles that angle 5 is not equal to are:

Answer:

Line A's slope is 2 and Line B's slope is 1/2.

Step-by-step explanation:

The slope of perpendicular lines is such that the slope of one line is the negative reciprocal of the slope of another line

Answer:

8 pens = 32

1 pen = 32 ÷ 8

= 4

Cost of one pen is $4.

The solution of the system of equation is as follows:

The system of equation can be solved algebraically using substitution method.

The system of equation can be solved when we find the value of x and y as follows:

y = 4x + 1

6x - 2y = 3

Let's substitute the equation(i) in equation(ii)

6x + 2(4x + 1) = 3

6x + 8x + 2 = 3

14x + 2 = 3

14x = 3 - 2

14x = 1

x = 1 / 14

let's find y as follows:

y = 4(1 / 14) + 1

y = 4 / 14 + 1

y = 2 / 7 + 1

y = 2 + 7 / 7

y = 9 / 7

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The transformation from the graph of f to the graph of g is reflection in the x-axis.

We are given the function f(x) = -4x + 8

Also it says that g(x) = -f(x)

                                 = 4x - 8

Since f(x) is a linear function, the graph of f(x) and hence the graph of g(x), both are straight lines. But the graph of g(x) will be a transformed image of the graph of f(x).

Here, if f(x) = y, then the transformation from f(x) to g(x) can be represented as, (x, y) -------> (x, -y)

This transformation corresponds to the reflection in the x-axis. When reflected along x-axis, the x- co-ordinate does not change, but the y- co-ordinate changes its sign. This is exactly what happens when the function f(x) is transformed to g(x) = -f(x).

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In  linear equation, y = -6 is the output .

What is a linear equation example?

We want to find the y value on the graph when x = -7

Got to x = -7 and find the value  of the blue line

y = -6

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The complete question is -

Find the output, y, when the input, x, is -7​

Answer:

B

Step-by-step explanation:

Let's go through each, step-by-step and simplify to see if we find a true number sentence:

A)

[tex]3\frac{1}{3} < \sqrt{7}?[/tex]

[tex]3.3333 < 2.64575?[/tex] Not true

B)

[tex]4.8 < \sqrt{32}?[/tex]

[tex]4.8 < 5.65685?[/tex] True

Knowing B is true, we have found our answer and don't need to go any further.

y = -3x - 8

Slope-intercept form: y = mx + b

Given: y + 2 = -3(x + 2)

Simplify:

y + 2 = -3x - 6

y = -3x - 6 - 2

y = -3x - 8

We have: m = -3, and b = -8

Answer:

y=-3x-8

Step-by-step explanation:

First make y by itself

y=-3(x+2)-2

Distribute the -3

y=-3x-6-2

Combine like terms

y=-3x-8

The total number of  ways 7 red marbles can be chosen is 95,567,472 i.e., option b is correct.

12 marbles are chosen in which 7 are red marbles and remaining marbles, which are 5, are blue marbles.

In order to find in how many ways 7 red marbles can be chosen we will follow the steps mentioned below:

Out of 18 red marbles 7 are chosen and out of 15 blue marbles 5 are chosen. So, we can write

Total number of  ways 7 red marbles can be chosen= [tex]18C_{7}[/tex] × [tex]15C_{5}[/tex]

Total number of  ways 7 red marbles can be chosen= [tex](\frac{18!}{7! (18-7)!} )[/tex][tex](\frac{15!}{5! (15-5)!})[/tex]

Total number of  ways 7 red marbles can be chosen= 31824 × 3003

Total number of  ways 7 red marbles can be chosen=  95,567,472

Thus, we can conclude that in 95,567,472 number of  ways 7 red marbles can be chosen.

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