Each 12 foot tall steel column is a rectangular prism, with a volume of 24 cubic feet. Steel is mostly composed of
iron and carbon (carbon represents 4% of its mass). The chemical formula for one steel molecule is Fe3C.
The mass of 1 cubic foot of steel is 490lbs.
9. If the depth of each column is one half its width, what are the dimensions (length, width and depth) of each
column?
10. How much iron was used to make one column?

The minimum value of the function f(x) =0. 9x2+3. 4x-2. 4 is -3.77 and its parabolic curve is upward because of its minimum value.

Let's consider the equation of a function.

f(x) = \(0.9x^{2} + 3.4x -2.4\)

Now, divide each and every element and assume that a, b, and c are coefficients of the function given.

a: 0.9

b: 3.4

c: -2.4

The sign of the coefficient of a determines the exposure of the parabola. Since a >  0, the parabola is open upwards and has a minimum value.

We can find the "x" of the vertex using the following expression.

x(v) = -b/2a = -3.4/(0.9)

x(v) = -3.77

We can find the "y" of the vertex by replacing this x in the equation

y(v) = 0.9(-3.77)² + 3.4(-3.77) -2.4

y(v)  = -2.42

The minimum value of the function is -3.77

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Given: The volume of helium balloon = 0.503 cubic feet

To Find: The volume of balloon in units of cubic centimeters1 cubic foot = 28.3168 litres

1 litre = 1000 cubic centimeters

So, 1 cubic foot = 28.3168 * 1000 = 28316.8 cubic centimeters

Therefore, the volume of the helium balloon in cubic centimeters would be:0.503 cubic foot = 0.503 * 28316.8 cubic centimeters= 14,221.80 cubic centimeters (approx). Therefore, the volume of the balloon in units of cubic centimeters is 14,221.80 cubic centimeters (approx).

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Answer:

1/2

Step-by-step explanation:

1/3 + 1/6 = 1/2

Answer:

The largest possible value of x is 2 + √8

Step-by-step explanation:

Given;

x² + y² = 4(x + y)

This is an equation of circle

x² + y² = 4x + 4y

x²- 4x + y² - 4y = 0

complete the square by taking half of coefficient of x and y, then add the squares to both sides;

x²- 4x + (-2)² + y² - 4y + (-2)² = (-2)² + (-2)²

factorize

(x - 2)² + (y - 2)² = √8

This circle has its center at  (2, 2)  with a radius of  √8

The largest x-value occurs at the right end of the circle = x value of the center plus the radius = 2 + √8

Answer:

\(\frac{7}{3}-\frac{2}{3}+\sqrt{3}-3\sqrt{3}=\frac{5}{3}-2\sqrt{3}\)    

Step-by-step explanation:

Given the expression

\(\frac{7}{3}\:-\:\frac{2}{3}\:+\:v^3\:-\:3v^3\)

solving the expression

\(\frac{7}{3}\:-\:\frac{2}{3}\:+\:\sqrt{3}-3\sqrt{3}\)

combine the fractions i.e \(\frac{7}{3}-\frac{2}{3}=\frac{5}{3}\)

\(\frac{7}{3}\:-\:\frac{2}{3}\:+\:\sqrt{3}-3\sqrt{3}=\frac{5}{3}+\sqrt{3}-3\sqrt{3}\)

add similar elements  i.e \(\sqrt{3}-3\sqrt{3}=-2\sqrt{3}\)

                                 \(=\frac{5}{3}-2\sqrt{3}\)      

Thus,

\(\frac{7}{3}-\frac{2}{3}+\sqrt{3}-3\sqrt{3}=\frac{5}{3}-2\sqrt{3}\)                        

Answer:

A is the answer

the test of the options are not the answer

Given |x - 2| <= 4, which of the following equation is C. x - 2 <= 4 && x - 2 >= -4.

The absolute value of (x - 2) represents the distance between x and 2 on the number line. The inequality |x - 2| <= 4 means that the distance between x and 2 is less than or equal to 4.

To solve for x, we can break it down into two inequalities:
1. x - 2 <= 4, which means x <= 6
2. -(x - 2) <= 4, which means -x + 2 <= 4, then -x <= 2, then x >= -2

Combining these two inequalities, we get:
x - 2 <= 4 && x - 2 >= -4

Therefore, the correct answer is C.

When solving an inequality involving absolute value, it's helpful to break it down into two separate inequalities and then combine them. In this case, we found that the correct answer is C.

