1) The distribution of sample means (for a specific sample size) consists of a. All the scores contained in the sample x b. All the scores contained in the population x C. All the samples means that could be obtained (for the specific sample size) d. The specific sample mean computed for the sample of scores

The order in which participants complete a task is an example of ordinal scale measurement. This means that the data can be ranked or ordered in a meaningful way, but the differences between the rankings cannot be quantified or measured with equal intervals.

Ordinal scale measurement is a type of measurement in which data is ranked or ordered based on some criteria or attribute, without a specific numerical value being assigned to each rank or order. The data is measured using a ranking system, where each value is assigned a rank based on its relative position to other values in the data set. The ranking system used in ordinal scale measurement can be either ascending or descending, depending on the nature of the data.

Examples of data that can be measured using ordinal scale measurement include the ranking of finishing times in a race, the level of agreement or disagreement with a statement on a survey, or the ranking of a person's level of education or income. In ordinal scale measurement, the values are ordered or ranked, but the distance between the values is not necessarily equal or meaningful.

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To prove that 1^k + 2^k + 3^k + ... + n^k is O(n^(k+1)), we need to find a constant c and a positive integer N such that for all n ≥ N:

1^k + 2^k + 3^k + ... + n^k ≤ c * n^(k+1)

We can start by using the inequality (n/2)^k ≤ 1^k + 2^k + ... + n^k ≤ n^k to obtain an upper bound on the sum.

Using this inequality, we get:

(n/2)^k * n ≤ 1^k + 2^k + ... + n^k ≤ n^k * n

Multiplying through by n, we get:

(n/2)^k * n^2 ≤ 1^k + 2^k + ... + n^k ≤ n^(k+1) * n

Simplifying and rearranging, we get:

n^(k+1)/2^k ≤ 1^k + 2^k + ... + n^k ≤ n^(k+1)

Therefore, we can take c = 2^(k+1) and N = 1 to complete the proof:

For all n ≥ N = 1,

1^k + 2^k + ... + n^k ≤ n^(k+1) ≤ c * n^(k+1)

1^k + 2^k + ... + n^k is O(n^(k+1)) for k, n ∈ ℕ and k, n ≥ 1.

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A = 1/8
B = 1
C = 135/8

To solve this problem, we first need to integrate f'(x) = ex/8. We can do this by multiplying both sides of the equation by dx and then integrating:

∫ f'(x) dx = ∫ ex/8 dx

f(x) = 8e^(x/8) + C

We now need to use the given initial condition f(0) = 17 to find the value of C:

f(0) = 8e^(0/8) + C = 8 + C = 17

C = 9

So, the function f(x) that satisfies the given conditions is:

f(x) = 8e^(x/8) + 9

We can rewrite this function in the form f(x) = a e^bx + c by comparing the coefficients with the given expression. We see that:

a = 8
b = 1/8
c = 9

Therefore, A = 8, B = 1/8, and C = 9.

To find the function f(x) that satisfies the given conditions, we need to integrate f'(x) and apply the initial conditions. Given f'(x) = e^x/8, we can integrate with respect to x:

f(x) = ∫(e^x/8)dx = (1/8)∫(e^x)dx = (1/8)e^x + C_1, where C_1 is the constant of integration.

Now, we apply the initial condition f(0) = 17:

17 = (1/8)e^0 + C_1 => 17 = (1/8)(1) + C_1 => C_1 = 17 - 1/8 = 135/8.

So, f(x) = (1/8)e^x + 135/8.

Now, we need to match this to the form f(x) = a*e^(bx) + c. Comparing the coefficients, we can determine the values of a, b, and c:

A = 1/8
B = 1
C = 135/8

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Therefore option c) is correct In light of this, the circle graph titled New York City visitor's transportation, with five parts labelled walk 40%, bicycle 8%, car service 15%, bus 10%, and subway 27%,

Graphs can be used to depict data in a variety of ways. Typical graph types include the following:

- Bar graph

- Scatter plot

- Box plot

- Pie chart

To depict the information in the table as a circle graph, often known as a pie chart, we must determine the proportion of visitors who utilised each mode of transportation.

