You have five identical pieces of equipment. There is a 1 in 10 chance that each piece will fail in a year. What is the likelihood that NONE of the pieces fail during a year?

Answers

Answer 1

Assuming failures are independent (not due to design flaw), the probability of no failures is
.. (1 -0.1)^5 = 0.59049

Answer 2

The probability that none of the five identical pieces of equipment will fail during a year is approximately 59.049%, calculated using the statistical independence of each piece's probability of not failing, which is 0.9, raised to the power of 5.

The question is asking for the probability that none of the five pieces of equipment fails within a year when there is a 1 in 10 chance of failure for each piece of equipment. To calculate this, we use the principle of statistical independence. If the chance that one piece of equipment does not fail is 9 in 10 (or 0.9), then the probability that all five do not fail is 0.9 raised to the power of 5.

Mathematically, this is calculated as:

[tex](0.9)^5[/tex]= 0.9 * 0.9 * 0.9 * 0.9 * 0.9

Performing the multiplication, the probability that none of the five pieces fail during a year is approximately 0.59049.

In conclusion, there is a 59.049% chance that none of the identical pieces of equipment will fail during a year, assuming that the failures are statistically independent events.

Related Questions

13) Suppose a coffee cup has a diameter of 8 cm and a height of 9 cm. What is the volume of the cup? (to nearest whole number)

Answers

A coffee cup is in e shape of cylinder
Radius is 4 cm (half of diameter)
Height = 9 cm
Volume of cylinder = pi x r^2 x h
The answer is 452.16 or can be rounded to 452 cubic cm

Answer:

[tex]452\ cm^{3}[/tex]

Step-by-step explanation:

we know that

the volume of a cylinder (coffe cup) is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=8/2=4\ cm[/tex] -----> the radius is half the diameter

[tex]h=9\ cm[/tex]

substitute

[tex]V=\pi (4^{2})(9)=452.4\ cm^{3}[/tex]

Round to the nearest whole number

[tex]452.4\ cm^{3}=452\ cm^{3}[/tex]

Marie earns $96 in interest each year on an investment what is the rate of simple interest if her principal was $800

Answers

[tex]\bf ~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$96\\ P=\textit{original amount deposited}\to& \$800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to &\stackrel{each~year}{1} \end{cases} \\\\\\ 96=800(r)(1)\implies \cfrac{96}{800}=r \\\\\\ 0.12=r\implies r\%=100\cdot 0.12\implies r=\stackrel{\%}{12}[/tex]

The rate of simple interest that Marie earns on her $800 investment is 12% per year, calculated by dividing the annual interest earned ($96) by the principal amount ($800).

To find the rate of simple interest, we can use the formula Interest = Principal * rate * time. Given that Marie earns $96 in interest each year on an investment and her principal was $800, we can rearrange the formula to solve for the rate.

The formula for simple interest is:

Interest = Principal * rate * time

Assuming the interest earned is for one year, we have:

$96 = $800 * rate * 1 year

To find the rate, we divide both sides by $800:

rate = $96 / $800

rate = 0.12

Converting into a percentage, the simple interest rate is 12% per year.

A ladder is leaning against the side of a building. The building and the ground form a right angle. How high on the building will the ladder touch if the ladder is 10 ft long and the base of the ladder is 6 ft from the base of the building?

Answers

The given question describes a right triangle with the hypotenuse as 10 ft and one of the legs as 6 ft.

We can make use of Pythagoras theorem to evaluate the length of the other side.

We know that by Pythagoras theorem, the square root of the sum of the squares of the legs of a right triangle gives the hypotenuse. Let the length of the required leg be x, then

[tex] x^2+6^2=10^2\\ \\ \Rightarrow x^2=100-36=64\\ \\ \Rightarrow x=\sqrt{64}=8. [/tex]

Therefore, the ladder reached 8 ft high on the building.