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The area of the shaded shape is 60 \(m^{2}\).

This question uses the area formula for rectangles, which states that the area of a rectangle is equal to its length multiplied by its width.

The formula for the area of a rectangle is A = lw, where l is the length of the rectangle and w is the width of the rectangle

To work out the area of the shaded shape, we need to calculate the area of the rectangle (5m x 12m) and subtract the area of the smaller rectangle (8m x 9m).

The area of the rectangle = 5m x 12m = 60\(m^{2}\)

The area of the small rectangle = 8m x 9m = 72\(m^{2}\)

Therefore, the area of the shaded shape = 60\(m^{2}\) - 72\(m^{2}\) = -12\(m^{2}\)

The answer is 60\(m^{2}\).

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Answer:

Here we want to create a histogram of:

Number of houses Vs day.

First you need to create a rectangular coordinate axis.

In the x-axis you will divide the days as:

day 1, day2, day3 etc

in the y-axis you will measure the number of houses visited.

then, for the first day our height will be 12 units

for the second day, our height will be 28 units...

and so on.

Remember that for histograms you need to use columns.

Then, our histogram will look like:

Answer:

hope it helps you.........

Answer:

10/14 - 7/14 = 3/14 :D

Step-by-step explanation:

you have to find the common denominator, in this case its 14. then, whatever number you multiplied the denominator by, you have to multiply the numerator by. so, 5/7x2= 10/14, and 1/2x7 = 7/14, then its just 10-7 which equals 3

Answer:

You can also demonstrate a proof of the sum of interior angles of triangles and apply a formula, a + b + c = 180° a + b + c = 180 ° , where a , b , and c are the interior angles of the triangle.

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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Among any group of 20 people (where any two people are either friends or enemies), there are either four mutual friends or four mutual enemies.

Let's assume there is a group of 20 people. Choose a person, say person A. There are two Probablities: A has at least 10 friends, or A has at least 10 enemies. Without loss of generality, let's assume A has at least 10 friends.

Now consider the 10 friends of A. Either they are all friends with each other, or there are two among them who are enemies. In the first case, we have found a group of four mutual friends (A and the other three). In the second case, let's say B and C are enemies.

If B and C are both friends with A, then we have found a group of four mutual enemies (B, C, and the two friends of A who are enemies with each other).

If either B or C is not friends with A, then we have found a group of four people (A, B, C, and one of A's friends who is an enemy of B or C) who are either four mutual friends or four mutual enemies.

Hence, among any group of 20 people, there are either four mutual friends or four mutual enemies.

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There are 11 prime dates in it.

The prime numbers between 1 and 30 are 1, 2,3,5,7,11,13,17,19,23,29

Relative prime:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Hence There are 11 prime dates in the month of June.

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Answer: 10

Step-by-step explanation:

Since exactly 1 in every $n$ consecutive dates is divisible by $n$, the month with the fewest relatively prime days is the month with the greatest number of distinct small prime divisors. This reasoning gives us June ($6=2\cdot3$) and December ($12=2^2\cdot3$). December, however, has one more relatively prime day, namely December 31, than does June, which has only 30 days. Therefore, June has the fewest relatively prime days. To count how many relatively prime days June has, we must count the number of days that are divisible neither by 2 nor by 3. Out of its 30 days, $\frac{30}{2}=15$ are divisible by 2 and $\frac{30}{3}=10$ are divisible by 3. We are double counting the number of days that are divisible by 6, $\frac{30}{6}=5$ days. Thus, June has $30-(15+10-5)=30-20=\boxed{10}$ relatively prime days.

The numerical value of x and the length of side ST are 2 and 6 respectively.

An equilateral triangle is simply a triangle with all three sides having the same length.

Given that;

First, we determine the value of x.

Since all three sides are equal;

RS = TR

2x + 2 = 5x - 4

Solve for x

5x - 2x = 2 + 4

3x = 6

x = 6/3

x = 2

Now, for side ST.

ST = 3x

Plug in x=2

ST = 3( 2 )

ST = 6

Therefore, the value of x is 2 and side length of ST is 6.

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Professor Rodgers can select the group of 4 students in 11880 ways.

Here the professor has to select 4 students from a group of 12. hence we see that

to select the first student, the professor can do so in 12 ways.

To select the second student, the professor now has 11 students left. Hence he can do in 11 ways.

To select the third student, he is left with 10 students, hence the thirst student can be selected in 10 ways

The fourth student can be selected in 9 ways.