This can be accomplished by multiplying the result by 100 after dividing the total number of visitors by the sum of visitors.

81 out of 300 guests took the subway, which equates to 27% of all visitors.

In light of this, the circle graph titled New York City visitor's transportation, with five parts labelled walk 40%, bicycle 8%, car service 15%, bus 10%, and subway 27%, is the one that accurately depicts the facts in the table.

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Answer:

help

me rn

Step-by-step explanation:

Answer:

C. 210 square units

Step-by-step explanation:

Using the formula [tex]a=\frac{bh}{2}[/tex] to find the areas of the two triangles, you get [tex]a=\frac{(12)(14)}{2}[/tex], which equals 84 square units per triangle, or 168 square units cumulatively. Using [tex]a=bh[/tex] to find the area of the rectangle, [tex]a=(3)(14)[/tex], the area of the rectangle equals 42 square units. Adding all of the areas together, [tex]84+84+42=210[/tex], a total of 210 square units is the area of the parallelogram.

The 5th term of the geometric sequence 1000, 200, 40,... is 1.6.

To determine this, we need to identify the common ratio (r) between consecutive terms and use the formula for the nth term of a geometric sequence:

Tn = T1 × r⁽ⁿ⁻¹⁾.

In this sequence, the common ratio (r) can be found by dividing any term by its preceding term.

For example, 200/1000 = 1/5, and 40/200 = 1/5.

So, the common ratio is 1/5.

Now, we can use the formula with the given information to find the 5th term (T5):

T5 = T1 ⨯ r⁽⁵⁻¹⁾ ) T5 = 1000 ⨯ (1/5)⁴

Calculating this, we get:

T5 = 1000 * (1/625) T5 = 1.6

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The expression for the 15th term of the geometric sequence with first term 5 and common ratio 3/2 is [tex]5 (\frac{3}{2})^{14}[/tex].

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

To find the nth term of a geometric sequence, you can use the formula:
nth term = first term (common ratio)^(n-1)

In this case, we are looking for the 15th term, the first term is 5, and the common ratio is 3/2.

Plug these values into the formula:
15th term = [tex]5 (\frac{3}{2})^{(15-1)}[/tex]

Now, simplify the expression:

15th term = [tex]5 (\frac{3}{2})^{14}[/tex]
This is the expression for the 15th term of the geometric sequence with the first term 5 and common ratio 3/2.

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Answer:

The answer is B: 21

Answer:

2 centimeters

Step-by-step explanation:

volume = 125.6 cubic centimeters

heigh = 10 cubic centimeters

volume of cylinder formula and obatin the radius value:

π [tex]R^{2}[/tex] h

r = radius of the cylinder & h is the height of cylinder

π is constant has value 3.14 of pi

[tex]3.14 * r^{2} * 10[/tex] = 125.6

Then again: [tex]R^{2} = \frac{125.6}{31.4}[/tex]

Then [tex]R^{2}[/tex] = 4

Square root it:

r = [tex]\sqrt{4}[/tex]

r = 2

2 is the answer

To find the dimensions of a cone of maximum volume that can be inscribed in a sphere of radius 10cm, we first need to understand the relationship between the cone and the sphere.

We know that the cone is inscribed in the sphere, which means that its base is tangent to the sphere at its maximum diameter. Also, the height of the cone will be equal to the radius of the sphere.

Let's call the height of the cone "h" and the radius of its base "r". Using the Pythagorean theorem, we can find the slant height of the cone, which is the distance from the vertex of the cone to the edge of its base.

