a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 205.8-cm and a standard deviation of 0.5-cm. for shipment, 22 steel rods are bundled together. find the probability that the average length of a randomly selected bundle of steel rods is greater than 206.1-cm. p(m > 206.1-cm)

Answer:

There are several measurements that a professional engineer would need to make in order to design and construct a bridge over a stream for a farmer's sheep to graze. These measurements may include:

Width and depth of the stream: The engineer will need to determine the width and depth of the stream in order to determine the size and type of bridge that is needed.

Soil composition and stability: The engineer will need to assess the soil composition and stability of the area surrounding the stream in order to determine the foundation and support structure needed for the bridge.

Water flow: The engineer will need to measure the water flow in the stream in order to determine the load-bearing capacity of the bridge and to ensure that it is able to withstand the forces of the water.

Distance between the two banks: The engineer will need to measure the distance between the two banks of the stream in order to determine the length of the bridge and ensure that it is long enough to span the stream.

Height of the banks: The engineer will need to measure the height of the banks of the stream in order to determine the height of the bridge and ensure that it is tall enough to allow the sheep to pass under it.

The equation of the Parabola is (y - 6 )² = 28 (x + 1)  of the given focus and directrix.

Given directrix x = -8

we know that    x = h - a = -8

              h -a =  -8  ...(i)

Given Focus  = ( 6,2)

we know that the Focus of the Parabola

        ( h + a , k ) = (6,2)

  comparing  h + a = 6 ...(ii)

                 k = 2

solving (i) and (ii) and adding

  h - a + h+ a = -8 +6

          2 h = -2

             h = -1

  Put h = 6 in equation (i)

 ⇒     h - a = -8

 ⇒   -1 + 8 = a

 ⇒      a = 7

The equation of the Parabola ( h,k) = (-1 , 7)

( y - k )² = 4 a ( x - h )

(y - 7 )² = 4 (7) (x -(-1))

(y - 6 )² = 28 (x + 1)

Hence, the equation of the Parabola is (y - 6 )² = 28 (x + 1)  of the given focus and directrix.

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Answer:

0.4 x 10^-1

Step-by-step explanation:

4 x 10^0

=> 4

=> 0.4 x 10^-1

Although part of your question is missing, you might be referring to this full question: What are the vertex and range of y = |2x + 6| + 2?

(0, 2); 2 < y < ∞

(0, 2); −∞ ≤ y < ∞

(−3, 2); 2 < y < ∞

(−3, 2); −∞ ≤ y < ∞

The vertex of the function is (–3, 2) and the range of the function is 2 < y < ∞.

The given modulus function:

y = |2x + 6| + 2

Now, we get two equations out of the absolute value function:

y = 2x + 6 + 2

y = 2x + 8

and

y = –2x – 6 + 2

y = –2x – 4

The vertex of the function will be at a point where these two equations are equal. So, we can calculate the vertex as follows:

2x + 8 = –2x – 4

2x + 2x = –4 – 8

4x = –12

x = –3

If x = –3, then y = 2(–3) + 8 = –6 + 8 = 2

Thus, the vertex of the function is (–3, 2).

Now, the values that y can take will range from 2 to infinity as y cannot take values below the vertex.

Thus, the range of the function is 2 < y < ∞.

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Answer: Least 1/2

Step-by-step explanation: Middle 2/3

Greatest 5/6

Answer:

Least 1/2

Middle 2/3

Greatest 5/6

Step-by-step explanation:

First,5 divided by 6,is 0.83(in to 1 decimal point)

Then 2 divided by 3 is 0.67(in to 1 decimal point)

Last 1 divided by 2 is 0.5(in to 1 decimal point)

So is 5/6 is greatest and 2/3 is in the middle and the least is 1/2.

The number of students who like dressmaking and catering only is 7.

The number of students who did not choose any of the 3 vocations is 12.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

Total students = 40

The Venn diagram is given below.

The number of students who like dressmaking and catering only.

= 7

Total number of students who like at least one vocation.

= 28

The number of students who did not choose any vocation.

= 40 - 28

= 12

Thus,

7 students like dressmaking and catering only.

12 students did not choose any vocation.

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When a spring of stiffness K = 120N/m supporting a smooth cylinder of mass 6kg is subjected to a force of 60N, the velocity it moves downward when compressed a distance of 0.2m is 1.79m/s.

Therefore, the answer is 1.79m/s.

The compression of spring, say x₀ at equilibrium position can be determined by

F = Kx₀

mg = Kx₀

6 × 9.81 = 120 × x₀

Therefore x₀ = 0.4905m

When force F = 60N is applied the spring is compressed more and let new compression of spring be x₁. Then when string compresses additional s distance

x₁ = x₀ + s

Then spring force, F₁ = Kx₁

F₁ = 120 × (0.4905 + s)

F₁ = 58.86 + 120s

Let the cylinder accelerates downward at a m/s², then

60N + mg = ma + F₁

60 + 6×9.81 = 6a + 58.86 + 120s

a = (10 - 20s) m/s²

dv/dt = 10 - 20s

We know that ds/dt = v, that is 1/dt = v/ds

Therefore, vdv/ds = 10 - 20s

vdv = (10 - 20s)ds

Integrating both sides

v²/2 = 10s - 10s²

v = √(20s - 20s²)

At s = 0.2m,

v = √(20×0.2 - 20×0.2²)

v = 1.79m/s

--The question is incomplete, answering to the question below--

"The 6kg smooth cylinder is supported by the spring having a stiffness of kAB = 120 N/m. Determine the velocity of the cylinder when it moves downward s = .2m from its equilibrium position, which is caused by the application of the force F = 60 N. (The 60 N force is not present in the equilibrium position.)"

