the solution of the equation y+2=_2 is​

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

y=-5

Step-by-step explanation:

When the x-value on the graph is equal to -4, the y-value is equal to -5

Answer:

6x + 2 m

Step-by-step explanation:

Given:

A (area) = (24x^2 + 8x) m^2

l (side length) = 4x m

Find: b (base) - ?

In order to find the base of the rectangle, you have to divide its area by the side length:

\(b = \frac{24 {x}^{2} + 8x}{4x} = \frac{4x(6x + 2)}{4x} = 6x + 2\)

Answer:

base = 6x + 2 m

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = base × width

given A = 24x² + 8x and width = 4x , then

24x² + 8x = base × 4x (divide both sides by 4x )

\(\frac{24x^2+8x}{4x}\) = base

\(\frac{24x^2}{4x}\) + \(\frac{8x}{4x}\) = base , then

base = 6x + 2 m

Answer:

12m + 9

Step-by-step explanation:

3(5m) is 15m

3(3) is 9

which makes 15m + 9

then 15m - 3m is 12m

Answer:

12m+9

Step-by-step explanation:

You first need to distributive the 3 into the parentheses:

3(5m +3) - 3m

15m + 9 - 3m

Next, you need to combine like terms:

15m + 9 - 3m

12m + 9

So the correct answer is 12m + 9. Hope this helps!

Approximately 9.63% of the energy consumed by the person would be derived from protein.

To calculate the percentage of energy derived from protein, we need to first convert the amount of protein consumed from grams to calories. Protein provides approximately 4 calories per gram. Therefore, 65 grams of protein would provide:

65 grams * 4 calories/gram = 260 calories

This gives us 260 calories from protein.

To find the percentage of energy derived from protein, we can divide the calories from protein by the total calories consumed and multiply by 100:

260 calories / 2700 calories * 100% ≈ 9.63%

Therefore, approximately 9.63% of the energy consumed by the person would be derived from protein.

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Answer:

400 square inches

Step-by-step explanation:

surface area= summation of area of all the faces the object has

out object has 2 triangular faces, and 3 rectangular faces

S.A = 2(0.5bh) + LW +LW+LW

= 2(0.5 x 8 x 15) + (15x7) + (17 x 7) + (7×8)

= 120+105+119+56

= 400 square inches

The statements that are true concerning the study that was carried out by the pharmaceutical company include the following: This study uses random sampling, This study uses blinding and This study uses a control group. That is option A, B and E.

A pharmaceutical company is defined as the company that has been certified to manufacture and distribute drugs such as the children's vitamin.

While selecting sample for the study, it was stated that 500 children grouped by age was randomly selected.

Out of the total samples, 250 was given the vitamin while the remaining half was given a placebo ( a blind) which would serve as concealment of the group allocation from them as they are serving as the control.

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Answer:

A,B,C,

Step-by-step explanation:

PLATO

Answer:

To create a matrix for this linear system, we can arrange the coefficients of the variables and the constants into a matrix as follows:

| 1 3 2 | | x | | 26 |

| 1 -3 4 | x | y | = | 2 |

| 2 1 1 | | z | | 8 |

To solve the system using row reduction, we can perform elementary row operations to transform the matrix into row echelon form or reduced row echelon form. I will use the latter approach for simplicity:

| 1 0 0 | | x | | 6 |

| 0 1 0 | x | y | = | 5 |

| 0 0 1 | | z | | -1 |

Therefore, the solution to the system is x = 6, y = 5, and z = -1.

g''(6) represents the second derivative of the function g(y) with respect to y, evaluated at y = 6, g''(6) is equal to 3888.

For g''(6), we need to take the second derivative of g(y) with respect to y and then evaluate it at y = 6. Let's go through the steps to find g''(6).

First, let's calculate the integral of f(x) with respect to t:

∫₀³ t² dt

Integrating t² with respect to t gives us:

[1/3 * t³] from 0 to 3

Substituting the limits of integration:

[1/3 * 3³] - [1/3 * 0³]

= 1/3 * 27 - 0

= 9

Therefore, the integral of f(x) with respect to t is 9.

Now, we can find g(y) by substituting the integral of f(x) into the expression for g(y):

g(y) = y⁴ * f(x) dx

     = y⁴ * ∫₀³ t² dt

     = 9 * y⁴

Now, we need to find the second derivative of g(y) with respect to y. Let's differentiate g(y) twice:

g'(y) = d/dy (9 * y⁴)

      = 36 * y³

g''(y) = d/dy (36 * y³)

       = 108 * y²

Finally, to find g''(6), we substitute y = 6 into the expression for g''(y):

g''(6) = 108 * (6)²

      = 108 * 36

      = 3888

Therefore, g''(6) is equal to 3888.

In summary, g''(6) represents the second derivative of the function g(y) with respect to y, evaluated at y = 6.

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Answer:

2.4

Step-by-step explanation:

all you have to do is divide 12 by 5

The statement that applies to Simon as a person is; C: His annual deductible will be $800.