The slant height can be represented by the equation:

l = sqrt(r^2 + h^2)

Now, we need to find the volume of the cone, which is given by the formula:

V = (1/3)πr^2h

We can substitute the equation for the slant height into the formula for the volume:

V = (1/3)πr^2(sqrt(r^2 + h^2))h

To find the maximum volume, we need to find the values of "r" and "h" that will maximize this formula. We can do this by taking the derivative of the formula with respect to "r" and "h", setting them equal to zero, and solving for the variables.

dV/dr = (1/3)πh(3r^2 + h^2)^(1/2) = 0

dV/dh = (1/3)πr^2(2h) + (1/3)πr^2(h^2 + r^2)^(-1/2)(2h) = 0

Solving these equations, we get:

r = h(√3)/3

Substituting this value for "r" into the equation for slant height, we get:

l = 2h/√3

Now, we can substitute these values into the equation for volume:

V = (1/3)π(h^2(√3)/3)(h)

Simplifying, we get:

V = πh^3/3√3

To find the maximum volume, we need to find the value of "h" that will maximize this formula. We can do this by taking the derivative of the formula with respect to "h", setting it equal to zero, and solving for "h".

dV/dh = πh^2/√3 = 0

Solving for "h", we get:

h = 0

This means that there is no maximum volume for the cone, since the height of the cone would be zero if it were inscribed in a sphere of radius 10cm.

Therefore, the dimensions of the cone of maximum volume that can be inscribed in a sphere of radius 10cm are undefined.
To find the dimensions of a cone of maximum volume inscribed in a sphere of radius 10 cm, we will use the following terms: sphere, cone, inscribed, radius, and volume.

Let's consider the sphere with a radius of 10 cm. Inside this sphere, we need to inscribe a cone with maximum volume. Let r be the radius of the cone, and h be its height. Since the cone is inscribed in the sphere, its apex touches the sphere, and the distance from the apex to the center of the sphere is also 10 cm.

Using the Pythagorean theorem, we can write:
r^2 + (h - 10)^2 = 10^2

The volume of the cone (V) is given by:
V = (1/3)πr^2h

Our goal is to maximize V with respect to r and h. We can first solve for h in terms of r from the Pythagorean equation and substitute it into the volume equation:
h = 10 + √(100 - r^2)

Now, the volume equation becomes:
V = (1/3)πr^2(10 + √(100 - r^2))

To find the maximum volume, we can use calculus and find the critical points by taking the derivative of V with respect to r and setting it equal to zero. After solving for r, we get r ≈ 5√2 cm. Now, we can find the corresponding height using the earlier equation for h: h ≈ 10 + 5√2 cm.

So, the dimensions of the cone of maximum volume that can be inscribed in a sphere of radius 10 cm are approximately r ≈ 5√2 cm and h ≈ 10 + 5√2 cm.

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1) The linear model for the data points (0.25, 0.5) and (2,0) is y = -0.5x + 1.

2) The slope of the line that best fits the data points is -20/37.

Using the point-slope form of the equation of a line and the coordinates of any one of the data points, we can find the equation of the line:

y - (-3) = (-20/37)(x - 7)

Simplifying this equation, we get:

y = (-20/37)x + 361/37

For the data points (0.25, 0.5) and (2,0), we can find the linear model in a similar way.

First, we find the slope of the line passing through the two points:

slope = (0 - 0.5) / (2 - 0.25) = -0.5

Next, we can use the point-slope form of the equation of a line to find the equation of the line. Choosing (2,0) as the point on the line, we get:

y - 0 = (-0.5)(x - 2)

Simplifying this equation, we get:

y = -0.5x + 1

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The volume of the rectangular prism, given the length, width and height, would be 1/20 cubic inches.

To find the volume of a rectangular prism, you multiply the height, breadth, and length together. In this case, the dimensions are:

Height (h) = 4/5 inches

Breadth (b) = 1/4 inches

Length (l) = 1/4 inches

Volume (V) = h x b x l

V = (4/5) x (1/4) x (1/4)

Now, multiply the fractions:

V = (4 x 1 x 1) / (5 x 4 x 4)

V = 4 / (5 x 16)

V = 4 / 80

V = 1 / 20

So, the volume of the rectangular prism is 1/20 cubic inches.

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The particle's velocity decreasing most rapidly ar t = 0

Hence Option A is correct.

Given that,

The acceleration of moving particle is,

a(t) = (t - 8)sint

We have to find the particle's velocity,

The velocity is the derivative of the particle's position function.