Select all of the following expressions that are equal to 2.5.
5 ÷ 2
-2(-1.25)
(-0.5)^2
-1 + (-1.5)

Answers

the first one, the second one, the fourth one

answer is
a) 5/2 = 2.5
b) -2(-1.25)

The heights (in inches) of 13 plants are 6, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 16, and 17. What is the interquartile range of this data set? A) 3.5 B) 6 C) 10.5 D) 11

Answers

The given heights:

6, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 16, 17.

The first step is to find Median in order to divide the above series into lower and upper quartiles.

To find the median, just cross out the first and the last value until you left with the single value, as the number of elements is odd.

Like first 6 would cancel the last 17,
second number 9 would cancel the second last number 16,
and so on.

By doing above exercise, we are left with 11.

So the median = 11.

Now any number below the median 11 would be in lower quartile series, while other half would be in upper one.

To find the lower quartile, find the median of 6, 9, 10, 10, 10, 11:
Now the numbers are even; therefore, we would do the above-mentioned exercise of cancelling first and the last element until we are left with just 2 elements:

The two elements are: 10, 10.
Take average = (10 + 10) / 2 = 10

So lower quartile = 10

To find the upper quartile, find the median of 12, 12, 13, 14, 16, 17:
Now the numbers are even; therefore, we would do the above-mentioned exercise of cancelling first and the last element until we are left with just 2 elements:

The two elements are: 13, 14.
Take average = (13 + 14) / 2 = 13.5

So Upper quartile = 13.5

The interquartile range = Upper Quartile - Lower Quartile = 13.5 - 10.0 = 3.5

So the correct option is (A) 3.5

-i

In order to find the interquartile range we need to find the first, second and third quartiles. These three numbers are called quartiles (think quarters = 4) because they divide the data into 4 groups. In order to find these quartiles we need the data to be in order (least to greatest) which your data already is.

Let's first find the second quartile. This is also known as the Median. It is the middle value in your list of numbers. The middle number in your data is 11.

6, 9, 10, 10, 10, 11, (11 = Median), 12, 12, 13, 14, 16, 17

There are six numbers to the left of the middle number and six to the right. We have divided the data into two groups.

The first quartile is the middle number of the first group. Since there are 6 numbers there technically isn't a middle number, so we take the average of the two numbers closest to the middle. These are in parenthesis below:
6, 9, (10), (10), 11
Since the two number are the same (10) their average is also 10. The first quartile (denoted q1 = 10).

Now let's look at the numbers to the right of the median. Again there are 6 numbers here so none is technically in the middle but I have put in parenthesis the two closest to the middle.
12, 12, (13), (14), 16, 17.
The third quartile q3 is the average of 13 & 14. This is found by adding 13 + 14 and dividing the sum by 2. The third quartile is 13.5

Going back to our original list of data we have now split the data into four groups of 3 numbers each as follows:
6, 9, 10, (q1= 10), 10, 10, 11, (Median = 11), 12, 12, 13, (q3=13.5), 14, 16, 17

The interquartile range is the third quartile minus the first quartile. Here it is 13.5 - 10 = 3.5. It gives the range (the distance) between the first and third quartiles.

Can someone help me?

Answers

There are 1+3 = 4 people from brazil (focus on row2)
There are 4+3+2 = 9 people who scored exactly 85 points (look at column 2)

So there are 4+9 = 13 people who are from brazil or scored exactly 85 points. Subtract out those who fit both criteria. So we'll subtract off 3 people
13-3 = 10

There are 10 people who fit the criteria out of 19 total. The 19 is from adding up all the values in the table.

