the radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. how fast is the surface area changing when the radius is 10 centimeters? hint: the surface area is . rate of change of surface area

According to Zaller's Receive-Accept-Sample (RAS) model, individuals who are most susceptible to the message of a political action committee launching a new advertisement aimed at expanding health insurance to low-income Americans through increased government funding would be those who both receive and accept the message.

The RAS model suggests that individuals have varying levels of political knowledge and are exposed to different sources of information. Those who are more likely to receive the message are individuals who are politically interested and engaged, while those who are more likely to accept the message are individuals who have limited political knowledge and are less critical of the information presented to them.

Therefore, in the context of the advertisement aiming to expand health insurance to low-income Americans, the most susceptible individuals would be those who are politically interested but have limited political knowledge. These individuals may be more likely to accept the message without critically evaluating its content.

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Answer:(-5.6, -1.4)

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Let the unknown number be x.

8 = -4(1) + x

8 = -4 + x

x - 4 = 8

x = 8 + 4

x = 12

Answer:

\(a_{n}\) = - 4n + 12

Step-by-step explanation:

The n th term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and d = a₂ - a₁ = 4 - 8 = - 4 , then

\(a_{n}\) = 8 - 4(n - 1) = 8 - 4n + 4 = - 4n + 12

$7.50 : 3 pounds >>> c

$3.75 : 5 pounds >>> a

$6.00 : 4 pounds >>> d

$13.50 : 6 pounds >>> b

i hope this helps! :D

Answer:

12x2+21x

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

It is a polynomial with degree 2 ( as it has x^2 as its highest power)

Answer:

Present Value = \(X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ]\)

Step-by-step explanation:

To find - If discount rate is 12%, the present value of Rs X received at the end of each year for the next five years is equal to .... ?

Solution -

We know that, formula for finding the Present vale is given by

Present value = Future value / (1 + r)ⁿ

where r is the rate of interest

and n is Number of periods

Now,

Here in the question, we have

r = 12% = 12/100 = 0.12

n = 5

Also, Given that, we have received Rs X at the end of each year

So,

Present Value = \(\frac{X}{(1 + 0.12)^{1} } + \frac{X}{(1 + 0.12)^{2} } + \frac{X}{(1 + 0.12)^{3} } + \frac{X}{(1 + 0.12)^{4} } + \frac{X}{(1 + 0.12)^{5} }\)

                        = \(X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ]\)

⇒Present Value = \(X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ]\)

The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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According to Chebyshev's theorem, at least 69 percent of any set of observations will be within 1.8 standard deviations of the mean.

Standard deviations of the mean = 1.8 s

According to Chebyshev's theorem at least (1 - 1/k^2)×100% observations will lie within k standard deviation from the mean.

The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 1/(1.8)^2)×100%

The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 1/3.24)×100%

The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 0.31)×100%

The proportion of observations that will be within 1.8 standard deviations of the mean = 0.69 × 100%

The proportion of observations that will be within 1.8 standard deviations of the mean = 69%

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Answer:

10/15 - 3/15= 7/15

Step-by-step explanation:

none

Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

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If 16 such parts are tested then the probability that the sample mean is

(a) less than 104 is 0.7881  and (b) is between 98 and 104 is 0.4435 .

In the question ,

it is given that ,

the lifetime of an electrical part follows a random variable ,

the mean of the random variable is = 100 hours ,

the standard deviation of the random variable is = 20 hours ,

the sample (n) is = 16

So , the standard error = 20/√16 = 20/4 = 5

the z value for 104 is is

= (104 - 100)/5 = 0.8

Part (a)

the probability the sample mean is less than 104 is ,

= P(X < 104)

= P(Z < 0.8)

From the z table values ,

= 0.7881

Part (b)

the probability that the sample mean is between 98 and 104 is ..

the z value for 98 , z = (98 - 100)/5

= -0.4

z value for 104 is = (104 - 100)/5

= 0.8

So , P(98 < X < 104) = P(-0.4 < Z < 0.8)

= 0.7881 + 0.654 - 1

= 0.4435

Therefore , the required probability are (a) 0.7881 and (b) 0.4435 .

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Answer: $351

Step-by-step explanation:

We need to setup two equations:

If you're taking the monthly cost: y = 468x, where x is the number of months.

If you're paying upfront: y = 12(0.25(39))x = 117x, where x is the number of years

So in one year, you will save (468-117) = $351 by paying upfront.

A square marble column is 12 meters long and 2 square meters in cross-cut area, it is supporting a load of 25 tons. The stress on the marble column is 1.042E7 N/m^2, and the strain is 2E-4.

