A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 169 cm and a standard deviation of 2.2 cm. For shipment, 10 steel rods are bundled together.

Answer the following rounding to three decimals where appropriate.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm.

P(M > 168.58) = ???

well, let's find out how much she made on each week

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]

It will take about 711.12 minutes or approximately 11.85 hours to test all 400 units.

To find out how long it will take to test 400 units, we need to use the information given in the problem. We know that the quality expert can test 18 units in 32 minutes. We can use this information to find out how long it will take to test one unit.

First, we need to find out how many units can be tested in one minute:

18 units / 32 minutes = 0.5625 units per minute

This means that the quality expert can test 0.5625 units per minute. To find out how long it will take to test one unit, we can divide 1 by 0.5625:

1 / 0.5625 = 1.7778 minutes per unit

So it takes about 1.7778 minutes to test one unit. To find out how long it will take to test 400 units, we can multiply this value by 400:

1.7778 minutes per unit * 400 units = 711.12 minutes

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The initial value (a) of the exponential function f(x) = 4ˣ is 1.

The standard form of an exponential equation is:

y = abˣ

where a is the initial value and b is the multiplication factor.

If b > 1, it is a growth function and if b < 1, it is a decay function.

Given the exponential function:

f(x) = 4ˣ

The initial value (a) = 1 and the multiplication factor (b) = 4.

The graph of the exponential function f(x) = 4ˣ is attached below.

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Answer:

[tex]2x=20\sqrt{10}\; \textsf{ft} \approx 63.25\; \sf ft[/tex]

[tex]6x=60\sqrt{10}\; \textsf{ft} \approx 189.74\; \sf ft[/tex]

Step-by-step explanation:

Assuming the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the value of x and then find the measurers of the side lengths.

[tex]\large{\boxed{a^2+b^2=c^2}[/tex]

where:

From inspection of the given diagram:

Substitute these values into the formula and solve for x.

[tex]\begin{aligned} (2x)^2+(6x)^2&=200^2\\2^2\cdot x^2+6^2\cdot x^2&=40000\\4x^2+36x^2&=40000\\40x^2&=40000\\x^2&=1000\\x&=\sqrt{1000}\\x&=\sqrt{100 \cdot 10}\\x&=\sqrt{100}{\sqrt{10}\\x&=10\sqrt{10}\end{aligned}[/tex]

Substitute the found value of x into the expression for each side length.

[tex]2x=2 \cdot 10\sqrt{10}=20\sqrt{10}[/tex]

[tex]6x=6\cdot 10\sqrt{10}=60\sqrt{10}[/tex]

Therefore, the exact side lengths of the given right triangle are:

[tex]20\sqrt{10}\; \textsf{ft}, \;\;60\sqrt{10}\; \textsf{ft}, \;\; 200\; \textsf{ft}[/tex]

The side lengths to the nearest hundredth are:

From the given triangle, x has a value of 35°.

As a result, one of the triangle's sides has been stretched to create an exterior angle of 125° outside angle.

Angles that are always located near one another, sharing a similar vertex and common side but not overlapping, are said to be adjacent angles.

According to the above figure, the tringle's exterior angle is 125°, and y is an adjacent angle to that.

Now, 125°+ y =180°

y = 180°-125°

y = 55°

As a result, the supplied triangle's value for y is 55°.

The sum of the triangle law,

55°+ 90° + x  = 180°

x = 35°

Therefore the value of x = 35°

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Step-by-step explanation:

| Equation | Solution |

| 6+x=15 | x = 9 |

| 9x = 18 | x = 2 |

The table would look like:

| Equation | Solution |

| 6+x=15 | X |

| 9x = 18 | X |

The subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

From the question, we have the following parameters that can be used in our computation:

O = (3, 2)

A = (-7, 5)

B = (-7, 2)

The distance between (or length of) the coordinates is calculated as

Length = √[(x2 - x1)² + (y2 - y1)²]

Using the above as a guide, we have the following:

OB = √[(3 -- 7)² + (2 - 2)²]

OB = √[(3 -- 7)² + 0²]

OB = √[(3 -- 7)²]

OB = 3 -- 7

AB = √[(-7 -- 7)² + (5 - 2)²]

AB = √[0² + (5 - 2)²]

AB = √[(5 - 2)²]

AB = 5 - 2

Hence, the subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

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The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

The given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

Now,

From the given information,

The operation we are to carry out is:

Add -4(row 1) to row 3

This means we are to multiply the first row by -4. Then, we will add the results to the corresponding elements on the third row (row)

Multiplying by -4

-4 × [ 1     2    1   | -5

     -4   -8   -4  | 20

Now, we will add the result from the multiplication to the corresponding elements in row 3

Adding the results to corresponding elements in row 3

   4    -1     6  |  -8

+  -4   -8   -4  | 20

------------------------

   0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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In a case wehereby you have $12,000 to invest and want to keep your money invested for 8 years the investment option that will earn you the most money is c.4.175% compounded annually

When an investment is compounded annually, it means that the interest earned on the investment is added to the principal amount once a year, and the interest is then calculated on the new total amount for the next year.

