what is the probability that, of 6 such types of devices, at least 3 will function for at least 15 hours? what assumptions are you making?

The density function of area is is ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}}).

A random variable can be defined as a variable whose value is unknown or as a function that assigns numerical values to each of the outcomes of an experiment. It can also be defined as a rule that assigns a numerical value to each outcome in a sample space.

The density function (1.4-5)P(x) = an exp(-ax), if x0,0, if x>0, where an is any positive real number, defines the exponential random variable.

radius R has df f(r) ={\lambdae}^{-\lambdar}

area Y= *r2

r = \pm (Y/(\pi))1/2

hence P(Y<y) =F(Y) =P( *r2<y) =P(r<+/- (Y/( ))1/2 ) = \int_{{-y/\pi}^{1/2}}^{{(y/\pi)}^{1/2}}{\lambdae}^{-\lambdar} dr

= e^{{\lambda(y/\pi)}^{1/2}}- e^{{-\lambda(y/\pi)}^{1/2}}

Therefore P(df of y) = f(y) = d/dyf(y) =(d/dy) (e^{{\lambda(y/\pi)}^{1/2}}- e^{{-\lambda(y/\pi)}^{1/2}})

= ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}})

Therefore the density function of area is ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}})

To learn more about exponential random variable visit

https://brainly.com/question/10900747

#SPJ4

Answer:

mother....... pure the water by boilingit

Problem 1:

[tex]sin(75^o)=sin(45^o+30^o)\\sin(A+B)=sinAcosB+cosAsinB\\sin(45^o+30^o)=sin45^ocos30^o+cos45^osin30^o\\\frac{1}{\sqrt{2} } *\frac{\sqrt{3} }{2} +\frac{1}{\sqrt{2} } ]\times\frac{1}{2} \\\frac{\sqrt{3} }{2\sqrt{2} } +\frac{1}{2\sqrt{2} } ---- > \frac{\sqrt{3}+1}{2\sqrt{2} } (ANS)[/tex]

Problem 2:

[tex]cos135^o=-cos45^o=-\frac{1}{\sqrt{2} }[/tex]

Explanation:

Cos 135° is an angle in the second quadrant.

In the second quadrant, cos is negative. [tex]cos\theta=\frac{x}{r}[/tex]

[tex]cos135=cos(180-45)=-cos45^o[/tex]

An angle of 45°  is found in a right-angled triangle of sides [tex]1:1:\sqrt{2}[/tex]

[tex]cos45^o=\frac{1}{\sqrt{2} }[/tex]

[tex]cos135^o=-cos45^o=-\frac{1}{\sqrt{2} }[/tex]

Note that [tex]\sqrt{2}[/tex] is an irrational number and cannot be given as an exact decimal.

Little messy math, but thanks for asking the question.

- Eddie

Answer: 154

Step-by-step explanation:

= [tex]11x\frac{42}{3} \\[/tex]

= 154

Step-by-step explanation:

since it is a right-angled triangle, the principle of Pythagoras has to be fulfilled :

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), which is in our case (x + 32).

a and b are the legs.

so

(x + 32)² = x² + (x + 31)²

x² + 64x + 1024 = x² + x² + 62x + 961

2x + 1024 = x² + 961

x² - 2x - 63 = 0

as 63 = 7×9

and -9 + 7 = -2

we can conclude that this quadratic equation is the same as the following factorization :

(x + 7)(x - 9) = 0

we have 2 solutions :

x = -7

x = 9

as x is also the length of a side, the negative solution does not make any sense.

so, x = 9 is our solution.

that means the sides of the triangle are

x = 9

x + 31 = 40

x + 32 = 41

and the perimeter of the triangle is

9 + 40 + 41 = 90

33% is the increasing percentage in the size of the graduating class.

The formula for percentage increase = Final number - Initial number x 100

                                                                              Initial number

Or, it can be also written as

Percentage increase =   Increase       x 100

                                       Initial number

Given that:

The final number of students = 266

The initial number of students = 200

Therefore, putting the value in the formula. We get,

Percentage increase = 266 - 200   x 100

                                           200

Percentage increase = 66   x 100

                                      200

Percentage increase = 33 %

Hence, the increase percentage from the previous year to this year of the students of the class graduating is 33%.

To learn more about the percentage increase visit: https://brainly.com/question/11200803

#SPJ1

Answer:2.4

Step-by-step explanation:

Based on the information given the unit rate per pound is 2.4.

Using this formula

Unit rate per pound=Costs/Pounds

Where:

Cost=$3.36

Pounds=1.4 pounds of grapes

Let plug in the formula

Unit rate per pound=$3.36/1.4

Unit rate per pound=2.4

the unit rate per pound is 2.4.

It will take 2.32 years for Michael to reach USD 25000.

The interest one earns on interest is known as compound interest. In other words, the process of adding interest to a loan's or deposit's principal is known as compound interest.