Hence, Professor can select the group in 12 X 11 X 10 X 9 ways

= 11880 ways.

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Answer:

One segment is 8.89 long and the other one is: 11.11 long

Step-by-step explanation:

Recall that the bisector of a triangle divides the opposite side it intersects into two segments that are proportional to the other two sides of the triangle.

In our case the bisector is generated on the angle opposite to the size 20 side (it is the smallest angle in the triangle since it is opposite to the smallest side). This bisector divides the side of length 20 into a segment of length x and a segment of length 20-x.

The proportionality indicated by the bisector theorem gives;

\(\frac{20-x}{x} =\frac{30}{24}\)

and we can solve for "x":

\(\frac{20-x}{x} =\frac{30}{24}\\24\,(20-x)=30\,x\\480-24\,x=30\,x\\480=54\,x\\x=480/54\\x\approx8.89\)

Then the other segment is:  20 - 8.89 = 11.11

To fcalculate the magnitude of the average force exerted on the ball by the club, we can use the equation:

F_av = Δp/Δt

where F_av is the average force, Δp is the change in momentum, and Δt is the time of contact.

Given:

Mass of the ball, m = 65.0 g = 0.065 kg

Time of contact, Δt = 0.00340 s

Final velocity of the ball, v_f = 56.0 m/s

Initial velocity of the ball, v_i = 0 (assuming the ball is initially at rest)

The change in momentum, Δp, can be calculated using the equation:

Δp = m * (v_f - v_i)

Substituting the given values:

Δp = 0.065 kg * (56.0 m/s - 0)

Now we can calculate the magnitude of the average force:

F_av = Δp/Δt

Substituting the values:

F_av = (0.065 kg * 56.0 m/s) / 0.00340 s

Calculating the result gives us:

F_av ≈ 1070 N

Therefore, the magnitude of the average force exerted on the ball by the club is approximately 1070 N.

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The probability of selecting a piece of pottery is 7/26, and when converted to a percentage and rounded to the nearest whole percent, it is approximately 27%.

An archaeologist uncovers 26 artifacts from a site. The types of artifacts are shown below. The horizontal axis represents tools, pottery, and coins. The vertical axis represents the number of artifacts and ranges from 0 to 16, in increments of 2. The number of artifacts of tools is 14. The number of artifacts of pottery is 7. The number of artifacts of coins is 5.

The total number of artifacts at the site = 26

Number of pottery artifacts = 7

Probability of selecting a piece of pottery = Number of pottery artifacts/Total number of artifacts

Probability of selecting a piece of pottery = 7/26

If we want to express this probability in a percentage, we can convert it by multiplying it by 100.

Thus,Probability of selecting a piece of pottery = 7/26 = 0.269 = 26.9% (rounded to the nearest whole percent)

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Answer:

The answer you are looking for is right here

Step-by-step explanation:

https://www.pinterest.com/pin/439734351089479667/

The number of minutes that she practices in 5 weeks will be 980 minutes.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Shandra rehearses the piano for 392 minutes in about fourteen days. Expecting she rehearses a similar sum consistently.

Let 'x' be the number of minutes that she practices in 5 weeks.

Then the number of minutes that she practices in 5 weeks will be given as,

x / 5 = 392 / 2

Simplify the equation, then we have

x / 5 = 392 / 2

x / 5 = 196

x = 980 minutes

The number of minutes that she practices in 5 weeks will be 980 minutes.

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The volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48 is 384.

In the given question, we have to find the volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48.

Cut by a plane at x = x(0) = constant, then z= 48-6x-8y while you are moving with y at x=x(0) constant

At this plane (x = x(0)), an element of area will be dA = z dy and an element of volume dV = dA dx

So , V = \(\int\int zdydx\)

v = \(\int_{0}^{8}\int_{0}^{(48-6x)/8}(48-6x-8y)dy.dx\)

v = \(\int_{0}^{8}[48y-6xy-4y^2]_{0}^{(48-6x)/8}dx\)

v = \(\int_{0}^{8}[48\times((48-6x)/8)-6x\times((48-6x)/8)-4((48-6x)/8)^2-0]dx\)

v = \(\int_{0}^{8}[9/4(x-8)^2]dx\)

Let u = x-8

v = \(9/4\int_{0}^{8}(u)^2\)

v = \(9/4\left[\frac{(u)^3}{3}\right]^{8}_{0}\)

v = \(3/4[(x-8)^2]_{0}^{8}\)

v = 3/4[(8-8)^3+(0-8)^3]

v = 3/4[0-(-512)]

v = 384

The volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48 is 384.