To determine the stress on the marble column, we can use the formula: stress = load/area. The load is given as 25 tons, which is equivalent to 25000 kg.

The area of the cross-cut is 2 square meters. Substituting these values, we get stress = 25000 kg / 2 m^2 = 12500 kg/m^2 = 1.25E7 N/m^2. To find the strain, we can use the formula: strain = stress/elastic modulus.

The elastic modulus for marble is given as 50E9 N/m^2. Substituting the values, we get strain = 1.25E7 N/m^2 / 50E9 N/m^2 = 2E-4.

Therefore, the stress on the marble column is 1.042E7 N/m^2, and the strain is 2E-4.

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# Complete/Translate Question:- A SQUARE MARBLE COLUMN IS 12 METERS LONG AND 2 SQUARE METERS IN CROSS-CUT AREA, IT IS SUPPORTING A LOAD OF 25 TONS. IF IT IS CONSIDERED THAT THE MODULE OF ELASTICITY CORRESPONDING TO THE MARBLE IS 50E9 N/M2 PLEASE I NEED IT FOR TODAY

To determine average high school GPA of students we would need access to dataset that includes birth dates and  high school GPAs of the students. Without specific data, it is not possible to provide an average GPA.

Collecting the required data involves accessing student records or conducting surveys to gather information on birth dates and high school GPAs. Once the data is obtained, the average GPA can be calculated by summing up the GPAs of all students born during April, May, and June of 2005 and dividing it by the total number of students in that group.

It's important to note that the average GPA will be specific to the dataset or sample of students used for the calculation. If the dataset is representative and unbiased, the average GPA can provide an estimation of the average performance of students born during those months in 2005. However, if the dataset is limited or not representative, the calculated average may not accurately reflect the overall average high school GPA of all students born during that period.

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The cube of the load acting on each revolution is 4.5 × 4.5 × 4.5

= 91.125 kN³

The mean cubic load is calculated by taking the average of the cube of the load acting on each revolution over one complete cycle.

= [ (9 × 9 × 9) + (4.5 × 4.5 × 4.5) ] / 15

= (729 + 91.125) / 15

= 48.875 kN³

The mean cubic load is 48.875 kN³, which is approximately 6.72 kN (cube root of 48.875).

The mean cubic load is 6.72 kN.

The given radial load acting on a rotating body is a repeating cycle.

For the first 5 revolutions, the radial load is 9 kN and for the next 10 revolutions, it is reduced to 4.5 kN.

The load variation repeats itself over and over.

The mean cubic load is the average of the cube of the load acting on a rotating body over one complete cycle.

To calculate the mean cubic load, we first need to calculate the load acting on each revolution of the cycle, and then calculate the cube of the load acting on each revolution.

Finally, we take the average of the cube of the load acting on each revolution over one complete cycle.

Load acting for the first 5 revolutions = 9 kN

Load acting for the next 10 revolutions = 4.5 kN

The entire cycle consists of 15 revolutions.

The load acting on each revolution in the first 5 revolutions is 9 kN. Therefore, the cube of the load acting on each revolution is

9 × 9 × 9 = 729 kN³

The load acting on each revolution in the next 10 revolutions is 4.5 kN. Therefore, the cube of the load acting on each revolution is 4.5 × 4.5 × 4.5 = 91.125 kN³

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Answer:

t - 7

Step-by-step explanation:

Answer: t - 7

Step-by-step explanation:

You have “7 less than a number t”, meaning, you have a variable t, and you want to find what 7 less than that is.

So, we would use subtraction.

We would get:

t - 7

Hope this helps! :)

0.8465 is the probability that the system operates if the probability that each component functions equals to 0.90, 0.99, and 0.95 respectively.

As the components are in a series system, this means that all the components have to function in order for the system to operate, and the failure of any one of the components to function will result in the system not operating.

Therefore, the probability for the system to operate is the probability that all the components c1, c2, and c3 function together

The probability of multiple events occurring together can be found by multiplying the probabilities of each event by one another.

Therefore;

Probability = 0.90 × 0.99 × 0.95

Probability = 0.84645

Rounding it off to 4 decimals as follows;

Probability = 0.84645 = 0.8465

Therefore, the probability that the system operates is calculated to be 0.8465.

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Step-by-step explanation:

ab = (x - 3)(x + 3)

multiply

ab = x² + 3x - 3x - 9

Simplify

ab = x² - 9

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

2ab = 2(x² - 9)

Distribute

2ab = 2x² - 18

To solve the initial value problem  \(dy/dx = 2x\) with the initial condition y(0)=2 in Python, we can use an appropriate numerical method, such as Euler's method or the built-in function odeint from the scipy.integrate module.

