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3 years ago

1^2 + 4^2 + 7^2 + ... + (3n - 2)^2 = n(6n^2-3n-1)/2

1 answer:

7 0

Use math induction proof method will be usefully

for n=1 will get

1^2 = 1(6*1^2 -3*1 -1)/2
1 = 1(6-4)/2
1 = 1(2)/2
1 = 1

suppose true for n=k and prove for k = k+1

hope this will help you

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How many times heavier is a 8 1/4 pound fish than a 6 7/8 pound fish

icang [17]

Answer:

Step-by-step explanation:

Divide 8 1/4 by 6 7/8 and the answer will be 1.2 times heavier.

8 1/4 is 8.25 and 6 7/8 is 6.875 in decimal point and again:

8.25 divided by 6.875 is 1.2.

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1 year ago

The table shows the distance traveled over time while traveling at a constant speed.

Setler79 [48]

Answer:1,200 meters per minute

Step-by-step explanation:

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3 years ago

Read 2 more answers

Choose the correct reasoning of when a projectile reaches its highest point. A. A projectile reaches its highest point when its

alexira [117]

Answer: A projectile reaches its highest point when its vertical velocity component is zero.

Step-by-step explanation:

In projectile motion, objects moves in parabolic path.

Projectile motion is a type of motion in which an object moves in a bilaterally symmetrical, parabolic path. Projection motion happens when the force is applied at the start of the trajectory (where the object follows) which follows an interference which is gravity. Gravity takes over and afterwards the object accelerates downwards. The acceleration is constant so the vertical velocity (Vy) varies linearly. The maximum height of the projectile which is the highest height is reached when the vertical velocity (Vy) is equal to zero.

After the projectile reaches its maximum height which is its highest point, it begins to drop downwards.

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2 years ago

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a

spin [16.1K]

Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

5 0

2 years ago

An apartment rents for $800 a month the monthly rent is expected to increase $15 each year what will the rent at the end of the

Nataly [62]

To find this you would do 800 + 15x where x is the amount of years.

For 9 years it would be 800 + 15(9) which is 800 + 135.

At the end of 9 years, the apartment's rent would be $935. I hope that's utilities included because... yikes...

5 0

3 years ago