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3 years ago

A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work.

1 answer:

4 0

$\displaystyle S_k = \sum\limits_{i=1}^k{i(i+1)} = \dfrac{k(k+1)(k+2)}{3} \\ \\ S_{k+1} = \sum\limits_{i=1}^{k+1}{i(i+1)} = \dfrac{(k+1)(k+1+1)(k+1+2)}{3}=\\ \\ = \dfrac{(k+1)(k+2)(k+3)}{3}$

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If a man walks at the rate of 2 ft./s how many minutes will it take him to walk 720feet

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Answer:

It would take 6 minutes.

Step-by-step explanation:

720/2=360

360/60=

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3 years ago

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What is the ratio 44/12 in simplest form

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Answer:

44/12 = 11/3 = 3 2/3

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A wheel on a piece of machinery makes one revolution every minute (60 seconds.) How many degrees does it move in 10 seconds?

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Answer:

It moves 6 degrees a second that means it moves 60 degrees in 10 seconds.

Step-by-step explanation:

360/60=6

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3 years ago

What is the most precise classification of the quadrilateral formed by connecting in order the midpoints of the figure below? Sh

AlekseyPX

Answer:

Rhombus

Step-by-step explanation:

The given trapezoid has vertices at M(-4,0), J(-2,4), K(2,4), and L(4,0).

Use the midpoint formula: $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

To obtain the midpoint of MJ:

$A=(\frac{-4+-2}{2},\frac{0+4}{2})=(-3,2)$

Similarly, the midpoint of of JK is B=(0,4), the midpoint of KL is C=(3,2), and the midpoint of LM is D=(0,0).

Now use the slope formula;

$m=\frac{y_2-y_1}{x_2-x_1}$

To find the slope of AB = $\frac{4-2}{0--3}=\frac{2}{3}$

The slope of BC = $\frac{2-4}{3-0} =-\frac{2}{3}$

The slope of CD= $\frac{0-2}{0-3}=\frac{2}{3}$

The slope of AD= $\frac{0-2}{0--3}=-\frac{2}{3}$

We can see that the slope of the opposites sides are parallel, CD is parallel to AB and AD is parallel to BC.

The product of the slopes of the adjacent sides is not -1.

Hence the shape formed by connecting the midpoint of the isosceles trapezoid is a parallelogram.

Obviously the side lengths are equal since we connected all midpoints.

The parallelogram is a rhombus.

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3 years ago

The probability of a train arriving on time and leaving on time is 0.8. The probability of the same train arriving on time is 0.

lys-0071 [83]

To help you with this topic, I would suggest you revise probability trees.

P(train arriving) = 0.8
P(train arriving on time) = 0.84
P(train arriving late) = 0.86

0.8 x 0.86 = 0.688

Answer: 0.688

Hope it helped :)

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