Let the particle starts at rest,

Integrate the acceleration function to get the velocity function,

⇒ v(t) = ∫ a(t) dt

         = ∫ (t-8) sint dt

         = -cos(t) (t-8) - sint + C

Where C is the constant of integration.

To find C, Use the initial condition that the particle starts at rest, so,

⇒ v(0) = 0.

Substituting this into the velocity function, we get,

⇒ 0 = -cos(0) (0-8) - sin(0) + C

⇒ C = 8 So the velocity function is,

⇒ v(t) = -cos(t) (t-8) - sint + 8

Now, we have to find when the velocity is decreasing most rapidly.

This occurs when the velocity function's derivative,

The acceleration, is at a maximum.

So we need to find the maximum of the acceleration function,

⇒ a'(t) = cos(t) sint + (t-8) cost

To find the maximum,

Take the derivative of a'(t) and set it equal to zero,

⇒ a''(t) = cos(t) cost - sint + cost - sin(t)

⇒ a''(t) = 2cost - sint - sin(t)

Setting a''(t) = 0, we get,

⇒ 2cost - sint - sin(t) = 0

We can use the identity cos²(t) + sin²(t) = 1 to solve for cos(t),

⇒ cos(t) = √(1 - sin²(t))

Substituting into the equation above, we get,

⇒ 2√(1 - sin²(t)) - sint - sin(t) = 0

Squaring both sides and simplifying, we get,

⇒ sin²(t) + 4sin(t) - 4 = 0

Using the quadratic formula, we get,

⇒ sin(t) = (-4 ± sqrt(16 + 16))/2

            = -2 ± 2sqrt(2)

Now t∈ [0, 8]

Hence,

At t = 0 its velocity decreases rapidly.

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4

subtract 2 from 6, because when you subtract 5 from 2 you will get 3

To solve this problem, we need to set up an equation where we solve for t, the time in years. The city will have a population of 200,000 in the year 2008.

To find the year when the population reaches 200,000, we need to solve the equation P = 142,000e^(0.014t) for t, with P = 200,000.

Step 1: Set P = 200,000
200,000 = 142,000e^(0.014t)

Step 2: Divide both sides by 142,000
(200,000 / 142,000) = e^(0.014t)

Step 3: Calculate the result of the division
1.4085 ≈ e^(0.014t)

Step 4: Take the natural logarithm of both sides
ln(1.4085) ≈ 0.014t

Step 5: Solve for t
t ≈ ln(1.4085) / 0.014

Step 6: Calculate the value of t
t ≈ 10.3

Since t represents the number of years after 1990, we can now determine the year when the population will reach 200,000.

Year = 1990 + t
Year = 1990 + 10.3

Since we can't have a fraction of a year, we'll round up to the nearest whole year.

Year = 1990 + 11

Year = 2001

The city will have a population of 200,000 in the year 2001.

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The probability of an event that is almost certain to occur is closest to 1. In the given options, the number that best represents this probability is 0.99.

What Is Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes. Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes,  i.e {(H, H), (H, T), (T, H), (T, T)}.The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.

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Step-by-step explanation:

Exponetial growth:

8% growth per year would be

  Population (t) = 604 000 ( 1.08) ^t       where t is years since 1990

Suppose u(x,0) = sin(πx) + ∑ [tex]5/n^{10}[/tex] sin(2nπx). n=1 If u(x, t) represents the temperature of a rod at a position x and time t, then at time t the midpoint has the temperature U(1/2, t) = 2.718.

The solution to the given heat equation with the given initial and boundary conditions is:

u(x,t) = ∑ (2/nπ) sin(nπx) e^(-n^2π^2t/16), n=1 [infinity]

Using this solution, we can find the temperature at the midpoint x=1/2:

U(1/2, t) = ∑ (2/nπ) sin(nπ/2) e^(-n^2π^2t/16), n=1 [infinity]

Plugging in t=0, we get:

U(1/2, 0) = ∑ (2/nπ) sin(nπ/2), n=1 [infinity]

Using the identity sin(nπ/2) = 1 if n is odd, and 0 if n is even, we can simplify this expression:

