The amount of time in REM sleep can be modeled with a random variable probability density function given by F ( x ) = x 1600 where 0 ≤ x ≤ 40 Y x is measured in minutes. 1. Determine the probability that the amount of time in REM sleep is less than 7 minutes. 2. Determine the probability that the amount of time in REM sleep lasts between 13 and 24 minutes.

The problem involves maximizing profit in a factory that produces products X and Y. Constraints include labor time, material availability, testing equipment usage, and minimum production requirements.

(a) To maximize profit, we need to define the objective function. Let x be the number of units of product X and y be the number of units of product Y produced. The objective function can be expressed as Z = 6x + 4.5y, representing the total profit.

The constraints can be formulated as follows:

1. Labor time constraint: 30x + 15y ≤ 60 hours (converted to minutes)

2. Material constraint: 2.5x + 2y ≤ 500 kilograms

3. Testing equipment constraint: Testing time for X ≥ 8 hours (converted to minutes)

4. Minimum production requirement: x ≥ 40 units of product X, y ≥ 80 units of product Y

5. Non-negativity constraint: x ≥ 0, y ≥ 0

(b) By graphing the system of inequalities on graph paper, the feasible region can be shaded. The feasible region represents the intersection of all the constraints.

(c) To find the weekly production that maximizes profit, we need to optimize the objective function within the feasible region. This can be done using linear programming techniques.

By solving the problem, we can determine the values of x and y that maximize the objective function Z. The expected maximum profit will be the value of Z at the optimal solution.

Note: The specific calculations and graphical representation will require numerical values and graphing tools to provide an accurate solution.

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Given,

principal(P)=$4000

Term Length (t)=4 years

Interest rate(i)=12%.

Let, I be the amount of interest of 4 years. Then,

Now, the monthy interest is

MOnthly payment is $105.

Therefore, the first payment of installment will go towards principal by

Hence, option (B) is correct.

We were given that:

At equilibrium, we have:

Answer:

11+12+13+14=50

Step-by-step explanation:

Just estimate. We know that 15 times 4 = 60, so it has to be less than that. We know that 10 times 4 is 40, so it has to be in that range. Just do trial and error to find the exact answer. I'm editing this now and I realized that I didn't answer the question. I don't know how to write the equation using N but the first integer is 11.      

Answer:

2.0*10^4

Step-by-step explanation:

\(5.2 *10^5\) words

26 categories

\(\frac{5.2 *10^5}{26} =\frac{520 000}{26} =20 000\)

\(2.0*10^4\)

so there is an average of 2.0*10^4 words per letter

Answer:

None

Step-by-step explanation:

For me, the easier way to see that the answer is 30 students (12 years and older) is to convert the 60% to a decimal, 0.60, and multiply by the total number of students:

(0.06)*(50) = 30 students are 12 and older.

None of the listed answers make sense to me.  Yes, a couple have the correct answer, but their derivation is incorrect.

100 ÷ 20 = 50   [who, what??]

100 ÷ 2 = 50       [who, what, why??]

60 ÷ 2 = the number of students who are 12 years old.  [Correct, but where did the 2 come from?]

60 ÷ 20 = 3 students  [gimmee a break]

30 of the 50 students are 12 years old. [Yes, but what is the calculation that led to this conclusion?]

To determine the exact concentration of the solution made, one can divide the mass of the solute with the volume of the solution.

A solution is the substance formed by the mixture of solute in solvent. The solute may or may not be dissolved in the solution. One can determine the exact concentration of the solution if the mass of solute added in the specific volume of solution is known. If the solution is made by someone else, then its concentration can be determined by process of titration.

The concentration of a solution is expressed in the form of moles or grams per unit liter. If the solution is unknown and only its dissolved chemical is known, then titration will help in determining the closest value of concentration if performed without human error. In titration, the use of glassware that that is more precise than the flasks, beakers, and graduated cylinders are used.

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Refer to complete question below:

How do we determine concentration a solution? If it is a solution that we have made up, we can readily do the calculations required. But what if it is a solution that someone else has made? What technique can be used to gather information about a solution that we are given with no other information than the name of the chemical dissolved.

Answer:

R=22% , T=8yrs , P=$250

I=PRT/100

I=250×22×8/100

I=$440.00

The Interest that's earned will be $440.