What is Insurance in-network?

We are aware of the following information regarding in-network insurance:

Simon will most likely have a yearly deductible of $800 and it is less probable that he will not pay anything after meeting this annual deductible because in-network doctors serve to lower the cost of insurance to the individual.

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The options missing in the question are;

a. The cost of his annual physical will be 50% after deductible

b. The maximum amount that he can expect to pay out-of-pocket is $6,000.

c. His annual deductible will be $800.

d. Once he hits his annual deductible of $800, he will incur no additional costs for health care services for the rest of the calendar year.

Answer:

5/6 = v + 2/7

Step-by-step explanation:

5/6 = v + 2/7  

23/42 - v = 0

5/6 = 1/7 (7 v + 2)

Answer:

23/42 = v

Step-by-step explanation:

5/6=v+2/7

Multiply each side by the common denominator, 42

42( 5/6=v+2/7)

35 = 42v + 12

Subtract 12 from each side

35-12 = 42v

23 = 42 v

Divide each side by 42

23/42 = v

Answer:

if this is a trig problem then x is 44

Step-by-step explanation:

Serenity is going to invest in an account paying an interest rate of 4.4% compounded continuously therefore Serenity would need to invest $400 to the nearest hundred dollars, for the value of the account to reach $670 in 11 years.

This is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

We can solve the problem by :

1+(0.044÷365)= 1.0001205479

Yearly impounding factor, 1.0001205479^365=1.0449795838

For a period of 11 years, maturity factor,1.0449795838^11 = 1.6225043167.

$1 becomes $1.6225043167.

If Maturity value is to be,$670 which is amount to be invested,

670÷ 1.6225043167 = 412.942

To the nearest 100 dollars is $400.

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The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800.  The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.

Let variable x = number of associates, assigned to the case

Let variable y = number of partners assigned to the case.

The system of equations to describe this are:

800 x + 1800 y = 17600

y = x + 2

Plugging equation 2 in equation 1, we get,

800 x + 1800(x+ 2) = 17600

2600 x + 3600 = 17,600

Collect like terms

2400 x = 14,000

Divide both side by 2400x

x = 14,000 / 2400

x = 5.8

x = 6 (Approximately)

So,

y = x + 2

y = 5.8 +3

y = 7.8

y = 8 (Approximately)

Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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Answer:

4. d = 4

5. d = 8.8

6. d = 6

7. d = 10

8. d = 3

9. d = 1

Step-by-step explanation:

4. (-5, 2), (-5, 6)

    (x₁, y₁)  (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-5 - (-5))² + (6 - 2)²

d = √(-5 + 5)² + (4)²

d = √(4)²

d = √16

d = 4

5. (4.5, -3.3), (4.5, 5.5)

       (x₁, y₁)      (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4.5 - 4.5)² + (5.5 - (-3.3)²

d = √(0)² + (5.5 + 3.3)²

d = √(8.8)²

d = √77.44

d = 8.8

6. ((5(1/2), (-7(1/2)) and ((5(1/2), (-1(1/2))

         (x₁,     y₁)                   (x₂,     y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(11/2) - (11/2)² + (-3/2) - (-15/2))²

d = √(d)² + ((-3/2) + (15/2)²

d = √(6)²

d = √36

d = 6

7. (-2(1/4)), -8) and (7(3/4), -8)

        (x₁,   y₁)               (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(31/4) - (-9/4))² + (-8 - (-8))²

d = √(31/4) + (9/4))² + (-8 + 8)²

d = √(10)²

d = √100

d = 10

8. (5(1/4)), (-3(1/4) and ((5(1/4), (-6(1/4))

         (x₁,     y₁)                    (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(21/4) - (21/4))² + (-25/4) - (-13/4))²

d = √(-25/4) + (13/4))²

d = √(-3)²

d = √9

d = 3

9. (-1(1/2)), (-6(1/2) and ((-2(1/2), (-6(1/2))

          (x₁, y₁)                        (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-5/2) - (-3/2))² + (-13/2) - (-13/2))²

d = √(-5/2) + (3/2))²

d = √(-1)²

d = √1

d = 1

I hope this helps!

Answer:

Calories from both fat and carbohydrates = 900 calories/day

Step-by-step explanation:

Number of calories eaten by Sandra per day = 2000 calories/day

Calories from fat = \(\frac{1}{4}\) of the total number of calories per day

OR

Calories from fat = \(\frac{1}{4}\times 2000 = 500\ calories/day\)

Calories from carbohydrates = \(\frac{1}{5}\) of the total number of calories per day

OR

Calories from carbohydrates = \(\frac{1}{5}\times 2000 = 400\ calories/day\)

To find the total number of calories from both fat and carbohydrates, we need to add the calories from fat and calories from carbohydrates as calculated above.

