The graph represents the direct variation function between earnings in dollars and hours worked.

A coordinate plane showing Store Clerk Pay, Hours Worked on the x-axis and Total Earnings in dollars on the y-axis. A line starting at (0, 0) and passing through (4, 30), (8, 60) and (12, 90)
Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?

E = 1.5h
E = 7.5h
E = 13h
E = 15h

It only seeks a single value and does not involve collecting data to draw general conclusions.

"Which employee worked the most hours in the previous month?" is not a statistical question because it only seeks a single value and does not involve collecting data to draw general conclusions.

On the other hand, "What is the average number of hours worked by employees in the previous month?" is a statistical question because it involves collecting data on all employees and using it to draw general conclusions about the entire workforce.

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Answer:

irrational

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

Answer:

0.42

Step-by-step explanation:

To solve the problem, we need to add the probability of picking a club to the probability of picking a face card, and then subtract the probability of picking a club that is also a face card (because we would have counted it twice).

There are 13 clubs in a standard deck, so the probability of picking a club is 13/52 or 0.25.

There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck, so the probability of picking a face card is 12/52 or 0.23.

However, there are 3 cards that are both clubs and face cards (the jack of clubs, queen of clubs, and king of clubs), so we need to subtract the probability of picking one of those cards. There are 3 of them out of 52 total cards, so the probability of picking a club that is also a face card is 3/52 or 0.06.

Therefore, the probability of picking a club OR a face card is:

0.25 + 0.23 - 0.06 = 0.42 (rounded to two decimal places).

So the answer is 0.42.

Answer:

Hope you understand not to sure but that's what I got

The amount of cash generated is 78.75 Million.

Price-sales ratio, often known as the P/S ratio or PSR, is a stock valuation indicator. It is computed by dividing the market capitalization of the company by its most recent fiscal year's revenue, or, equivalently, by dividing the share price of the stock by its revenue per share.

The sales ratio will be calculated as below:-

Sales= $450  Million

Fixed Assets= $225  Million

% of capacity utilized. . 65%

Sales at full capacity = actual sales/%of capacity used = 692.31 millions dollars .

Target FA = Full capacity FA/sales = FA/Capacity sales = 32.50%

(225*65% = 146.25, 146.25/450 = 32.50%)

Optimal FA = sales * targeted FA/Sales Ratio = 450*32.50% = 146.25

Cash Generated = Actual FA-optimal FA = 225-146.25 = 78.75 millions dollars

Therefore, the amount of cash generated is 78.75 Million.

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Answer:

In the instruction above, it gives us some helpful information.

2 days with no professional sports game.

3 forms of ratio --> a to b, a : b, a / b

1) Remember there are 365 days in a year.

Days without games to Days in a year --> 2 to 365

Days without games : Days in a year --> 2 : 365

Days without games / Days in a year --> 2 / 365

2) Now there is a plot twist. It ask days with games. To find that we need to subtract 365 - 2 = 363 days with games.

Days with games to Days in a year --> 363 to 365

Days with games : Days in a year --> 363 : 365

Days with games / Days in a year --> 363 / 365

3) Days with games to Days without games --> 363 to 2

Days with games : Days without games --> 363 : 2

Days with games / Days without games --> 363 / 2

Hope this helps and sorry for not answering you. For some reason I was not getting any notification, but it is fixed now. Thank you :) !!

Answer:

4.428571429

Step-by-step explanation:

You have to do 8+6 then 62 divided by 14 and then thats what your x equals.

Answer:

x=9

Step-by-step explanation:

start with

6x+8=62

subtract 8 from each side

6x=54

divide each side by 6

x=9

Answer:

D) 8x+5

Step-by-step explanation:

3(2x-1)+2(x+4)

6x-3+2x+8

6x+2x-3+8

8x-3+8

8x+5

Answer:

x = (-5,10)

Step-by-step explanation:

Answer:

-1 and -5

Step-by-step explanation:

-1x-5= 5

-1+-5= -6

The number of ways which he can choose 4 courses if more than 2 must be science is; 224 ways.

Combination of outcomes;

He can choose from 4 humanities courses and 8 science courses.

If the condition requires that he chooses more than 2 science courses, it follows that;

He can only choose three science courses and only 1 humanities courses.

8C3 x 4C1 = 56x 4 = 224

On this note, the number of ways he can choose the required 4 courses is; 224 ways.

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27 can be written as a product of 3 and 9, where 9 is a perfect square.

