How to make a scatter plot

Find the circumference of a circle with the diameter of 10 inches. Leave your answers in form of pi

MrRa [10]

Answer:

Circumference = 10π

Step-by-step explanation:

First identify the circumference formula as such:

2πr (where r ⇒ radius, π ⇒ pi)

Knowing 2 times the radius (2r) in the formula can be rewritten as the diameter, the formula itself can be rewritten as:

πd (where d ⇒ diameter, π ⇒ pi)

If we know the diameter = 10 inches, substitute in the circumference formula πd to get:

π * 10 inches = 10 * π inches = 10π inches

4 0

3 years ago

Need help in this question

Shtirlitz [24]

Answer:

C!

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Write out the first four terms of the series to show how the series starts. Then find the sum of the series or show that it dive

Nostrana [21]

Answer:

The first four terms of the series are

$(9+3),(\frac97+\frac35),(\frac9{7^2}+\frac3{5^2}),(\frac9{7^3}+\frac3{5^3})$

$\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$ = 14.25

Step-by-step explanation:

We know that

Sum of convergent series is also a convergent series.

We know that,

$\sum_{k=0}^\infty a(r)^k$

If the common ratio of a sequence |r| <1 then it is a convergent series.

The sum of the series is $\sum_{k=0}^\infty a(r)^k=\frac{a}{1-r}$

Given series,

$\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$

$=(9+3)+(\frac97+\frac35)+(\frac9{7^2}+\frac3{5^2})+(\frac9{7^3}+\frac3{5^3})+.......$

The first four terms of the series are

$(9+3),(\frac97+\frac35),(\frac9{7^2}+\frac3{5^2}),(\frac9{7^3}+\frac3{5^3})$

Let

$S_n=\sum_{n=0}^\infty \frac{9}{7^n}$ and $t_n=\sum_{n=0}^\infty \frac{3}{5^n}$

Now for $S_n$ ,

$S_n=9+\frac97+\frac{9}{7^2}+\frac9{7^3}+.......$

$=\sum_{n=0}^\infty9(\frac 17)^n$

It is a geometric series.

The common ratio of $S_n$ is $\frac17$

The sum of the series

$S_n=\sum_{n=0}^\infty \frac{9}{7^n}$

$=\frac{9}{1-\frac17}$

$=\frac{9}{\frac67}$

$=\frac{9\times 7}{6}$

=10.5

Now for $t_n$

$t_n= 3+\frac35+\frac{3}{5^2}+\frac3{5^3}+.......$

$=\sum_{n=0}^\infty3(\frac 15)^n$

It is a geometric series.

The common ratio of $t_n$ is $\frac15$

The sum of the series

$t_n=\sum_{n=0}^\infty \frac{3}{5^n}$

$=\frac{3}{1-\frac15}$

$=\frac{3}{\frac45}$

$=\frac{3\times 5}{4}$

=3.75

The sum of the series is $\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$

= $S_n+t_n$

=10.5+3.75

=14.25

4 0

3 years ago

Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership wit

ivann1987 [24]

Answer:

Number of months spent in first gym = 9

Number of months spent in second gym = 3

Step-by-step explanation:

Let she spent x months in a year at first gym and y months in a year at second gym

Now, there are 12 months in one year

⇒ x + y = 12

y = 12 - x .......(1)

Now, total money she spent in one year = $825

⇒ 75·x + 50·y = 825 .........(2)

Putting value of y from equation (1) in equation (2)

75·x + 50·(12 - x) = 825

⇒ 75·x - 50·x + 600 = 825

⇒ 25·x = 225

⇒ x = 9

Now, putting this value of x in equation(1)

⇒ y = 12 - 9

⇒ y = 3

Hence, number of months spent in first gym = 9

And number of months spent in second gym = 3

7 0

3 years ago

What is the angle of rotation for the following figure?<br> 120°<br> 90°<br> 60°<br> 45°

il63 [147K]

120 i think because if the sun rotates it will move at a 120 angle

4 0

3 years ago