The formula for compound interest calculation is given as,

[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where,

Here, the compound interest (A) is USD 25000, r is 9.6%, n is 12 months (1 year), and P is USD 20000. Using these we have to find t,

[tex]\begin{aligned}20000\left(1+\frac{0.096}{12}\right)^{12t}&=25000\\20000(1.008)^{12t}&=25000\\1.008^{12t}&=1.25\\12t \ln{(1.008)} &=\ln{(1.25)}\\12t\times0.008&=0.223\\t&=\mathrm{2.32\;years}\end{aligned}[/tex]

Therefore, the answer is 2.32 years.

To know more about compound interest:

https://brainly.com/question/26457073

#SPJ4

Answer:

(top to bottom)104.04...6800...272...3

Step-by-step explanation:

68 can go into 7075, 104 times.

68 goes into 275 4 times.

275-272=3

Step-by-step explanation:

6+7=13,13+7=20,20+7=27,27+7=(34)!

Answer:

14

Step-by-step explanation:

first add inside the parentheses 4+7=11

then add three 11+3=14

Answer: 3 + 11 = 14

Step-by-step explanation: Follow PEMDAS (Parentheses, exponent, multi, divi, add, subtract.)

Answer: y = 4

Step-by-step explanation:

First, we have to look at the triangle and understand which sides match each other. The side measure of EF matches the side of KH. Since we know these are congruent sides, we can set them equal to each other in an equation. So,

7y - 11 = 17.00

Now we add 11 to both sides, isolating the variable.

7y = 28.00

Now, we divide by 7 on both sides.

7y/7 = 28/7

y = 4

There are 12 players of right handed, according to the question.

What do you mean by percentage?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

According to data in the given question,

We have given data:

A local little league has a total of 60 players of whom 20% are right-handed.

Let x be the total number of players that are right-handed.

The value of x can be found as follow:

x = 20% of 60

x = (20/100)60

x = 0.2(60)

x = 12

Therefore, the total number of players that are right-handed is 12, if the local little league has a total of 60 players of whom 20% are right-handed.

To learn more about percentage, visit:

brainly.com/question/14979505?referrer=searchResults

#SPJ4

 To prove that given is perpendicular we have show that one make right angle, i.e. 90 degree.

A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with that other line. In other words, two lines become perpendicular to one another if they connect at a right angle.

For proof of perpendicular-

Theorm 1 : If two lines intersect to form a pair of lines with a "congruent angle," then the lines are perpendicular to one another. Angles that are equivalent to one another are known as congruent angles.

Theorm 2 : Four right angles will be formed if two perpendicular lines cross.

Theorm 3 : The "adjacent acute angles" are complimentary if two of their sides are perpendicular. As you presumably remember, acute angles are angles that are fewer than 90 degrees, whereas adjacent angles are angles that are next to one another.

To know more about perpendicular visit:

https://brainly.com/question/18271653

#SPJ4

Answer:

yes

Step-by-step explanation:

24 * 2 represents 24 × 2

I am not a fan of the use of the asterix to represent multiplication

Ron jump is less than 10 feet. Ron jump is actually 5.45 feet.

Stacey long jump was 10 feet. That is 5/6 foot longer than Ron's long jump.

Let's find if Ron jump more or less than 10 feet's.

Therefore,

Ron's Jump = x

Hence,

x + 5 / 6 x = 10

6x + 5x / 6 = 10

cross multiply

6x + 5x = 60

11x = 60

x = 60 / 11

x = 5.45

Therefore, Ron jump less than 10 feet.

learn more on length in feet here: https://brainly.com/question/16792596

#SPJ1

Of the following statements regarding time-series methods, the statement that is false is a simple moving average of three periods is identical to exponential smoothing with an alpha equal to 0.33. (Option D)

In mathematics, a time series refers to a series of data points indexed or listed or graphed based on the time order. Generally, a time series is a sequence captured at successive equally spaced points in time and hence is a sequence of discrete-time data. Time-series methods are used in forecasting. It comprises of analytical methods in order to obtain meaningful statistics and other characteristics of the data. Time series forecasting is a model used to predict future values based on previously observed values. From the given options, the time-series methods that is false is is a simple moving average of three periods is identical to exponential smoothing with an alpha equal to 0.33.

Learn more about Time-series methods:

https://brainly.com/question/28481953

#SPJ4

Answer:

6, 8

Step-by-step explanation:

just replace x with the number

2(2)+2

4+2

6

2(3)+2

6+2

8

Hopes this helps please mark brainliest

Answer:

  (2, 8)

Step-by-step explanation:

You want the image coordinates of (8,-2) after 90 degree counterclockwise rotation.

The transformation of (x, y) coordinates that does a 90° CCW rotation about the origin is ...

  (x, y) ⇒ (-y, x)

Applying this transformation to the given point, we have ...

  (8, -2) ⇒ (2, 8)

The rotated point is (2, 8).

