A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet?

Answer:

The sampling method used is a stratified sampling method

Step-by-step explanation:

sampling is the selection of a predetermined representative subpopulation from a larger population, to estimate the characteristics of the whole population.

Stratified sampling: Here, the total population are divided into subcategories (strata) before sampling is done. The strata are formed based on some common characteristics. In our example, the times of the day (morning, afternoon and evening) has widely varying atmospheric conditions which will add biases to the measurement of air quality. For example, the air in the morning if compared to the afternoon in an industrial area may be purer because of minimal industrial activity, hence effective comparison will be made by stratification.

The probability of making the wrong decision is approximately 0.0082.

According to the central limit theorem, the distribution of the sample mean of a large number of independent and identically distributed random variables approaches a normal distribution. In this case, the random variable is the number of odd outcomes in 100 rounds of the roulette.

As each outcome has an equal probability of being odd, the distribution of the number of odd outcomes is binomial with parameters n=100 and p=1/2.

Using the mean and variance of a binomial distribution, we have:

mean = np = 100 x 1/2 = 50

variance = np(1-p) = 100 x 1/2 x (1 - 1/2) = 25

The standard deviation of the distribution is the square root of the variance, which is 5. Therefore, the z-score for a count of 55 is:

z = (55 - 50) / 5 = 1

Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1 (i.e., a count of 55 or more) is approximately 0.1587. However, we are interested in the probability of making the wrong decision, which is the probability of a count of 55 or more given that the roulette is fair.

This probability is equal to the significance level of the test, which is the probability of rejecting the null hypothesis (fair roulette) when it is actually true.

Assuming a significance level of 0.05, the probability of making a Type I error (rejecting a true null hypothesis) is 0.05. Therefore, the probability of making the wrong decision is approximately 0.05 x 0.1587 = 0.0082.

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If v=<8,3,5> w=<2,2,2>, the cosine of the angle between vectors v and w is approximately 0.93294.

To find the cosine of the angle between vectors v and w, we will use the formula:
cos(θ) = (v • w) / (||v|| ||w||)
where θ is the angle between the vectors, v • w is the dot product of v and w, and ||v|| and ||w|| are the magnitudes of v and w, respectively.
First, let's find the dot product (v • w):
v • w = (8 * 2) + (3 * 2) + (5 * 2) = 16 + 6 + 10 = 32
Next, let's find the magnitudes of v and w:
||v|| = √(\(8^2 + 3^2 + 5^2\)) = √(64 + 9 + 25) = √98
||w|| = √(\(2^2 + 2^2 + 2^2\)) = √(4 + 4 + 4) = √12
Now, let's find the cosine of the angle between v and w:
cos(θ) = (32) / (√98 * √12) = 32 / (9.899494936611665 * 3.4641016151377544) ≈ 0.93294

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The cosine of the angle between v and w is 0.9332

To find the cosine of the angle between v and w, we can use the formula:

cos(Ф) = (v.w) / (||v|| ||w||)

where Ф is the angle between v and w, the . represents the dot product, and || || represents the magnitude or length. First, let's calculate the dot product of v and w:

v.w = 8*2 + 3*2 + 5*2 = 32

Next, let's calculate the magnitudes of v and w:

||v|| = sqrt(8^2 + 3^2 + 5^2) = sqrt(98)

||w|| = sqrt(2^2 + 2^2 + 2^2) = sqrt(12)

Now we can substitute these values into the formula:

cos(Ф) = (v.w) / (||v|| ||w||)
cos(Ф) = 32 / (sqrt(98) * sqrt(12))
cos(Ф)= 32 / (sqrt(1176))
cos(Ф) = 32 / 34.29
cos(Ф)= 0.9332

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The probability that a car chosen to random will need:

A) no repairs: 72%

B) No more than one repairs: 89%

C) some repairs: 11%

The total amount of cars that will need some type of repair is 28%; 17% will need to be repaired once + 7% will need to be repaired twice + 4% will need to be repaired more than two times.

The amount of cars that wouldn´t need any type of repairs is the total amount of cars minus the percentage that need some type of repair:                

                                   100% - 28% = 72%.

The amount of cars that will need no repairs or only one repair is the total amount of cars minus the percentage that need more than one of repair:

                             100% - (7% + 4%) = 89%.

The amount of cars that need some repairs is the sum of those cars that need two repairs plus those that need three or more repairs:

                                  7% + 4% = 11%

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The solution set of the given homogeneous system in parametric vector form is x = k[-1 1 0] where k is a constant.

