A tower that is 159 feet tall casts a shadow 172 feet long. Find the angle of elevation of the sun to the nearest degree

Answer:

Step-by-step explanation:

The mean and standard deviation of the total time are µx = 66 and σx = 3.17, so the correct answer is (D) µx= 66 σx= 3.17.

To find this:

The total time to complete all three tasks is the sum of the time taken for each task. The mean time to complete all three tasks (µx) can be calculated by adding the mean time for each task: µx = 36 + 22 + 8 = 66. The standard deviation (σx) of the total time can be calculated using the standard deviation of each task and the square root of the number of tasks (n).

Using the formula: \(\sigma x = \frac{\sqrt{\sigma1^2 + \sigma2^2 + \sigma3^2}}{\sqrt n}\),

where σ1, σ2, σ3 are the standard deviations of each task, n = 3.

Plugging in the values, we get

\(\sigma x = \sqrt(2.5^2 + 1.8^2 + 0.75^2)/\sqrt3 \\= \sqrt{6.25 + 3.24 + 0.5625}/\sqrt3 \\= \sqrt{10.0525}/\sqrt3 = 3.17\)

Hence, the mean and standard deviation of the total time are µx = 66 and σx = 3.17, so the correct answer is (D) µx= 66 σx= 3.17.

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Answer:

3x+9 ≥15

Step-by-step explanation:

three times x

3x

9 more than

3x+9

is at least 15

3x+9 ≥15

Answer:

Permanent Magnets and Electromagnets: What are the Differences? A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. ... An electromagnet is made from a coil of wire which acts as a magnet when an electric current passes through it.

Step-by-step explanation:

Electromagnets differ from regular magnets in that they require an electric current to generate a magnetic field.

Regular magnets, also known as permanent magnets, possess an inherent magnetic field due to the alignment of their atomic or molecular structure. They do not require an external power source.

On the other hand, electromagnets are made by wrapping a coil of wire around a magnetic core and passing an electric current through the wire. The electric current creates a magnetic field, and the strength of the magnetic field can be controlled by varying the current.

One key advantage of electromagnets is their ability to be turned on and off by controlling the electric current. This feature allows for a wide range of applications, such as in electric motors, generators, speakers, magnetic levitation systems, and more, where the magnetic field needs to be controlled or modulated. In contrast, regular magnets have a constant magnetic field that cannot be easily manipulated.

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Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.

-----------------------------

x-y=-2

3x+y=10

---------------

4x=8

x=8/4=2

2-y=-2

y=2-(-2)=2+2=4

To find the angle of least nonnegative measure that is coterminal with θ = -570°, we can add or subtract multiples of 360° until we get an angle between 0° and 360°.

We can start by adding 360° to -570°:

-570° + 360° = -210°

This is still negative, so we can add another 360°:

-210° + 360° = 150°

This is between 0° and 360°, so the angle of least nonnegative measure that is coterminal with θ = -570° is 150°. Therefore, 0c is 150°.

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Answer:

-19.68

-1/10x+8/5

25 1/3

-50

22.75

Step-by-step explanation:

Answer:

6) 22.75gallons

7) -50feets

8) 25⅓ inches

9)2/5

10) -19.68

Answer:

1/2 × |AB| × |OE|

Step-by-step explanation:

use the formula for finding the area of a triangle.

It depicts how a plant first grows swiftly from time t₁ to time t₂.

It indicates consistent height during a dry period from time t₂ to time t₃.

It depicts consistent increase from time t₃ forward.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

From t₁ to t₂ it represents plant grows quickly at first.

From t₂ to t₃ it represents constant height during a dry spell.

From, t₃ on wards it represents growth at a steady pace.

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If we reflect across the y-axis and then reflect again across the y-axis , it will give result an image that maps onto itself , Option B is the right answer.

The reflection of the point (x,y) across the x-axis is the point (x,-y), across the y-axis is the point (-x,y). , across the line is the point (y, x)

The 90 degree counterclockwise rotation of a point (x, y) is the point (-y, x)

The 180 degree counterclockwise rotation of a point (x, y) is the point (-x, -y)

The 270 degree clockwise rotation of a point (x, y) is the point (-y, x)

Therefore on application of these rules

For Case A

The point will be (-y , x)

For Case B

The point will be (x,y)

Therefore Option B is the answer.

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Answer:

B ($905)

Step-by-step explanation:

Plug in $17 for the h value in the equation, and you get this:

c = 50 (17) + 55

c = 850 + 55

c = 905

So the answer is $905 for 17 hours of work (plus the service fee)

Answer:

60%

Step-by-step explanation:

I know it is

Answer:

60

Step-by-step explanation:

5 percent (calculated percentage %) of what number equals 3? Answer: 60.

