Lightbulbs. A company produces lightbulbs. We know that the lifetimes (in hours) of lightbulbs follow a bell-shaped (symmetric and unimodal) distribution with a mean of 7,161 hours and a standard deviation of 564 hours. Use the Empirical Rule (68-95-99.7 rule) to answer the following question: The shortest lived 2.5% of the lightbulbs burn out before how many hours

Step-by-step explanation:

[tex]\tan^2 \theta - 3\tan \theta + 2 = 0[/tex]

Let [tex]x = \tan \theta[/tex]

We can then write

[tex]x^2 -3x + 2 = 0\:\:\Rightarrow\:\:(x - 2)(x - 1) = 0[/tex]

or

[tex](\tan \theta - 2)(\tan \theta - 1) = 0[/tex]

The zeros occur when

[tex]\tan \theta = 2\:\:\:\text{or}\:\:\:\tan \theta = 1[/tex]

or when [tex]\theta = 63.4°[/tex] or [tex]\theta = 45°[/tex].

Answer:

The right answer is "0.3193".

Step-by-step explanation:

According to the question,

Mean,

[tex]\frac{1}{\lambda} = 13[/tex]

[tex]\lambda = \frac{1}{13}[/tex]

As we know,

The cumulative distributive function will be:

⇒ [tex]1-e^{-\lambda x}[/tex]

hence,

In the first 5 years, the probability of failure will be:

⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]

                    [tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]

                    [tex]=1-e^(-\frac{5}{13})[/tex]

                    [tex]=1-0.6807[/tex]

                    [tex]=0.3193[/tex]

The cordent plan of the answer is 2

Answer:

The scale factor will just be 2

Step-by-step explanation:

The length of PQ is twice as larger than the length of AB.

so from 12 to 6 or 6 to 12, we multiply 6 by 2 which equals to 12

Answer:

0.4444 = 44.44% probability that it is NOT raining

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Technician not detected.

Event B: Not raining.

Probability the technician is not detected:

0.3 of 0.25(raining).

0.08 of 0.75(not raining). So

[tex]P(A) = 0.3*0.25 + 0.08*0.75 = 0.135[/tex]

Probability the technician is not detected and it is not raining:

0.08 of 0.75. So

[tex]P(A \cap B) = 0.08*0.75 = 0.06[/tex]

Given that the technician will NOT be detected, what is the probability that it is NOT raining?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.135} = 0.4444[/tex]

0.4444 = 44.44% probability that it is NOT raining

Answer:

Hello?

Step-by-step explanation:

Answer:

SAS=side angle side

there is two side and one angle

Answer:

SAS theorem

explanation:

Answer:

0.03 more flour per cupcake

Step-by-step explanation:

3.12/8 = 0.39

2.52/7 = 0.36

0.39 - 0.36 = 0.03

Hope this helps c:

This is one single number. The number is slightly larger than 163 thousand.

====================================================

Explanation:

Consider four slots labeled A,B,C,D

We have....

There's a countdown going on (46,45,44,43) when filling up the slots. This countdown is because we cannot reselect any specific person for multiple slots at the same time.

If order mattered, then we'd have 46*45*44*43 = 3,916,440 permutations possible.

However, order doesn't matter. For any group of 4 people, there are 4! = 4*3*2*1 = 24 ways to arrange them. So we must divide the previous result over 24 to get (3,916,440)/24 = 163,185

This means there are 163,185 different combinations and this is the number of possible samples of size 4 from a population of 46 people. The order of any sample doesn't matter.

Answer:

67. A

68. D

Step-by-step explanation:

I don't remember exactly the explanation, but I recommend you try to learn more about number lines sometime when you aren't under stress from schoolwork, because they're pretty simple questions to answer once you get a better understanding of them!

Answer:

Determine the conditional probability distribution of X given that Y = 1 and Z = 2. Round your answers to two decimal places (e.g. 98.76).

answer:

Given that Y = 1 :  2/5

Given that Z = 2 : 3/5

Step-by-step explanation:

The conditional probability distribution of X     F x | yz^( x )

Given that Y = 1

F x | yz . ( x | yz )  = 2/5

Given that z = 2

= 3/5

attached below is the detailed solution

Answer:

yes

Step-by-step explanation:

its correct because divide by 2/ 28/16=14/8

maybe

Answer:

1

Step-by-step explanation:

3^0

Anything raised to the zero power is 1

3^0 =1

Answer:

1

Step-by-step explanation:

Anything to the power of 0 is 1

Eg: 5⁰ = 1

a⁰= 1

(-12)⁰ = 1

Answer:

[tex]P = 8 + 2\sqrt{26}[/tex]

Step-by-step explanation:

Given

[tex]W = (-2, 4)[/tex]

[tex]X = (2, 4)[/tex]

[tex]Y = (1, -1)[/tex]

[tex]Z = (-3,-1)[/tex]

Required

The perimeter

First, calculate the distance between each point using:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2[/tex]

So, we have:

[tex]WX = \sqrt{(-2- 2)^2 + (4-4)^2 } =4[/tex]

[tex]XY = \sqrt{(2- 1)^2 + (4--1)^2 } =\sqrt{26}[/tex]

[tex]YZ = \sqrt{(1- -3)^2 + (-1--1)^2 } =4[/tex]

[tex]ZW = \sqrt{(-3--2)^2 + (-1-4)^2 } =\sqrt{26}[/tex]

So, the perimeter (P) is:

[tex]P = 4 + \sqrt{26} + 4 + \sqrt{26}[/tex]

[tex]P = 8 + 2\sqrt{26}[/tex]

Answer:

its D.

