As an employee of the architectural firm of Brown and Farmer, you have been asked to design a silo to stand adjacent to an existing barn on the campus of the local community college. You are charged with finding the dimensions of the least expensive silo that meets the following specifications.


The silo will be made in the form of a right circular cylinder surmounted by a hemi-spherical dome.

It will stand on a circular concrete base that has a radius 1 foot larger than that of the cylinder.

The dome is to be made of galvanized sheet metal, the cylinder of pest-resistant lumber.

The cylindrical portion of the silo must hold 1000π cubic feet of grain.

Estimates for material and construction costs are as indicated in the diagram below.


The design of a silo with the estimates for the material and the construction costs.


The ultimate proportions of the silo will be determined by your computations. In order to provide the needed capacity, a relatively short silo would need to be fairly wide. A taller silo, on the other hand, could be rather narrow and still hold the necessary amount of grain. Thus there is an inverse relationship between r, the radius, and h, the height of the cylinder.



The construction cost for the concrete base is estimated at $20 per square foot. Again, if r is the radius of the cylinder, what would be the area of the circular base? Note that the base must have a radius that is 1 foot larger than that of the cylinder. Write an expression for the estimated cost of the base.



Surface area of base = ____________________


Cost of base = ____________________

A sample that does not represent the entire group of interest is called a biased sample.

A biased sample is a sample that doesn't reflect the real-world population it is supposed to represent. It happens when the sample is chosen in such a way that some members of the population are less likely to be included than others.

Therefore, a biased sample may not be an accurate representation of the entire population.

For example, if a researcher wants to know how many people in a given area have access to the internet and chooses a sample of people from a high-income neighborhood, the results may be biased because people from low-income areas may have lower rates of internet access.

A biased sample can lead to inaccurate conclusions, and therefore, it's important to ensure that the sample is representative of the population. A random sample, on the other hand, ensures that all members of the population have an equal chance of being included in the sample.

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Answer:

\( m\widehat {BDA} = 222\degree \)

Step-by-step explanation:

\( m\widehat {BDA} = 360\degree -(m\widehat {AC} +m\widehat {CB}) \)

\( m\widehat {BDA} = 360\degree - (90\degree +48\degree) \)

\( m\widehat {BDA} = 360\degree - 138\degree \)

\( m\widehat {BDA} = 222\degree \)

Given the equation below:

Using distributive to simplify as shown below:

Collect like terms

Divide through by 2

Hence, the value of a is 20

Answer: 89.7

Step-by-step explanation:

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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(a)i. Evaluating the constant:

\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)

Therefore, the probability density function is:

\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:

From the graph, it is observed that the density function is skewed to the left.

(b)i. The mean:

\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)

ii. The second moment about the origin:

\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)

Therefore, the variance is:

\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)

iii. The standard deviation:

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)

i. The cumulative distribution function:

\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)

ii. The probability density function can be obtained by differentiating the cumulative distribution function:

\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)

iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)

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Answer:

when the coefficient of x^2 is negative

Step-by-step explanation:

Answer:

The slope between those two points is 2

Step-by-step explanation:

Answer:

The slope is:

\(m = 2\)

Step-by-step explanation:

Use the slope formula:

\(m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Use both points (4,0) and (0,-8) for the slope formula:

\(m = \frac{-8-0}{0-4}\)

-Then, you solve:

\(m = \frac{-8-0}{0-4}\)

\(m = \frac{-8}{-4}\)

\(m = 2\)

So, therefore, the slope is \(2\) .

(-∞,-10)∪(-10,-2)∪(-2,∞)

Or

\(\left\{x|x\ne-2,-10\right\}\)

Both are correct.

Answer:

Remainder = (-4)

Step-by-step explanation:

f(x) = 5\(x^{5} + 1\)

x + 1 = 0

x = -1

f(-1) = 5*\((-1)^{5} + 1\)

      = 5 * (-1) + 1

      = -5 +1

      = -4

This statement is false. In a weighted, connected graph with edge weights not necessarily distinct, if one Minimum Spanning Tree (MST) has k edges of a certain weight w, it is not guaranteed that any other MST must also have exactly k edges of weight w.

1. In a weighted graph, each edge has a weight (or cost) associated with it.
2. A connected graph means there is a path between any pair of vertices.
3. An MST is a subgraph that connects all the vertices in the graph, without any cycles, and with the minimum possible total edge weight.