Answer:

After 17,190 years, the amount of carbon-14 left would be approximately 5 mg.

The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the remaining carbon-14 decays. To calculate the amount of carbon-14 remaining after 17,190 years, we can use the formula:

A = A0 * (1/2)^(t/T)

where:

A0 is the initial amount (80 mg)

t is the time elapsed (17,190 years)

T is the half-life (5,730 years)

A = 80 * (1/2)^(17,190/5,730)

A = 80 * (1/2)^3

A = 80 * (1/8)

A = 10 mg * 1/2

A = 5 mg

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

the wizard will have 237 millimeters of potion left unused.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, A wizard need to prepare 735 ml of a magic drink, The recipe contains of watermelon juice coconut water and potion in a ratio of 21:11:3.

This means that for every 21 parts of watermelon juice, there are 11 parts of coconut water and 3 parts of potion.

Let's assume that the total volume of the magic drink is 21x + 11x + 3x = 35x, where x is a constant that represents the ratio factor.

To find the actual volume of the magic drink, we need to solve for x using the given total volume of 735 ml:

35x = 735

x = 21

This means that the actual volume of watermelon juice in the magic drink is 21x = 21 * 21 = 441 ml,

and the actual volume of coconut water is 11x = 11 * 21 = 231 ml.

Since the wizard has 300 ml of potion, which is more than the required 3x = 3 * 21 = 63 ml of potion for the magic drink,

the wizard only needs to use 63 ml of potion. Therefore, the unused portion of potion is:

300 ml - 63 ml = 237 ml

Thus, the wizard will have 237 millimeters of potion left unused.

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When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

In working with two variables related by a regression equation, the marginal change in a variable is the amount that it changes when the other variable changes by exactly one unit.

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Answer:

The two number are :

x = 1411

y = 1079

Step-by-step explanation:

Let the two numbers = x and y

The sum of two numbers is 2490

x + y = 2490..... Equation 1

If 6.5 percent of one no. is equal to 8.5 percent of the other,

Hence:

6.5% of x = 8.5% of y

0.065x = 0.085y

Make x the subject of the Formula

x = 0.085y/0.065

x = 1.308y

We substitute 1.308y for x Equation 1

x + y = 2490..... Equation 1

1.308y + y = 2490

2.308y = 2490

y = 2490/2.308

y = 1078.8561525

y = 1079

x + y = 2490..... Equation 1

x = 2490 - y

x = 2490 - 1079

x = 1411

Answer:

3 5,7,9,11,13,16,17 19,21,23,25,27,29

Answer:

60 years

Step-by-step explanation:

If there is 200 feet of fencing available, the maximum possible area of the corral is 5000 Feet.

In the question, if there is 200 feet of fencing available, then we have to find the maximum possible area of the corral.

The formula of area of rectangle is:

A = L × B, where L is the length of the rectangle and B is the breadth of the rectangle.

The A = 200 feet and rectangular area is enclosed using the creek as one side and fencing for the other three sides, to create a corral.

So, L + 2B = 200

Subtract L on both side, we get

2B = 200 - L

Divide by 2 on both side, we get

B = 100 - L/2

A = f(L)

A = L·(100 - L/2)

A = 100L - \(L^2\)/2

Now finding the derivative.

A' = \(\frac{df(L)}{dL}\)

A' = -L + 100

Let A' = 0

-L + 100 = 0

Subtract 100 on both side, we get

-L = -100

L = 100 feet

Now putting the value of L in B = 100 - L/2.

B = 100 - 100/2

B = 100 - 50

B = 50 feet

The maximum possible area of the corral = 100 × 50

The maximum possible area of the corral = 5000 Feet

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The G force for particles rotating at 2000 rpm when the distance from the axis of rotation to the particle is 0.1 m is 4,335.5.