The formula for calculating simple Interest will be:

= PRT/100

where,

P = $250

R = 22%

T = 8 years

Therefore, the simple interest will be:

= (250 × 22 × 8) / 100

= 44000/100

= 440

Therefore, the simple interest is $440.

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An equation is formed of two equal expressions. The correct options are C, D, and E.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of x in the given equation is,

\(\dfrac35 (30x-15) = 72\\\\(6x - 3) = 72\\\\6x -3 = \dfrac{72}3\\\\6x = 24 + 3\\\\x = 4.5\)

Substitute the value of x in other option to check if the equations are equal are not. Therefore, the options can be written  as,

A.) 18x - 15 = 72

18(4.5) - 15 = 66

Thus, this will not return the same value.

B.) 50x - 25 = 72

50(4.5) - 25 = 200

Thus, this will not return the same value.

C.) 18x - 9 = 72

18(4.5) - 9 = 72

Thus, this will return the same value.

D.) 3(6x - 3) = 72

3[6(4.5) - 3] = 72

Thus, this will return the same value.

E.) x = 4.5

Thus, this will return the same value.

Hence, the correct options are C, D, and E.

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To find the volume of the solid generated by revolving the region bounded by the curves y = √√√x and x = 2y about the line x = 5, we can use the method of cylindrical shells. The volume can be obtained by integrating the product of the height of each shell, the circumference of the shell, and the thickness of the shell.

To apply the cylindrical shell method, we divide the region into thin vertical shells parallel to the axis of revolution (x = 5). Each shell has a height given by the difference between the upper and lower functions, which in this case is x = 2y - √√√x. The circumference of each shell is given by 2πr, where r is the distance between the axis of revolution and the shell, which is x - 5.

To calculate the volume of each shell, we multiply the height, circumference, and the thickness of the shell (dx). The thickness is obtained by differentiating the x-coordinate with respect to x, which is dx = dy/dx * dx. Since x = 2y, we can substitute y = x/2.

Now we can set up the integral to find the total volume:

V = ∫(2πr * h * dx)

V = ∫(2π(x - 5)(2y - √√√x) * (dy/dx) * dx)

V = ∫(2π(x - 5)(2(x/2) - √√√x) * dx)

By evaluating this integral over the appropriate limits of x, we can find the volume of the solid generated by revolving the region bounded by the given curves about the line x = 5.

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Answer:

Step-by-step explanation:

These probabilities may be given in the problem statement or may need to be estimated based on past data or assumptions. Once we have these probabilities, we can use the multiplication rule to calculate the joint probability.

To find the probability that the next driver will use entrance 1 and park for more than two hours, we can use the multiplication rule of probability.

The multiplication rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the two events are:

The driver uses entrance 1

The driver parks for more than two hours

Let P(E1) be the probability that the next driver uses entrance 1, and let P(MT2) be the probability that the next driver parks for more than two hours.

Then, the probability that both events occur together is given by:

P(E1 and MT2) = P(E1) × P(MT2)

So, to find the probability that the next driver will use entrance 1 and park for more than two hours, we need to know the individual probabilities of these events.

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Answer:

G

Step-by-step explanation:

An equation of proportionality has the form

y = kx ← k is the constant of proportionality

y = 25x ← has this form with k = 25

y = 5x ← has this form with k = 5

The required equation is y = 25x with k = 25 → G

The mover is communicating that the weight of the table and 4 chairs combined, represented as t+4C, is greater than or equal to 100 pounds.

The expression t+4C represents the total weight of the table and 4 chairs. The mover's invoice states that this total weight is greater than or equal to 100 pounds, which means that the combined weight of the table and chairs is at least 100 pounds. Therefore, the correct answer is D, "The table and 4 chairs weigh at least 100 pounds."

To solve this mathematically, we can use algebraic inequalities. The inequality t+4C >_ 100 can be rearranged as t >_ 100-4C. This means that the weight of the table t must be greater than or equal to 100 minus four times the weight of a single chair C.

If each chair weighs less than 25 pounds, then the total weight of the table and 4 chairs combined will be at least 100 pounds. So D is correct answer.

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Answer:

it is shifted up three points

Step-by-step explanation:

Answer:

For the top row, 3 and 4, respectively

For the bottom row, 60 and 150, respectively

Step-by-step explanation:

w increases by 1 every time and d increases by 30

Answer:

for 2 weeks it is $60 and for $90 dollars its 3 weeks and for $120 is 4 weeks  and for 5 weeks its $150.