For example, if you invest $12,000 at an annual interest rate of 8%, compounded annually, at the end of the first year you will earn the interest of ( $12,000 x 8%) = $960

Then new total amount after one year will be $12,000 + $960 = $12 960 ,

This process will continue for each year of the investment and the  formula to calculate the future value (FV) of an investment compounded annually is: FV = P(1 + r)^n

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complete quesation:

You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.

a.

3.99% compounded monthly

b.

4% compounded quarterly

c.

4.175% compounded annually

d.

4.2% simple interest

It will take Lisa and Felipe approximately 4.95 hours to fill the order by working together.

To solve this problem, we can use the formula:

1/T = 1/T₁ + 1/T₂

where T is the time taken to complete the job when both Lisa and Felipe work together, T₁ is the time taken by Lisa to complete the job, and T₂ is the time taken by Felipe to complete the job.

Substituting the given values into the formula, we get:

1/T = 1/9 + 1/11

Simplifying the right-hand side of the equation, we get:

1/T = (11 + 9)/(9 x 11)

1/T = 20/99

Multiplying both sides by 99, we get:

T = 99/20

Therefore, working together, Lisa and Felipe can complete the job in 4.95 hours, or approximately 4 hours and 57 minutes.

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The force applied to the input piston is  136.25 N.

This problem can be solved using the principle of hydraulic systems, which states that pressure in a confined fluid is transmitted equally in all directions.

Thus, we can equate  the pressure on the input piston to the pressure on the output piston, and solve for the force on the input piston. That is:

P₁ = P₂

F₁/A₁ = F₂/A₂    (Pressure = Force/Area)

F₂ = 2000 * 9.81 = 19620 N   (F = mg)

A₁ = π * r₁² = π * 5² = 25π cm²

A₂  = π * r₂ ² = π * 60² = 3600π cm²

F₁ = F₂/A₂ * A₁

F₁ = (19620/3600π) * 25π

F₁ = 136.25 N

Therefore, the force applied to the input piston is  136.25 N.

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Question in English

A machine shop lift has input and output pistons of 5 cm and 60 cm radius respectively. With this device, a 2000 kg car is kept lifted. What is the force applied to the intake piston?

Answer: 70, 6

Step-by-step explanation:

(a)  For <F  that is the same as <D.  The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same

All of the angles are = 180   if you subtract <E, you are left with 140 to be split between <F and <D

<F= 70

(b) all of the sides are the same because all the angles are the same

so AB=6

Answer:ina can row 6mph in still water and 2 mph in current

Step-by-step explanation:

The year in which  the number of vehicle miles of travel in City A was 140 billion is 9.79 years. Thus, the linear model suggests that the number of vehicle miles traveled in city A was 140 billion in the 10th year approximately.

The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models.

To derive the number of year,

140 = 2.86t + 112

Subtracting 112 from both sides gives:

28 = 2.86t

Dividing both sides by 2.86 gives:

t ≈ 9.79 years

See attached graph.

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Answer:

x = 3, -5/2

Step-by-step explanation:

First, you move the 15 onto the left of the equation by subtracting it from both sides.

Second, you plug your info into the quadratic equation.  (1 +- sqrt(1+4*15*2))/4

The perimeter of rectangle RSTU is 21 cm.

The area of the rectangle RSTU is 27 cm².

A rectangle is a quadrilateral that has opposite side equal to each other and opposite side parallel to each other.

Therefore, let's find the perimeter of the rectangle RSTU and the area of RSTU.

Hence,

Let's find the width of the rectangle MNPQ

14 = 2(4 + w)

14 = 8 + 2w

14 - 8 = 2w

2w = 6

w = 6 / 2

w = 3 cm

Therefore, using similar ratio,

4 / 6 = 3 / RU

cross multiply

4RU = 18

RU = 18 / 4

RU = 4.5 cm

Therefore,

Perimeter of the rectangle RSTU = 2(6 + 4.5)

Perimeter of the rectangle RSTU = 2(10.5)

Perimeter of the rectangle RSTU =21 cm

Area of the rectangle RSTU = 4.5 × 6

Area of the rectangle RSTU = 27 cm²

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Answer:

Step 1:

Let x = number of years

Let y = Value of the laptop after x years

Step 2:

Write an equation that expresses the value of the laptop after x years y = 0.8((4700)x)

Step 3:

Set the equation equal to 1000 and solve for x

1000 = 0.8((4700)x)

1 = 0.8(4700)x

1/0.8 = 4700x

1.25 = 4700x

x = (1.25/4700)

Answer: The laptop will be worth $1000 or less after 0.0026608 years.