Divide the two values to get 10/19

Answer: 10/19

in the diagram, the areas of ADC and DCB are in a ratio of 3:4. what are the coordinates of point C

Answers

the complete question in the attached figure

we know that

dAB=dAC+dCB

dAC=√((8-1)²+(-2+9)²)=√98

Area triangle ADC=dAC*CD/2

Area triangle DCB=dCB*CD/2

Area triangle ADC/Area triangle DCB=3/4

[dAC*CD/2]/[dCB*CD/2]=3/4

dAC=(3/4)*dCB-----------------------> equation (1)

dAB=dAC+dCB=√98

dAC=√98-dCB------------------------ > equation (2)

(1)=(2)

(3/4)*dCB=√98-dCB------------------> (7/4)*dCB=√98

dCB=(4/7)√98

dAC=√98-dCB-------- > √98-(4/7)√98-----à (3/7) )√98

dAC=(3/7) )√98

find the slope point A (1.-9) and point B (8,-2)

m=(-2+9)/(8-1)=7/7=1-------------- > 45°

dAC=(3/7)√98

the component x of dAC is

dACx=(3/7)√98*cos45°=(3/7)√98*√2/2=(3/7)√196=3

the component y of dAC is

dACy=dACx=3

the coordinates of the point C are

point A(1.-9)

Cx=Ax+dACx----------> 1+3=4

Cy=Ay+dACy----------> -9+3=-6

the coordinates C(4,-6)

the answer is C(4,-6)

Answer:

C(4,-6) is correct on plato

Step-by-step explanation:

The temperature of a liquid during an experiment can be modeled by the function f(x)=3.8cos(πx20)+2.2 , where f(x) is the temperature in °C and x is the number of minutes into the experiment.

What is the lowest temperature the liquid reached during the experiment?

Answers

we have that
the function is f(x)=3.8cos(πx20)+2.2

using a graph tool
see the attached figure

the answer is
the lowest temperature the liquid reached during the experiment is -1.6 °C

helpppppppppppppppppp

Answers

The answer is -1

[tex]cot \frac{3π}{4} [/tex] = 1 ÷ [tex]tan \frac{3π}{4} [/tex]

the trig unit circle
[tex]tan \frac{3π}{4} [/tex] = [tex] - tan \frac{π}{4} [/tex]
= -1

Remember,
[tex]cot \frac{3π}{4} [/tex] = 1 ÷ [tex]tan \frac{3π}{4} [/tex]
= 1 ÷ -1
= -1

By definition, Cot(α)=Adjacent leg/Opposite leg

Then, when you substitute the values, you obtain:

Cot(3π/4)=-(√2/2)/(√2/2)

When you simplify the expression, you have the following result:

Cot(3π/4)=-1

What is the exact value of Cot(3π/4)?

The answer is: The exact value of Cot(3π/4) is -1

Anybody have the proper answer to this

Answers

Radius = 11 / 2 = 5.5

A = π * 5.5 * 5.5

A = 30.25 π

3025 / 100 π mm^2

The radius of the circle is half its diameter.
.. r = d/2
.. r = (11 mm)/2 = (11/2) mm

The area is given by
.. A = π*r^2
.. = π(11/2 mm)^2

.. A = (121/4)π mm^2

Find the 200th term, given the first term and the common difference. A1=34 and d=15

Answers

Try this solution:
1. it is arithmetic progression, where a₁=34 and d=15. Formula for aₓ is aₓ=a₁+d(x-1);
2. a₂₀₀=34+15*(200-1)=3019.

answer: 3019.
P.S. if it is possible check the arithmetic part.

Michaela uses measuring tape to measure a piece of paper. The measuring tape has an accuracy to the nearest centimeter. She uses her measurements to calculate the area of the piece of paper. Which of the answer choices show the degree of precision she can use to report the area?

Answers

Where are the answer choices?

The lengths of pregnancies are normally distributed with a mean of 264 days and a standard deviation of 15 days. if 36 women are randomly selected, find the probability that they have a mean pregnancy between 264 days and 266 days.