Here's an example code snippet in Python that solves the given initial value problem using Euler's method:

import numpy as np

import matplotlib.pyplot as plt

def f(x, y):

   return 2*x

def euler_method(f, x0, y0, h, num_steps):

   x = np.zeros(num_steps+1)

   y = np.zeros(num_steps+1)

   x[0] = x0

   y[0] = y0

   for i in range(num_steps):

       y[i+1] = y[i] + h * f(x[i], y[i])

       x[i+1] = x[i] + h

   return x, y

x0 = 0

y0 = 2

h = 0.1

num_steps = 10

x, y = euler_method(f, x0, y0, h, num_steps)

plt.plot(x, y)

plt.xlabel('x')

plt.ylabel('y')

plt.title('Solution of dy/dx = 2x')

plt.show()

In this code, we define the function f(x, y) that represents the right-hand side of the differential equation. Then, we implement the Euler's method in the euler_method function, which takes the function f, the initial values x0 and y0, the step size h, and the number of steps num_steps as inputs. The method iteratively calculates the values of x and y using the Euler's method formula. Finally, we plot the solution using matplotlib.pyplot. Running the code will generate a plot showing the solution of the initial value problem dy/dx = 2x with y(0)=2 over the specified range of x-values.

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Answer:

(2, -10)

(4, -15)

(6, -20)

Step-by-step explanation:

First you should simplify the equation.

-5x=10+2y

-5x-10=2y

-2.5x-5=y

Then put in any number in for x. since we have a decimal I'll make the numbers I put in even the keep the solution whole numbers.

Putting in 2 gives you -10 so (2, -10) is a solution.

Putting in 4 gives you -15 so (4, -15) is a solution.

Putting in 6 gives you -20 so (6, -20) is a solution.

There will be 6.11 acres in a piece of property measuring 620' x 430'

To calculate the number of acres in a piece of property, you need to convert the measurements from feet to acres.

1 acre is equal to 43,560 square feet.

Given that the property measures 620' x 430', you can calculate the area in square feet by multiplying the length by the width: 620' x 430' = 266,600 square feet.

To convert the area from square feet to acres, divide the square footage by 43,560: 266,600 square feet / 43,560 = 6.11 acres (rounded to two decimal places).

Therefore, the piece of property measures approximately 6.11 acres.

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Given: A 180 degree rotation of a vertical angle will always map to the other vertical angle

To Determine: The prove that the vertical angles are congruent

Draw and label to vertical lines with an angle

The 180 degree rotation of the vertical angle BOC would give:

Note that the other vertical would be AOD

The students should respond that

Hence, the 180 degree rotation of a vertical angle will always map to the other vertical angle which are congruent to each other because:

The vertical angles are vertically opposite to each other

Answer:

\(1.66\)

or 2/3

Answer:

2/3

Step-by-step explanation:

Since triangles ADE and ABC are similar we can calculate the value of x using similarity ratio

AD/AB = ED/CB

3/2 = 1/x cross multiply expressions

3x = 2 divide both sides by 3

x = 2/3

Answer:

180.34cm

Step-by-step explanation:

Multiply 12x5=60, then multiply 60x2.54=152.4, then multiply 11x2.54=27.94, then add 152.4+27.94 of it together, which is 180.34

Answer:

Domain: -2≤ x≤ 0

Range: -2≤ x≤ 2

The relation is a Function

Step-by-step explanation:

The Domain is all the x values.

All the x values are either equal to or greater than -2, and less than or equal to =-0

The Range is all the y values.

Apply the same logic as the domain.

A function is where no x values are the same, and since in this graph we see no vertical line, indicating the same x value, it means it is a function

Answer:

24 coins

Step-by-step explanation:

We give the dimes a unknown number like y since the nickels are twice as much we give it 2y we multiply the numbers with their value and form an equation like 2y×5+y×10=160 find the value of y then get value of 2y+y to get the number of coins

The number of students who took more than 15 minutes to complete their homework = 5

First of all, observe the given data and understand the frequency of students in each category.

To find the number of students who took more than 15 minutes to complete their homework calculate the sum of the students who took 16 to 20 minutes and 21 to 25 minutes since they are all taken more than 10 minutes.

Here we have

A frequency table that shows the number of minutes to complete the work  

From the table

3 students will take 1 to 5 minutes

8 students will take 6 to 10 minutes  

11 students will take 11 to 15 minutes  

4 students  will take 16 to 20 minutes    

1 student  will take 21 to 25 minutes

The number of students who took more than fifteen minutes

= 4 + 1 = 5

Therefore,

The number of students who took more than 15 minutes to complete their homework = 5

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Answer:

7

Step-by-step explanation: