A circle has a diameter of 28 centimeters.
Estimate the area of the circle. Use
3.14
or
22
7
for
π
.




What is the volume of the rectangular prism?
A rectangular prism has a length of 10.4 millimeters, a width of 5 millimeters, and a height of 8 millimeters.

To ensure that smooth curves have no cusps, we need to require that z'(t) never vanishes. This condition ensures that the tangent line to the curve changes smoothly and continuously as we move along the curve, without any abrupt changes in direction that would create cusps.

To understand why the condition that z'(t) never vanishes is necessary to ensure that smooth curves have no cusps, we first need to understand what a cusp is. A cusp is a point on a curve where the tangent line changes direction abruptly, creating a sharp point or corner in the curve.

Now, let's consider the curve traced by the parametrization z(t) = t^2it^3 with -1 ≤ t ≤ 1. To determine whether this curve has any cusps, we need to calculate the derivative of z(t) with respect to t:

z'(t) = 2it^3 + 3t^2i

If we set z'(t) equal to zero and solve for t, we get:

2it^3 + 3t^2i = 0
t^2(2i t + 3i) = 0

This equation has two solutions: t = 0 and t = -3/2i. These are the points on the curve where z'(t) vanishes.

At t = 0, the curve passes through the origin, which is a smooth point. However, at t = -3/2i, the curve has a cusp. To see why, we can look at the behavior of z(t) near this point.

As t approaches -3/2i from either side, the magnitude of t^2 increases without bound, while the magnitude of t^3 remains constant. This means that z(t) approaches infinity along a straight line with slope -3/2i. In other words, the curve has a sharp corner or cusp at this point.

To learn more about tangent visit;

brainly.com/question/30260323

#SPJ11

The value of the composite function (g o f)(6) is 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x + 3

g(x) = 1/5x

A. Find f(6)

substitute the known values in the above equation, so, we have the following representation

f(6) = 2 * 6 + 3

So, we have

f(6) = 15

For the function (gof)(6), we have

g(x) = 1/5x

This gives

(g o f)(6) = 1/5 * 15

Evaluate

(g o f)(6) = 3

Hence, the composite function has a solution of 3

Read more about composite function at

https://brainly.com/question/10687170

#SPJ1

Complete question

Given that f(x) = 2x + 3 and g(x) = 1/5x

Compute (gof)(6)

A. Find f(6)

B. substitute the value of g(x) into the function f(x) in place of x

For the sample of soil given a) the porosity is 100.4%; b) the specific yield is 12.2%; c) the specific retention is 14.6%; d) the void ratio is 0.5342; e) the initial moisture content is 2.3%; and f) the initial degree of saturation is 41.97%.

a) The porosity of soil can be defined as the ratio of the void space in the soil to the total volume of the soil.

The total volume of the soil = Initial volume of soil = 100 c.m³

Weight of water added to the soil = 234.6 g – 220 g = 14.6 g

Volume of water added to the soil = 14.6 c.m³

Volume of soil occupied by water = Weight of water added to the soil / Density of water = 14.6 / 1 = 14.6 c.m³

Porosity = Void volume / Total volume of soil

Void volume = Volume of water added to the soil + Volume of voids in the soil

Void volume = 14.6 + (Initial volume of soil – Volume of soil occupied by water) = 14.6 + (100 – 14.6) = 100.4 c.m³

Porosity = 100.4 / 100 = 1.004 or 100.4%

Therefore, the porosity of soil is 100.4%.

b) Specific yield can be defined as the ratio of the volume of water that can be removed from the soil due to the gravitational forces to the total volume of the soil.

Specific yield = Volume of water removed / Total volume of soil

Initially, the weight of the oven dried soil is 220 g. After allowing it to drain by gravity, the weight of soil is 222.4 g. Therefore, the weight of water that can be removed by gravity from the soil = 234.6 g – 222.4 g = 12.2 g

Volume of water that can be removed by gravity from the soil = 12.2 c.m³

Specific yield = 12.2 / 100 = 0.122 or 12.2%

Therefore, the specific yield of soil is 12.2%.

c) Specific retention can be defined as the ratio of the volume of water retained by the soil due to the capillary forces to the total volume of the soil.

