Oscar measured an Italian restaurant and made a scale drawing. The scale he used was 1 millimeter = 1 meter. What scale factor does the drawing use?Simplify your answer and write it as a ratio, using a colon.

We can see here that the data set approximately periodic. The period and amplitude is: Periodic with a period of 4 and an amplitude of about 30.

The size or magnitude of a wave or vibration is measured by its amplitude in physics. It describes the greatest deviation of a wave from its equilibrium or rest state, or the greatest intensity of an electromagnetic or sound wave.

When referring to waves, amplitude is commonly calculated as the distance between a wave's peak or trough and its resting position.

We can deduce that the values are being repeated at regular interval of four (4).

For the amplitude:

\(Amplitude: \frac{140 - 74}{2}\)

Amplitude = 33 ≈ 30.

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Answer:

x is any integer except for -1

Step-by-step explanation:

If you substitute -1 for x, the denominator value would be 0, or undefined.

For this reason, x cannot be -1, which is mathematically known as an extraneous value.

The exact value of sin(pi/3) is √3. By definition, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(pi/3) = √3/1 = √3.

The exact value of sin(pi/3) can be determined using trigonometric properties and identities.

First, we know that pi/3 is equivalent to 60 degrees. In a unit circle, the point corresponding to 60 degrees forms an equilateral triangle with the origin and the x-axis. This triangle has side lengths of 1, 1, and √3.

To find the sine of pi/3, we consider the side opposite the angle (pi/3) in the triangle. In this case, the opposite side has a length of √3. The hypotenuse of the triangle is 1, as it is the radius of the unit circle.

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Answer:

Thus, the greatest number of rides I can go on is 15 rides

Step-by-step explanation:

I have $35.50 to spend for admission plus rides in the amusement park.

Admission costs $13. That leaves me with

$35.50 - $13 = $22.50

to spend on rides.

Considering each ride costs $1.50, we can find the maximum number of rides by dividing the remaining money by the cost per ride as follows:

$22.50 / $1.50 = 15

Thus, the greatest number of rides I can go on is 15 rides

what's up? 5 gallons ≈ 19 liters  (THIS IS U.S. GALLON, THE OTHER ANSWER HAS IMPERIAL GALLON IF THAT IS WHAT YOU NEED)

best of luck with your studies

Answer:

0

Step-by-step explanation:

If 4x + b = 4x, then b = ?

Let's solve!

4x + b = 4x

Minus 4x on both sides

b = 4x - 4x

b = 0

We can check, does 4x + 0 = 4x?

Yes, it works.

Hope this helps :)

Have a nice day!

Answer:

23.5 is half of 47

Step-by-step explanation:

hope it help and if it not what you meant please tell me I will help you out

The angles A and C in the triangle with sides AC = 24, BC = 15, and angle B = 74 degrees are approximately 29.16 degrees and 45.84 degrees, respectively.

To find angles A and C in the triangle, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of the included angle.

Let's denote the angles opposite to the sides with lengths 24, 15, and AB as A, B, and C, respectively. Then, the Law of Cosines gives us:

AB^2 = AC^2 + BC^2 - 2ACBCcos(B)

AB^2 = 24^2 + 15^2 - 22415cos(74)

AB^2 ≈ 758.76

AB ≈ 27.54

Now, we can use the Law of Sines, which relates the ratios of the lengths of the sides to the sines of the opposite angles:

sin(A) / AB = sin(B) / BC

sin(A) / 27.54 = sin(74) / 15

sin(A) ≈ 0.4927

A ≈ sin^-1(0.4927) ≈ 29.16 degrees

sin(C) / AB = sin(B) / AC

sin(C) / 27.54 = sin(74) / 24

sin(C) ≈ 0.6863

C ≈ sin^-1(0.6863) ≈ 45.84 degrees

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sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

The sine expression is given as

sin^4x

The above means

sin x raised to the power of 4

This in other words, the expression is represented as

(sin(x))^4

Express 4 as 2 + 2

(sin(x))^(2 + 2)

Apply the law of indices

(sin(x))^2 * (sin(x))^2

This gives

sin^2(x) * sin^2(x)

Hence, sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

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The inference from the information is A. No, the equation is not a good fit because the sum of the residuals is a large number.

It should be noted that line of best fit simply means a line through a scatter plot of data points which shows the relationship between the points.

In this case, the inference from the information is that the equation is not a good fit because the sum of the residuals is a large number.

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Answer:

1000

Step-by-step explanation:

Round the 6 in 600, this is 1 significant figure.6 rounds up to 10 making 1000

The number can be 601, 602, 603, ....... 699

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.

If the number is round down to 600 then it's depend on round off

If the round off should be at hundred place, then number can be

601,602,  ..................649.

If we round off the above number then it will be 600 which has 1 significant figure.

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consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. Suppose probability a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded.a fraction in lowest terms. 21/36

The sample space given in the question is the set S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} The event that the sum of the numbers showing face up is at least 9 is represented by the set E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}.

To compute the probability of this event, we need to count how many elements are in the set E and divide this number by the total number of elements in the set S. There are 18 elements in the set E and 36 elements in the set S. Therefore, the probability of the event is 18/36, which can be simplified to 21/36.