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The value of TC = 5.9

According to the given figure of the triangle ABC, (refer to the attached figure)

The length of perpendicular bisector AC is = m

The length of perpendicular bisector BC is = n

The point at which line m and line n are intersecting = T

Given the value of TA = 5.9

According to the corner theorem.

AC = CF

So, ΔTFA ≅ ΔTFC

⇒ TA = TC = 5.9

Therefore, The value of TC = 5.9

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Answer:

putting more than question is against app rules but alr

Part A: The value of each of the houses after a fixed number of years can be described by a linear function. This is because the value of each house increases at a constant rate, with the same amount added each year.

Part B: The function for House 1 could be written as f(x) = 294,580 + 8,937.6x, and the function for House 2 could be written as f(x) = 295,000 + 9,000x.

Part C: After 25 years, the value of House 1 will be approximately $750,834.40, and the value of House 2 will be approximately $753,000. The difference in value between the two houses after 25 years will be approximately $2,165.60, which is not a significant difference in the overall value of the houses. Therefore, either house would be a good choice for Belinda to purchase.

The value of the old fare to the nearest cent will be $423.08. Then the correct option is B.

Any product's quantity is presented as if it were a percentage of one hundred. The proportion can be written as 1/4 of 100. One hundred percent is symbolized by the symbol %. The sign for it is the letter "%".

The cost of an aircraft ticket from New Orleans to Boston expanded to $550. This is a 30% expansion.

Let 'x' be the old fare. Then the equation is given as,

(1 + 0.30) x = $550

Simplify the equation, then we have

(1 + 0.30) x = $550

1.30 x = $550

x = $550 / 1.30

x = $423.08

The worth of the old admission to the closest penny will be $423.08. Then the right choice is B.

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The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder [tex]\frac{x^2}{25} +\frac{y^2}{9}[/tex] is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

[tex]\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)[/tex]

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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The number of years that the deposit was held for is 3 years.

From the information, Mr. Johnson deposited $2000 in an account that earns simple interest at an annual interest rate of 6%. and he received $360 as interest at the end of the tenure.

It should be noted that simple interest is Illustrated as:

I = PRT

Therefore, T = Interest / Principal × Rate

Time = 360 / (2000 × 6%)

Time = 360 / 120

Time = 3 years

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The approximate probability that at least 45 of 50 patients can be cured with the drug is 0.788.

To find the approximate probability that at least 45 of 50 patients can be cured with the drug, we can use the binomial formula. The binomial formula allows us to calculate the probability of a certain number of success out of a set of trials given a certain probability of success for each trial. In this case, we have a probability of success of 0.9 and 50 trials. Therefore, the probability of at least 45 of the 50 patients being cured with the drug is 0.788. This can be calculated using the binomial formula or a binomial probability calculator.

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[tex]-4w+ 2 = 14[/tex]

Subtract 2 from both sides:

[tex]-4w+2-2=14-2[/tex]

[tex]-4w=12[/tex]

Divide both sides by -4:

[tex]\dfrac{-4w}{-4} =\dfrac{12}{-4}[/tex]

[tex]= \fbox{w = -3}[/tex]

Answer:

w = -3

Step-by-step explanation:

-4w + 2 = 14

-4w + 2 - 2 = 14 - 2 (Subtract 2 from both sides)

-4w = 12

-4w/-4 = 12/-4 (Divide -4 from both sides)

w = -3

Answer:

x = 1          y = 0

Step-by-step explanation:

-8x + y = -8

6x - y = 6

y have the same coefficient but one is negative and the other is positive therefore we add both the equations

we get:

-2x = -2

divide both sides by -2

x = 1

now as we have the value of x we can input this into any one of the starting equations

-8x + y =-8

-8(1) +y = -8

-8 + y = -8

add 8 to both sides

y = 0

Answer:

(1, 0 )

Step-by-step explanation:

- 8x + y = - 8 → (1)

6x - y = 6 → (2)

adding (1) and (2) term by term will eliminate y

- 2x + 0 = - 2

- 2x = - 2 ( divide both sides by - 2 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

- 8(1) + y = - 8

- 8 + y = - 8 ( add 8 to both sides )

y = 0

solution is (1, 0 )

Answer: The distance between the two parallel lines is 11/12.

Step-by-step explanation:

The distance between two parallel lines can be found by calculating the difference between the y-intercepts of the two lines. In this case, the y-intercept of the first line is (-1/4,0), and the y-intercept of the second line is (-7/6,0). The difference between these y-intercepts is (-1/4 - (-7/6)) = 11/12. Therefore, the distance between the two parallel lines is 11/12.

i didn't learn it.. so im not sure.. but i thimk 3

Answer:

2.64 square meters.