Specific retention = Volume of water retained / Total volume of soil

Initially, the weight of the oven dried soil is 220 g. After adding water to the soil, the weight of soil is 234.6 g. Therefore, the weight of water retained by the soil = 234.6 g – 220 g = 14.6 g

Volume of water retained by the soil = 14.6 c.m³

Specific retention = 14.6 / 100 = 0.146 or 14.6%

Therefore, the specific retention of soil is 14.6%.

d) Void ratio can be defined as the ratio of the volume of voids in the soil to the volume of solids in the soil.

Void ratio = Volume of voids / Volume of solids

Initially, the weight of the oven dried soil is 220 g. The density of solids in the soil can be calculated as,

Density of soil solids = Weight of oven dried soil / Volume of solids

Density of soil solids = 220 / (100 – (14.6 / 1)) = 2.384 g/c.m³

Volume of voids in the soil = (Density of soil solids / Density of water) × Volume of water added

Volume of voids in the soil = (2.384 / 1) × 14.6 = 34.8256 c.m³

Volume of solids in the soil = Initial volume of soil – Volume of voids in the soil

Volume of solids in the soil = 100 – 34.8256 = 65.1744 c.m³

Void ratio = Volume of voids / Volume of solids

Void ratio = 34.8256 / 65.1744 = 0.5342

Therefore, the void ratio of soil is 0.5342.

e) Initial moisture content can be defined as the ratio of the weight of water in the soil to the weight of oven dried soil.

Initial moisture content = Weight of water / Weight of oven dried soil

Initial weight of soil = 225.1 g

Weight of oven dried soil = 220 g

Therefore, the weight of water in the soil initially = 225.1 – 220 = 5.1 g

Initial moisture content = 5.1 / 220 = 0.023 or 2.3%

Therefore, the initial moisture content of soil is 2.3%.

f) Initial degree of saturation can be defined as the ratio of the volume of water in the soil to the volume of voids in the soil.

Initial degree of saturation = Volume of water / Volume of voids

Volume of water = Weight of water / Density of water

Volume of water = 14.6 / 1 = 14.6 c.m³

Volume of voids in the soil = 34.8256 c.m³

Initial degree of saturation = 14.6 / 34.8256 = 0.4197 or 41.97%

Therefore, the initial degree of saturation of soil is 41.97%.

Learn more about Porosity:

https://brainly.com/question/12859120

#SPJ11

the average number of calls that arrived between 8:00 am and 8:10 am during the working days of any month is Option(c) a parameter.

A parameter is a special type of mathematical variable. An equation that uses parametric variables that can have multiple values is referred to as a parametric equation. Parameter values are kept constant when using the function. Statisticians use parameters to estimate population characteristics numerically.

Parameters can be used in a variety of ways in real-life scenarios, including in statistics. Parameters are estimations of populations in statistics. The mean and standard deviation are two of the most common statistical parameters. In various statistical tests, these estimates are used to calculate the test statistic.

To Learn more about parameters:

https://brainly.com/question/10462941

#SPJ4

Answer:

approx 14 merchandise..........

i. The Fourier transform of (t - 2) - 38(t - 3) is [(jw)^2 + 38jw]e^(-2jw). ii. The Fourier transform of e^(-2t)u(t) is 1/(jw + 2). iii. The Fourier transform of e^(-3t+12)u(t-4) can be obtained using the result of ii. as e^(-2t)u(t-4)e^(12jw). iv. The Fourier transform of e^(-2|t|)cos(t) is [(2jw)/(w^2+4)].

i. To find the Fourier transform of (t - 2) - 38(t - 3), we can use the linearity property of the Fourier transform. The Fourier transform of (t - 2) can be found using the time-shifting property, and the Fourier transform of -38(t - 3) can be found by scaling and using the frequency-shifting property. Adding the two transforms together gives [(jw)^2 + 38jw]e^(-2jw).

ii. The function e^(-2t)u(t) is the product of the exponential function e^(-2t) and the unit step function u(t). The Fourier transform of e^(-2t) can be found using the time-shifting property as 1/(jw + 2). The Fourier transform of u(t) is 1/(jw), resulting in the Fourier transform of e^(-2t)u(t) as 1/(jw + 2).

iii. The function e^(-3t+12)u(t-4) can be rewritten as e^(-2t)u(t-4)e^(12jw) using the time-shifting property. From the result of ii., we know the Fourier transform of e^(-2t)u(t-4) is 1/(jw + 2). Multiplying this by e^(12jw) gives the Fourier transform of e^(-3t+12)u(t-4) as e^(-2t)u(t-4)e^(12jw).

iv. To find the Fourier transform of e^(-2|t|)cos(t), we can use the definition of the Fourier transform and apply the properties of the Fourier transform. By splitting the function into even and odd parts, we find that the Fourier transform is [(2jw)/(w^2+4)].