U(1/2, 0) = ∑ (2/(2n-1)π), n=1 [infinity]

This is a divergent series, so we cannot find its exact value. However, we can approximate it by truncating the series at a large enough value of N:

U(1/2, 0) ≈ ∑ (2/(2n-1)π), n=1 to N

For example, if we take N=10, we get:

U(1/2, 0) ≈ 3.8197

Therefore, at time t, the midpoint of the rod has the temperature U(1/2, t) ≈ ∑ (2/nπ) sin(nπ/2) e^(-n^2π^2t/16), n=1 to N, which depends on the value of t and the number of terms included in the series approximation.
At time t, the midpoint of the rod has the temperature:

U(1/2, t) = sin(π(1/2)) * e^(-16(π^2)t) + ∑ [5/n^10 * sin(2nπ(1/2)) * e^(-16(2nπ)^2t)]. n=1 to ∞

Here, e represents the base of the natural logarithm (approximately 2.718).

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The value of c 5y^2 dx 12xy dy, where c is the boundary of the semiannular region d in the upper half-plane between the circles x^2 + y^2 = 1 and x^2 + y^2 = 9, is -94.5 - 2.5 = -97.

To evaluate c 5y^2 dx 12xy dy, we need to first determine the boundary of the semiannular region d in the upper half-plane between the circles x^2 + y^2 = 1 and x^2 + y^2 = 9.

The boundary of d consists of two curves: the outer circle x^2 + y^2 = 9 and the inner circle x^2 + y^2 = 1. We can parameterize the outer circle as x = 3cos(t) and y = 3sin(t), where t varies from 0 to pi.

We can parameterize the inner circle as x = cos(t) and y = sin(t), where t varies from pi to 0.

Using these parameterizations, we can express c 5y^2 dx 12xy dy as the sum of two integrals:

integral from 0 to pi of 5(3sin(t))^2 (-3sin(t) dt) + 12(3cos(t))(3sin(t))(3cos(t) dt)
integral from pi to 0 of 5(sin(t))^2 (cos(t) dt) + 12(cos(t))(sin(t))(cos(t) dt)

Simplifying these integrals, we get:

integral from 0 to pi of -135sin^3(t) dt + 108cos^2(t)sin^2(t) dt
integral from pi to 0 of 5sin^2(t)cos(t) dt + 12cos^2(t)sin(t) dt

Using trigonometric identities, we can evaluate these integrals to get:

-94.5
-2.5

Therefore, the value of c 5y^2 dx 12xy dy, where c is the boundary of the semiannular region d in the upper half-plane between the circles x^2 + y^2 = 1 and x^2 + y^2 = 9, is -94.5 - 2.5 = -97.

To evaluate the given integral, we need to understand the given boundary and region. In this case, the region is a semiannular region, which is in the upper half-plane between two circles with equations x^2 + y^2 = 1 and x^2 + y^2 = 9.

First, let's parameterize the boundary C. We can use polar coordinates for this, where x = r * cos(θ) and y = r * sin(θ).

For the inner circle (x^2 + y^2 = 1), r = 1, and θ ranges from 0 to π.
For the outer circle (x^2 + y^2 = 9), r = 3, and θ ranges from 0 to π.

Now, let's evaluate the given integral:

∫∫_D (5y^2 dx + 12xy dy)

Using Green's theorem, we can rewrite this as:

∮_C (12xy dx - 5y^2 dy)

Now, we have two parts of the boundary - inner and outer circles.

For the inner circle (r = 1):
x = cos(θ), y = sin(θ), dx = -sin(θ)dθ, dy = cos(θ)dθ, θ ranges from 0 to π.

∫(12(cos(θ))(sin(θ))(-sin(θ)dθ) - 5(sin(θ))^2(cos(θ)dθ)) from 0 to π

For the outer circle (r = 3):
x = 3cos(θ), y = 3sin(θ), dx = -3sin(θ)dθ, dy = 3cos(θ)dθ, θ ranges from 0 to π.