Step-by-step explanation:

To find the surface area of a cuboid, you need to find the area of each of the six faces and add them together. A wooden cuboid with an open flame base that has a square surface with 1.2 meter sides and a height of 0.25 meters would have a surface area of 1.2 * 1.2 + 4 * (1.2 * 0.25) = 1.44 + 1.2 = 2.64 square meters. This is because the base of the cuboid has an area of 1.2 * 1.2 = 1.44 square meters, and each of the four sides has an area of 1.2 * 0.25 = 0.3 square meters. The total surface area of the cuboid is therefore the sum of these areas: 1.44 + 4 * 0.3 = 2.64 square meters.

Answer: 50%

Step-by-step explanation:

Take 2.62 divided by 5.24, then times 100 = 50%

Then take 100% - 50% = 50%

The percentage discount is 50%

Yes, the starting position of these players form a perpendicular line.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Using Trigonometry

sin [tex]\theta[/tex] = 33.33/100

sin [tex]\theta[/tex] = 0.3333

[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)

[tex]\theta[/tex] = 19.469

cos 19.469 = B/ 100

0.9428 = B/ 100

B= 94.28

tan  [tex]\theta[/tex] = P/B

tan  [tex]\theta[/tex] = 94.28/ 33.33

[tex]\theta[/tex] = 70.5

Using Angle Sum property

< 3= 180 - (70.5 + 19.5)

<3 = 180 - 90

<3 = 90

Hence, they form perpendicular line.

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In a dice, there is a six side

Probability of occurring a score = 1/18

                                           = 1*2/18*2

                                               = 2/36

                                        =   preferred outcome/ Total outcome

Only 5 is a number that has occurred twice

The score that has a probability of occurring of 1/18 is 5.

The two dice having different values 30/36 = 5/6 (because the probability of the two dice having equal values is 6/36 = 1/6.)

The probability of the second dice being less than the first dice is the same as the probability of the first dice is less than the second dice: (5/6) / 2 = 5/12.

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The given statement is true for tabulation method representing the variable different categories and summarize it in tabulation method makes the calculation simple.

As given in the question,

Therefore, the given statement of representing the variable different categories and summarize it in tabulation method makes the calculation simple is a true statement.

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Answer:

3.11(0) = 0

Step-by-step explanation:

D. 3.11(0) = 0 is an example of the identity property of 1. The identity property of 1 states that any number multiplied by 1 is equal to itself. In this case, 3.11 is multiplied by 0, which is equal to 0.

Step-by-step explanation:

photo is not clear post again.

Answer:

18

Step-by-step explanation:

this seems to be an equilateral triangle so all sides are equal

5r+8=9r

-5r.   -5r

8=4r

/4 /4

2=r

now fill it in

5(2)+8

10+8

18

hopes this helps

18 inches is not a possible length for the third side of a triangle

What is the triangle inequality theorem?

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.

By triangle inequality theorem:

This theorem states that the sum of any two sides of a triangle must be greater than the third side.

As per the statement:

A triangle has two sides of lengths 8 inches and 10 inches.

Let the third side be x.

The Sum of the two sides is:

8 + 10 = 18

By triangle inequality theorem:

18 > x

or

x < 18

⇒ the length of the third side must be less than 18

From the given options:

Length of third sides 12, 16, and 17 which are less than 18.

the value which could the length of the third side be are: 12, 16, and 17.

Hence, 18 inches is not a possible length for the third side of a triangle

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π/16 is the area enclosed by the curve r= sin(4θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = [tex]\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta[/tex]

where a and b is the boundary at which r=0

so after equation r=0

sin(4θ) =0

=> sin(4θ) =0

=> 4θ = 0,π

=> θ = 0, π/4

so a=0 , b= π/4

now  

  A =  [tex]\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta[/tex]   ------(i)

so   [tex]r^2[/tex] = (sin(4θ))^2

=>   [tex]sin^2[/tex]( 4θ )

ans we know that

cos(2α) = 1 -  [tex]2sin^2[/tex]2 α

so     [tex]sin^2[/tex]= (1- cos(8θ) )/2

putting the value of r in the equation (i) we get :-

A = [tex]\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta[/tex]

=> 1/4*  [tex]\int\limits^b_a {(1-cos8\theta) } \, d\theta[/tex]

here a=0 and b=π/4

after putting the value and solving the integral

A = π/16

so A is the area enclosed by r=sin(4θ) is π/16

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The length of the wall in her drawing is given as follows:

5.6 inches.

A scaling measurement represents the proportion of a total dimension, as it is the ratio between the length of the drawing with the actual length of the object.

On her drawing a 10-foot wall is 8 inches, hence the scale measurement for this problem is given as follows:

8 inches/10 feet = 0.8 inches per feet.

The scale means that each feet of an actual object is represented by a length of 0.8 inches on the drawing.

Audrey wants to add a 7 foot wall to the drawing, meaning that the length of the drawing is given as follows:

7 x 0.8 = 5.6 inches.

(applying the proportion found from the scale measurement).

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