A system of linear equations is referred to as homogeneous if all of the constants on the right-hand side of the equation are equal to zero. Homogeneous systems of linear equations are linear, which means that the equations are additive and homogeneous.

The system is solved using the steps given below:

Solution  Step 1:

Rewrite the given equations in the form of matrix

AX= 0 where X = [x1,x2,x3]T   and A is the matrix of the given system.

Therefore, the system can be represented as

[2 2 4;1 -4 -4] [x1;x2;x3] = 0

Step 2:

Find the reduced row echelon form of the matrix [A|0]

Step 3:

Let x3 = k, a free variable, and express all variables as functions of x3.

Step 4: Write the general solution of the system in the form of

X = c1v1 + c2v2

where c1 and c2 are constants and v1, v2 are the vectors found from step 3.

For the given homogeneous system

2x1 + 2x2 + 4x3 = 0x1 - 4x1 - 4x2 - 8x3 = 0

Step 1: The matrix of the given system is [2 2 4;1 -4 -4] [x1;x2;x3] = 0

Step 2: The augmented matrix of the system is [2 2 4 0;1 -4 -4 0]

Reducing the matrix to echelon form, we get [2 2 4 0;0 -6 -6 0]

Reducing the matrix to reduced row echelon form, we get [1 0 -1 0;0 1 1 0]

Step 3:

Let x3 = k, a free variable, then x1 = k and x2 = -k.

Hence the solution set of the given system is

x = x2 - 7x2 + 21x3 = 0 X3 x=x3 can be expressed as:

x = k[-1 1 0] + 0[0 -7 21]

Therefore, the solution set of the given homogeneous system in parametric vector form is x = k[-1 1 0] where k is a constant.

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In summary, the composition of two functions, f ∘ g, combines the outputs of the function g as inputs to the function f.

The composition of two functions, f ∘ g, is a new function that is formed by applying the output of the function g as the input of the function f.

To find the composition of f ∘ g, follow these steps:

1. Start with the function g(x) and evaluate it for a given input value, let's call it 'a'. This will give you g(a).
2. Take the output g(a) and use it as the input for the function f(x). Evaluate f(x) with this input value to get f(g(a)).
3. The final result f(g(a)) is the value of the composition of the two functions f ∘ g at the input 'a'.

In terms of composition notation, f ∘ g is read as "f composed with g" or "f of g". It represents the order in which the functions are applied: g is applied first, and then f is applied to the result of g.

In summary, the composition of two functions, f ∘ g, combines the outputs of the function g as inputs to the function f.

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Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

Answer:

59049.

Step-by-step explanation:

It is given that, 2 years later, two years ago, the population of this same city was 81,000 and today it is 65,610.

So, graph passing through (2,81000) and (-2,65610).

The general exponential function is

\(y=ab^x\)

where, a is initial value or present year population and b is growth factor.

Since graph passing through (2,81000) and (-2,65610), therefore the above equation must be satisfied by these points.

\(81000=ab^2\)    ...(1)

\(65610=ab^{(-2)}\)    ...(2)

Multiplying (1) and (2), we get

\(81000\times 65610=ab^2\times ab^{-2}\)

\(5314410000=a^2\)

Taking square root on both sides.

\(72900=a\)

Substitute a=72900 in (1).

\(81000=72900b^2\)

\(\dfrac{81000}{72900}=b^2\)

\(\dfrac{10}{9}=b^2\)

Taking square root on both sides.

\(\dfrac{\sqrt{10}}{3}=a\)

So, the population function is

\(y=72900\left(\dfrac{\sqrt{10}}{3}\right)^x\)

Substitute x=-4 in the above equation, to find the population of four years ago.

\(y=72900\left(\dfrac{\sqrt{10}}{3}\right)^{-4}\)

\(y=72900(0.81)\)

\(y=59049\)

Therefore, the population of four years ago is 59049.

The scalar surface integral ∫∫s x² ds over the closed cylinder S is equal to the integral over the curved lateral surface:

∫∫s x² ds = ∫∫s (9cos²θ) √(9(dθ²) + dz²).

To evaluate the scalar surface integral ∫∫s x² ds over the closed cylinder S, we need to parameterize the surface S and calculate the corresponding vector surface integral.

The surface S consists of two parts: the curved lateral surface and the top and bottom surfaces. Let's consider each part separately.