In mathematics, a perfect square is an integer that is equal to the square of another integer. In other words, a perfect square is a non-negative integer that can be expressed as the product of an integer with itself.

To write 27 as a product of two integers such that one of the factors is a perfect square, we need to find a perfect square that divides 27.

The perfect square that divides 27 is 9, which is equal to \(3^2\).

So, we can express 27 as the product of two factors, 3 and 9. One of the factors, 9, is a perfect square because it is equal to \(3^2\). Therefore, we have written 27 as a product of two integers where one of the factors is a perfect square.

We can also express 27 as 1 x 27 or 27 x 1, but neither of these representations includes a perfect square as a factor.

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Answer:

200 ml

Step-by-step explanation:

She uses a ml of solution a.

She uses b ml of solution b.

Equation of the amount of each solution:

a = b - 100

Equation of the amount of alcohol:

0.11a + 0.2b = 51

0.11(b - 100) + 0.2b = 51

0.11b - 11 + 0.2b = 51

0.31b = 62

b = 200

Answer: 200 ml

After solving the equations, we know that a total of 25 ladies attended the party.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

So, take dudes as x and ladies as y.

Now, form the required 2 equations as follows:
2x + y = 45 ...(1)

x + y = 35 ...(2)

Work on equation (2):

x + y = 35

x = 35 - y

Now, substitute x = 35 - y in equation (1):

2x + y = 45

2(35-y) + y = 45

70 - 2y + y = 45

-y = -25

y = 25

Since ladies were charged $1 for each ticket, then 25 ladies attended the party.

Therefore, after solving the equations, we know that a total of 25 ladies attended the party.

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Answer: serbia

Step-by-step explanation:

Answer:

x=16

Step-by-step explanation:

Answer: A. x < 2

Step-by-step explanation:

         We will isolate the variable with inverse operations.

Given:

  3x – 2 < 4

Add 2 to both sides of the equation:

  3x < 6

Divide both sides of the equation by 3:

  x < 2

        A. x < 2

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.

The model of the height of a Ferris wheel is represented by a sinusoidal model, which is presented below:

h = A + B · sin ωt     (1)

Where:

Sinusoidal functions are bounded functions, the minimum height of the Ferris wheel represents the lower bound of the function and the maximum height is the upper bound. Therefore, the minimum height of the rider is:

\(h_{min} = 39\,m - 30 \,m\)

\(h_{min} = 9\,m\)

By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.

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The expression of the statement that is given above can be written as follows: 262144y³ + 27.

To determine how to express the given statement the following should be carried out.

When a number is said to be cubed, it means that the number should be times by itself three consecutive times.

That is (64y + 3)³. This means that various components should be multiplied by itself three times. That is,

= 64×64×64(y)³ + 3×3×3

= 262144y³ + 27.

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Answer:

8494.87 is the actual answer but the rounded version is 8494.9

Step-by-step explanation:

3.142×52^2=8494.866535

8494.9 nearest tenth

Answer:

\(y = - [ \frac{1}{t - \frac{28}{9} } + t ]\)

Step-by-step explanation:

Solution:-

- A change of variable is a technique employed in solving many differential equations that are of the form: y ' = f ( t , y ).

- Considering a differential equation of the form y' = f ( αt + βy + γ ), where α, β, and γ are constants. A substitution of an arbitrary variable z = αt + βy + γ is made and the given differential equation is converted into a form: z ' = g ( z ).

- This substitution basically allow us to solve in-separable differential equations by converting them into a form that can be separated, followed by the set procedure.

- We are to solve the initial value problem for the following differential equation:

                              \(y' = ( t + y ) ^2 - 1 , y ( 3 ) = 6\)

First Step: Make the appropriate substitution

- We will use a arbitrary variable ( z ) and define the our substitution by finding a multi-variable function f ( t , y ) that is a part of the given ODE.

- We see that the term ( t + y ) is a multi-variable function and also the culprit that doesn't allow us to separate our variables.

- Usually, the change of variable substitution is made for such " culprits ".

- So our substitution would be:

                               \(z = t + y\)

Second Step: Implicit differential of the substitution variable ( z ) with respect to the independent variable

- In the given ODE we see that the variable ( t ) is our independent variable. So we will derivate the supposed substitution as follows:

                              \(\frac{dz}{dt} = 1 + \frac{dy}{dt} \\\\\frac{dy}{dt} = -1 + \frac{dz}{dt}\)

Remember: z is a multivariable function of "t" and "y". So we perform implicit differential for the variable " z ".