∫(12(3cos(θ))(3sin(θ))(-3sin(θ)dθ) - 5(3sin(θ))^2(3cos(θ)dθ)) from 0 to π

Now, add these two integrals, simplify, and evaluate to find the answer.

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the value of ∠C is 20°

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The answer is ∠C= 20 degree

We have given:

AB= 5

AC = 14

and we have to find ∠c to the nearest degree.

So,

We know that:

tan(C)= AB/AC

tan(C)= 5/14

tan(C)= 0.3571

C=20 degree

Thus the value of ∠C is 20°

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The time it takes for a sunflower seed to hit the ground is approximately 3.1 seconds.

To solve this problem, we need to find how long it takes the distance function to reach a value of 150 feet (the height of the balcony). When the sunflower seed falls to the ground, the distance to the balcony is zero.

The expression can be set like this:

[tex]d(t) = 16t^2 = 150[/tex]

Solving for t gives:

[tex]t^2 = 150/16[/tex]

t = sqrt(9.375) seconds

therefore, Rounded to the nearest tenth of a second the time it takes for a sunflower seed to hit the ground is approximately 3.1 seconds.

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The correct answer is option c. 95%. Reaching out two standard errors on either side of the sample proportion gives us an interval of 95% confidence.

This is due to the fact that two standard errors on either side of the sample proportion will cover around 95% of the population's cases.

We can typically determine the true proportion in the population using this range of two standard errors on either side of the sample proportion.

This is because it helps us identify any potential outliers in the population and provides a range of population proportions for which we may be 95% certain.

We are 95% certain that the true percentage is capable inside the interval if we stretch out two standard errors on either side of the sample proportion.

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If m and n are odd numbers, then we will have:

In the diagram we can see a 3 by 5 checkboard, it has:

3*5 = 15 boxes.

And there we can count that we have 8 black ones and 7 white ones.

As long as both numbers are odd, the product will be odd, so we always will have one more black box than whites boxes, and that is because we will start having more black boxes (and end) like in the given diagram.

Then we will have that m*n is odd.

Then the number of white boxes is (m*n - 1)/2

And the number of black boxes is 1 more than that, it can be written as:

(m*n - 1)/2 + 1 = (m*n + 1)/2

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a) To find the profit when 60 units are sold, we plug x = 60 into the profit function:

P(60) = -2.75(60)^2 + 1025(60) - 3000 = $37,500

Therefore, the profit when 60 units are sold is $37,500.

b) The average profit per unit when 60 units are sold is:

average profit per unit = total profit / number of units sold

average profit per unit = P(60) / 60 = 37500 / 60 = $625/ unit

Therefore, the average profit per unit when 60 units are sold is $625 per unit.

c) To find the rate that profit is changing when exactly 60 units are sold, we take the derivative of the profit function with respect to x and evaluate it at x = 60:

P'(x) = -5.5x + 1025

P'(60) = -5.5(60) + 1025 = $660

Therefore, the rate that profit is changing when exactly 60 units are sold is $660 per unit.

d) To find the rate that profit changes on average when the number of units sold rises from 60 to 120, we use the average rate of change formula:

average rate of change = (P(120) - P(60)) / (120 - 60)

We can find P(120) by plugging x = 120 into the profit function:

P(120) = -2.75(120)^2 + 1025(120) - 3000 = $67,500

Therefore,

average rate of change = (67500 - 37500) / (120 - 60) = $600 per unit

Therefore, the rate that profit changes on average when the number of units sold rises from 60 to 120 is $600 per unit.

e) To find the number of units sold when profit stops increasing and starts decreasing, we need to find the maximum point of the profit function. We can do this by finding the x-coordinate of the vertex:

x = -b / 2a = -1025 / (2(-2.75)) = 186.36

Since we can't sell a fraction of a unit, the number of units sold when profit stops increasing and starts decreasing is 186 units.

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Answer:

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Given is the special 30°×60°×90° right triangle.

It has a property that, the length of the hypotenuse is twice the length of the side opposite to 30° angle.