1. Curved Lateral Surface:

The equation x² + y² = 9 represents a circle in the xy-plane with radius 3. We can parameterize this circle using cylindrical coordinates as follows:

x = 3cosθ

y = 3sinθ

z = z

where 0 ≤ θ ≤ 2π and 0 ≤ z ≤ 4.

To calculate the surface element ds on the curved lateral surface, we can use the formula:

ds = √(dx² + dy² + dz²)

ds = √((dx/dθ)² + (dy/dθ)² + dz²)

ds = √((-3sinθ dθ)² + (3cosθ dθ)² + dz²)

ds = √(9(dθ²) + dz²)

The integral of x² over the curved lateral surface can be written as:

∫∫s x² ds = ∫∫s (9cos²θ) √(9(dθ²) + dz²)

2. Top and Bottom Surfaces:

The top and bottom surfaces are flat, so we can directly calculate their areas and multiply them by x² = 0 (since z = 0 on the bottom surface and z = 4 on the top surface).

Area of the bottom surface = π(3²) = 9π

Area of the top surface = π(3²) = 9π

Therefore, the integral of x² over the bottom and top surfaces is:

∫∫s x² ds = 0 ∫∫(bottom) x² ds + 0 ∫∫(top) x² ds = 0

Finally, the scalar surface integral ∫∫s x² ds over the closed cylinder S is equal to the integral over the curved lateral surface:

∫∫s x² ds = ∫∫s (9cos²θ) √(9(dθ²) + dz²)

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Answer:

Range : { -5,1,7}

Step-by-step explanation:

Take the values in the domain and substitute into the equation

x = -3

y = -2(-3) +1 = 6+1 =7

x = 0

y = -2(0) +1 = 0+1 =1

x = 3

y = -2(3) +1 = -6+1 =-5

The range is the y values

We put then in order from smallest to largest

Range : { -5,1,7}

The area of the shaded region A = 44.22

What is area of circle?

The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr2. π is approx 3.14 or 22/7.

1) Area of circle, Ac = π r^2

Ac = π (6)^2

Ac = 113.10

2) Area of triangle, At

The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile, the 3 angles at the center is 120 degrees each since a circle is 360 degree.

We know that the radius (line from center point to corner) is equivalent to 6. Using the cosine law, we can calculate for the length of one side.

s^2 = 6^ + 6^2 – 2 (6) (6) cos 120

s^2 = 108

s = 10.4

Since this is an equilateral triangle therefore all sides are equal. The area for this is:

At = (sqrt3 / 4) * s^2

At = 46.77

3) Area of segment, As is given as:

As = [ (r^2) / 2 ] ( θ rad – sin θ )

As = [(6^2) / 2] (120 * π / 180 – sin 120)

As = 22.11

Therefore the area of shaded region is:

A = 113.10 - 46.77 - 22.11

A = 44.22

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1999, is the smallest value of n for which Sₙ( sum of sequence terms ) >10000.

The best way to solve this problem is to write down the series and try to find out some pattern follows by terms , hopefully you can find a pattern (for example, you have a repeating series of numbers).

4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, … You can see that the sequence (4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3) is repeated. There are 12 numbers in this sequence, and their sum is 60.

Divide 10,000 by 60, we get

10,000 = 60 * 166 + 40, so there are 166 sets and we need more than 40 numbers in total. Requires at least 12 x 166 = 1992 numbers and some numbers totaling over 40. Now, we have to add starting from 4, 7 such that some of adding terms reach the number >40.

4 + 7 + 1 + 8 + 9 + 7 + 6 = 42 > 40, so we need 7 more numbers. So, the total number needed for Sn > 10,000 is

1992 +7 = 1999.

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Answer:

1200

Step-by-step explanation:

400+50+150*8+3000=7800

9000-7800

Answer:

6,600

Step-by-step explanation:

9000 − 3000 + 600 =

6600

(I don't know if this what you wanted but I hope it will help)

Answer: A) 87

The median value is the second quartile (Q₂), which is 87.

Answer:

A: 87

Step-by-step explanation:

Sorry for this very late response. But if anyone is not sure if answer A is correct, it is. I can confirm this because I just took the test. I hope I could help! (:

The place value of the digit 6 when it is moved one place to the left in the number 18,564 is the hundreds place.

To determine the place value of the digit 6 when it is moved one place to the left in the number 18,564, we need to understand the concept of place value in our number system.

In the given number, 18,564, each digit represents a specific place value based on its position. Starting from the rightmost digit, the place values increase by powers of 10 as we move towards the left.

Let's analyze the number 18,564 to find the place value of the digit 6 when it is moved one place to the left.