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Answer: Two dice

Step-by-step explanation:

For the two dice, there are 5 possible: (6, 2);(5, 3);(4, 4);(3, 5);(2, 6)

So two dice, the probability is 5/36 = 30/216

For three dice, the number of favorable cases is 21

The probability is 21/216

So the two dice are more likely

Answer:

the rules regarding the vertex of a quadratic function are:

the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.

Hope This Helps!!!

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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a) Since the new score is less than the average score, it will decrease the average.

a) Since the new score is less than the average score, it will decrease the average.

b) Sum of 27 scores = 27*79

Hence,

New average = (79*27 + 63)/28 = 78.43

c) Since the variability would increase in the overall data, the standard deviation increases.

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A p-value is a measure of the strength of evidence against the null hypothesis in a statistical hypothesis test. It represents the probability of obtaining the observed data or more extreme results, assuming that the null hypothesis is true.

In general, a smaller p-value provides stronger evidence against the null hypothesis. Therefore, in the given scenario, a p-value of 0.02 would provide stronger evidence against the null hypothesis compared to a p-value of 0.03.

A p-value of 0.02 indicates that there is a 2% chance of obtaining the observed data or more extreme results if the null hypothesis is true. This suggests that the observed data is relatively unlikely under the assumption of the null hypothesis, providing stronger evidence against it.

On the other hand, a p-value of 0.03 indicates that there is a 3% chance of obtaining the observed data or more extreme results if the null hypothesis is true. Although this still suggests that the observed data is unlikely under the null hypothesis, it is not as strong evidence as a p-value of 0.02.

In summary, a lower p-value indicates that the observed data is less likely to occur under the null hypothesis, providing stronger evidence against it. Therefore, a p-value of 0.02 would provide stronger evidence against the null hypothesis compared to a p-value of 0.03.

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Answer:

C ; 20 weeks

Step-by-step explanation:

\(y=0.25x+18\\23=0.25x+18\\23-18=0.25x+18-18\\5=0.25x\\\frac{5}{0.25}=\frac{0.25x}{0.25} \\20=x\)

Answer:

66.75

Step-by-step explanation:

Your answer will be:

(9.5-(9.5*.25))*6 = 42.75

(8-(8*.25))*4 = 24

Add 42.75 + 24 and that gives you the total

66.75

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

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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

We have a polynomial \(x^4-x^3+6x^2-13x+7=0\) which is a degree- 4 polynomial also known as a Bi-Quadratic polynomial. The roots of the polynomial \(x^4-x^3+6x^2-13x+7=0\) are\(x=1 , x=1, x= \frac{-1+3\sqrt{3}\iota }{2}, x= \frac{-1-3\sqrt{3}\iota }{2}\)

Given Polynomial:- \(x^4-x^3+6x^2-13x+7=0\)

Using the method of hit and trial we assume x=1

On putting the value of \(x=1\) in the equation we obtain the resultant 0.

So, \((x-1)\) is a root of the polynomial \(x^4-x^3+6x^2-13x+7=0\)

By factorizing the polynomial we get:

\(x^4-x^3+6x^2-13x+7=0 = (x-1)(x^3+6x-7)\)

\(x^4-x^3+6x^2-13x+7=0 = (x-1)(x-1)(x^2+x+7)\)

We know that \((x^2+x+7)\) is a Quadratic Equation.

The formula for the roots of the Quadratic Equation is:

\(x=(\frac{-b\pm\sqrt{b^2-4ac} }{2a} )\)

Considering the equation \((x^2+x+7)\) here \(a=1\), \(b=1\), and \(c=7\)

Putting the values in the formula we obtain:

\(x=\frac{-1\pm\sqrt{1^2-4\cdot1\cdot7} }{2\cdot1}\)

\(x=\frac{-1\pm\sqrt{1-28} }{2}\)

\(x=\frac{-1\pm\sqrt{-27} }{2}\)

\(x= \frac{-1+3\sqrt{3}\iota }{2}, x= \frac{-1-3\sqrt{3}\iota }{2}\)

Therefore, the roots of the 4-degree polynomial \(x^4-x^3+6x^2-13x+7=0\) are  \(x=1 , x=1, x= \frac{-1+3\sqrt{3}\iota }{2}, x= \frac{-1-3\sqrt{3}\iota }{2}\)

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The complete question is:-

Find the roots of the polynomial x⁴ - x³ + 6x² - 13x + 7 = 0.