However, there can be multiple MSTs for a given graph, and their edge weights distribution might not be the same. This is because MSTs are primarily focused on minimizing the total weight, not necessarily preserving the number of edges with a specific weight. Different MSTs may use different sets of edges to achieve the minimum total weight, so they might not have the exact same count of edges with weight w.

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Answer:

611 divided by 78

Step-by-step explanation:

7.83333333333 round to 7.83

Answer:

When X = 24

Step-by-step explanation:

Use derivative to locate the turning point.

48 - 2X = 0, => X = 24

The probability of getting three aces is  0.0015

The probability of getting exactly one ace is 0.2887.

To solve these probability problems, we can use combinations and the concept of equally likely outcomes.

(a) Probability of getting three aces:

We have four aces in the deck. To choose 3 aces out of 4, we can use combinations: C(4, 3) = 4.

The remaining 2 cards in the hand must be chosen from the remaining 48 non-ace cards. So, we have C(48, 2) = 1,128.

The total number of possible 5-card hands is C(52, 5) = 2,598,960.

Therefore, the probability of getting three aces is:

P(three aces) = (4 * 1,128) / 2,598,960 ≈ 0.0015

(b) Probability of getting exactly one ace:

Similar to part (a), we have C(4, 1) = 4 ways to choose one ace.

The remaining 4 cards in the hand must be chosen from the remaining 48 non-ace cards. So, we have C(48, 4) = 194,580.

The probability of getting exactly one ace is:

P(exactly one ace) = (4 * 194,580) / 2,598,960 ≈ 0.2887

(c) Probability of getting no aces:

There are no aces in the hand. We need to choose all 5 cards from the 48 non-ace cards:

P(no aces) = C(48, 5) / C(52, 5) ≈ 0.6718

(d) Probability of getting at least one ace:

This is the complement of getting no aces. So, we have:

P(at least one ace) = 1 - P(no aces) ≈ 1 - 0.6718 ≈ 0.3282

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From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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The measure of the interior non-adjacent angle as required in the task content is; 95°.

Recall; It follows from the triangle exterior angle theorem that the measure of exterior angle of a triangle is equal to the sum of the two opposite interiors angles.

On this note, if the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, the sum of the two angle measures is therefore;

x + x - 32.

where, x is the measure of the interior non-adjacent angle.

Hence, x + x - 32 = 158

2x = 158 + 32

2x = 190

x = 95°.

Ultimately, the measure of the interior non-adjacent angle is; 95°.

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Answer:

23. c

24.b

25. box 2

26. 48, 26

Step-by-step explanation:

The company that charges more for a 5-mile ride is Callie's cab.

1. Tasha's taxi :

   Let us consider the equation, y = 3x + 5

Here,

A. Let us consider 1 mile, that is,  x = 1.

   So, y = 3(1) +5

         y = $8

   Every ride should include the pickup fee also.

   The total cost for one mile is $8

B. Let us consider 5 mile, that is,  x = 5.

   So, y = 3(5) +5

         y = $20

   Every ride should include the pickup fee also.

   The total cost for 5 miles is $20

2. Callie's cab:

A. Let us consider 1 mile,

    So, Total cost = 4 + 3

                           =$7

    Every ride should include the pickup fee also.

    The total cost for one mile is $7

B. Let us consider 5 miles,

    So, Total cost = 4(5) + 3

                           =$23

    Every ride should include the pickup fee also.

    The total cost for 5 miles is $23

The company that charges a higher pickup fee is Tasha's taxi.

The company that charges more per mile is Tasha's taxi.

The company that charges more for a 5-mile ride is Callie's cab.

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Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Since the derivative is negative, it indicates that raising prices will decrease city revenue (Option B).

The demand function for city bus rides is given as P = 100 - 10Q, where P represents the price of a ride and Q represents the quantity of rides demanded.

Currently, the price of a ride is 60.

To determine the quantity demanded at this price, we can plug the price into the demand function:

60 = 100 - 10Q

10Q = 40

Q = 4

So, at a price of 60, the quantity demanded is 4 rides.

The current city revenue can be calculated as Revenue = P*Q, which is 60×4 = 240.

Now, let's consider a hypothetical increase in price (ΔP).

This increase will lead to a decrease in the quantity demanded (ΔQ). Since revenue is a product of price and quantity (P*Q), we need to determine the net effect of increasing the price on revenue.

Let's use the demand function to find the new quantity demanded, Q' = Q - ΔQ, after the price increase:

P' = P + ΔP

100 - 10(Q - ΔQ) = P + ΔP

To analyze the impact of a price increase on revenue without specific values for ΔP, we can use calculus.