Third Step: Plug in the differential form in step 2 and change of variable substitution of ( z ) in the given ODE.

- The given ODE can be expressed as:

                            \(\frac{dy}{dt} = ( t + y ) ^2 - 1\\\\\frac{dz}{dt} - 1 = ( z ) ^2 - 1\\\\\frac{dz}{dt} = z ^2 \\\) ... Separable ODE

Fourth Step: Separate the variables and solve the ODE.

- We see that the substitution left us with a simple separable ODE.

Note: If we do not arrive at a separable ODE, then we must go back and re-choose our change of variable substitution for ( z ).

- We will progress by solving our ODE:

                            \(\frac{dz}{z^2} = dt\\\\\int {\frac{1}{z^2} } \, dz = \int {1} \, dt\\\\-\frac{1}{z} = t + c\\\\\frac{1}{z} = - (t + c )\\\\z = -\frac{1}{t + c}\)

Where,

                     c: The constant of integration

Fifth Step: Back-substitution of variable ( z )

- We will now back-substitute the substitution made in the first step and arrive back at our original variables ( y and t ) as follows:

                           \(t + y = - \frac{1}{t + c} \\\\y = - [ \frac{1}{t + c} + t ]\)  

Sixth Step: Apply the initial value problem and solve for the constant of integration ( c )

- We will use the given initial value statement i.e y ( 3 ) = 6 and evaluate the constant of integration ( c ) as follows:

                           \(y ( 3 ) = - [ \frac{1}{3 + c} + 3 ] = 6 \\\\\frac{1}{3 + c} = -9\\\\3 + c = -\frac{1}{9} \\\\c = - \frac{28}{9}\)

Seventh Step: Express the solution of the ODE in an explicit form ( if possible ):

                          \(y = - [ \frac{1}{t - \frac{28}{9} } + t ]\)

Answer:

7k-4

Step-by-step explanation:

(-3)(2.5)+(-3)(-k)+(0.5)(7)+(0.5)(8k)

-7.5+3k+3.5+4k

Then you combine like terms

-7.5k+3k+3.5+4k

(3k+4k)+(-7.5+3.5)

7k+-4

Answer:

Step-by-step explanation:

a) To determine the endogenous variables, we need to identify the variables that are determined within the model equation. In the given model, the endogenous variable is Y (output or national income).

b) Let's find Y, C, and T step-by-step:

Start with the equation Y = C + I0 + g0.

Substitute C from the equation C = a + b(y - T).

Y = (a + b(y - T)) + I0 + g0.

Substitute T from the equation T = d + tY.

Y = (a + b(y - (d + tY))) + I0 + g0.

Expand the equation:

Y = a + by - bd - btY + I0 + g0.

Rearrange the equation to isolate Y:

Y + btY = a + by - bd + I0 + g0.

Y(1 + bt) = a + by - bd + I0 + g0.

Y = (a + by - bd + I0 + g0) / (1 + bt).

Now, Y is expressed in terms of the exogenous variables a, b, d, I0, g0, and the endogenous variable Y itself, along with the parameter t.

To find C and T, we can substitute the obtained Y value back into the respective equations:

Substitute Y into the equation C = a + b(y - T):

C = a + b(y - T) = a + b(y - (d + tY)) = a + by - bd - btY.

C = a + by - bd - bt[(a + by - bd + I0 + g0) / (1 + bt)].

Now, C is expressed in terms of the exogenous variables a, b, d, I0, g0, and the endogenous variable Y, along with the parameter t.

Substitute Y into the equation T = d + tY:

T = d + tY = d + t[(a + by - bd + I0 + g0) / (1 + bt)].

Now, T is expressed in terms of the exogenous variables d, t, and the endogenous variable Y, along with the parameters a, b, I0, and g0.

It's important to note that in the given model, there is only one endogenous variable, Y (national income/output). C and T are determined based on the values of Y and the exogenous variables.

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

1. f = 35g - 12, g is the independent variable and f is the dependent variable.

2. r = 17q - 5, the independent variable is q, and the dependent variable is r.

3. Number of weeks is the independent variable and the number of pencils is the dependent variable.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

1. In the linear function f = 35g - 12, The independent variable is 'g' and the dependent variable is 'f'.

2. In the linear function r = 17q - 5, the Independent variable is 'q' and the dependent variable is 'r'.

3. In this context independent variable is weeks and the dependent variable is the number of pencils.

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