Answer:

1 year

Step-by-step explanation:

4700 x .8= 3760

4700 - 3760 = 940$

In 1 year the laptop will be $940

Step-by-step explanation:

Here is a graph from Desmos....you should be able to see where the function is > 0

The equation of the line passing through the point (-3,-4) and parallel to the x-axis is y = -4.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept

Given that; the line passing through the point (-3,-4) and parallel to the x-axis.

A line that is parallel to the x-axis has a slope of 0, because the y-coordinate of any point on the line does not change as the x-coordinate varies.

Hence;

The equation of the line passing through the point (-3,-4) and parallel to the x-axis can be written in the form y = b, where b is a constant.

To determine the value of b, we substitute the coordinates of the given point (-3,-4) into the equation y = b:

-4 = b

Note that: y = b, where b is a constant.

y = -4

Therefore, the equation of the line y = -4.

Option C) y = -4 is the correct answer.

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Answer:

n=7

Step-by-step explanation:

[tex] \frac{n}{4} \times 4 = 7 \\ \frac{4n}{4} = 7 \\ 4 \times \frac{4n}{4} = 7 \times 4 \\ 4n = 28 \\ \frac{4n}{4} = \frac{28}{4} \\ n = 7 [/tex]

Answer:

x = 3,

y = -2

Step-by-step explanation:

Let's write the given equations into a system:

{2x - y = 8,

{3x + 2y = 5;

Let's make y the subject from the 1st equation:

-y = 8 - 2x / × (-1)

y = 2x - 8

Replace y in the 2nd equation with its value from the 1st one:

3x + 2(2x - 8) = 5

Expand the brackets:

3x + 4x - 16 = 5

Collect like-terms:

7x = 5 + 16

7x = 21 / : 7

x = 3

y = 2 × 3 - 8 = -2

The probability that the marble choose is not green is 9/10

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.

Probability is expressed as;

probability = sample space/total outcome

total number of marble = 8+6+2+4 = 20marbles

Probability that it is green = 2/20 = 1/10

therefore probability that Is not green = 1-1/10

= 10-1)/10

= 9/10

therefore the probability that a marble chosen is not green is 9/10.

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Answer:

53yd

Step-by-step explanation:

SA1 = 2(4×2)

= 2×8

= 16

SA2 = 2(4×3)

= 2×12

= 24

SA3 = 2(3×2)

= 2×6

= 12

TOTAL SA

16+24+13

= 53

The height of the person on the ferris wheel can be modeled by the equation:

h = 20sin(π/4*t) + 21

where h is the height in meters above the ground, t is the time in minutes, and 21 meters is added to account for the height of the platform.

needs more explanation

(1) The result of the row operation R₂ ↔ R₃ is [ -5   1    0    8]

                                                                            [  8  8    -7   5 ]

                                                                            [ 2   2     6   -5]

(2) The result of the row operation  3R₁ ↔ R₁ is  [24  - 27   -21   - 18]

                                                                                [8       9      -4      -5]

                                                                                 [2       2       -7     -8]

The result of the row operation in the matrix is calculated as follows;

R₂ ↔ R₃, implies changing row 2 and row, and the result would be;

[ -5   1    0    8]

[  8  8    -7   5 ]

[ 2   2     6   -5]

The result of obtained from 3R₁;

3R₁ = [24  - 27   -21   - 18]

3R₁ ↔ R₁ is determined as; (the row interchange)

[24  - 27   -21   - 18]

[8       9      -4      -5]

[2       2       -7     -8]

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Answer: To factorize x² + 18x, we can first find the greatest common factor (GCF) of the two terms, which is x:

x(x + 18)

This is the fully factorized form of x² + 18x.

Answer:

-----------------------

Given equation to solve:

The result of the first step:

The second step:

And its result is:

The matching choice is C.

Answer:

  A.  P

Step-by-step explanation:

You want to identify the point that represents a striking deviation in the given box plot.

The interquartile range for this box plot is the difference between the upper and lower quartiles:

  29 -26 = 3

The "fence" that is 1.5 times the IQR below the lower quartile is ...

  26 -3·1.5 = 21.5

Point P lies beyond this fence, so is considered an outlier in the data set.

Point P represents a striking deviation, choice A.

<95141404393>

The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.

The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.

plot the y-get at (0,1),

x = - b/2a

To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is

f(3/4) = 1/8.

Plot the vertex at (3/4, 1/8).

Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.

To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.

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