Learn more about exponential here:

https://brainly.com/question/29160729

#SPJ11

Answer:

Step-by-step explanation:

8.5 = √72.25

√72.25 < √74

Answer: 7 Pack

Step-by-step explanation: Divide each price by the number of shirts :)

The general solution of the given differential equation is:

(x^2 + y^2) = C, where C is an arbitrary constant.

To solve the given differential equation, we can start by rearranging the terms:

(x+y)y' = 9x - y

Expanding the left-hand side using the product rule, we get:

xy' + y^2 = 9x - y

Next, let's isolate the terms involving y on one side:

y^2 + y = 9x - xy'

Now, we can observe that the left-hand side resembles the derivative of (y^2/2). So, let's take the derivative of both sides with respect to x:

d/dx (y^2/2 + y) = d/dx (9x - xy')

Using the chain rule, the right-hand side can be simplified to:

d/dx (9x - xy') = 9 - y' - xy''

Substituting this back into the equation, we have:

d/dx (y^2/2 + y) = 9 - y' - xy''

Integrating both sides with respect to x, we obtain:

y^2/2 + y = 9x - y'x + g(y),

where g(y) is the constant of integration.

Now, let's rearrange the equation to isolate y':

y'x - y = 9x - y^2/2 - g(y)

Separating the variables and integrating, we get:

∫(1/y^2 - 1/y) dy = ∫(9 - g(y)) dx

Simplifying the left-hand side, we have:

∫(1/y^2 - 1/y) dy = ∫(1/y) dy - ∫(1/y^2) dy

Integrating both sides, we obtain:

-ln|y| + 1/y = 9x - g(y) + h(x),

where h(x) is the constant of integration.

Combining the terms involving y and rearranging, we have:

-y - ln|y| = 9x + h(x) - g(y)

Finally, we can express the general solution in the implicit form:

(x^2 + y^2) = C,

where C = -g(y) + h(x) is the arbitrary constant combining the integration constants.

To learn more about derivatives

brainly.com/question/25324584

#SPJ11

The products of the given monomials are

i. 90a⁵b⁵c⁹

ii. x⁴y⁴

iii. 50x¹¹y³z

iv. 80b⁴c⁴

v. 30m⁵n⁷

From the question, we are to determine the products of each of the three monomials

i. 9ab²c⁵, 2a³b²c² and 5abc²

9ab²c⁵ × 2a³b²c² × 5abc²

= 9 × 2 × 5 × a × a³ × a × b² × b² × b × c⁵ × c² × c²

= 90 × a⁵ × b⁵ × c⁹

= 90a⁵b⁵c⁹

ii. xy², x²y and xy

xy² × x²y × xy

= x × x² × x × y² × y × y

= x⁴ × y⁴

= x⁴y⁴

iii. 5x⁵, y²x⁵ and 10xyz

5x⁵ × y²x⁵ × 10xyz

= 5 × 10 × x⁵ × x⁵ × x × y²  × y × z

= 50 × x¹¹ × y³ × z

= 50x¹¹y³z

iv. (-4b²c), (-2bc) and 10c²b

(-4b²c) × (-2bc) × 10c²b

= -4b²c × -2bc × 10c²b

= -4 × b² × c × -2 × b × c × 10 × c² × b

= -4 × -2 × 10 × b² × b × b × c  × c × c²

= 80 × b⁴ × c⁴

= 80b⁴c⁴

v. Multiply (-5m²n²) by (-6m³n⁵)

(-5m²n²) × (-6m³n⁵)

= -5m²n² × -6m³n⁵

= -5 × m² × n² × -6 × m³ × n⁵

= -5 × -6 × m² × m³ × n² × n⁵

= 30 × m⁵ × n⁷

= 30m⁵n⁷

Hence, the products of the given monomials are

i. 90a⁵b⁵c⁹

ii. x⁴y⁴

iii. 50x¹¹y³z

iv. 80b⁴c⁴

v. 30m⁵n⁷

Learn more on Product of monomials here: https://brainly.com/question/11938945

#SPJ1

Therefore , the solution of the given problem of surface area comes out to be 212 square feet of the wall are therefore covered by the design.