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The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

To determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.

1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.

2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.

3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.

To find the total number of possible outcomes, we multiply the number of outcomes for each event together:

Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)

Total number of outcomes = n × 6 × 52

Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

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Answer:

The 16 ounces at 1.76.

Step-by-step explanation:

Divide total cost by the quantity to get cost per unit.

Ounces Cost Cost/Ounce

60      5.40          0.09  

28      2.24          0.08  

16       1.76           0.11  

The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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Answer:

The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.

Answer:

D.

Step-by-step explanation:

6a² = surface area for cube

6(5)² = 150

2\(\pi\)(r)(h)+2\(\pi\)r²  = surface area cylinder

2\(\pi\)(2)(3)+2\(\pi\)(4) = 20pi

150 + 20pi = 212.8318531

Answer:

The answer is:

390= 15a+8c

40=a+c

Answer:

A)      \(y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ]\)

B)       \(\frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p\)

Step-by-step explanation:

- The following initial value problem is given as follows:

                      \(my'' + cy' + ky = F(t) \\\\y(0) = 0\\y'(0) = 0\)

- The above equation is the Newtonian mathematical model of a spring-mass-dashpot system. The displacement ( y ) and velocity ( y' ) are zeroed at the initial value t = 0.

- The equivalent mass ( m ) , damping constant ( c ) and the equivalent spring stiffness ( k ) are given as follows:

                      \(m = 2 kg\\\\c = 8 \frac{kg}{s} \\\\k = 80 \frac{N}{m} \\\\\)

- The system is subjected to a sinusoidal force F ( t ) given. We will plug in the constants ( m , c, and k ) and applied force F ( t ) into the given second order ODE.

                      \(2y'' + 8y' + 80y = 20sin(6t)\)

- The solution to a second order ODE is comprised of a complementary function ( yc ) and particular function ( yp ).

- To determine the complementary function ( yc ) we will solve the homogeneous part of the given second order ODE. We will assume the independent solution to the homogeneous ODE takes the form:

                           \(y = e^-^a^t\)

Where,

                          a: The root of the following characteristic equation

- Substitute ( y ) into the given ODE as follows:

                          \(( 2a^2 + 8a + 80 )*e^-^a^t = 0\\\\2a^2 + 8a + 80 = 0\)

- Solve the above characteristic quadratic equation:

                           \(a = 2 +/- 6i\)

- The complementary solution for the complex solution to the characteristic equation is of the form:

                           \(y_c = e^-^\alpha^t * [ Acos (\beta*t) + Bcos (\beta*t) ]\)

Where,

                          a = α ± β

Therefore,

                           \(y_c = e^-^2^t * [ Acos (6t) + Bcos (6t) ]\)

- To determine the particular solution we will scrutinized on the non-homogeneous part of the given ODE. The forcing function F ( t ) the applied force governs the form of the particular solution. For sinusoidal wave-form the particular solution takes form as following:

                           \(y_p = Csin (6t ) + Dcos(6t )\)

Where,

                           C & D are constants to be evaluated.

- Determine the first and second derivatives of the particular solution (yp) as follows:

                            \(y'_p = 6Ccos(6t) - 6Dsin(6t)\\\\y''_p = -36Ccos(6t) - 36Dcos(6t)\\\)

- Plug in the particular solution ( yp ) and its derivatives ( first and second ) into the given ODE.

        \(-72Csin(6t) - 72Dcos(6t) + 48Ccos(6t) - 48Dsin(6t) + 80Csin(6t) + 80Dcos(6t) = 20sin(6t) \\\\sin(6t)* ( 8C -48D ) + cos(6t)*(8D + 48C ) = 20sin(6t)\\\\D + 6C = 0\\\\C - 6D = 2.5\\\\C = \frac{5}{74} , D = -\frac{15}{37}\)

- The particular solution can be written as follows:

                        \(y_p = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)\)

- Now we use the principle of super-position and combine the complementary and particular solution and form a function of general solution as follows:

                        \(y_g = y_c + y_p \\\\y_g = e^-^2^t* [ Acos(6t) + Bsin (6t) ] + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)\)

- To determine the complete solution of the given ODE we have to calculate the constants ( A and B ) using the given initial conditions as follows:

                        \(y_g ( 0 ) = 1*[A(1) + 0 ] + 0 - \frac{15}{37}(1) = 0\\\\A = \frac{15}{37}\\\\y'_g = -2e^-^2^t*[Acos(6t) + Bsin(6t) ] +e^-^2^t*[-6Asin(6t) + 6Bcos(6t) ] + \\\\\frac{15}{37}cos(6t) +\frac{90}{37}sin(6t) \\\\y'_g(0) = -2*[A(1) + 0] + 1*[0 + 6B] + \frac{15}{37}(1) +0 = 0\\\\B = \frac{15}{6*37} = \frac{5}{74}\)

- The complete solution to the initial value problem is:

           \(y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ]\)          

- To determine the long term behavior of the system we will apply the following limit on our complete solution derived above:

                 \(Lim (t->inf ) [ y_g ] = \frac{15}{37}cos(6t)* [ 0 - 1 ] + \frac{5}{74}sin(6t)* [ 0 + 1 ]\\\\Lim (t->inf ) [ y_g ] = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p\)

- We see that the complementary part of the solution decays as t gets large and the particular solution that models the applied force F ( t ) is still present in the system response when t gets large.