Using this property, set up equation and solve for y:

The angle (xy)° is complementary with 30° angle, therefore it is:

Substitute 10 for y into equation to find the value  of x:

So the missing values are:

Answer: 52:3

Step-by-step explanation:

We know that the surface area formula for the cylinder is 2pi r h + 2 pi r^2. We can assume that the radius of the base circle is 1 inch, as it will not change the outcome of the surface area given that both the base circles have the same radius. Plugging in for r and h, we get 16pi + 2pi, equal to 18pi. Applying this to the larger cylinder, we get 24 pi + 288 pi which is 312 pi. Dividing 312 pi by 18 pi, we get 312/18, which in the most straightforward form is 52/3. This means the ratio of the surface area from the larger cylinder to the smaller cylinder is 52:3.

In order to determine the dimension of the subspace of R3 spanned by the given vectors, we need to find the number of linearly independent vectors in the set.

For example, if we have two vectors in R3, we can determine if they are linearly independent by checking if one vector is a scalar multiple of the other. If they are linearly independent, they span a two-dimensional subspace of R3.

If we have three vectors in R3, we can use the same method to check if they are linearly independent. If they are, they span a three-dimensional subspace of R3. If they are not linearly independent, we can use row reduction to find a linearly independent subset of the vectors, which will span a subspace of lower dimension.

In general, the dimension of the subspace of R3 spanned by n vectors will be at most n, and it will be exactly n if and only if the vectors are linearly independent.

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The CDF of Y=X is [tex]F_{Y}(y) =1-exp(-2y)[/tex] for y ≥ 0, and 0 otherwise and the PDF of Y is [tex]2 exp(-2  y)[/tex] for y ≥ 0, and 0 otherwise.

Given that X has an exponential PDF with λ = 2, we'll first find the CDF of Y = X, and then determine the PDF of Y.

(a) To find the CDF of Y = X, we first need to consider the PDF of X, which is given by:

[tex]f_{X}(x) = \lambda \times exp(-\lambda \times x)[/tex] for x ≥ 0, and 0 otherwise.

Since λ = 2, the PDF of X becomes:

[tex]f_{X}(x) = 2 \times exp(-2 \times x)[/tex] for x ≥ 0, and 0 otherwise.

Now, to find the CDF of [tex]Y = X (F_{X}(y))[/tex], we need to integrate the PDF of X from 0 to y:

[tex]F_{Y}(y) = \int_{0}^{y}(2 \times exp(-2 \times x)) dx [/tex].

Upon integrating and evaluating the integral, we get:

[tex]F_{Y}(y) =1-exp(-2y)[/tex] for y ≥ 0, and 0 otherwise.

(b) To find the PDF of Y ([tex]f_{Y}(y)[/tex]), we need to differentiate the CDF of Y ([tex]F_{Y}(y)[/tex]) with respect to y:

[tex]f_{Y}(y) = \frac{d(F_{Y}(y))}{dy}[/tex].

Differentiating [tex]F_{Y}(y)[/tex] with respect to y, we get:

[tex]f_{Y}(y) = 2 \times exp(-2 \times y)[/tex] for y ≥ 0, and 0 otherwise.

So, the PDF of Y ([tex]f_{Y}(y)[/tex]) is the same as the PDF of X ([tex]f_{X}(x)[/tex]), which is

[tex]2 exp(-2  y)[/tex] for y ≥ 0, and 0 otherwise.

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Answer:

y = -20x - 12

Step-by-step explanation:

Solve for y by simplifying both sides of the equation, then isolating the variable.

Hope this helps!

The calculated value of x in the right triangle is 7

To find the value of x, we can use the trigonometric ratios of sine, cosine, and tangent.

In this problem, we know that the hypotenuse is 14 units and the angle between the hypotenuse and the base is 30 degrees. Let's label the adjacent side (the side adjacent to the 30-degree angle) as a and the opposite side (the altitude) as x.

Then, using the definition of sine, cosine, and tangent, we can write:

sin(30°) = x/14

cos(30°) = a/14

tan(30°) = x/a

So, we have

x/14 = 0.5

Solving for x, we get:

x = 7

Therefore, the value of x in simplest form is 7

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