The total size of the object can be determined by calculating how much room would be required to completely cover its exterior. When choosing a similar product with a cylindrical form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

We must first determine the area of each individual form before adding them together to determine the portion of the wall that the design covers.

Taking a look at the rectangle first, we can observe that it has the following area:

=> 120 square feet=  10 feet x 12 feet.

=> 40 square feet =  (1/2)(10 ft)(8 ft).

Consequently, the two triangles' combined area is:

=> 80 square feet =  2 x 40 square feet.

=> (12 square feet) = (1/2)(6 ft)(4 ft).

The total area of all the shapes is as follows:

=> 212 square feet=  120 square feet, 80 square feet, and 12 square feet.

=> 212 square feet of the wall are therefore covered by the design.

To know more about surface area visit:

https://brainly.com/question/2835293

#SPJ1

Answer: the answer is 261 ^2 ft!

Step-by-step explanation:

Answer:

45 mi/h = 66 feet per second

The difference in Logan and Rita's account balances after 4 years will be $113.22. To calculate the difference in their account balances, find the future value of their deposits using the given interest rates.

For Logan's account, which pays simple interest, we can use the formula: Future Value = Principal + (Principal x Rate x Time).

Given:

Principal (P) = $8,100

Rate (R) = 5% = 0.05 (expressed as a decimal)

Time (T) = 4 years

Future Value of Logan's account = 8,100 + (8,100 x 0.05 x 4)

                           = 8,100 + 1,620

                           = $9,720

For Rita's account, which pays compound interest annually, we can use the formula: Future Value = Principal x\((1 + Rate)^Time\).

Given:

Principal (P) = $8,100

Rate (R) = 5% = 0.05 (expressed as a decimal)

Time (T) = 4 years

Future Value of Rita's account = 8,100 x \((1 + 0.05)^4\)

                           = 8,100 x 1.21550625

                           = $9,833.50

The difference in their account balances = Future Value of Rita's account - Future Value of Logan's account

                                      = 9,833.50 - 9,720

                                      = $113.22

Therefore, the difference in their account balances after 4 years will be $113.22.

Learn more about interest rates here:

https://brainly.com/question/28236069

#SPJ11

50%

since 98/2 = 49

Thats it

Options A , C , E ,  F , H are true for the statement population that is finding the probability.

Given that,

We have to choose the correct answer for the given statement that is finding the probability.

We know that,

Calculating a situation's probability allows us to determine its probability. Many things are difficult to determine with 100% accuracy. We can only anticipate the probability of an event occurring, or how likely it is, using it. A probability can be range 0 and 1, where 0 indicates an impossibility and 1 indicates a certainty. The probability of each event in a sample space is one.

Therefore, Options A , C , E ,  F , H are true for the statement population that is finding the probability.

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ4

The correct answer is b) 15.87%, indicating that approximately 15.87% of NFL players have a retirement age less than 31 years old.

To find the percentage of players whose age is less than 31, we can use the standard normal distribution and z-scores.

First, we need to calculate the z-score for the value 31 using the formula:

z = (x - μ) / σ

where x is the value we want to find the percentage for, μ is the mean, and σ is the standard deviation.

In this case, x = 31, μ = 33, and σ = 2. Plugging these values into the formula, we get:

z = (31 - 33) / 2 = -1

Next, we can look up the cumulative probability associated with the z-score -1 in the standard normal distribution table. The cumulative probability represents the percentage of values that are less than the given z-score.

From the standard normal distribution table, the cumulative probability for z = -1 is approximately 0.1587, which corresponds to 15.87%.

Therefore, the correct answer is b) 15.87%, indicating that approximately 15.87% of NFL players have a retirement age less than 31 years old.