1. Write down the number: 18,564

2. Identify the digit 6: It is located in the thousands place (the fourth digit from the right).

3. Move the digit 6 one place to the left: This means we need to divide the number by 10. The resulting number is 1,856.4 (since the decimal point moves along with the digits).

4. Determine the new place value of the digit 6: After moving the digit one place to the left, the digit 6 now occupies the hundreds place (the third digit from the right) in the number 1,856.4.

Therefore, the place value of the digit 6 when it is moved one place to the left in the number 18,564 is the hundreds place.

In summary, when the digit 6 is moved one place to the left in the number 18,564, its new place value becomes the hundreds place in the resulting number 1,856.4.

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Answer:

a. 2

Step-by-step explanation:

\(4x-5=-6x+15\)

add 6x to both sides

\(10x-5=15\)

add 5 to both sides

\(10x=20\)

divide both sides by 10

\(x=2\)

Answer:

(a)  2

Hope it helps

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Thank you

Answer:

x=23

Step-by-step explanation:

1/6 as a decimal is 0.16666667 but i rounded it to 0.2

so the equation is the 0.2(3x-9)-9=3

then i did 0.2 times 3x =0.6x

then 0.2 times -9= -1.8

so the equation now looks like this:

0.6x-1.8x-9=3

so i add 1.8 and 9 to 3 which gives you 13.8

then the equation looks like this:

0.6x=13.8

then you do 13.8 divided by 0.6 which equals 23.

hope this helps

tell me if i got it right or wrong

Answer:

70 percent

Step-by-step explanation:

140/200 = 7/10 = 0.7 = 70 percent

We can conclude that the difference engine rule for the given function f(n) = 6n^2 - 5n^4 is as follows:

First Difference Function: -20n^3 - 30n^2 - 8n + 1

Second Difference Function: -90n^2 - 122n - 51

To calculate the difference functions for the given function f(n) = 6n^2 - 5n^4, we need to find the differences between consecutive terms. Let's calculate the first few differences:

f(n) : 6n^2 - 5n^4

f(n + 1) : 6(n + 1)^2 - 5(n + 1)^4

Now, let's expand and simplify these expressions:

f(n) : 6n^2 - 5n^4

f(n + 1) : 6(n^2 + 2n + 1) - 5(n^4 + 4n^3 + 6n^2 + 4n + 1)

Expanding further:

f(n + 1) : 6n^2 + 12n + 6 - 5n^4 - 20n^3 - 30n^2 - 20n - 5

Next, we subtract f(n) from f(n + 1) to find the first difference:

f(n + 1) - f(n) : (6n^2 + 12n + 6 - 5n^4 - 20n^3 - 30n^2 - 20n - 5) - (6n^2 - 5n^4)

Simplifying:

f(n + 1) - f(n) : 6n^2 + 12n + 6 - 5n^4 - 20n^3 - 30n^2 - 20n - 5 - 6n^2 + 5n^4

Combining like terms:

f(n + 1) - f(n) : 12n + 6 - 20n^3 - 30n^2 - 20n - 5

Further simplifying:

f(n + 1) - f(n) : -20n^3 - 30n^2 - 8n + 1

Therefore, the first difference function is -20n^3 - 30n^2 - 8n + 1.

To find the second difference function, we need to calculate the differences between consecutive terms of the first difference function:

f(n + 1) - f(n) : -20(n + 1)^3 - 30(n + 1)^2 - 8(n + 1) + 1 - (-20n^3 - 30n^2 - 8n + 1)

Expanding and simplifying:

f(n + 1) - f(n) : -20(n^3 + 3n^2 + 3n + 1) - 30(n^2 + 2n + 1) - 8n - 8 + 20n^3 + 30n^2 + 8n - 1

Combining like terms:

f(n + 1) - f(n) : -20n^3 - 60n^2 - 60n - 20 - 30n^2 - 60n - 30 - 8n + 20n^3 + 30n^2 + 8n - 1

Simplifying further:

f(n + 1) - f(n) : -90n^2 - 122n - 51

Therefore, the second difference function is -90n^2 - 122n - 51.

From the calculations, we can conclude that the difference engine rule for the given function f(n) = 6n^2 - 5n^4 is as follows:

First Difference Function: -20n^3 - 30n^2 - 8n + 1

Second Difference Function: -90n^2 - 122n - 51

The difference engine rule shows how the values of the function change as n increases, and it provides a way to predict future values based on the differences between consecutive terms.