Given,The diameter of the microcarrier = 250 μm

The density of the microcarrier = 1.02 g/cm3

The volume of the culture = 50 liters

The height of the culture = 1 m

The density of the culture solution without microcarrier = 1.00 g/cm3

The viscosity of the culture solution without microcarrier = 1.1 cP

To find,The time needed to settle the cells completely

Formula used,Vs = 2g(ρp - ρm)/9μ

Where,Vs = Settling velocity

g = acceleration due to gravityρ

p = density of particleρ

m = density of medium

μ = viscosity of medium

Calculation,

Volume of the microcarrier,V = 4/3πr3V

= 4/3 × π × (250 × 10-6/2)3

V = 8.68 × 10-12 m3

Mass of the microcarrier,

m = ρV = 1.02 × 8.68 × 10-12m

= 8.85 × 10-12 kg

Radius of the microcarrier,r = 250 × 10-6/2 =

125 × 10-6 m

Total mass of the system = Mass of microcarrier + Mass of culture solution without microcarrierM

= m + ρV

= 8.85 × 10-12 + 1.00 × 50 × 10-3M

= 8.9 × 10-11 kg

Density of the system,ρ = M/V = 8.9 × 10-11/(π/4 × 1 × 12)

= 1.2 kg/m3 (Approx)

Viscosity of the system,μ = 1.1 × 10-3 Pa.s

= 1.1 × 10-6 N.s/m2

Settling velocity,Vs = 2g(ρp - ρm)/9μ

= 2 × 9.81 (1200 - 1020)/(9 × 1.1 × 10-6)

Vs = 70.87 × 10-3 m/s

Height of the culture left after settling,

h = height of culture - height of the microcarrier

= 1 - (250 × 10-6) = 0.99975 m

Time taken to settle completely,

t = h/Vst = 0.99975/0.07087

t = 14091.2 sec = 3.91 hours (Approx)

Therefore, the time needed to settle the cells completely is 3.91 hours (Approx).

Given,Rotational speed, ω = 2000 rpm

= 209.44 rad/s

Distance from the axis of rotation to the particle, r = 0.1 m

To find,G force, G

Formula used,

G = rω2/G

Calculation,

G = rω2/G

= 0.1 × 209.442/9.81G

= 4,335.5

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We can plot the vector r(t) and the vector N(T) at the given value of t = T.

To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.

First, let's find the derivative of r(t):

r'(t) = cos(t)i + (cos(t) - tsin(t))j + k

Next, we'll normalize the vector r'(t) to obtain the unit vector:

||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)

Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:

N(t) = r'(t) / ||r'(t)||

Let's evaluate the principal unit normal at t = T:

N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||

To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.

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Answer: 13.8

Step-by-step explanation:

Answer:

13.8

Step-by-step explanation:

If a Markov chain has a valid transition matrix without absorbing states, we can find the steady-state probabilities by solving the equation πP = π or by using other methods such as eigenvalues and eigenvectors.

Let's denote the transition matrix as P. In your case, the given transition matrix is:

P = [0.6 0.3 0.1

0.1 0.8 0.1

0.6 0 0.4]

To find the steady-state probabilities, we need to solve the equation πP = π, where π is the probability vector we want to find.

πP = π

π(P - I) = 0

By finding the null space of (P - I), we can find the steady-state probabilities. However, the given matrix P does not have a steady-state distribution because one of its rows (the third row) contains only zeros. This means that state 3 is an absorbing state, meaning once you reach state 3, you can never leave it.

In such cases, the long-term behavior of the Markov chain depends on the initial distribution. If we start with a non-zero probability in state 3, the chain will remain in state 3 forever. If the initial distribution does not have a non-zero probability in state 3, the chain will never reach that state.

Therefore, for the given transition matrix, we cannot calculate the long-term probabilities for each state since there is an absorbing state present. It's important to note that the presence of an absorbing state affects the long-term behavior of the Markov chain.

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Answer:

terminating

Step-by-step explanation:

"terminating decimal" since it ends. It does not go on for ever like 6.2222...

x 2, and the second side is expressed by  2x-25 , The value of x is 5.

What is isosceles triangles ?

An isosceles triangle is a triangle with two sides of equal length. These two sides are called the legs and they are congruent. The third side is called the base and it is not necessarily congruent to the legs. The angle opposite to the base is called the vertex angle.

To solve for x, we can start by isolating x on one side of the equation.

We can do this by subtracting x^2 from both sides ,

x^2 - x^2 = 2x-25 - x^2

we get 0 = 2x - 25 - x^2

Now we can add x^2 to both sides ,

x^2 = 2x - 25

Now we can move the -25 to the other side of the equation ,

x^2 - 2x + 25 = 0

Now we can factor the left side of the equation ,

(x-5)(x-5) = 0

Now we can solve for x by setting each factor equal to zero ,

x-5 = 0 , x = 5

x 2, and the second side is expressed by  2x-25 , The value of x is 5.

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Answer:

1/4

Step-by-step explanation:

First, add up the marbles:

2 + 9 + 7  = 18

Multiply by 2 because you pick two:

18 × 2 = 36

Simplify:

9/36 = 3/12 = 1/4

Hope this helped.