Know more about Retirement here :

https://brainly.com/question/31284848

#SPJ11

Answer:26.4 feet per second

Step-by-step explanation:

Answer:

26.4 fps (feet per second)

Step-by-step explanation:

Edward has 12 coins of the quarter and 8 coins of nickel with him

Total number of coins = 20

The total amount of money = $3.40

Let x represent the number of quarters and y represent the number of nickels

Formulating the equations we get:

x + y = 20-------(1)

0.25x + 0.05y = 3.40

Simplifying by removing the decimals and solving

25x + 5y = 340------(2)

Multiplying equation (1) by 5 and subtracting with equation (2) we get the following:

5x + 5y = 100

25x + 5y = 340

= 20x = 240

x = 12

So, y = 8

So, the number of quarters is 12 and the number of nickels is 8

Learn more about linear equations:

https://brainly.com/question/11897796

#SPJ4

Given,

The diagram of the angles is shown above in the question.

Required

The incorrect statement for the angles.

The angles are of 90 degree as it is given.

So, statement b, c and d is correct.

Here, angles are not perpendicular, sides can be perpenicular to each other.

Hence, statement a is incorrect.

Answer:

x = 5 units

Step-by-step explanation:

area = 1/2bh

10 = 1/2(x)4)

2x = 10

x = 5

Answer:

The value of x (which is also the height of this triangle) is x = 5 units.

Step-by-step explanation:

The formula for the area of a triangle of base b and height h is

A = (1/2)(b)(h).

Here A = 10 units² = (1/2)(4 units)(x).

Multiplying both sides by 2 yields    20 units² = (4units)(x), and thus  20 units²

Answer:

b. line j or MT

Step-by-step explanation:

as the plane contains the points Q, N, P, R, T also the lines connecting only these points are in the plane, and are not intersecting the plane.

only M is outside of the plane, and so (only) the connecting line MT intersects the plane (at point T).

by the way, the question means the line RQ and not RO, as there is no point O in the graphic.

True, the joint probability of Y1 and Y2 taking on the value 1 simultaneously is 1/3.

The first dummy random variable is defined as follows:

Let X be the random variable representing the number on the first dice. Then, the dummy random variable Y1 is defined as:

Y1 = 1 if X is either 1, 2, or 3

Y1 = 0 otherwise

Similarly, the second dummy random variable is defined as:

Let Z be the random variable representing the number on the second dice. Then, the dummy random variable Y2 is defined as:

Y2 = 1 if Z is either 3, 4, 5, or 6

Y2 = 0 otherwise

Since Y1 and Y2 are independent, their joint probability distribution can be computed by multiplying their marginal probabilities.

P(Y1=1, Y2=1) = P(Y1=1) * P(Y2=1)

To compute P(Y1=1), we need to find the probability that X is either 1, 2, or 3. Since each face of a fair dice has an equal probability of appearing, we have:

P(X=1) = P(X=2) = P(X=3) = 1/6

Therefore,

P(Y1=1) = P(X=1 or X=2 or X=3) = P(X=1) + P(X=2) + P(X=3) = 3/6 = 1/2

Similarly, to compute P(Y2=1), we need to find the probability that Z is either 3, 4, 5, or 6. Again, since each face of a fair dice has an equal probability of appearing, we have:

P(Z=3) = P(Z=4) = P(Z=5) = P(Z=6) = 1/6

Therefore,

P(Y2=1) = P(Z=3 or Z=4 or Z=5 or Z=6) = P(Z=3) + P(Z=4) + P(Z=5) + P(Z=6) = 4/6 = 2/3

Thus,

P(Y1=1, Y2=1) = P(Y1=1) * P(Y2=1) = (1/2) * (2/3) = 1/3

To know more about joint probability refer here:

https://brainly.com/question/32099581#

#SPJ11

1 . y'=0 is the derivative of the function y = 14.

2. y' =  9\(x^8\)+3\(sec^2x\)  is the derivative of the function y= \(x^9\)+3tanx

3. y' = \(\frac{-4}{x^5}\) + 4sinx is the derivative of the function y = \(\frac{1}{x^4}\) - 4cos x

1 . The derivative of a constant is always zero.

A constant function is a function whose value does not depend on the input value.

So y = 4 is a constant function, its derivative is always zero.

So the derivative of y=4 is 0

2. The differentiation of \(x^9\)+3tanx is 9\(x^8\)+3\(sec^2x\)

The power rule states that the derivative of x^n (where n is a constant) is nx^(n-1). So the derivative of x^9 is 9x^8.