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The partial fraction expansion of the Laplace transform of (s - 2) / [(s + 2)(s + 3)] is 2 / (s + 2) - 1 / (s + 3).

To find the partial fraction expansion of the given Laplace transform, we need to decompose the fraction into simpler fractions. The expression is:

(s - 2) / [(s + 2)(s + 3)]

To decompose this, we assume that the fraction can be expressed as the sum of two terms:

(s - 2) / [(s + 2)(s + 3)] = A / (s + 2) + B / (s + 3)

Now, we need to find the values of A and B. To do this, we can multiply both sides of the equation by the denominator (s + 2)(s + 3):

(s - 2) = A(s + 3) + B(s + 2)

Expanding and equating the coefficients of the corresponding powers of s:

s - 2 = (A + B) s + (3A + 2B)

By comparing the coefficients, we get the following system of equations:

1 = A + B (coefficient of s)

-2 = 3A + 2B (constant coefficient)

Solving this system of equations, we find A = 2 and B = -1.

Therefore, the partial fraction expansion of the given Laplace transform is: (s - 2) / [(s + 2)(s + 3)] = 2 / (s + 2) - 1 / (s + 3)

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Answer:

Step-by-step explanation:

Let x be the variable.

One fourth times the difference of ten and x is 2/3

1/4 (10 - x) = 2/3

10 - x = 3/2

-x = 3/2 - 10

x = -3/2 + 10

x = 13/2

The answer is:

\(\rm{\dfrac{1}{4}(10-d)=\dfrac{2}{3}}\)

Work/explanation:

First, the variable is d

Then, the difference of 10 and d is 10 - d.

One-fourth is 1/4.

The equation is : \(\rm{\dfrac{1}{4}(10-d)=\dfrac{2}{3}}\).

The fractions reduced to standard form are -2/5, 1/5, 1/2 and 5/11 for 1), 2), 3), and 4) respectively

To reduce a fraction to standard form, you need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that can be evenly divided into both the numerator and the denominator.

Given:

1) -18/45

The GCD of 18 and 45 is 9. Thus:

-18/45 = -2/5

2) -3/-15

The GCD of 3 and 15 is 3. Thus:

-3/-15 = 1/5

3) 28/56

The GCD of 28 and 56 is 28. Thus:

28/56 = 1/2

4) 45/99

The GCD of 45 and 99 is 9. Thus:

45/99 = 5/11

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1)-6/15

2)1/5

3)1/2

4)5/11

1) -18/45

⇒-6/15

2)-3/-15

⇒-1/-5

⇒1/5

3)28/56

⇒4/8

⇒1/2

4)45/99

⇒15/33

⇒5/11

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Answer:

D. 29

Step-by-step explanation:

If a = 6 and b = 5, fill in the numbers in place of the variables (letters) in 4a + b

= 4•6 + 5

= 24 + 5

= 29

4a means 4 times a. Multiply first, and then add.

Independent events are not affected by previous events, that is, the probability of a new event doesn't change from the previous event. However, disjoint sets mean they don't have any data in common, which means the intersection of such sets is impossible. In other words, the events are exclusive, if one occurs, then the other can't occur.

Having said that, we can deduct that scenario 1 represents an independent exclusive event because the occurrence of one event excludes the other. The main reason is that there's just one orange marble.

Answer:

you just need to get 93 and times it my the number next to it and you will get your answer which is 257

The distance across the lake based solely on the length of Cade's shadow and the timing of the tree's shadow reaching the other side of the lake cannot be determined.

What is distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Disagree. Without additional information or measurements, it is not possible to determine the distance across the lake just from the length of Cade's shadow and the timing of the tree's shadow reaching the other side of the lake.

To determine the distance across the lake, we would need to use similar triangles or trigonometry to relate the length of Cade's shadow to the height of the tree, the angle of the sun's rays, and the distance across the lake.

However, we do not have any information about the height of the tree or the angle of the sun's rays, so we cannot use trigonometry to calculate the distance across the lake.

Therefore, we cannot determine the distance across the lake based solely on the length of Cade's shadow and the timing of the tree's shadow reaching the other side of the lake.

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Answer:

C

Step-by-step explanation:

\(12x\sqrt{900x^2y^4z^6}= \\\\12x\sqrt{30^2x^2(y^2)^2(z^3)^2}= \\\\12x(30xy^2z^3)= \\\\360x^2y^2z^3\)

Therefore, the correct answer is choice C. Hope this helps!!