Answers

Given that a sample of 36 women is selected, the probability that the mean is between 264 days and 266 days will be found as follows:
the std deviation of the sample will be:
σ/√n
plugging the values we obtain:
15/√36
=15/6
=2.5
hence the z-score when x=264 will be:
z=(264-264)/2.5
z=0
thus:
P(x<264)=P(z<0)=0.5

the z-score when x=266 will be:
z=(266-264)/2.5
z=0.8
hence
P(x<266)=P(z<0.8)=0.7881
thus
P(264<x<266)=P(0.5<z<0.7881)
=0.7881-0.5
=0.2881

Answer: 0.2881

The probability that a randomly selected group of 36 women will have a mean pregnancy length between 264 days and 266 days is 0.2881. The percentage is 28.81%.

The correct probability that the mean pregnancy length of 36 randomly selected women falls between 264 days and 266 days is given by the cumulative distribution function (CDF) of the normal distribution with a mean of 264 days, a standard deviation of 15 days, and a sample size of 36.

To find this probability, we first need to determine the standard error of the mean (SEM), which is calculated by dividing the standard deviation by the square root of the sample size:

[tex]\[ SEM = \frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{36}} = \frac{15}{6} = 2.5 \][/tex]

To find the z-scores corresponding to the mean pregnancy lengths of 264 days and 266 days. The z-score for a value x is calculated by:

[tex]\[ z = \frac{x - \mu}{SEM} \][/tex]

For 264 days:

[tex]\[ z_{264} = \frac{264 - 264}{2.5} = 0 \][/tex]

For 266 days:

[tex]\[ z_{266} = \frac{266 - 264}{2.5} = \frac{2}{2.5} = 0.8 \][/tex]

Now, we look up these z-scores in the standard normal distribution table or use a calculator to find the corresponding probabilities.

The probability of a z-score less than 0 is 0.5, and the probability of a z-score less than 0.8 is approximately 0.7881.

The probability that the mean pregnancy length is between 264 days and 266 days is the difference between these two probabilities:

[tex]\[ P(264 < \bar{x} < 266) = P(z < 0.8) - P(z < 0) \] \[ P(264 < \bar{x} < 266) = 0.7881 - 0.5 \] \[ P(264 < \bar{x} < 266) = 0.2881 \][/tex]

Therefore, the probability that a randomly selected group of 36 women will have a mean pregnancy length between 264 days and 266 days is approximately 0.2881.

To express this as a percentage, we multiply by 100:

[tex]\[ 0.2881 \times 100 \approx 28.81\% \][/tex]

The answer is: 28.81%.

Classify the number as natural, whole, integer, rational, and/or irrational. Select all terms that are correct. 7√

Answers

i took the test the answer is Irrational i hope this helps :)

I think It would be irrational. I hope this helps you and others to come out :)

Solve the system of equations. 2.5y + 3x = 27 5x – 2.5y = 5 What equation is the result of adding the two equations? –8x = 328x = 325y + 8x = 328x – 5y = 32 What is the solution to the system? (–4, 6)(–2.75, 8.6)(2.75, 3.5)(4, 6)

Answers

a) The result of adding the two equations is
.. (2.5y +3x) +(5x -2.5y) = (27) +(5)
.. 8x = 32 . . . . . . . . . . . . . . . . . . . . . . . your 2nd selection

b) The solution to the system is (4, 6), your 4th selection.
.. This is the only choice with x=4, the solution to part (a).

Answer:

8x=32

(4,6)

Step-by-step explanation:

Factor ab + bc + b2 + ac.

Answers

ab + bc + b² + ac =
(b² + bc)+(ab + ac) =
b(b+ c)+a(b + с) =
(b + c)(b + a)

(ab + b^2) + (bc + ac).

{So we can get the terms with the same variables together}

Factoring out the GCF from each term:

b(a + b) + c(a + b).

Then, factoring out a + b yields:

(a + b)(b + c).

I hope this helps!