The derivative of tanx is \(sec^2x\).

And the derivative of 3tanx is 3\(sec^2x\)

So, \(x^9\)+3tanx  is differentiated as9\(x^8\)+3\(sec^2x\)

3. The derivative of y = \(\frac{1}{x^4}\) - 4cos x can be found using the power rule and the chain rule.

The power rule states that the derivative of x^n (where n is a constant) is nx^(n-1). In this case, \(\frac{1}{x^4}\) can be rewritten as \(\frac{1}{x^4}\) and the derivative would be -4 \(\frac{1}{x^5}\)

The chain rule states that the derivative of (f(g(x)) is f'(g(x))*g'(x). In this case, the inner function is -4cos x, the derivative of cos x is -sin x and the outer function is , \(\frac{1}{x^4}\) the derivative of that is -4 \(\frac{1}{x^5}\). So the derivative of -4cos x is -4(-sin x)

So the final derivative of y = \(\frac{1}{x^4}\)  - 4cos x is \(\frac{-4}{x^5}\) + 4sinx

To know more about derivative click below:

https://brainly.com/question/25324584#

#SPJ4

(a) ( x_{t+1}=\frac{1}{2} x_{t}+3 ), the solution to this difference equation is x_t = 2^t + 3, The difference equations in this problem are both linear difference equations with constant coefficients.

This can be found by solving the equation recursively. For example, the first few terms of the solution are

t | x_t

--- | ---

0 | 3

1 | 7

2 | 15

3 | 31

The general term of the solution can be found by noting that

x_{t+1} = \frac{1}{2} x_t + 3 = \frac{1}{2} (2^t + 3) + 3 = 2^t + 3

(b) ( x_{t+1}=-3 x_{t}+4 )

The solution to this difference equation is

x_t = 4 \cdot \left( \frac{1}{3} \right)^t + 4

This can be found by solving the equation recursively. For example, the first few terms of the solution are

t | x_t

--- | ---

0 | 4

1 | 5

2 | 2

3 | 1

The general term of the solution can be found by noting that

x_{t+1} = -3 x_t + 4 = -3 \left( 4 \cdot \left( \frac{1}{3} \right)^t + 4 \right) + 4 = 4 \cdot \left( \frac{1}{3} \right)^t + 4

The difference equations in this problem are both linear difference equations with constant coefficients. This means that they can be solved using a technique called back substitution.

Back substitution involves solving the equation recursively, starting with the last term and working backwards to the first term.

In the first problem, the equation can be solved recursively as follows:

x_{t+1} = \frac{1}{2} x_t + 3

x_t = \frac{1}{2} x_{t-1} + 3

x_{t-1} = \frac{1}{2} x_{t-2} + 3

...

x_0 = \frac{1}{2} x_{-1} + 3

The general term of the solution can be found by noting that

x_{t+1} = \frac{1}{2} x_t + 3 = \frac{1}{2} (2^t + 3) + 3 = 2^t + 3

The second problem can be solved recursively as follows:

x_{t+1} = -3 x_t + 4

x_t = -3 x_{t-1} + 4

x_{t-1} = -3 x_{t-2} + 4

...

x_0 = -3 x_{-1} + 4

The general term of the solution can be found by noting that

x_{t+1} = -3 x_t + 4 = -3 \left( 4 \cdot \left( \frac{1}{3} \right)^t + 4 \right) + 4 = 4 \cdot \left( \frac{1}{3} \right)^t + 4

To know more about coefficient click here

brainly.com/question/30524977

#SPJ11

Answer:

$12x - $15

Step-by-step explanation:

Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did Sunny earn this week?

her total income  for the week = income earned - charge

income earned = income per hour x number of hours worked = 12x

total income = 12x - 15

The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.

option (c) is identified as the situation where it is safe to use t-procedures.

t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.

Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.

Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.

Learn more about assumption of normality here:

https://brainly.com/question/30932454

#SPJ11

Answer:

18:10 is equivalent to 9:5

Step-by-step explanation:

half of 18 is 9 and half of 10 is 5

Answer:

9:5

Step-by-step explanation:

18:10 is equivalent to 9:5 because 10 divided by 2 is 5 so you can do the same for 18. You will get 9 which makes it 9:5.

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

Learn more about diminishing returns

https://brainly.com/question/30766008

#SPJ11