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2 years ago

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A light bulb manufacturer claims that the lifetime of the bulbs is normally distributed with a mean of 5000 hours and a standard

deviation of 250 hours. If 20000 bulbs are produced on a particular day, what percentage of the bulbs will have a lifetime of between 4750 and 5500 hours?

1 answer:

daser333 [38]2 years ago

8 0

Answer:

88

Step-by-step explanation:

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The tax on each video

dimulka [17.4K]

Answer:

69.66

Step-by-step explanation:

3 0

2 years ago

Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference

Bezzdna [24]

Since $a_1,a_2,a_3,\cdots$ are in arithmetic progression,

$a_2 = a_1 + 2$

$a_3 = a_2 + 2 = a_1 + 2\cdot2$

$a_4 = a_3+2 = a_1+3\cdot2$

$\cdots \implies a_n = a_1 + 2(n-1)$

and since $b_1,b_2,b_3,\cdots$ are in geometric progression,

$b_2 = 2b_1$

$b_3=2b_2 = 2^2 b_1$

$b_4=2b_3=2^3b_1$

$\cdots\implies b_n=2^{n-1}b_1$

Recall that

$\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n$

$\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2$

It follows that

$a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)$

so the left side is

$2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n$

Also recall that

$\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}$

so that the right side is

$b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)$

Solve for $c$ .

$2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}$

Now, the numerator increases more slowly than the denominator, since

$\dfrac{d}{dn}(2n(n-1)) = 4n - 2$

$\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2$

and for $n\ge5$ ,

$2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2$

This means we only need to check if the claim is true for any $n\in\{1,2,3,4\}$ .

$n=1$ doesn't work, since that makes $c=0$ .

If $n=2$ , then

$c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0$

If $n=3$ , then

$c = \dfrac{12}{2^3 - 6 - 1} = 12$

If $n=4$ , then

$c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N$

There is only one value for which the claim is true, $c=12$ .

3 0

2 years ago

The following table shows the final scores for a group of mini golf reset adventure Land find the median number of strokes

solong [7]

The median would be the middle data point. Let’s list the points

25, 26, 31, 39, 32, 57

Put them in order from least to greatest

25, 26, 31, 32, 39, 57

There is an even amount of data so take the two center points and divide by 2

31 + 32 = 63

Divide by 2

31.5

There would be an average of 31.5 strokes

7 0

2 years ago

Read 2 more answers

Ronin kicks a ball over the gate of the first floor balcony. The function h(t)=-36t^2+288t+9 can be used to model the height of

ale4655 [162]

Answer: 4 seconds

Step-by-step explanation:

Given: The function $h(t)=-36t^2+288t+9$ can be used to model the height of the ball where t is the time in seconds after the ball kicked and h(t) is the height in feet.

Differentiate the given function with respect to t , we get

$h'(t)=-36(2)t+288=-72t+288$

Put h'(t)=0

$\Rightarrow\ -72t+288=0\Rightarrow\ t=\dfrac{288}{72}\\\\\Rightarrow\ t=4$

Also, $h''(t)=-72$

By second derivative test, h(t) is maximum at t=4.

Hence, the time in Devon which the ball reaches it maximum height = 4 seconds

3 0

2 years ago

What does <br><br>"mixed number in its lowest form." mean?

Viktor [21]

Answer:

ok so it basically means reducing a mixed number to its simplest form.

4 0

3 years ago

Read 2 more answers