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2 years ago

The amount of time a certain brand of light bulb lasts is normally distributed with a

1 answer:

3 0

The interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.

<h3>What is empirical rule?</h3>

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

$P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%$

Here, we had where mean of distribution of X is \mu and standard deviation from mean of distribution of X is \sigma

The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1400 hours and a standard deviation of 50 hours. Thus,

$\mu=1300\\\sigma=90$

Using the empirical rule, the interval of hours represents the lifespan of the middle 68% of light bulbs is,

$P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(1300- 90 < X < 1300+ 90) = 68\%\\P(1210 < X < 1390) = 68\%$

Thus, the interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.

Learn more about empirical rule here:

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Please help me. Thank you very much.

Alika [10]

Hello!

Your answer would be C.

Multiply 3 x 8 x 5 and 2 x 5 x 6 and add both products together and you get 120 cm3.

Hope it helps you :)

5 0

3 years ago

Department started out with 100 pencils and 200 pens during the lat quarter of this year they lost 4% of the pens and 2% of the

o-na [289]

Answer:

The remaining number of the pencil = 98

The remaining number of the pens = 192

Step-by-step explanation:

Here, according to the question:

The number of pencils at the starting at the quarter = 100

The percentage of the lost pencil over the year = 2%

Now, calculating the lost pencil, we get:

2% of 100 = $\frac{2}{100} \times 100 = 2$

⇒The number of lost pencil over the year = 2

So,Number of remaining Pencil = Total pencil - Number of pencil lost

= 100 - 2 = 98

The number of pens at the starting at the quarter = 200

The percentage of the lost pens over the year = 4%

Now, calculating the lost pens, we get:

4% of 200 = $\frac{4}{100} \times 200 = 8$

⇒The number of lost pens over the year = 8

So,Number of remaining Pens = Total pens - Number of pens lost

= 200 - 8 = 192

Hence, the remaining number of the pencil = 98

And and the remaining number of the pens at the end of the year = 192

6 0

2 years ago

Consider the differential equation x^2 y''-xy'-3y=0. If y1=x3 is one solution use redution of order formula to find a second lin

Anastasy [175]

Suppose $y_2(x)=y_1(x)v(x)$ is another solution. Then

$\begin{cases}y_2=vx^3\\{y_2}'=v'x^3+3vx^2//{y_2}''=v''x^3+6v'x^2+6vx\end{cases}$

Substituting these derivatives into the ODE gives

$x^2(v''x^3+6v'x^2+6vx)-x(v'x^3+3vx^2)-3vx^3=0$

$x^5v''+5x^4v'=0$

Let $u(x)=v'(x)$ , so that

$\begin{cases}u=v'\\u'=v''\end{cases}$

Then the ODE becomes

$x^5u'+5x^4u=0$

and we can condense the left hand side as a derivative of a product,

$\dfrac{\mathrm d}{\mathrm dx}[x^5u]=0$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}[x^5u]\,\mathrm dx=C$

$x^5u=C\implies u=Cx^{-5}$

Solve for $v$ :

$v'=Cx^{-5}\implies v=-\dfrac{C_1}4x^{-4}+C_2$

Solve for $y_2$ :

$\dfrac{y_2}{x^3}=-\dfrac{C_1}4x^{-4}+C_2\implies y_2=C_2x^3-\dfrac{C_1}{4x}$

So another linearly independent solution is $y_2=\dfrac1x$ .

3 0

2 years ago

X + x(x + y) + y; use x = 4, and y = 1

leva [86]

$\huge\text{Hey there!}$

$\huge\text{x + x(x + y) + y}$

$\huge\text{= 4 + 4(4 + 1) + 1}$

$\huge\text{= 4 + 4(5) + 1}$

$\huge\text{= 4 + 20 + 1}$

$\huge\text{= 24 + 1}$

$\huge\text{= 25}$

$\huge\boxed{\textsf{Therefore, your answer is: 25}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\huge\boxed{\frak{Amphitrite1040:)}}$

5 0

2 years ago

Read 2 more answers

Which expression equals the sum 1+2+3+4+5+6..

otez555 [7]

Answer:

7 * 3

7+7+7

3+3+3+3+3+3+3

2+2+2+2+2+2+2+2+2+2+1

(2*10)+1

(10*1)+11....

...and so on

Step-by-step explanation:

I don't know what type of expression you are looking for

7 0

2 years ago