Step-by-step explanation:

She gets payed $30 every week since 1 week=30 that means its adding 30 dollars each week.

Answer:

i. 70%

ii. 70%

Step-by-step explanation:

Since in the question,  it is given that 60% of everyone is ordered tacos so 40% of everyone is ordered enchiladas

i. Now if half ordered tacos that means out of these 30 orders enchiladas.

since 30 ordered tacos that means 70% ordered enchiladas

ii. Now for 3 by 4 we have to assume the number of people who ordered only  enchiladas be x

So,

For both,  it would be 0.75 x

And, the number of people who did not order is 40 as 60 tacos are ordered by people

So, the percentage is

= 40 × 0.75 + 40

= 30 + 40

= 70%

Answer:

x represents the number of level 1 tickets; y represents the number of level 2 tickets

Here, x represents the number of level 1 tickets; y represents the number of level 2 tickets. Therefore, option C is the correct answer.

Given that, the total number of seats=50,000, the cost of level 1 tickets=$150, the cost of level 2 tickets=$250 and the total cost=$125,000.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Let the number of level 1 tickets be x and the number of level 2 tickets be y.

Now, x + y = 50,000 and 150x + 250y = 125,000.

Therefore, option C is the correct answer.

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Horizontal translation for a parabola is changed by the value of a variable, h, that is subtracted from x before the squaring operation.

Our reference parabola has the following equation:

And the equation that includes a horizontal translation looks like this:

The sign of h is determined by whether the translated parabola is on the right (positive sign) or on the left (negative sign) side of the reference parabola, in this case, the vertex of the parabola is translated 3 units to the left, then h equals -3, replacing this value for h, we get:

Then, the correct answer is option D, G(x) = (x+3)^2

There is no upper limit if the ratio raises x to a higher power. The limit is 0 if the ratio causes the power of x to be reduced to zero.

A ratio is an expression for an ordered pair of numbers, a and b, where b is not equal to zero and the expression is written as a/b. A ratio is created by combining two ratios. Assuming a ratio of one boy to three girls, this would suggest that 3/4 of the population is female and only 1/4 is male. A part can be an amount, a percentage, or the difference between two or more objects.

Here,

The ratio of, say, the highest-degree words serves as the upper bound as x grows.

There is no upper bound on how much the ratio can raise the power of x. The limit is 0 if the ratio causes the power of x to be reduced to zero.

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Answer:

C)

Step-by-step explanation:

Answer:

D) 1:1

Step-by-step explanation:

Answer:

4,52

Step-by-step explanation:

32+5x=y

pls let me know is it was right

if it was pls give brainlest

The value of the function at, x = 3, x = 0 and x = - 2 are 3, 0, and - 2.

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.

Given, A function f(x) = x, Now this is an identity function as y = x.

Now, At x = 3,

f(3) = 3.

At x = 0,

f(0) = 0.

At, x = - 2,

f(-2) = - 2.

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The final result should be a circle with center (2, 3) and a radius of 4 units.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center; equivalently, it is a curve drawn by a point that moves in a plane so that its distance from that point is constant.

Let's choose the point (x, y) as (2, 3).

Using graph paper with a scale of 1cm = 1 unit, we can draw the graph of a circle with center (2, 3).

Here's how you can draw the circle:

Mark the point (2, 3) on the graph paper. This will be the center of the circle.

Determine the radius of the circle. Let's say the radius is 4 units. Starting from the center point (2, 3), measure a distance of 4 units in all directions (up, down, left, and right). Mark these points on the graph paper.

Connect the marked points to form a circle. You can use a compass or any round object with a diameter equal to the radius to draw a smooth curve passing through the marked points.

Label the circle as "C" to indicate that it represents a circle.

Note: The accuracy of the circle drawing may depend on the precision of the graph paper and the tools used.

The final result should be a circle with center (2, 3) and a radius of 4 units.

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Answer:

y = x + 3

Step-by-step explanation:

Given: (6,9)  (14, 17)

\(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{17-9}{14-6}=\frac{8}{8}=1\)

slope, m = 1

Equation of line ⇒ y=mx+b

y = 9 , x = 6 , m = 1, b = ?

9 = 1*6 + b

9 = 6 + b

b = 9 - 6 = 3

Therefore, the equation of line will be:

y = 1x + 3

y = x + 3

Answer:

If you mean the angle at X... 70°

Step-by-step explanation: