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2 years ago

Find a closed form for

1 answer:

5 0

$S_n=1\cdot1!+2\cdot2!+\cdots+n\cdot n!$
$S_n=(1+1-1)\cdot1!+(2+1-1)\cdot2!+\cdots+(n+1-1)\cdot n!$
$S_n=(2\cdot1!-1\cdot1!)+(3\cdot2!-1\cdot2!)+\cdots+\bigg((n+1)n!-\cdot n!\bigg)$
$S_n=(2!-1!)+(3!-2!)+\cdots+\bigg((n+1)!-1\cdot n!\bigg)$
$S_n=-1!+(n+1)!$
$S_n=(n+1)!-1$

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The length of a rectangle is 20 units more than its width. The area of the rectangle is x4−100.

Mice21 [21]

Answer:

$1. x^2-10$ because the area expression can be rewritten as $(x^2-10)(x^2+10)$ which equals $(x^2-10)((x^2-10)+20).$

Step-by-step explanation:

Area of the rectangle $=(x^4-100)$

$x^4-100=(x^2)^2-10^2\\$Applying difference of two squares: a^2-b^2=(a-b)(a+b)\\(x^2)^2-10^2=(x^2-10)(x^2+10)$

Since the length of a rectangle is 20 units more than its width.

$Width: x^2-10\\Length=x^2+10=x^2-10+20$

The correct option is therefore 1.

4 0

2 years ago

Read 2 more answers

The following differential equation is separable as it is of the form dP/dt = g(P)h(t).

dedylja [7]

Answer:

$P(1-P) = Ae^t$

Step-by-step explanation:

given differential equation is

$\frac{dP}{dt} =P-P^2\\\frac{dP}{dt} = g(P) h(t)\\g(P) = P-P^2\\h(t) = 1$

So this is separable

We separate as

$\frac{dP}{P-P^2} =1dt\\\frac{dP}{P(1-P)} =1dt$

Resolve into partial fractions to solve this

$dP(\frac{1}{P}+ \frac{1}{1-P} ) = 1dt\\ln P(1-P) = t+C\\P(1-P) = Ae^t$

So solution is $P(1-P) = Ae^t$

7 0

2 years ago

Chiko bought 75 shares of stock at $19.58 per share. He received dividends of $73.42 during the year. At the end of the year, hi

shtirl [24]

Answer: 1,468.5

Step-by-step explanation:

Hi, to answer this question we simply have to multiply the price of each share of stock ($19.58) by the number of shares of stock bought (75 ).

Mathematically speaking:

Price per share x number of shares = 19.58 x 75 = $1,468.5

His purchase price was 1,468.5

Feel free to ask for more if needed or if you did not understand something.

3 0

2 years ago

The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hour

ikadub [295]

Mean = 12000
Standard Deviation = 2000

We have to find how many standard deviations is 14,500 away from the mean.
This can be achieved by calculating the z-score

Z-score tells us how many standard deviations above or below is a sample value from the mean. A positive z value shows, sample value is above the mean.

z score can be calculated as = (Sample Value - Mean )/Standard Deviation)
So,
Z-score = $\frac{14500-12000}{2000} =1.25$

This means, 14,500 is 1.25 standard deviations above the mean value 12,000.

4 0

2 years ago

Read 2 more answers

Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this p

goldfiish [28.3K]

Answer:

0.0406, 0.8284,0.7887

Step-by-step explanation:

Given that Mattel Corporation produces a remote-controlled car that requires three AA batteries

X is N(34, 5.5)

Hence sample size of 25 would follow a t distribution with df = 24

This is because sample size <30