Step-by-step explanation:

took test

Answer:

[tex]14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]

Step-by-step explanation:

In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:

[tex]cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}[/tex]

So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: [tex]\frac{1}{15}x^{2}[/tex] so for

[tex]cos(\frac{1}{15}x^{2})[/tex]

the modified series will look like this:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}[/tex]

So we can use some algebra to simplify the series:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}[/tex]

which can be rewritten like this:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]

So finally, we can multiply a 14x to the series so we get:

[tex]14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]

We can input the x into the series by using power rules so we get:

[tex]14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]

And that will be our answer.

The freezing point of water is 0°C or 32°F while the boiling point of  water is 100°C or 212°F.

Temperature is the measure of the degree of hotness or coldness of a substance or place. It is usually expressed Fahrenheit and Celsius scale. Temperature indicates the direction of heat flow.

The freezing point of water is 0°C or 32°F while the boiling point of  water is 100°C or 212°F.

Find out more on Temperature at: https://brainly.com/question/24746268

Answer:

The total distance Allie traveled was 0.81 miles.

Step-by-step explanation:

Since Allie rode her bike up a hill at an average speed of 12 feet / second, and she then rode back down the hill at an average speed of 60 feet / second, and the entire trip took her 2 minutes, to determine what is the total distance she traveled, the following calculation must be performed:

12 + 60 = 72

72 x 60 = 4320

1000 feet = 0.189394 miles

4320 feet = 0.8181818 miles

Therefore, the total distance Allie traveled was 0.81 miles.

Answer:

Purplemath

Introduces reflections in the x- and y-axes. ... To see how this works, take a look at the graph of h(x) = x2 + 2x – 3. ... The previous reflection was a reflection in the x-axis. ... f (x – b) shifts the function b units to the right.

Answer:

Parallelogram.

Step-by-step explanation:

Because parallelogram has its opposite sites equal.

Answer:

a. 7 ÷ 4 yes

b. 4 ÷ 7 no

c. [tex]\frac{7}{4}[/tex] yes

d. [tex]\frac{4}{7}[/tex] no

e. 7 × [tex]\frac{1}{4}[/tex] yes

f. [tex]1\frac{3}{4}[/tex] yes

Step-by-step explanation:

hope this helps ^^

Answer:

{-6,0,2,4}

Step-by-step explanation:

Answer:

ur answer is correct

A =xy

A = 1.6×0.3 = 0.48

Answer:

Answer:

Y' = - 1

Step-by-step explanation:

Y' = - 2x +3

So y' (2,2) =-2*2 +3= - 1

Answer:

ok so if she gets paid 372 we just multiply this by 4 since there's 4 weeks in a month then we multiply by 4 so

372*4*12=17856

now we just multiply 831.33 by 2 since she is paid semimonthly and we multiply by 12

831.33*2*12=19951.92

now we just subtract

19951.92-17856=2095.92

so she gets paid 2095.92 more dollars per year

Hope This Helps!!!

9514 1404 393

Answer:

  P' = (3, -5)

Step-by-step explanation:

Rotation 180° about the origin is the same as reflection across the origin. The transformation is given by ...

  (x, y) ⇒ (-x, -y) . . . . . . the signs of the coordinates are both changed

  P(-3, 5) ⇒ P'(3, -5)

Answer:

bottom graph

Step-by-step explanation:

f(x) = |3q-6|

because you have absolute value there are 2 possibilities

y= +(3q-6) and y= -(3q-6)

to find where the graph intersects the x-axis make y=0 because there the y coordinate is 0, so we have...

3q-6 =0 and -3q+6 =0

3q= 6 and -3q =-6

q=2 and q=2

the bottom graph has the intersection with x-axis only at 2, so is the correct one

9514 1404 393

Answer:

  bottom graph shown

Step-by-step explanation:

It can be helpful to rearrange the equation to either of the equivalent forms ...

  f(x) = |3(x -2)|

or ...

  f(x) = 3|x -2|

_____

The first of these forms represents a horizontal compression of the absolute value function by a factor of 3, then a right-shift by 2 units. This matches the bottom graph shown.

__

The second of these forms represents a horizontal right-shift by 2 units, and a vertical expansion by a factor of 3. This matches the bottom graph shown.

__

The attached graph shows the function given here along with the absolute value parent function.

_____

Additional comment

The transformations we're usually interested in are ...

g(x) = k·f(x) . . . . vertically scaled (stretched) by a factor of k

g(x) = f(kx) . . . . .horizontally compressed by a factor of k

g(x) = f(x) +k . . . shifted up by k units

g(x) = f(x -k) . . . . shifted right by k units

In many cases, as here, horizontal scaling and vertical scaling are indistinguishable as to which caused a given effect.

Answer:

Old number = 150

Step-by-step explanation:

Given information;

Percentage decreased = 22%

New number obtain = 117

Find:

Old number

Computation:

Old number = New number obtain[100 / (100 - 22)]

Old number = 117[100 / (100 - 22)]

Old number = 117[100 / (78)]

Old number = 11,700 / 78

Old number = 150