What is the point called where the perpendicular bisectors of the sides of a triangle intersect

Answers

Answer: Circumcenter

This is the center of the circle that goes through the three vertices of the triangle. This circle is known as the circumcircle. It is the smallest circle possible in which the circle encompasses the triangle and none of the triangle spills outside the circle.

Which statement best describes the polynomial 2x + 8?

A. first degree polynomial with two terms

B. first degree polynomial with eight terms

C. second degree monomial

D. second degree binomial

Answers

There are two (2) terms, "2x" and "8", making it a "binomial" (the "bi" prefix meaning "two"). The only variable is x, and its power is 1, making the "2x" term a first-degree term. Since the highest degree of any term is 1, the polynomial is first degree.

Selection A is appropriate.

Write a real world problem that you would represent with the equation 4x+5=37.

Answers

Bob was 5 feet off the ground. He travels 4 feet every single second. How long will it take for him to reach 37 feet?

4x + 5 = 37

4x + 5 (-5) = 37 (-5)

4x = 32

4x/4 = 32/4

x = 8

It will take Bob ~8 seconds to reach 37 feet*

*Problem & answer

hope this helps

Solve the system of equations using the linear combination method. {5m+3n=41 {3m−6n=9 Enter your answers in the boxes. m = n =

Answers

These are linear equations that can be solved simultaneously;
5m+3n=41
3m-6n=9 (multiplying the first equation by 3 and the second by 5)

15m+9n=123
15m-30n= 45 (subtracting the two equations)
39n = 78
n = 2,
and for m, 3m = 9+6(2)
= 21
m = 7
Therefore, n=2 and m=7

Answer:

n=2 m=7

Step-by-step explanation:

You asked your classmates to name their favorite type of music. You found that 12 students like rock, 8 like rap, 6 like R&B, and 4 like jazz. Suppose you made a pie chart to display the data. How many degrees of the circle should represent rock music?

Answers

first we should write the total numbers:
12+8+6+4=30
then we should divide the number 30 by 360(because the pie chart is 360 degrees):
[tex]360 \div 30 = 12[/tex]

now we should multiply 12(the number of students who likes rock) by 12
[tex]12 \times 12 = 144[/tex]
the answer is 144 degrees

How do you write
2/4
as a percentage?

Answers

you would right 2 fourths in a percentage is 50%

2/4 is 50% your welcome

helppppppppppppppppppppppppppppppppppppp

Answers

The expression x²-14x+31=63 is a quadratic equation. To solve it, you must order it:

x²-14x+31-63=0

x²-14x-32=0

Then, you must apply the quadratic formula, which is shown below:

x=(-b±√(b^2-4ac))/2a

So you have the values of a,b and c:

a=1

b=-14

c=-32

When you substitute those values in the quadratic formula, you obtain:

x=(-(-14)±√((-14)^2-4(1)(-32))/2(1)

x1=-2

x2=16

So, the correct option is the third one: x=-2 or x=16

Jermaine did this work to solve an equation. Did he make an error?

Answers

The solution for the below equation is required:

4x + 6 - x = 2x + 3

The work done by the Jermaine is presented below :

4x + 6 - x = 2x + 3

5x + 6 = 2x + 3

Instead of adding 4x with -1x to make it 3x , he added 4x with 1x to make it 5x.

So, the correct option is

Jermaine did make an error. He should have combined 4x and -1x to make 3x

3x + 6 = 2x + 3

Hope it helps..!!

Answer:

Step-by-step explanation:

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc is th

The gum you like to is on sale. it is regularly priced at $1.59. Write and equation that will help determine how much you’ll save if you buy the pack today.
S=sale price
C=cost savings

Answers

c=s-1.59 that should be the answer see ya

What is the answer to this problem?

Answers

Hey there!

To start, an isosceles triangle is any triangle with two sides of the same length.

In this case, you are given two measurements: 20 and 30.

This means that the third side of the triangle can either be 20 or 30, since two of the sides must equal one another.