The derivative of the revenue function with respect to price, d(P×Q)/dP, will indicate whether revenue increases or decreases as price increases.

Taking the derivative, we get:

d(P×Q)/dP = Q - P/10

At the current price P=60, the derivative evaluates to:

Q - P/10 = 4 - 60/10 = 4 - 6 = -2

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Multiply the numerator and denominator by the conjugate of the denominator:

\(\dfrac{6+9i}{-1+4i} \times \dfrac{-1-4i}{-1-4i} = \dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2}\)

Simplify:

\(\dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2} = \dfrac{-6-9i-24i-36i^2}{1-16i^2} = \dfrac{-6-33i-36i^2}{1-16i^2} = \dfrac{-6-33i+36}{1+16} = \boxed{\dfrac{30-33i}{17}}\)

9514 1404 393

Answer:

Step-by-step explanation:

Looking at the numbers individually, we have ...

16 = 4×4

42 = 2×3×7

6 = 2×3

17 = 1×17 (prime)

12 = 3×4

49 = 7×7

24 = 2×3×4

7 = 1×7 (prime, a multiple of 7)

11 = 1×11 (prime)

8 = 2×4

__

Multiples of 4:

  16, 12, 24, 8

Multiples of 7:

  42, 49, 7

Multiples of neither:

  6, 17, 11

77 is the sum of their integers  squares .

What in math is an integer?

Let the numbers be ( n - 1 ), n , ( n + 1 )

according to question

  ( n - 1 ) (n) ( n + 1 ) = 8( n + n - 1 + n + 1 )

  n( n² - 1 ) = 8(3n)

   ( n² - 1 ) = 24

    n²= 25

    n = 5

since n is positive integer n = 5

thus required numbers are 4,5,6

4² + 5² + 6² = 77

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Answer:

\(\displaystyle =\frac{0.5\text{ ft}}{\text{day}}\)

The weed grows at a rate of 0.5 feet per day.

Step-by-step explanation:

The weed grows at a rate of 0.25 inches per hour.

And we want to convert this rate into feet per day.

We have that:

\(\displaystyle \frac{0.25\text{ in}}{\text{hr}}\)

We knowt that there are 12 inches in one foot.

And since we want to cancel the inches, we can write our conversion factor as ft / 12 in.

We also know that there are 24 hours in one day.

And since we want to cancel the hours, we can write our conversion factor as 24 hr / day.

Hence:

\(\displaystyle \frac{0.25\text{ in}}{\text{hr}}\cdot\frac{\text{ft}}{12\text{ in}}\cdot \frac{24\text{ hr}}{\text{day}}\)

Multiply and cancel common terms. So:

\(\displaystyle =\frac{0.5\text{ ft}}{\text{day}}\)

The weed grows at a rate of 0.5 feet per day.

Answer:

10.63cm

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2

(square root of 32)^2+(9)^2=113^2

The square root of 113 is 10.63.

I hope this helps :)

A ........,.......,,......,.,...

Answer:

(0.5, -3)

Step-by-step explanation:

(-3, -1) (4, -5)

midpoint formula

(x1 + x2) /2, (y1 + y2) /2

-3 + 4 = 1 / 2 = 0.5

-1 + -5 = -6 / 2 = -3

Answer:

47x 8y 3

Step-by-step explanation:

To find the exact length of the curve given by x = et − 9t, y = 12et/2, 0 ≤ t ≤ 3, we can use the arc length formula:
L = ∫(a to b) √[dx/dt]^2 + [dy/dt]^2 dt
Substituting the given values, we get:
L = ∫(0 to 3) √[e^t - 9]^2 + [6e^(t/2)]^2 dt
Simplifying the expression under the square root, we get:
L = ∫(0 to 3) √(e^(2t) - 18e^t + 81 + 36e^t) dt
L = ∫(0 to 3) √(e^(2t) + 18e^t + 81) dt
L = ∫(0 to 3) (e^t + 9) dt
L = [e^t + 9t] from 0 to 3
L = [e^3 + 9(3)] - [e^0 + 9(0)]
L = e^3 + 27 - 10.99
L ≈ 25.5
Therefore, the exact length of the curve is approximately 25.5 units.

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The solution of the given fraction can be gotten through filling the boxes with the following values respectively;

8/100 + 9/10 = 98/100

A fraction is defined as the representation of a part of a whole value in the form of a numerator and denominator.

The given fraction;

8/100 + 9/10 = ?

Find the lowest common multiple of the denominator = 100.

= 8/100 + 9/10

= 8 + 90/100

= 98/100

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