The least number of votes necessary from each group to pass the policy is 596 votes from technical managers and 119 votes from administrative managers.

We know that 30% of technical managers vote in favor, which means 0.3x technical managers will vote in favor.

Similarly, 60% of administrative managers vote in favor, which means 0.6y administrative managers will vote in favor.

The total number of managers who vote in favor is given by the sum of technical and administrative managers who vote in favor:

0.3x + 0.6y

We want this total number of votes to be at least 250, so we can write the inequality:

0.3x + 0.6y ≥ 250

Since the total number of managers in the company is 715, we also have the constraint:

x + y ≤ 715

To find the least number of votes from each group necessary to pass the policy, we can solve this system of inequalities.

0.3x + 0.6y ≥ 250 ---(1)

x + y ≤ 715 ---(2)

To simplify equation (1), we can multiply both sides by 10 to remove the decimal:

3x + 6y ≥ 2500

Now, we have the following system:

3x + 6y ≥ 2500 ---(3)

x + y ≤ 715 ---(4)

To solve this system, we can use a method like substitution or elimination.

Let's solve using the elimination method:

Multiply equation (4) by 3:

3x + 3y ≤ 2145 ---(5)

y ≥ 118.33

Since y represents the number of administrative managers, it must be a whole number, so we take the next higher integer, y = 119.

Substitute this value of y into equation (4):

x + 119 ≤ 715

x ≤ 596

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Answer:

option C

Step-by-step explanation:

Answer:

c number is right anwer .... . .... ..

From the inventory ratios of  24 8, 33.4 and 53.8 of  Dunn and Bradstreet report. It can be concluded that

The problem is seeking expression of ratios in percentage

Ratios represents part or share of a whole while percentage refers to a fraction of hundred

Calculation of the whole among the ratios 24 8 : 33.4 : 53.8 is done by adding up

= 24 8 + 33.4 + 53.8

= 108

Expressing as ratio 53.8 a percentage, we have

= 53.8/108 * 100

= 0.4981 * 100

= 49.81%

approximately 50%

We can therefore say that inventory of 53.8 or more is 50%

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Parabolas are used to represent curved functions

The shortest distance between the parabola and the point is \(x = -\frac 1{2}\)

The parabola is given as:

\(y=(7x+5)^{1/2}\)

Rewrite as:

\(y=\sqrt{7x+5}\)

Let p represent a point on the parabola.

So, we have:

\(P(x,\sqrt{7x + 5})\)

Next, calculate the distance between P and the point (3,0) using the following distance formula:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2\)

So, we have:

\(d = \sqrt{(x- 3)^2 + (\sqrt{7x + 5})^2\)

\(d = \sqrt{x^2- 6x + 9 + 7x + 5}\)

Evaluate the like terms

\(d = \sqrt{x^2+ x + 14}\)

Square both sides

\(d^2 = x^2+ x + 14\)

The shortest distance is then calculated as:

\(x = -\frac b{2a}\)

Where:

a = 1, b = 1 and c = 14

So, we have:

\(x = -\frac 1{2*1}\)

\(x = -\frac 1{2}\)

Hence, the shortest distance between the parabola and the point is \(x = -\frac 1{2}\)

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Answer:

It's say's this on internet

Step-by-step explanation:

First graph. Then, identify the domain and range.

The domain is all of the possible values of the line, related to the input variable (X-axis).

The range represents all of the possible values of the vertical axis, or the output of the equation (Y-axis).

If you look at the graphed line, you'll probably notice that if it went on forever, it would cover every possible value (thus, the infinite values of both the input and output). In other words, you could plug in any number for X and get a corresponding value for Y, and it would be right on that line.

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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clothing,fuel,groceries and utility bill

Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

The values of the expressions are;

z³³

d⁻¹⁶

Note that index forms are described as forms used in the representation of numbers or variables too large or small.

Some rules of index forms are;

Then, from the information given, we have that;

(z⁻⁴/z⁶  × z⁵/z⁻⁶)⁻¹¹

Subtract the exponents, we have;

(z⁻² × z⁻¹)⁻¹¹

expand the bracket

z²² ⁺ ¹¹

z³³

(d⁴)⁻³/(d⁶)⁻²  ÷  (d⁴/d⁶)⁻⁸

expand the brackets

d⁻¹²/d¹²  ÷    (d⁻²)⁻⁸

subtract the exponents

d⁰  ÷  d¹⁶

d⁻¹⁶

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Answer:

x = 20°

Step-by-step explanation:

here's your solution

=>. we know that, sum of two opposite interior angle is equal to one exterior

=> (3x)° + (3x -20)° = (7x - 40)°

=> 6x - 20° = 7x - 40

=> - x = - 20

=> x = 20

hope it helps

Answer:

20°

Step-by-step explanation:

C.20 is the correct answer.