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Nookie1986 [14]
2 years ago
11

The number of peanuts in bags is normally distributed with a mean of 172.5 peanuts and a standard deviation of 1.9 peanuts.

Mathematics
1 answer:
ValentinkaMS [17]2 years ago
5 0
-2.368 tell me if I’m wrong
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For the following telescoping series, find a formula for the nth term of the sequence of partial sums
gtnhenbr [62]

I'm guessing the sum is supposed to be

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}

Split the summand into partial fractions:

\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}

1=a(5k+4)+b(5k-1)

If k=-\frac45, then

1=b(-4-1)\implies b=-\frac15

If k=\frac15, then

1=a(1+4)\implies a=\frac15

This means

\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}

Consider the nth partial sum of the series:

S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)

The sum telescopes so that

S_n=\dfrac2{14}-\dfrac2{5n+4}

and as n\to\infty, the second term vanishes and leaves us with

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17

7 0
3 years ago
leandra has 40 coins that total 7.15 all of her coins are dimes,d, and quarters,q, which system of equations models this situati
navik [9.2K]

Answer:

40 = d+q

7.15=0.10d+0.25q

there are 19 dimes and 21 quarters.

3 0
3 years ago
I need help graphing 2x - 6y = 42 I'm just really lazy​
solong [7]

Answer:

We can use slope intercept form to get the points needed. Y= -7+1/3x The points are (0,-7) and (3,-6)

Step-by-step explanation:

Subtract 2x from the left side and place it over to the right side with the 42. Now we have -6y= 42-2x. From here we divide by -6 and we get y= -7+1/3x. We know that are slope is 1/3 which the one is the rise and the 3 is the run. We also know that our y intercept is -7. We plot the points at (0,-7) and (3,-6)

3 0
3 years ago
Braydon is performing the four arithmetic operations on 14 and 2.
Luda [366]
The answer is 14 divided by 2
4 0
3 years ago
If cot theta= 4/3, find csc theta
Marrrta [24]

Answer: Option d.

Step-by-step explanation:

The trigonometric identity needed is:

csc^2\theta=cot^2\theta+1

Knowing that cot\theta=\frac{4}{3}:

Substitute it into csc^2\theta=cot^2\theta+1:

csc^2\theta=(\frac{4}{3})^2+1

Simplify the expression:

csc^2\theta=(\frac{4}{3})^2+1\\\\csc^2\theta=\frac{16}{9}+1\\\\csc^2\theta=\frac{25}{9}

Solve for csc\theta. Apply square root at both sides of the expression:

\sqrt{csc^2\theta}=\±\sqrt{\frac{25}{9}}

csc\theta=\frac{5}{3}

8 0
2 years ago
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