Calories from both fat and carbohydrates = Calories from fat + Calories from carbohydrates = 500 + 400 = 900 calories/day

The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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Pentagon ABCDE, when rotated 90 degrees clockwise about the origin, forms Pentagon A'B'C'D'E', where the x and y-coordinates are switched and the y-coordinate is negated, and the vertices remain the same.

In this question, we are given that Pentagon ABCDE is rotated 90 degrees clockwise about the origin to form Pentagon A'B'C'D'E'.We can observe that the vertices of the Pentagon ABCDE and Pentagon A'B'C'D'E' are still the same. However, the positions of the vertices change from (x, y) to (-y, x). This means the x and y coordinates are switched and the y coordinate is negated.Let's take a look at how the vertices are transformed:

Pentagon ABCDE Vertex

A(-1, 2) Vertex B(2, 4) Vertex C(3, 1) Vertex D(2, -1) Vertex E(-1, 0)Pentagon A'B'C'D'E'Vertex A'(-2, -1)Vertex B'(-4, 2)Vertex C'(-1, 3)Vertex D'(1, 2)Vertex E'(0, -1)Therefore, Pentagon ABCDE, when rotated 90 degrees clockwise about the origin, forms Pentagon A'B'C'D'E', where the x and y-coordinates are switched and the y-coordinate is negated, and the vertices remain the same.

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Answer:

D

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

100 inches
Let's use "x" to represent the length of a side of the smaller polygon, and let's use "y" to represent the corresponding length of a side of the larger polygon. We're told that the ratio of the side lengths is 3/5, so we can set up the equation:

y/x = 5/3

We're also told that the perimeter of the smaller polygon is 60 inches, so we can set up another equation using the fact that the smaller polygon has "n" sides:

nx = 60

Now, we want to find the perimeter of the larger polygon, which also has "n" sides. We can use the equation we set up earlier to write "y" in terms of "x":

y/x = 5/3

y = (5/3)x

Now we can substitute this expression for "y" into the formula for the perimeter of the larger polygon:

Perimeter of larger polygon = nx = n(5/3)x = (5/3)(nx) = (5/3)(60) = 100

So the perimeter of the larger polygon is 100 inches.

Answer:

1.  ≠

2. =

Step-by-step explanation:

Cross products mean you multiply the top of the first one by the bottom of the second one and compare it to multiplying the bottom of the first one by the top of the second one.

1. 7*10 is not equal to 5*15, so the answer is not equal.

2. 6*20 is equal to 8*15, so the answer is equal

The value of sin(θ) is approximately 0.921 and the value of cos(θ) is approximately 0.391.

To find the value of each variable using sine and cosine, we need to set up a right triangle with the given information. Let's label the sides of the triangle as follows:

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h2 = s2 + t2

h2 = 31.32 + 13.32

h2 = 979.69 + 176.89

h2 = 1156.58

h = √1156.58

h ≈ 34.0

Now that we know the length of the hypotenuse, we can use sine and cosine to find the values of the variables:

sin(θ) = s / h

sin(θ) = 31.3 / 34.0

sin(θ) ≈ 0.921

cos(θ) = t / h

cos(θ) = 13.3 / 34.0

cos(θ) ≈ 0.391

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Answer:

7g + 3n - 2

Step-by-step explanation:

when you subtract you 'add the opposite'; subtracting a negative is the same as adding a positive

for example, using the above statement we can rewrite the problem as:

7g - 6 + 3n + 4

we can combine -6 and 4 to get -2

7g + 3n - 2 or 7g + 3n + (-2)

To determine the points where the probability distribution function is a maximum for the given states of a particle in a three-dimensional box, we need to find the values of x, y, and z that maximize the wave function. In this case, we are given two different states: (a) n_X = 1, n_Y = 1, n_Z = 1, and (b) n_X = 2, n_Y = 2, n_Z = 1. We will find the points where the probability distribution function is a maximum for each state.

(a) For the state n_X = 1, n_Y = 1, n_Z = 1, the wave function is given by Ψ(x, y, z) = √(8/L^3) * sin(πx/L) * sin(πy/L) * sin(πz/L). To find the maximum points, we need to maximize the absolute value of this function. Since sin oscillates between -1 and 1, the maximum value of the wave function occurs at the points where sin(πx/L) = 1, sin(πy/L) = 1, and sin(πz/L) = 1. This means the maximum points are at (x, y, z) = (L, L, L).

(b) For the state n_X = 2, n_Y = 2, n_Z = 1, the wave function is given by Ψ(x, y, z) = √(8/L^3) * sin(2πx/L) * sin(2πy/L) * sin(πz/L). Similarly, we need to find the points where sin(2πx/L) = 1, sin(2πy/L) = 1, and sin(πz/L) = 1. This gives us the maximum points at (x, y, z) = (L/2, L/2, L).

In summary, for the state n_X = 1, n_Y = 1, n_Z = 1, the maximum points of the probability distribution function are at (x, y, z) = (L, L, L). For the state n_X = 2, n_Y = 2, n_Z = 1, the maximum points are at (x, y, z) = (L/2, L/2, L).

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