Because the question is asking for the greatest possible perimeter of the triangle, it would only make sense that the third side would have to be 30 units in length to make the greatest possible perimeter since it is the possible length that is greatest in value (20 < 30).

Therefore, knowing that the sides of the triangle are now 20, 30, and 30, add the lengths up to find the perimeter:
20+30+30
=80

Therefore, the largest possible value of the perimeter would be 80 units.

Hope this helps and I hope you have a marvelous day! :)

Trapezoid RSTV∼trapezoid WXYZ .

What is the scale factor of a dilation from RSTV to WXYZ ?

a. 14/25

b. 4/5

c. 7/8

d. 7/10

Answers

Answer:

Correct option is D

Scale factor of dilation is [tex]\frac{7}{10}[/tex]

Step-by-step explanation:

Given the two similar figures

Trapezoid RSTV∼trapezoid WXYZ

We have to scale factor of dilation from RSTV to WXYZ.

As the two trapezoid are similar therefore their ratio of corresponding sides gives the scale factor of dilation.

Hence, [tex]\text{scale factor of dilation is=}\frac{WX}{RS}=\frac{WZ}{RV}[/tex]

i.e [tex]\frac{28}{40}=\frac{35}{50}=\frac{7}{10}[/tex]

Hence, scale factor of dilation is [tex]\frac{7}{10}[/tex]

the elevation in denver colorado is 13 times greater than that of waikapu, hawaii. the sum of their elevations is 5600 feet. find the elevation of each city

Answers

h1 = waikapu height
h2 = denver height

A) 13 h1 = h2
B) h1 + h2 = 5,600

B) h1 + 13h1 = 5,600
B) 14h1 = 5,600
h1 = Waikapu height = 400 feet

h2 = 5,600 - h1
h2 = 5,600 -400
h2 = Denver height = 5,200

What is the perimeter of this equilateral triangle?
Equilateral triangle with one side labeled 13 meters.

Answers

An equilateral triangle has equal sides, so it would be 39.

Write an expression to represent: four more than the product of three and a number xxx.

Answers

The number is x

product of 3 and the x = 3x

four more = 3x + 4

Answer:

x-4

Step-by-step explanation:

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If y varies inversely as x and y is 6 when x is 12 what is x when y is 14.4 Persephoneby Walter Wykesyour laughter echoes stillin that bright field where you playedso carefree, a little goddessarms white as milkgathering flowers with your playmateswhen the earth shookand through the crumbling groundyour monstrous lover burstan uninvited guestsnatching you awayplucking your innocenceas you had plucked flowersonly moments beforehow you must have cried outmust have begged for your releasewhen your mother learned of the abductionher grief stopped the earth, the moon, the stars in their tracksthe world became eternal winterthere was no consolation, no solaceno moving onwhat an unexpected miracle when you returned to usa gift from the godsbut you are not the sameno longer that bright childa handful of seeds has sealed your fateand though all things flourish in your presenceyour laughter is colored by that other place, that dark loverand in your eyes cold winter reignsWykes, Walter. 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I forgot he was a poor Cabuli fruitseller, while I was but no, was I more than he? He was also a father.After reading this sentence the reader can most likely conclude that the narrator feels all of the following exceptA. disdainB. humilityC. kinshipD. shame Using radicals , write an equivalent expression for the expression 2 1/3 Which sentence is an example of personification? A.It was an open secret that she liked him. B.The dog was heavier than an elephant. C.Her words were like a knife to his heart. D.The storm pounded the roof of our home. How are amino acids assembled during translation? Please explain your answer! Thanks! Why do some believe the japanese were involved in her disappearance amelia earhart? The term Kikuyu BEST refers to which of these? A) an ethnic group B) a nationalist leader C) a colonial rebellion why was silk in demand in Europe and other parts of Asia 5% sales tax on a $81.08 bookcase Create a claim only from the following prompt (DO NOT WRITE AN ESSAY! 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