Answer:

mabey dis will help

Step-by-step explanation:

A =l X w

52.2 = 12 X w

w = 52.2 */* 12

After the subtraction, the simplified form of the mixed number is 33/4

Mixed numbers

Mixed fraction means a fraction represented with its quotient and remainder.

Given,

Here we have the mixed numbers 12 5/12 - 4 1/6

Now, we have to perform the subtraction in it and then we have to simplifies it.

Firs we have to convert the mixed numbers into normal fraction, for that we have to do the following:

12 5/12 = (12 x 12) + 5/12

=> (144 + 5)/12

=> 149/12

Similarly, when we simplifies the second one, then we get,

=> 4 1/6 = (6 x 4) + 1/6

=> (24 + 1) / 6

=> 25/6

Here the fractions have unlike denominators.

So, first we have to find the Least Common Denominator and rewrite the fractions with the common denominator.

Therefore, the LCD(149/12, 25/6) = 12

Now, we have to multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD.

=> 149/12 - 50/12

The two fractions now have like denominators so you can subtract the numerators.

Then:

=> 99/12

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 99 and 12 using GCF(99,12) = 3

So, the simplified form of the fraction is

=> 33/4

To know more about Mixed numbers here.

https://brainly.com/question/24137171

#SPJ1

The solution is

y=x+4

y=-2x-4

Slope of a Line :

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's slope in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate.

As a result, the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.

where the slope of a line is denoted by "m".

The graph of the equation y = mx + c has a slope of m, an intercept of m, and a y-intercept of c. In the slope-intercept version of the linear equation, m and c are real integer values.

To learn more about slope of a line visit: https://brainly.com/question/16180119

#SPJ9

The equation that represents the proportional relationship is y=14x. The correct option is D.

Given the table which shows a proportional relationship X=1,2,3 and Y=14,28,42.

We want to find an equation that represents the proportional relationship.

We will find the proportional relationship by dividing Y with X.

When X=1 and Y=14 then proportional relationship is

Y/X=14/1

Multiply both sides by X, we get

(Y/X)X=14X

Y=14X.....(1)

When X=2 and Y=28 then proportional relationship is

Y/X=28/2

Y/X=14

Y=14X.....(2)

When X=3 and Y=42 then proportional relationship is

Y/X=42/3

Y/X=14

Y=14X......(3)

From equation (1),(2) and (3) we get that the proportional relationship is Y=14X.

Hence, an equation that represents the proportional relationship when the table shows a proportional relationship is Y=14X.

Learn more about the proportional relationship from here brainly.com/question/12242745

#SPJ9

The domain of the given function h(x) = 1 - 3x is {-2, 1, -2, -5}.

The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.

The function is given in the question as:

h(x) = 1 - 3x    ....(i)

Here domain= {1, 0, 1, 2}

The range includes all possible y values of a set of ordered pairs.

Substitute the values of the domain i.e. x = 1, 0, 1, 2 in the equation (i),

h(x) = 1 - 3(1)

h(x) = 1 - 3

h(x) = -2

h(x) = 1 - 3(0)

h(x) = 1

h(x) = 1 - 3(1)

h(x) = 1 - 3

h(x) = -2

h(x) = 1 - 3(2)

h(x) = 1 - 6

h(x) = -5

Therefore, the domain of the given function is {-2, 1, -2, -5}.

Learn more about the domain and the range here:

brainly.com/question/21027387

#SPJ1

Answer:

10x^2 + 26x - 56

Step-by-step explanation:

10 x^2 -14x + 40x - 56 =

= 10x^2 + 26x - 56

Answer: 5x -2x = 8 +7, 3x = 15 x = 15/3) X= 5

Answer:

-2,2

4

Step-by-step explanation:

Answer:

4 people caught the bus

Step-by-step explanation:

hello here is number 4 & 6

6:

the graph for number 6 is listed below.

table:

(-2,5)

(-1,0)

(0,-3)

(1,-4)

(2,-3)

4:

all of them can be, look at the listed images below.

The average temperature last Sunday is 1.08T or (1 + 8/100)T.

Temperature simply means the hotness and coldness of a body.

In this case, last Sunday, the average temperature was 8 percent higher than the average temperature two Sundays ago.

This will be expressed as:

= T + (8% × T)

= T + (0.08 × T)

= T + 0.08T

= 1.08T

The temperature is 1.08T.

Learn more about temperature on:

brainly.com/question/24746268

#SPJ1

Given that a table is 6 feet long and 3 feet wide. You extend the length of the table by inserting two identical table leaves. The extended table is rectangular with an area of (18+6x) square feet.

The area of a rectangle is the product of the width and the length

The required values are given as;

6 + 2x

Here x represents the width of the leaves

Total length = (6 + 2x) feet

Width = 3 feet

Area, A = (6 + 2x) ft. × 3 ft. = (18 + 6x) ft.²

The expression that represents the length of the table is 6 + 2x

The variable x represents the width of the leaves

To learn more about expressions click here https://brainly.com/question/723406

#SPJ4